Aristotle, Metaphysics

Aristotle’s Metaphysics, translated by Thomas Taylor (1801). Edited by William C. Michael, O.P. for use in the Classical Liberal Arts Academy.

Aristotle, Metaphysics. Book 1, Chapter 1.

All men naturally desire to know. A token of which is the love of the senses; for, separate from utility, they are loved for themselves, and this is especially the case with the sense of seeing. For, as I may say, we choose to see, in preference to everything else, not only that we may act, but likewise when we have no intention of acting. But the cause is, that this sense in a most eminent degree makes us to know something, and renders many differences manifest. Animals therefore are produced naturally possessing sense; but from sense, in some of them memory is not ingenerated, and in others it is. And on this account, some animals are prudent, but others are more capable of discipline than those who are not able to exercise the power of memory. Those indeed are prudent without discipline, who are unable to hear sounds, such as bees, and other animals of this kind, if any such are to be found. But those learn, who together with memory possess the sense of hearing. Other animals therefore live from phantasy, and memory, and participate but a little of experience; but the human race lives from art also, and reasoning. But men derive experience from memory. For memory being often exercised about the same thing, gives perfection to the power of one’s experience. Hence experience appears to be nearly similar to science and art. But science and art proceed to men through experience. For experience, as Polus rightly observes, produces art, but unskillfulness chance. But art is then effected, when, from many conceptions of experience, one universal opinion about things similar is produced. For to have an opinion that to Callias, Socrates, and to many others severally considered, laboring under a certain disease, this particular thing is expedient, is the province of experience; but that it is expedient to all of this kind who are defined according to one species, and who are afflicted with this disease, such as the phlegmatic, or the choleric, or those who are in a fever from heat, is the province of art. With respect therefore to acting, experience seems in no respect to differ from art; but we see that the skillful more readily accomplish what they intend, and those who possess the reason of a thing without experience. But the cause of this is, that experience is a knowledge of particulars, but art of things universal. But all actions and generations are about that which is particular. For he who cures does not give health to man, unless by accident, but to Callias or Socrates, or someone of others who are thus denominated, and who happens to be a man. If anyone therefore possesses the reason of a thing without experience, and knows indeed that which is universal, but is ignorant of the individual it contains, he will often err in his attempts to cure. For that which is particular possesses a greater capability of being cured; but at the same time we are of opinion that to know, and to understand, belong rather to art than to the experience, and we think that artists are wiser than the experienced, because in all men wisdom is rather the consequence of knowledge than of anything else. But this takes place, because some know, and others do not know the cause of a thing. For the skillful indeed know that a thing is, but they do not know why it is; but the scientific know the why and the cause of a thing. On this account we consider those who in anything are master artists, as more honorable, as those who know more than manual operators, and likewise as more wise, because they know the causes of things which are made. But others, like certain inanimate beings, make indeed, but make destitute of knowledge, just in the same manner as fire burns. Inanimate beings, therefore, make each of these things by a certain nature; but manual artificers through custom; as being wiser, not from their engaging in active pursuits, but from their possessing reason, and knowing the causes of things. And, in short, it is a sign that a man possesses knowledge, when he is able to teach; and on this account we think that art is more science than experience: for the former are able, but the latter are not able, to teach. Further still, we do not think that any one of the senses is wisdom, although each is the most principle knowledge of particulars; but the senses do not assert the why respecting anything, as for instance, why fire is hot, but only that it is hot. It is probable, therefore, that the first inventor of any art, besides the common senses, was admired by men, not only because something of things invented was useful, but as being wise and differing from other men. But when many arts were discovered, some of which pertain to things necessary, but others to the conduct of life, from that time we have always considered those who know the causes of things as wiser than manual artificers, because their sciences do not regard utility. Hence all such things as contribute to the common purposes of this life being procured, those sciences were invented, which neither respect pleasure nor things necessary, and they were first discovered in those places in which men abounded in leisure. On which account the mathematical arts first originated about Egypt; for there the tribe of priests was permitted to be at leisure. In our moral treatises, therefore, we have declared what the difference is between art and science, and other things of a kindred nature. But that for the sake of which we engage in the present discourse, is the belief of all mankind, that what is called wisdom, is conversant with first causes and principles. So that, as we before energized, the skillful man appears to be wiser than those who merely energize from any one of the senses; the artist than the skillful; the architect than manual artificers; and the theoretic than fabricators. That wisdom, therefore, is a science about certain causes and principles, is evident.

Aristotle, Metaphysics. Book 1, Chapter 2.

But, since we investigate this science, we should consider from the speculation of what causes and principles science is wisdom. If anyone therefore shall apprehend the opinions which we entertain respecting a wise man, perhaps from this the thing proposed will become more evident. In the first place then, we are of opinion, that a wise man in the most eminent degree knows scientifically all that can be known; not possessing a science of things according to that which is particular, but according to that which is universal. In the next place, we consider him as a wise man, who is able to know things difficult, and which it is not easy for man to know. For, to perceive according to sense is common to all men; on the which account this is easy, and he who thus energizes is by no means wise. In the third place, we are of opinion, that he who is more accurate, and more capable of teaching the causes of things, is more wise respecting every science. Further still, that of sciences, that which is eligible for its own sake, and for the sake of knowing, partakes more of wisdom than that which is eligible for the sake of things which are contingent; and that the more principal science partakes more of wisdom than that which is subservient. For it is not proper that the wise man should be commanded, but that he should command; nor ought he to be persuaded by another, but one less wise ought to be persuaded by him. And such and so many are the opinions which we entertain respecting wisdom and wise men. But, among these, to know all things necessarily belongs to him who in the most eminent degree possesses universal science: for such a one in a certain respect knows all subjects. But things most eminently universal are nearly most difficult for man to know: for they are most remote from the senses. But the most accurate of the sciences are those which especially relate to things first. For those sciences which consist from fewer things, are more accurate than those which are denominated from addition; as arithmetic than geometry. But indeed that science is more doctrinal which speculates the causes of things: for those teach others, who about everything relate the causes. But to know, and to know scientifically for the sake of such knowledge, especially belongs to the science of that which is most eminently the object of scientific knowledge. For he who chooses to know scientifically for the sake of such knowledge, especially chooses that which is most eminently science. But such is the science of that which is most eminently the object of scientific knowledge and objects of this kind are things first and causes. For, through and from these, other things are known, but these are not known through things in subjection to them. But the most principle of sciences, and which is more a principle than the science which is in subjection, is that which knows on what account everything is to be done. But this is the good of everything; and universally that which is best in every nature. From all therefore that has been said, that name which is the object of our investigation falls into the same science. For it is necessary that this should be speculative of first principles and causes: for the good also, and that for the sake of which a thing subsists, is one among the number of causes. But that this science is not employed in making, is evident from those who first philosophized: for, both now and at first, men began to philosophize through wonder; at first indeed admiring such dubious particulars, as were of a more easy solution; but afterwards proceeding in this manner gradually, they began to doubt about things of greater importance, such as concerning the properties participated by the moon, the sun, and the stars, and the generation of the universe. But he who doubts and wonders, is of opinion that he is ignorant; and, on this account, a philosopher in a certain respect is a lover of fables. For a fable is composed from things wonderful. So that if now and at first men philosophized, in order to fly from ignorance, it is evident that they pursued scientific knowledge for the sake of knowing, and not for the sake of any use. But the truth of this is also testified by that which has happened. For nearly all such things as are necessary being present, and which contribute both to ease and the conduct of life, prudence of this kind began to be investigated. It is evident therefore, that we seek after scientific knowledge for the sake of no other utility than that which arises from itself; and that as we call him a free man who exists for his own sake, and not for the sake of another, so this alone among the sciences is liberal; for this alone subsists for its own sake. On this account, too, the possession of it may justly be considered as not human. For in many respects human nature is servile; So that, according to Simonides, divinity alone possesses this honor; but it is unbecoming that man should only investigate the science which pertains to himself. But, if the poets say anything to the purpose, and a divine nature is naturally envious, it is likely that it would especially happen in this particular, and that all those would be unhappy who surpass the rest of mankind. For neither does a divine nature admit of envy; and poets (according to the proverb) speak falsely in many things. Nor is it proper to think that any other science is more honorable than a science of this kind. For that which is divine is also most honorable. But a thing of this kind will alone subsist twofold. For the science which divinity possesses is especially divine; and this will likewise be the case with the science of things divine, if there be such a science. But the science of which we are speaking alone possesses both these prerogatives. For divinity appears to be a cause and a certain principle to all things; and either alone or in the most eminent degree, divinity possesses such a science as this. All other sciences therefore are more necessary, but no one is better than this. But it is requisite in a certain respect to establish this science in an order contrary to that of the inquiries which men made from the beginning. For all men, as we have said, begin from wonder to investigate the manner in which a thing subsists; just as it happens to those, who have not yet contemplated the cause of those wonderful figures that move spontaneously, or the cause of the revolutions of the sun, or the reason of the incommensurability of the diameter of a square and its side. For it seems admirable to all men, that a thing which is not the least of things, should not be measured. But it is requisite they should end in the contrary, and in that which is better, according to the proverb, as is the case in these things when they learn them. For there is not anything which would appear more wonderful to a geometrician, than if the diameter should become commensurable to the side. And thus we have declared what the nature is of that science which is the object of our investigation, and what the mark to which the inquiry and the whole method ought to be directed.

Aristotle, Metaphysics. Book 1, Chapter 3.

But, since it is evident that it is requisite to consider the science of causes from its principle (for we then say that each particular is known when we know the first cause of it), and the causes are said to subsist in a fourfold respect, one of which we assert to be essence, and the subsisting as a certain particular thing (for the inquiry, on what account a thing exists, is referred to the last reason) and cause and principle form the first why: but a second cause is matter; and that which subsists as a subject: a third is that whence the beginning of motion is derived: but the fourth is the cause opposite to this, that for the sake of which a thing subsists, and the good (for this is the end of all generation).This being the case, though we have speculated sufficiently concerning these causes in our Physics, yet, at the same time, we shall take along with us in our inquiry those who prior to us have engaged in the speculation of beings, and have philosophized about truth. For it is evident that they also assert that there are certain principles and causes. A repetition, therefore, of what they have said will be of advantage to the present discussion. For, either we shall find another genus of cause, or we shall more firmly believe those we have just now enumerated.

The greater part then of those that first philosophized were of opinion that the principles of all things alone subsisted in the species of matter. For that from which all things subsist, from which they are first generated, and into which they are finally corrupted, the essence indeed remaining but becoming changed by participations, this, say they, is the element, and this is the principle, of things. Hence they were of opinion that neither is anything generated nor corrupted, because this nature is always preserved. Just as we say that Socrates is neither simply generated, when he becomes beautiful, or a musician, nor is corrupted when he loses these habits, because the subject, Socrates himself, remains; in like manner, neither is any one of other things, either generated, or corrupted. For it is requisite there should be a certain nature, either one, or more than one, from which other things are generated while it is itself preserved.

But with respect to the multitude and form of this principle, all philosophers do not assert the same. For Thales indeed, who was the leader of this philosophy, said that this principle is water. On this account he asserted that the earth is placed upon water, entertaining perhaps this opinion from seeing that the nutriment of all things was moist, that the hot itself was generated from this, and that from this animals lived. But that from which anything is generated is the principle of that thing period on this account, therefore, he formed this opinion, and because the seeds of all things have a moist nature. . But water is the principle of nature to things moist. But there are some who think that men of the greatest antiquity, who flourished long before the present generation, and who first theologized, entertained the very same opinion respecting nature. For they made Ocean and Tethys the parents of generation, and the solemn oath of the gods water, which is called Styx by the poets. For that which is the most ancient is the most honorable: but a solemn oath is the most honorable. That this opinion, therefore, respecting nature is very ancient, is perhaps not immanifest. Thales indeed is said to have discoursed in this manner respecting the first cause. For no one will think that Hippo deserves to be ranked with these, on account of the meanness of his cogitative part. Anaximenes and Diogenes placed air prior to water, and considered it as in the most eminent degree the principle of simple bodies. Hippasus the Metapontine, and Heraclitus the Ephesian, considered fire as the principle of all things. But Empedocles, who introduced four principles, besides those already mentioned added earth for the fourth. For According to him these always remain, and are not generated, but are mingled and separated in multitude and paucity, into one, and from one. But Anaxagoras the Clazomenian, who was prior in age to Empedocles, but posterior in his works, asserts that there are infinite principles. For he says, that nearly all things which consist of similar parts, such as water or fire, are thus generated and corrupted by concretion and separation alone; but that otherwise they are neither generated nor corrupted, but remain as things eternal. From these men, therefore, anyone might be led to think that cause alone belongs to that which is called the species of matter. But in consequence of their proceeding in this manner, the thing itself afforded them a passage, and compelled them to investigate. For though every corruption and generation is in the most eminent degree, from something, as subsisting from one, or from many things; yet, why does this happen, and what is the cause of it? For the subject itself does not make itself change. I say, for instance, that neither would nor brass is the cause that either of these is changed. Nor does wood make the bed, nor brass the statue, but something else, which is the cause of mutation. But to investigate this is to investigate another principle, which we should call that from whence motion derives its beginning. Those, therefore, who have entirely touched upon this method from the beginning, and who assert that the subject is one, have not rendered anything in this inquiry difficult to themselves; but some of those who assert that all things are one, as if vanquished by this inquiry, assert that the one is immovable, and likewise the whole of nature, not according to generation and corruption (for this is an ancient opinion, and acknowledged by all men), but also according to every other mutation. And this is the peculiarity of their doctrine.

Of those, therefore, who assert that the universe is alone one, it has so happened that no one has perceived a cause of this kind, except Parmenides; and this has happened to him so far as he admits that there is not only one, but, in a certain respect, two causes. But to those who admit that there are more than two causes, it belongs in a still greater degree to assert A cause of this kind; Such as those who consider as causes the hot and the cold, or fire and earth. For they use fire as possessing A motive nature; but water and earth, and things of this kind, as endued with a nature contrary to the motive. But after these and such like principles, as not being sufficient to generate the nature of things, again, being compelled, as we have said, by truth, they investigated that principle which is consequent to this. For perhaps neither earth, nor any other similar nature, is the cause that some things subsist, and that others are generated in a good and beautiful manner, nor is it probable that they entertained such an opinion. Nor, again, is it proper to ascribe a thing of such great importance to chance and fortune. He therefore who asserted that as in animals, so also in nature, there is a certain intellect, which is the cause both of the world, and of all order, will appear like one sober, when compared with those ancients that spoke rashly. We evidently know, therefore, that Anaxagoras touched upon these reasons; though Hermotimus the Clazomenian is said prior to him to have mentioned a cause of this kind. Those, therefore, who entertained this opinion, together with establishing a principle of things, which is the cause of their subsisting in a beautiful manner, established also a principle which is the cause of motion to things.

Aristotle, Metaphysics. Book 1, Chapter 4.

But someone may suspect that Hesiod first investigated a thing of this kind; and likewise that this is the case with any other who may have considered love or desire as a principle in beings, such, for instance, as Parmenides. For he also, devising the generation of the universe, says: “He produced Love the first of all the gods.” But Hesiod, “Chaos was generated the first of all things; but afterwards wide-bosomed Earth, and Love who excels among all the immortals:” as if it were fit that there should be a certain cause in beings which moves and comprehends things, and binds them together. With respect to these, therefore, we may be permitted afterwards to judge, which of them ought to rank as the first. But since the contraries to things good appear also to be inherent in nature, and not only order and the beautiful, but disorder and the base; and, since things evil are more in number than such as are good, hence a certain other philosopher has introduced friendship and strife, each, according to him, being the cause of evil and good. For, if anyone should follow and receive this doctrine in that part of his nature which reasons scientifically, and not according to what Empedocles has stammeringly asserted, he will find that friendship is the cause of things good, but strife of things evil. So that, if anyone should say that Empedocles in a manner asserts, and is the first who asserts, that good and evil are principles, he will perhaps speak well; since good is the cause of all things that are good, and evil of such as are evil. These, therefore, as we have said, thus far touched upon those two causes which we have defined in our physics; I mean the material cause, and that whence motion is derived: but yet they have touched upon these causes obscurely, and in no respect clearly, but just in the same manner as those do, who are unexercised in battles. For these advancing towards their opponents often strike excellent blows; but neither do these strike from science, nor do those seem to know what they assert. For they do not scarcely in any respect appear to use these principles, except in a small degree. For Anaxagoras uses intellect as a machine to the fabrication of the world, just as the gods are introduced in tragedies, when very difficult circumstances take place; and, when he doubts on what account it necessarily is, he introduces it by force. But, in other things, he considers everything else rather than intellect as the cause of generated natures. And Empedocles indeed uses causes more than Anaxagoras; but yet neither sufficiently, nor in these does he find that which is consentaneous. For in many places, According to him, friendship separates and strife mingles things together. For when the universe through strife is separated into the elements, then fire, and each of the other elements, is mingled into one. But when all things through friendship accord in one, it is necessary that the parts from each should be again separated. Empedocles therefore, in this respect, differing from those who were prior to him, was the first that, by making a division, introduced this cause; Not making one principle of motion, but such principles as are different and contrary. Further still, he was the first who asserted that the elements which are considered as belonging to the species of matter, are for; yet he does not use them as four, but as if they were alone two. For he uses fire indeed by itself, but its opposites, earth, air and water, as if they were one nature. But of this anyone may be convinced, by considering his verses. He, therefore, as we have said, speaks in this manner, and asserts that there are so many principles.

But Leucippus, and his associate Democritus, assert that the elements of things are “the full” and “the void”; affirming that the former is being, and the latter is non-being. And again of these, they call “the full” and the solid “being”, but “the void” and “the rare” non-being. On this account they say that being has not anymore subsistence than non-being, because neither has void less subsistence than body. But these are the causes of beings as matter. And, just as those who make the subject essence of things to be one, generate other things from the participations of this subject, and establish the rare and the dense as the principles of participations; in the same manner these also assert, that diversities are the causes of other things. But they say that these are three: figure, order, and position. For they assert that being differs from rysmos, diathege, and trope: but of these rysmos is figure, diathege is order, and trope is position: for the letter A differs from the letter N in figure, but the syllable AN from NA in order, and Z from N in position. But these men, in a manner similar to others, negligently omit to consider with respect to motion, whence it is derived, and how it subsists in beings. And thus far, as we have said, those prior to us appear to have investigated the two causes of things.

Aristotle, Metaphysics. Book 1, Chapter 5.

But among these, and prior to these, those who are called Pythagoreans, and who were the first that applied themselves to mathematics, gave the precedency to these disciplines; and, in consequence of being nourished in them, were of opinion that these are the principles of all beings. But since among these disciplines numbers are first by nature, and it appeared to them that in numbers more similitudes both to things which are, and to things in generation, are seen, than in fire, earth, and water (for this particular property of numbers is justice, that soul and intellect, and again another opportunity, and in a similar manner, as I may say, with respect to each of the rest); and further still, since they perceived the participated properties and reasons of harmonies in numbers, and since other things appeared in every respect to be naturally assimilated to numbers, but numbers are the first elements of every nature; hence they conceived the elements of numbers to be the elements of all things, and that all heaven is harmony and number; and such things as are acknowledged to be evinced both in numbers and harmonies, these they collected together and adapted to the participated properties and parts of the heavens, and to the whole order of things. Likewise, if anything was found anywhere to be much deficient, they supplied the defect, that the whole of their treatise might properly accord with itself. I say, for instance, since the decad appears to be perfect, and to comprehend all the nature of numbers, hence they say that the bodies which revolve in the heavens are ten; but as nine only are apparent they make the tenth to be the antichthon or the opposite earth. But these are considered by us more accurately in other places.

However, we have related these things that we may understand from these men what the principles are which they establish, and how they fall into the above mentioned causes. For it appears that they also considered number as a principle, as matter to beings, and as participated properties and habits. But they assert that the elements of number are the even and the odd; and that of these, the one is bounded, but the other infinite; and that the one is composed from both of these because it is both even and odd. They likewise assert that number consists from the one, and that numbers, as we have said, composed the whole of heaven. But others of these assert that there are ten principles, which are denominated according to coordination, namely:

• bound, the infinite:
• the odd, the even:
• the one, multitude:
• right hand, left hand:
• the masculine, the feminine:
• the quiescent, that which is in motion:
• the straight, the curved:
• light, darkness:
• good, evil:
• the square, the oblong.

Alcmaeon the Crotonian appears to have entertained this opinion: and neither he derived this dogma from them, or they from him. For Alcmaeon flourished when Pythagoras was an old man. But his doctrine was similar to that of these men. For he says that the multitude of human affairs receives a twofold division (meaning into contrarieties), yet not distinguished as they distinguished them, but defined in a casual manner: such as white, black; sweet, bitter; good, evil; the small, the great. He therefore spoke indefinitely concerning the rest: but the Pythagoreans declare how many, and what are the contrarieties. Hence thus much may be understood from both, that contraries are the principles of beings; but from the Pythagoreans we learn the number and quality of these principles: yet it is not clearly determined by them how they may be applied to the above mentioned causes. But they appear to dispose the elements as in the species of matter. For from these, as things inherent, they say that essence is composed and fashioned. From these things, therefore, the conceptions of the ancients, who asserted that the elements of nature were many, may be sufficiently seen.

But there are some who have discoursed about the universe as if it were one nature: yet all of them have not discoursed after the same manner, neither of that which subsists beautifully, nor of that which subsists according to nature. By no means, therefore, does the discourse concerning these men harmonize with the present speculation of causes. For they do not speak like certain physiologists, who, supposing being to be one, at the same time generate from the one, as from matter; but their assertions are of a different nature. For the physiologists who contend that being is one, when they generate the universe, at the same time add motion: but these men assert that the universe is immovable. Thus far, however, a discourse about these men is adapted to the present inquiry. For Parmenides appears to have touched upon the one according to reason, but Melissus according to matter. Hence the former asserts that the universe is finite, but the latter that it is infinite. But Xenophanes, who was the first that introduced this doctrine (for Parmenides is said to have been his disciple), did not assert anything clearly; nor does he appear to have apprehended the nature of either of these, but, looking to the whole of heaven, he says that the one is God. These men, therefore, as we have said, are to be dismissed in the present inquiry; two of them, indeed, entirely, as being a little too rustic, namely Xenophanes and Melissus. But Parmenides appears to have seen more than the these where to speak. For, besides being itself, he thought fit to consider non-being as nothing, and hence was necessarily of opinion that being is one, and nothing else; concerning which doctrine we have spoken more clearly in our Physics. But being compelled to follow the phenomena, and conceiving that, according to reason, the one had a subsistence, but, according to sense, the many, he again establishes two causes and two principles, namely the hot and the cold, or, in other words, fire and earth. But of these he disposes the one, namely the hot, according to being, but the other according to non-being. From what has been said, therefore, and from those wise men who adhered to reason, we now receive these particulars. From the first indeed, that the principle of things is corporeal (for water, and fire, and the like, our bodies); and of these some assert that there is one, but others that there are many corporeal principles; but both agree in placing these principles as in the species of matter. But from certain others who establish this cause, we receive besides this the principle whence motion is derived; and according to some there is one principle, but according to others there are two principles of this kind. As far, therefore, as to the Italic philosophers, and separate from them, others have spoken in a more becoming manner about these things, except, as we have said, that they used two causes; and of these some made the other cause, or that whence motion is derived, to be one, but others to be two. The Pythagoreans, after the same manner, said that there are two principles. But thus much they added, which is peculiar to them, that they did not think the finite, and the infinite, and the one, were certain other natures, such as fire, or earth, or any other similar thing; but they were of opinion, that the infinite itself, and the one itself, are the essence of these things of which they are predicated: and hence they asserted that number is the essence of all things. After this manner, therefore, they unfolded their opinion respecting these things, and began to speak about what a thing is, and to define; but they treated this affair in a very simple manner. For they defined superficially, and considered that in which a given definition is first inherent, as the essence of the thing; just as if anyone should think that the double and the duad are the same, because the double first subsists in two. But perhaps the double is not the same with the duad: and if it be not, one thing will be many; which consequence happens also to them. From those, therefore, who first philosophized, and from others, thus much may be received.

Aristotle, Metaphysics. Book 1, Chapter 6.

After the above mentioned philosophers, the business with Plato next succeeds, who in many things followed these Pythagoreans, but who also had some peculiar doctrines different from the philosophy of the Italics. For, when he was a young man, associating first of all with Cratylus, and being familiar with the opinions of Heraclitus, that all sensible things are perpetually flowing, and that there is no science respecting them, he afterwards adopted these opinions. But as Socrates employed himself about ethics, and entirely neglected the speculation respecting the whole of nature; In morals, indeed, investigating the universal, and being the first who applied himself two definitions; Hence Plato, approving this his investigation of universals, adopted thus much of his doctrine, that these definitions respect other things, and are not conversant with anything sensible. For he was of opinion, that it is impossible there should be a common definition of any sensible nature, as sensibles are always changing. Things of this kind, therefore, he denominated ideas, but asserted that all sensible things were denominated as different from, and as subsisting according to, these. For, According to him, the multitude of things synonymous is homonymous to forms according to participation; but he only changed the name participation. For the Pythagoreans say that beings are imitations of numbers; but Plato, changing the name, calls them participations of numbers. They omit, however, to investigate in common what the participation or imitation of forms is. Further still, besides things sensible, and forms, they say that the mathematics are things of a middle nature, differing indeed from sensibles in that they are eternal and immovable, but from forms in that they are certain similar multitudes, every form itself being only one thing. But, since forms are causes to other things, he was of the opinion that the elements of these are the elements of beings. He thought, therefore, that the great and the small were principles as matter, but the one as essence. For from these, through the participation of the one, forms are numbers. He asserted, indeed, that the one is essence, and that nothing else is called the one, in this respect speaking in a manner similar to the Pythagoreans; and, like them, he also considered numbers as the causes of essence to other things. But this is peculiar to him, to make the duad instead of the infinite considered as one, and to compose the infinite from the great and the small.

Further still: Plato asserts that numbers are different from things sensible; but the Pythagoreans say that they are things themselves, and do not place mathematics between these. The one, therefore, and numbers, were considered as different from things themselves, and not as the Pythagoreans consider them; and, as well as forms, were introduced in consequence of dialectic investigation. For the more ancient philosophers were not skilled in dialectic. Through the same investigation, also, Plato made the duad to be a different nature from the one, because numbers, except those that rank as first, are aptly generated from it, as from a certain express resemblance of a thing; though, indeed, the contrary to this happens to be the case. For it is not reasonable it should be so. For now they make many things from matter, but form generates once only. But one table appears to be produced from one matter. However, he who introduces form makes many tables. The male, too, is in a similar manner related to the female. For the female is filled from one copulation, but the male fills many. And yet these are imitations of those principles. Plato, therefore, has thus defined respecting the objects of investigation.

But it is evident, from what has been said, that he uses only two causes; That which relates to what a thing is, and that which subsists according to matter. For forms, according to him, are the causes to other things of essence; but the one is the cause of this to forms. And what is this cause which subsists according to matter? It is that subject matter through which forms are said to belong to things sensible; and the one is said to be in forms, because this is the duad, or the great and the small. Further still: he attributes to the elements the cause of subsisting well and ill, each to its proper element; And this, we say, some of the more ancient philosophers, namely Empedocles and Anaxagoras, have investigated. In a brief and summary manner, therefore, we have discussed who those were that have spoken, and how they have spoken, respecting principles and truth.

But, at the same time, we obtain thus much from them, that of those who have spoken concerning a principle and a cause, no one has said anything in addition to what we have delivered in our Physics; but all of them have spoken obscurely, though in a certain respect they appear to have touched upon these two period for some speak of principle as matter, whether they suppose there is one or many principles, and whether they consider principle as body, or as in corporeal: As Plato, when he speaks of the great and the small; Empedocles, of fire and earth, water and air; and Anaxagoras, of the Infinity of similar parts. But all these touched upon a cause of this kind; and besides these, those who have established as a principle either fire or water or that which is more dense than fire, but more attenuated than air; For some assert that the first element is a thing of this kind. These, therefore, had only an obscure conception of this cause; But certain others had some conception when the principle of motion is derived, namely those who make friendship and strife, or intellect, or love, a principle. But no one has clearly assigned the nature and essence of this principle. However, they especially speak respecting it who adopt the hypothesis of forms, and the things which subsist in forms. For neither do they consider forms and the things which forms contain as matter to sensibles, nor as if the principle of motion was derived from thence. For they say that they are rather the cause of immobility, and of things being at rest period but, according to them, forms impart the particular being which each individual of other things possesses; and the one imparts the same to forms. But that, for the sake of which actions, mutations and motions subsist after a certain manner, they denominate a cause; yet they do not assert that it is a cause, nor do they speak of it conformably to what it naturally is. For those who speak of intellect, or friendship, place these causes as a certain good, but do not speak of them as if for the sake of these either being or any generated nature subsists, but as if from them the motions of things were derived. In a similar manner, those who say that the one, or being, is a nature of this kind, assert indeed that it is the cause of essence; yet do not say that anything either is, or is generated, for the sake of this. So that in a certain respect it happens that they assert, and yet do not assert, that the good is a cause of this kind; for they speak not simply, but casually. That we have therefore rightly determined concerning causes, and respecting their number and quality, all these philosophers appear to testify, since they were not able to touch upon any other cause. And, besides this, that principles should be investigated, either all of them in this manner, or some one of four, is evident. But after this it is requisite that we should consider in what manner each of these speaks, and what are the doubts which arise respecting principles themselves.

Aristotle, Metaphysics. Book 1, Chapter 7.

It is evident, therefore, that those err manifoldly, who consider the universe as one, and as being one certain nature, as matter; and this corporeal, and possessing magnitude. For they only admit the elements of bodies, but not of things in corporeal, though at the same time things in corporeal have a subsistence. And besides this, endeavoring to assign the causes of generation and corruption, and physiologizing about all things, they take away the cause of motion. Further still, by placing essence as the cause of no one thing, and not considering the what; and besides this, thinking that there might easily be any principle of simple bodies (except earth), they did not attend to the manner in which, according to them, the generation of these from each other is accomplished; I mean fire and water, earth and air. For some things are generated from each other by concretion, and others by separation. But this, with respect to the being prior and posterior, differs much for that may appear to be the most elementary of all things, from which the elements are generated by a first concretion: but a thing of this kind will, among bodies consist of the smallest parts, and be the most attenuated; on which account, such as place fire as a principal speak in the highest degree conformably to this doctrine. But everyone acknowledges that a thing of this kind is also the element of other bodies. No one, therefore, of those later philosophers who speak of the one, has thought fit to consider earth as an element, on account of the magnitude of its parts. But each of the three elements has had a certain arbitrator; For some say that this is fire, others water, and others air though why, like the multitude do they not say that earth also is an element? For they say that earth is all things. Hesiod also asserts, that earth was the first thing generated among bodies; so that this opinion happens to be both ancient and popular. According to this reasoning, therefore, if anyone should say that anything belonging to these, except fire, is more dense than air, but more attenuated than water, he will not speak rightly. But if that which is posterior in generation is prior by nature, and that which is digested and mingled together is posterior in generation, the contrary of these will take place; for water will be prior to air, and earth to water. And thus much may suffice respecting those who establish one cause such as we have mentioned.

But the same things may be said, if anyone should think that there are many corporeal principles, as Empedocles, who says that the four elementary bodies are matter: for it is necessary that partly the same things, and partly such as are peculiar, should happen to him. For we see that the elements are generated from each other, as the fire and earth of the same body do not always remain. But we have spoken respecting these in our physics, and also respecting the cause of things moving, whether it is to be considered as one or two; nor is it to be thought that this has been asserted in a manner altogether irrational. But, in fine, those who speak in this manner must necessarily take away internal mutation. For the cold is not from the hot, nor the hot from the cold period and what contraries themselves will suffer, and what that one nature will be, which becomes fire and water, Empedocles does not say.

But if anyone should think that Anaxagoras asserts there are two elements, he will, in the highest degree, think according to reason; for though he does not clearly assert this, yet it follows from necessity, if anyone speaks conformably to his doctrine. It is indeed absurd to say, that at first all things were mingled together; both because it must happen that all things prior to this ought to have subsisted unmingled, and because everything is not naturally adapted to be mingled with everything. To which it may be added, that from this doctrine, participated properties and accidents must be separated from substances (for mixture and separation belong to the same things); yet if anyone follows, and at the same time accurately considers his assertions, he will perhaps appear to have advanced something new. For, at the time when nothing was separated, it is evident nothing could be said respecting that essence. I say, for instance, that it was neither white nor black, nor of any color between these; but that it was from necessity colorless: for otherwise it would possess some one of these colors. In like manner, it must have been tasteless: and, from the same reasoning, it could not have been anything else of the like kind. For it is not possible that it could possess any quality or quantity, or be any actual thing, since something of those things which are called partial forms would be inherent in it. But this is impossible, in consequence of all things (according to him) being mingled together; for they would now be separated. But he says that all things were mingled except intellect; and that this alone was unmingled and pure. Hence it comes to pass, that he proclaims, as principles, the one (for this is simple and unmingled), and another thing, as if it were being, such as we consider the indefinite to be, before it is bounded and participates of a certain form. So that this is asserted, indeed, neither with rectitude nor perspicuity; yet he wishes to say something similar to what more modern philosophers have said, and more agreeable to the present phenomena. But these philosophers only speak in a manner accommodated to the assertions respecting generation, corruption, and motion. For they nearly alone investigate an essence, principles and causes of this kind.

But with respect to such, indeed, as make all beings the subject of their speculation, and consider some beings as sensible and others as not sensible, it is evident that they inquire concerning both genera; and on this account anyone may be induced to dwell longer on the consideration of what they have said, well or ill, with respect to our present investigation. Those, therefore, who are called Pythagoreans, use principles and elements in a more incredible manner than physiologists. But the reason is, because they do not receive these from sensibles. For mathematical entities are without motion, except those things which pertain to astronomy. Yet notwithstanding this, they discourse about and discuss all things respecting nature. For they generate the heaven, and observe what happens respecting its parts, participated properties, and operations; and into these they resolve principles and causes, as agreeing with other physiologists, that whatever is sensible in being, and is comprehended by that which is called heaven. But, as we have said, and also as they assert, they speak sufficiently respecting causes and principles, and even ascend to a higher order of beings, and this more than is adapted to discourses concerning nature; but they are silent as to the mode in which motion, bound, and infinity, the even and the odd, these being alone the subjects of hypothesis, subsist; or how it is possible that generation and corruption can exist without motion and mutation; or how the operations of the bodies which resolve in the heavens can be accomplished.

Further still, whether anyone grants them that magnitude is from these, or whether this is shown to be the case; yet, at the same time, after what manner will some body’s possess levity, and others gravity, respecting which their hypotheses and assertions do not less accord with mathematical bodies than with sensibles? Hence they do not say anything respecting fire, or earth, or other bodies of this kind; and this, I think, because they do not assert anything which is their own concerning sensible natures. Again, how ought we to receive the assertion, that the participated properties of number, and number itself, are the causes of things which exist, and are produced in the heavens, both from the beginning, and at present, at the same time that there is no other number besides this number, from which the world is composed? For since, according to them, opinion and opportunity are in this part of the world, but a little higher or a little lower, injustice, and separation, or mixture, and they adduce demonstration that each of these is number, and it happens from this mode of reasoning, that there is now a multitude of constituted magnitudes, because these properties follow the respective places; since this is the case, whether is it owing to that number which is in the heavens that each of these exists, or to another number besides this? For Plato says it is owing to another number; though he also thought that numbers are these things, and are the causes of these; but that they are indeed intelligible causes, while these are nothing more than sensibles. Respecting the Pythagoreans, therefore, we shall speak no further at present; for it is sufficient to have thus much touched upon them.

But those who consider ideas as causes, in the first place exploring the cause of these things, introduce other things equal to these in number: just as if someone, wishing to numerate, should think that he cannot accomplish this if there are but a few things, but that he can numerate if he increases their number. For nearly forms are equal, or not less than those things, of which, investigating the causes, they proceed from these to those; for, according to each individual thing, there is a certain homonymous form, and besides the essences of other things, there is the one in many, both in these, and in eternal entities. Further still, forms do not appear to have a subsistence, according to any one of those modes by which we have shown them to subsist. Four, from some, the reasoning does not necessarily follow; and from others forms are produced of those things, of which we do not think there are forms; for, according to the reasons arising from the sciences, there are forms of all such things as there are sciences; and from that argument for ideas, which is founded in considering the one in the many, it follows, that there are also forms or ideas of negations. Likewise, in consequence of the ability to understand something of things corruptible, there will also be forms of corruptible natures; for there is a certain phantasm of these.

Further still, with respect to the most accurate of reasons, some make ideas of things relative, of which we do not say there is an essential genus, and some assert that there is a third man; and, in short, the reasons respecting forms subvert those things which, the assertions of forms are of opinion, have a subsistence prior to ideas themselves. For it happens that the duad is not first, but number, and that which has a relative is prior to that which has an essential subsistence. All such particulars likewise happen, as, being consequent to the opinions respecting forms, are adverse to principles. Again, from the notion according to which we say there are ideas, there will not only be forms of essences, but also of many other things: for there is one conception not only respecting essences, but also respecting other things; and sciences are not only sciences of essence, but also of other things; and ten thousand such like particulars happen. But, from necessity, and the opinions respecting forms, it follows that, if forms are participle, there are only ideas of essences: for they are not participated according to accident; but it is requisite that things should participate each idea, so far as each idea is not predicated of a subject. I mean, just as if anything participates of the double, this also participates of the perpetual, but according to accident. For it happens to the double to be eternal; so that forms will be essences; and these both here and there will signify essence. Or what will be the meaning of that assertion, that the one in many is something different from sensible things? And if there is the same form, both of ideas and their participants, there will be something common. For why, in duads, which are corruptible, and in many but eternal duads, is the duad said to be more one and the same than in this, and in some particular thing? But if there is not the same form, the name only will be common; and it will be just as if someone should call both Clinias and a piece of wood a man, at the same time that he perceives no communion whatever between them.

But someone may, in the most eminent degree, doubt what it is that forms contribute to such things as are eternal among sensibles, or to things which are generated and corrupted: for neither are they the causes of any motion, nor of any mutation whatever to these. Nor yet do they afford any assistance to the science of other things (for they are not the essence of these, since in this case they would reside in them); nor do they contribute to the being of other things, since they are not inherent in their participants. For thus, perhaps, they might be considered as causes, as a white color mixed with a body may be said to be the cause that the body is white. But that assertion, which was first made by Anaxagoras, and afterwards by Eudoxus and others, respecting the temperament of things from similar natures, may be easily confuted; for it is easy to collect many and impossible consequences in opposition to this opinion. But, indeed, neither do other things subsist from forms, according to any of those modes which are generally adduced. And to say that forms are paradigms, and that they are participated by other things, is to speak vainly, and to utter poetical metaphors. For, what is that which operates looking to ideas? For it is possible that anything may both be, and be generated similar, without being assimilated to that to which it is familiar; so that, Socrates both subsisting and not subsisting, some other may be generated such as Socrates is: and, in like manner, it is evident that this will follow, although Socrates should be eternal. Besides, there will also be many paradigms of the same thing; and consequently forms, as man, animal, biped; and at the same time, man himself, or the ideal man, will have a subsistence.

Further still, forms will not only be paradigms of sensibles, but also of forms themselves; as, for instance, genus, so far as genus, will be the paradigm of species: so that the same thing will be both paradigm and image. Again, it may seem to be impossible that essence should be separated from that of which it is the essence. So that how well ideas, since they are the essences of things, be separated from them? But, in the Phaedo, forms are said to be the causes, both that things are, and that they are generated; though, at the same time, participants will not be generated, even admitting the subsistence of forms, unless that which is motive subsists. And besides this, many other things are made, such as a house and a ring, of which we do not say there are forms: so that it is evident that other things may be, and may be generated, through such causes as we have just now mentioned.

Again, if forms are numbers, how will they be causes? Whether because beings are different numbers? As, for instance, man is this number, Socrates another, and Callias a number different from both. Why, therefore, are those the causes of these? For it is of no consequence, if those are eternal, but these not. But if it is because sensible natures are the reasons of numbers, as a Symphony, it is evident that there will be one certain thing, of which there are reasons or ratios. If, therefore, this one thing is matter, it is evident that numbers themselves also will be certain ratios of another thing to another thing. I say, for instance, if Callias is a ratio in numbers of fire and earth, water and air, and of certain other subjects, man himself also whether this idea is a certain number or not, will be a ratio of certain things in numbers, without being himself number, and will not through these things be some particular number.

Further still: from many numbers one number is produced; but how is one form produced from forms? But if form is not produced from forms, but from the unities which are in number, after what manner will the unities subsist? For, if they are of the same species, many absurd consequences will ensue; and if they are not of the same species, nor are the same with each other, nor all the rest the same with all, in what do they differ, since they are impassive? For these things are neither reasonable, nor conformable to intellectual conceptions. Besides, it will likewise be necessary to establish another certain genus of number with which arithmetic must necessarily be conversant; and all such things as by some are denominated media. How then do these things subsist, or from what principles do they derive their subsistence? Or why will they be media between things here and those? Besides, each of the unities which is in the duad will subsist from a certain something prior to them, namely the duad itself. This, however, is impossible. 

Further still: since every idea is number, why is it one? And besides this, if the unities are not different, it will be requisite to speak in the same manner as those who say that there are four or two elements: for each of these does not call that which is common an element; as, for instance, body, but fire and earth, whether body is something common or not. But now the assertion is just as if the one consisted of similar parts, like fire or water; but if this be the case, numbers will not be essences. It is, however, evident, that if the one is anything, and this is a principle, the one is predicated in a manifold respect; For it is impossible it should be otherwise. But we, who wish to reduce essences into principles, assert that length consists from the long and the short, and from the small and the large: that superficies is composed from the broad and the narrow; and body from the deep and the low. But how can a plane possess a line, or a solid a line and a plane? For the broad and the narrow are a genus different from that of the deep and the low. As, therefore, number is not inherent in these, because the much and the few are different from these, so it is evident that neither will any one of the superior subsist in any of the inferior natures. But neither is the broad the genus of the deep: for thus body would be a certain superficies.

Again: from what principles will points be composed? This genus, therefore, Plato opposes, as being a geometrical dogma; but he calls it the principle of a line; And often asserts that there are indivisible lines, though it is necessary there should be a certain bound of these. So that, for the same reason that there is such a thing as a line, a point also has a subsistence. And, in short, since wisdom investigates the cause of things apparent, this indeed we omit: for we say nothing respecting the cause whence the beginning of mutation is derived. But, thinking to assign the essence of things apparent, we say that there are other essences; and we in vain describe the manner in which those are the essences of these: for, as we have before observed, it is to no purpose to assert, that this is effected by participation. Nor, again, our ideas such causes as we perceive in sciences, and through which every intellect and every nature produces; nor do they touch upon any cause which we say is one of the principles. But, with those of the present day, the mathematical sciences generated philosophy, though they say it is requisite to be conversant with these disciplines for the sake of other things.

Further still, the subject matter itself may be considered as being rather mathematical matter, and as that which ought rather to be predicated and to be considered as the difference of essence and matter, such as the great and the small; Just as physiologists assert that the rare and the dense are the first differences of the subject matter. For those are certain excesses and defects. But respecting motion what ought we to think? For if these (namely excess and defect) are motions it is evident that forms will be moved: but if they are not motions, whence is motion derived? For the whole speculation respecting nature it will be taken away. And besides this, that which seems to be easy will not be accomplished, namely to demonstrate that all things are one. For all things do not become one by exposition, but a certain one itself, if anyone allows all things. Nor yet this, unless he admits that there is an universal genius. But this in certain things is impossible. Nor is there any reason in those things which are posterior to numbers, namely lengths, superficies and solids, with respect to the mode in which they are or will be; Nor do they possess any power. For these can neither be forms (for they are not numbers) nor things which have a middle subsistence (for those are mathematical), nor can they be things corruptible: but again these appear to be a fourth genus, different from those three. And, in short, it is impossible that anyone can find by investigation the elements of beings, unless he divides them, since they are manifoldly predicated; Especially, if he investigates from what elements they are composed. For it is not possible to admit those things from which action or passion, or the straight, consist; but, if it were possible, they could only be admitted as belonging to beings: so that either to investigate, or to think it possible to possess, the elements of all beings is not true. For, how can anyone learn the elements of all things? Since it is evident that he cannot possess any antecedent knowledge. For, as he who learns geometry may indeed previously know other things, but cannot have a prior knowledge of any of the particulars with which the science of geometry is conversant, and in which he is to be constructed; So likewise in other things. So that, if there be a certain science of all things, as some assert, he who possesses this science cannot have any pre-existent knowledge. But yet every discipline subsists through a prior knowledge, either of all things, or of certain particulars; And is accomplished, either through demonstration or through definitions. For it is requisite that those things should be foreknown from which definition consists. And the like takes place with respect to the knowledge which is acquired by induction. But if we possess an innate knowledge of things, it is wonderful how we happen to be ignorant that we possess the most excellent of sciences. Further still, how can anyone know from what particulars all things consist, and how will this be manifest? For this is dubious: for someone may doubt just as respecting certain syllables, since some assert that the syllable ZA, is composed from Σ, Δ, A; but others say it has a different sound, and not any one of those sounds that are known. Again, how can anyone, not possessing sense, no sensibles? Yet it is requisite he should, if those are elements of all things, from which things consist, just as composite sounds from their proper elements. From what has been said, therefore, it is evident that all philosophers seem to investigate, though obscurely, those causes which we have spoken of in our Physics, and that we are not able to assign any other cause different from some one of these. Four, in one respect, all these have been mentioned by philosophers prior to us; but in another respect they have been by no means mentioned. For the first philosophy, as being young, and that its first commencement, appears to stammer about everything. For Empedocles says, that bone consists from reason (namely form). But this is the very nature and essence of a thing period however, if this were admitted, in like manner flesh, and everything else, must either be reason or nothing; for, through this, both flesh and bone, and every other thing, subsist, and not through matter, which he calls fire and earth, and water and air. These things he would necessarily admit, if they were asserted by another person; but he does not speak clearly respecting them. Things of this kind, therefore, we have rendered manifest before. But such doubts as may arise respecting them we shall again relate; for, from these, we may perhaps be enabled to solve future doubts.

Aristotle, Metaphysics. Book 2, Chapter 1.

The speculation of Truth is partly difficult and partly easy; a token of which is this: that no one can speak of it according to its dignity, and that all men are not disappointed in the pursuit of it, but everyone asserts something respecting Nature; and though each of those who have philosophized has added nothing, or but a little, to this speculation, yet something of magnitude is produced from the assertions of all of them collected together. So that, if this appears to be the case, who, as we are accustomed to say proverbially, will miss the gate? In this respect, therefore, the speculation of truth will be easy; but that all those who philosophize should together possess a certain whole, while at the same time each is destitute of a part, evinces the difficulty of this speculation. But perhaps, since the difficulty is twofold, the cause of it is not in things themselves, but in us.

For, as are the eyes of bats to the light of day, so is the intellect of our soul to such things as are naturally the most splendid of all. But it is not only just to return thanks to those with whose opinions some one may accord, but likewise to those who have spoken more superficially; for they also contribute something, since they exercise our speculative habit: for, if Timotheus had not existed, we should not have had much modulation; and without Phrynis there would not have been such a person as Timotheus. The same thing may be said of those who have discoursed concerning truth: for from some of them we receive certain opinions; but others were the causes of their entertaining such opinions.

But it is right to call philosophy a science speculative of truth: for the end of speculative science is truth, but of practical science, a work: for practical men, if they consider how a thing subsists, yet do not speculate the cause of that thing by itself, but with relation to something else, and as connected with the present time. But we do not know truth without the knowledge of causes: and everything is in the most eminent degree that, among other things, according to which the synonymous is present with other things: thus, fire is most hot; for this is to other things the cause of heat. Hence that is most true, which is the cause to posterior natures of their being true; on which account it is necessary that the principles of things eternal should be always most true: for they are not sometimes true, nor is any thing the cause of being to them, but they are the cause of being to other things. And hence, such as is the being of every thing, such also is its truth.

Aristotle, Metaphysics. Book 2, Chapter 2.

But, indeed, that there is a certain principle, and that the causes of things are not infinite, neither according to a procession in a right line, nor according to species, is evident. For, neither can this thing proceed from that to infinity, as, for instance, flesh from earth, earth from air, air from fire, and so on, without any end of the procession; nor can this be the case with that cause whence the principle of motion is derived; as, for instance, that man is moved by the air, this by the sun, and the sun by strife, and so on without end. In like manner, with respect to the final cause, or that for the sake of which a thing subsists, neither is it possible in this to proceed to infinity; as that walking should be undertaken for the sake of health, health should be acquired for the sake of felicity, and felicity for the sake of something else; and that thus always one thing should subsist for the sake of another. In like manner, a procession to infinity is impossible, with respect to the formal cause; for, in those things which have mediums, so that something is last and something first, that which is first must necessarily be the cause of that which is posterior to it. For, if it were requisite for us to assign the cause of three things, we should say it is the first of the three; for it cannot be the last, since this is not the cause of anything: nor yet can it be the middle, for this is the cause only of one thing, viz. that which follows it. But it is of no consequence whether one, or many and infinite mediums are assumed. But with respect to things infinite in energy, and the infinite itself, all the parts are similarly mediums as far as to the extremity; so that, in short, if nothing is first, there is no cause.

But neither can a procession to infinity downwards take place, if in a procession upwards there is a principle of causes, viz. so that from fire water shall be produced, from water earth, and so always something else shall be generated. For one thing is generated from another in a twofold respect, not as this thing is said to take place after that, as the Olympic from the Isthmian games; but either as we say a man is generated from a boy undergoing a mutation, or air from water. We say, therefore, that a man is generated from a boy, as that which is generated from that which has already been generated, or as that which is perfect from that which is tending to perfection. For there is always a certain medium; so that, as generation is the medium between being and non-being, in like manner, that which is making subsists between that which is simply being, and that which is simply non-being. But he who is learning is becoming to be scientific: and this is the meaning of the assertion, that he who is scientific is generated from him who learns. But water is generated from air, in consequence of air being corrupted. Hence, in the former instances, the things adduced do not revert into each other, nor is a boy generated from a man. For, that which is making is not produced from generation, but subsists after generation. Thus, day is generated from the dawn, because it subsists after it; and, on this account, neither is the dawn generated from the day. But the other instances revert into each other.

In both these cases, however, it is impossible that a procession to infinity should take place. For, since there are mediums, in the one case, it is necessary there should be an end; and, in the other case, the things adduced revert into each other; for the corruption of one is the generation of the other. But, at the same time, it is impossible that the nature which is first should be corrupted, since it is eternal: for, since generation is not infinite in an ascending progression, it is necessary that the nature should not be eternal, from which being first corrupted something is generated. Besides, that for the sake of which other things subsist is the end; but a thing of this kind is that which does not subsist for the sake of another, but other things subsist for the sake of it; so that, if that which is last is of this kind, there will not be a procession to infinity. But, if there is not anything of this kind (or that which is last), there will not be that for the sake of which other things subsist.

Those, indeed, who introduce an infinite process are ignorant that they take away the nature of the good; though no one would attempt to do anything, if he were not to arrive at the end of his undertaking; nor would there be intellect in things of this kind. For he who possesses intellect always acts for the sake of something. For this is a limit; but the end is a limit. But neither can the formal cause be referred to another more copious definition; for always the prior definition is more the definition of a thing, but the posterior is not the definition of a thing. But where there is no first, neither is there that which is consequent to the first.

Further still: those who speak in this manner take away scientific knowledge. For it is not possible that anything can be known before we arrive at things indivisible: for how can things be understood, which are after this manner infinite? for the infinite here is not like that in a line, since there is no end to the divisions of a line; But we do not understand divisions unless we limit them; he, therefore, who passes through the infinite will not number the sections. Likewise, with respect to matter, it is necessary that it should be understood so far as it subsists in motion. But nothing can be infinite in energy; and if this be the case, that by which infinite can be known is not itself infinite. But if likewise the species of causes were infinite in multitude, neither thus could we obtain a knowledge of things; for we then think that we know when we know causes. But we cannot in a finite time pass through that which is infinite according to addition.

Aristotle, Metaphysics. Book 2, Chapter 3.

But affections happen according to habits. For we think that we ought to speak conformably to things to which we are accustomed; and things which are asserted contrary to those to which we have been accustomed appear more unknown to us, because they are strange and foreign. For that to which we are accustomed is more known. But the laws evince the great power of custom, in which things fabulous and puerile possess, through custom, greater power than the truth of knowledge. Some, therefore, will not attend to those who speak, unless they speak mathematically; and others do not approve what is said, unless it is spoken paradigmatically. There are also those who think that a poet should be adduced as a witness; and others expect that all things should be accurately delivered. To others, again, the accurate is painful; either because they are unable to comprehend it, or because they consider it as nothing more than micrology, or minute discussion. For the accurate possesses something of this kind; and hence, as in contracts minute attention, so in discourse accurate discussion, appears to some to be illiberal. On this account, it is requisite to be instructed how everything is to be admitted; because it is absurd at the same time to investigate science, and the manner in which science is to be obtained; for it is not easy to accomplish either of these. Mathematical accuracy of discussion is not, however, to be required in all things, but in those only which have no connection with matter: on this account such a mode of discussion is not physical; for the whole of nature perhaps is connected with matter. Hence, what nature is ought first to be considered; for thus the object of the physical science, and whether it is the province of one or of many sciences to speculate causes and principles, will be apparent.

Aristotle, Metaphysics. Book 3, Chapter 1.

In order to acquire that science which is the object of our investigation, it is necessary, in the first place, to enumerate the particulars respecting which it is first requisite to doubt. But these are the things of which there are different opinions, and whatever besides these may have been neglected and omitted. But, for those who wish to doubt, it is advantageous to doubt in a proper manner. For the power of acquiring posterior knowledge is derived from the solution of prior doubts. But it is not possible for any one to dissolve the bond of anything, who is ignorant with what it is bound. The doubting, however, of the dialectic part of the soul, or that part which reasons scientifically, manifests the bond respecting a thing. For, so far as this part of the soul doubts, so far it is similar to those who are bound; since neither he who is bound nor he who doubts is able to proceed any further. On this account it is requisite, in the first place, to contemplate all the difficulties, both for the sake of these things, and because those that investigate without having previously doubted resemble those who are ignorant whither they ought to go: and, besides this, neither can they know whether they have found, or not, the object of their search. For the end to these is not manifest; but is manifest to those who previously doubt in a proper manner. Further still, it is necessary that one should be better fitted to judge, who has heard all the opposite reasons which may be compared to the adversaries in a law-suit.

But the first doubt is respecting those things concerning which we have also doubted in the preface, viz. whether it is the province of one or of many sciences to speculate causes; and whether it belongs to this science, alone to consider the first principles of essence, or likewise to speculate concerning those principles from which all demonstrations are formed: such as, whether it is possible that one and the same thing can at the same time be affirmed and denied; and other things of this kind. And, if it is the business of this science to be conversant with essence, whether there is one or many sciences about all essences; and, if there are many, whether all of them are allied to each other, or some of them are to be called wisdom, and others something else. This, also, it is necessary to investigate, whether we must say that sensible experiences alone have a subsistence, or others besides these; and whether there is one genus or many genera of essences; according to the opinion of those who introduce forms, and place things mathematical between these and sensibles. These things, therefore, as we have said, must be considered; and likewise, whether the speculation is alone respecting essences, or also respecting the essential accidents of essences. And, besides this, whose province it is to speculate concerning the same and different, the similar and dissimilar, contraries, prior and posterior, and every thing else of this kind, about which those who are skilled in dialectic endeavour to speculate, making their inquiry from things probable alone.

Further still, respecting such things as are essential accidents to these; and not only what each of these is, but likewise if one is contrary to one. And again, whether genera are principles and elements, or those things which are inherent in a thing, and into which it is divided. And if this is the case with genera, whether they are such things as are predicated the last of all of individuals, or such things as are first; as, for instance, whether animal or man is a principle, and is more a principle than that which is an individual. But it is especially requisite to inquire, and seriously to consider, whether there is any essential cause besides matter, or not, and whether this is separate or not: likewise, whether it is one, or if there are many such causes; and whether there is any thing besides a collected whole, or that which is a composite (but I mean by a collected whole, when any thing is predicated of matter); or whether there is nothing besides: or whether this is the case with some things, and not with others; and, if this be the case, what kind of beings these are.

Further still, with respect to principles, whether they are bounded in number or species, viz. whether this is the case both with principles subsisting in reasons (formal causes), and those which subsist in a subject; and whether there are the same or different principles of things corruptible and incorruptible. Again, whether all principles are incorruptible, or whether the principles of things corruptible are themselves corruptible. Further still, that which is the most difficult of all, and possesses the greatest ambiguity, is, whether whether the one and being are, as the Pythagoreans and Plato say, nothing else than the essence of beings; or this is not the case, but something else is the subject. For instance, whether fire is the principle of all things, as Heraclitus says; or water, or air. And again, whether principles are things universal, or have a subsistence like particulars; and whether they subsist in capacity or energy.

Further still, whether they subsist in any other manner than as things motive; for these things may afford matter for abundant doubt. And, besides all this, whether numbers, lengths, figures, and points are certain essences or not; and if they are essences, whether they are separated from sensibles, or subsist in them. For, respecting all these particulars, it is not only difficult to discover the truth, but neither is it easy to doubt well in a rational manner.

Aristotle, Metaphysics. Book 3, Chapter 2.

In the first place, therefore, we must inquire regarding those things which we first mentioned, whether it is the province of one or many sciences to speculate on all the genera of causes: for how can it be the business of one science to know principles, since they are not contrary to each other? Besides, with many beings all things are not present. For, how is it possible that the principle of motion, or nature of the good, can subsist in things immovable? since everything which is essentially and through its own nature good is an end; and so is a cause, because other things are generated and subsist for its sake. But the end, and that for the sake of which a thing subsists, are the end of a certain action. But all actions are accompanied with motion: hence, it is not possible that in things immovable there can be this principle, or a certain good itself. On this account also, in the mathematical sciences, nothing is evinced through this cause, nor is any demonstration produced from it, because it is better or worse. But no one makes any mention whatever of any thing of this kind; so that certain of the sophists, such as Aristippus, revile these sciences on this account. For in other arts, says he, and even such as are sordid, as in the tectonic art and that of the currier, all things are asserted on account of the better or the worse; but the mathematical sciences do not pay any attention to things good and evil.

But again, if there are many sciences of causes, and each is conversant with a different cause, which of these must we assert to be that which we investigate? or, who, among those that possess these sciences, will have a scientific knowledge of the thing investigated? For it happens, that all the modes of causes are present with the same thing. Thus, for instance, in a house, the cause whence motion is derived is art, and the builder; but that for the sake of which it subsists is the work; the matter is earth and stones, and the form is the definition. From those things, therefore, which were formerly decided by us, viz. which of the sciences ought to be called Wisdom, it seems reasonable, that each should be thus denominated: for that science which is the most principal and the most honorable, and which it is not just other sciences that rank as servants should contradict, is the science of the end and the good (and, as it appears, ought to be called wisdom); for the rest subsist for the sake of this.

But, so far as wisdom is defined to be the science of first causes, and of that which is especially the object of knowledge, the science of essence may not unjustly vindicate to itself the name of wisdom. For, since the same thing may be known in many ways, we say, that he rather knows who knows a thing from its inherent properties, than he who knows from particulars which do not pertain to that thing. But, among these, one knows more than another; and this is especially the case with him who perceives what a thing is, and not of him who apprehends the quantity or quality of a thing, or what it is naturally adapted to do or suffer. Further still, in other things also, we then think that we know each of those things of which there are demonstrations, when we know what each is; as, for instance, we then know what the squaring of a right-lined figure is, when we know that it is the invention of a mean proportional; and in a similar manner, with respect to other things. But with respect to generations, actions, and all mutation, we then especially know, when we know the principle of motion. This, however, is another principle, and is opposite to that which ranks as the end; so that, to contemplate each of these causes may appear to be the province of another science.

With respect, however, to the principles of demonstration, it is doubtful whether the speculation of these is the province of one, or of many sciences–but I call the principles of demonstration those common opinions from which all men demonstrate–such as, it is necessary that every thing should be affirmed or denied; and, it is impossible for a thing at the same time to be and not to be; and such other propositions as are of a similar nature. Whether, therefore, is there one or a different science of these and of essence? And if there is one, whether or not must we denominate it that science which we now investigate? It is not, therefore, rational to suppose, that there is one science of these; for, why is it more the province of geometry than of any other science to speculate concerning these? If, therefore, it is in a similar manner the province of any science whatever, but it cannot be the province of all the sciences, as neither is it the peculiarity of the rest, so neither does it belong to that science which knows the essences of things, to know the principles of demonstration. And, at the same time, how will it be the science of these? For we now also know what each of these is. Other arts, therefore, use these as things known to them. But If there is a demonstrative science respecting them, it will be requisite there should be some subject genus, and that some of them should be participated properties, and others axioms. For it is impossible that there can be demonstration of all things; since it is necessary that demonstration should consist from certain things, be employed about a certain thing, and be of certain things. Hence it happens, that there is one particular genus of all things that are demonstrated; for all demonstrative sciences use axioms.

But if the science of essence is different from the science respecting these, which of them is the more principal, and naturally prior? for, universally, and in the most eminent degree, axioms are the principles of all things. But, if it is not the province of a philosopher, to whom does it belong to contemplate the truth and falsehood about these? And, In short, whether is there one science of all essences, or many sciences? If, therefore, there is not one science, what kind of essence must we establish as the object of this wisdom? But it is not rational to suppose, that there is one science of all essences; for there will also be one demonstrative science of all essential accidents; since every demonstrative science speculates, from common opinions, essential accidents about a certain subject. It is the business, therefore, of the same science, to speculate, from the same opinions, essential accidents about the same genus: for the consideration of the whole, or, that a thing is, is the province of one science; and it is likewise the employment of one science to speculate the particulars from which a thing consists, whether it is the same or a different science; so that the like will take place with respect to accidents–whether these sciences contemplate them, or one of these. Further still, whether the speculation is alone respecting essences, or also respecting things accidental to these. But my meaning is: if, for instance, a solid is a certain essence, and lines and planes, whether it is the province of the same or of another science to know these, and things accidental about each genus; for, if it is the province of the same science, it will be a certain demonstrative science, and the science of essence. But demonstration does not appear to be employed about the formal cause: but if it is the province of another science, what science will that be which speculates the accidents about essence? for, to assign this is very difficult.

Further still: whether must we say, that there are alone sensible essences, or others besides these? And whether is there one genus, or many genera of essences, according to the opinion of those who say that there are forms and natures subsisting between forms and things sensible, about which, according to them, the mathematical sciences are conversant? In what manner, therefore, we assert that forms are causes and essences subsisting by themselves, has been related by us in our first discourses respecting them; but as the consideration of them is attended with abundant difficulty, it is no less absurd to say, that there are certain natures besides those which are in the heavens, and that these are the same with sensibles, except that the former are eternal, but the latter corruptible. For they say, that there are man itself, and horse itself, and health itself; but they do not assert any thing else respecting these: and in this respect they are similar to those who acknowledge indeed that there are gods, but that they possess a human form; for, neither do the latter of these make any thing else than eternal men, nor do the former make ideas to be at all different from eternal sensible natures.

Again, if any one, besides forms and things sensible, places things between these, it will be attended with many doubts: for it is evident, that in a similar manner there will be lines, and each of the other genera, besides those that are sensible: so that, since astronomy is one of these, there will also be another heaven besides the sensible heaven, another sun and moon, and, in a similar manner, the other natures which the heavens contain. Though, how is it possible to believe that there are such things as these? For, neither is it rational to suppose, that this ideal heaven is immoveable, and it is entirely impossible that it should be moveable. A similar consequence will ensue respecting those objects about which the optic science is employed, and likewise with respect to harmonics in mathematics: for it is impossible that these should have a subsistence different from sensibles, through the same causes: for, if there are sensibles and senses which have a middle subsistence, it is evident that there will also be animals subsisting between them and things corruptible. But it may also be doubted, about what kind of beings it is requisite to investigate these sciences. For, if geodesy differs in this only from geometry, that the former of these is conversant with things which we perceive, but the latter with things which are not sensible; it is evident, that, besides the medicinal science, there will be a certain science between medicine itself, and the medicine which subsists among us. But how is this possible? for there will also be certain salubrious things, besides such as are sensible, and the salubrious itself. And, at the same time, neither is this true, that geodesy is conversant with sensible and corruptible magnitudes: for, these being corrupted, it also will be corrupted. But neither will astronomy be conversant with sensible magnitudes, nor with this visible heaven. For neither are sensible lines such as the geometrician speaks of, since nothing of sensibles is accurately straight or round: for a circle touches a rule not in a point, but as Protagoras said, confuting geometricians; nor are the motions and spiral revolutions of the heavens similar to those about which astrology discourses; nor have points the same nature as the stars.

But some assert, that there are such things as are said to subsist between forms and sensibles, which yet are not separate from sensibles, but in them. To enumerate to these men the impossibilities which attend this doctrine would require a long discourse: it is sufficient, therefore, to have speculated thus much respecting them: for neither is it rational that this should alone be the case with these, but it is evident that it would also happen that species would subsist in sensibles; since both these are the consequences of the same reasoning process. Further still: it would be necessary that two solids should be in the same place; and mathematical entities would not be immoveable, in consequence of subsisting in things sensible which are moved. And, in short, on what account can any one admit them to have a subsistence, and a subsistence in sensibles? for there will be a certain heaven besides heaven, except that it will not be separate, but in the same place; which is more impossible.

Aristotle, Metaphysics. Book 3, Chapter 3.

Respecting these things, therefore, there is great doubt, viz. how they may be admitted so that we may obtain the truth; and likewise respecting principles, whether it is requisite to consider genera as elements and principles, or rather those things from which, being inherent, everything first consists: as, for instance, the elements and principles of voice appear to be those things from which all voices are first composed, and not voice in common: and we say that those things are the elements of diagrams, the demonstrations of which are inherent in the demonstrations either of all or the greater part of other things. Further still: both those who assert that there is one element, and those who say that there are many, from which bodies are composed and from which they consist, assert that they are principles; as, for instance, Empedocles says that fire and water, and the natures which subsist together with them, are elements, from which, being inherent, things exist; but he does not speak of these as the genera of beings. Besides this too, if anyone is willing to consider the nature of other things, as, for instance, a bed, from what parts it consists, and how those parts are composed, he will then know the nature of it. From these reasons, therefore, principles will not be the genera of beings. But if we know everything through definitions, but principles are the genera of definitions, it is necessary also that genera should be the principles of things defined. And likewise, if to possess the science of beings is to possess the science of forms, according to which beings are predicated, in this case genera will be the principles of forms.

But some also of those who assert that the one, or being, or the great and the small, are the elements of beings, use these as genera. However, it is not possible to call both these principles; for there is one reason of essence; but the definition which is assigned through genera will be different from this, and likewise that which assumes those particulars from which, being inherent, a thing consists: to which we may add, if genera are in the most eminent degree principles, whether is it requisite to think that the first of genera are the principles of things, or the last genera which are predicated of individuals? For this is doubtful. For, if things universal are in a more eminent degree principles, it is evident that the highest genera will be the principles of things (for these are predicated of all things); and hence there will be as many principles of beings as there are first genera: so that both being and the one will be principles and essences; for these are especially predicated of all beings. But it is not possible that there can be only one genus of beings, and that this is either the one or being: for it is necessary that there should be differences of every genus, and that each should be one. But it is impossible either that species should be predicated of the proper differences of genus, or that genus should subsist without its species; so that, if either the one or being is genus, no difference will either be the one or being. But if there are not genera, neither will there be principles; since genera are principles. Further still, things subsisting between these, comprehended together with differences, will be genera as far as to individuals. But now this appears to be the case with some, and not with others; to which it may be added, that differences are in a greater degree principles than genera. But if these also are principles, there will be, as I may say, infinite principles, and especially if anyone establishes the first genus as a principle. But if the one is of a more primary nature, and the one is indivisible, but everything indivisible is either so according to quantity or according to species, and that which is according to species has a prior subsistence, but genera are more divisible into species, the one indeed will be predicated the last of all; for man is not the genus of particular men.

Further still: in those things in which there is prior and posterior, it is not possible that the thing which is predicated of these should be different from them. Thus, for instance, if the dyad is the first of numbers, there will not be any number besides the species of numbers; and, in a similar manner, neither will there be figures besides the species of figures. But, if this is the case with respect to these, scarcely will there be genera of other things besides species; for genera appear especially to be of these. But, in individuals, one thing is not prior and another posterior. Further still: wherever one thing is better and another worse, that which is better is always prior; so that none of these will be genus. Hence, those things which are predicated of individuals appear to be principles more than genera.
Again, it is not easy to say in what manner it is requisite to consider these as principles. For it is necessary that a principle and cause should exist exclusive of the things of which it is the principle, and that it should be able to subsist separate from them. But why should anyone think that anything of this kind exists besides that which is particular, except that it is predicated universally and of all things? But if on this account, then things more universal must be considered as principles in a more eminent degree; so that first genera will be principles.

Aristotle, Metaphysics. Book 3, Chapter 4.

But there is a doubt consequent to these things, which is the most difficult and the most necessary of all things to contemplate, and which is the subject of the present discourse. For, if there is nothing besides particulars, but particulars are infinite, how is it possible to possess the science of infinites? For, so far as there is a certain one and the same, and so far as there is something universal, so far we know all things. But if this is necessary, and if it is requisite that there should be something besides particulars, it will also be necessary that there should either be last or first genera besides particulars. That this, however, is impossible, we have just now doubted. Furthermore, if there is especially something besides the whole, when anything is predicated of matter, whether, if there is a certain form, it is necessary there should be something (universal) besides all individuals? Or, that there should be something universal besides some and not besides others? Or, is there universal besides individuals? If, therefore, there is nothing besides particulars, there will be nothing intelligible, but all things will be sensible, and there will not be science of anything, unless someone asserts that sense is science. Again, neither will there be anything eternal, nor anything immovable; for all sensible things are corrupted, and are in motion. But if there is nothing eternal, neither is it possible that there can be generation. For it is necessary that there should be something which is generated, and something from which it is generated, and that the last of these should be that which is unbegotten, if the progression of things stops, and it is impossible that anything can be generated from non-entity.

Further still: there being such things as generation and motion, it is necessary also there should be a boundary or end: for neither is any motion infinite, but of every motion there is an end; and it is not possible a thing should be generated which cannot possibly be generated. But that which is made necessarily is as soon as it is made. Again, if matter is, on account of its being unbegotten, it is much more rational that there should be essence, on which the being of matter depends: for, if neither essence is, nor matter, nothing whatever will have any subsistence. But, if this is impossible, it is necessary that form and species should be something besides the whole. But again, if anyone admits this, it is doubtful in what things he should admit it, and in what not. For it is evident that it cannot be admitted in all things; since we do not all admit that there is any house different from sensible houses. To which we may add, whether will there be one essence of all things, as for instance, of men? But this is absurd. For all things are not one of which the essence is one, but many and different. But this also is irrational. At the same time, too, how does matter receive each of these? And how is the whole (viz. sensible particulars) both these?

Further still: this also may be doubted respecting principles. For, if they are one in species, there will be nothing which is one in number, nor will there be the one itself and being itself. And how will it be possible to know scientifically, if there is not in all things a certain one? But indeed, if they are one in number, each of the principles also is one in number, and there are not different principles of different things as in sensibles; as, for instance, of this syllable, which is the same in species, the principles also are the same in species; for these also are different in number. But if this is not the case, and the principles of beings are one in number, there will not be anything besides the elements. For, to call a thing one in number, or to call it a sensible particular, differs in no respect; for, thus we call a sensible particular one in number; but universal, that which is common in these. Just, therefore, as if the elements of speech were bounded in number, it would be necessary that all the letters should be as many as the elements, since neither two nor more than two of them would be the same.

But a doubt in no respect less than this is omitted, both by those of the present day and the ancients, viz. whether there are the same or different principles of things corruptible and of things incorruptible. For, if there are the same principles, after what manner are some things incorruptible, but others corruptible? And what is the cause of this? Hesiod, indeed, and all such theologians alone paid attention to that which appeared probable to themselves, but neglected us. For, making principles to be gods, and asserting that all things originated from the gods, they say that those natures are mortal which have not tasted of nectar and ambrosia. But it is evident that they employ these names as expressive of things known to themselves, though, respecting the enunciation of these names, they speak beyond our conception. For, if the immortals touch these for the sake of pleasure, nectar and ambrosia are in no respect the causes of their being; but, if they are the causes of their being, how will the gods be eternal, since they require aliment? It is not, however, worth while to speculate seriously respecting those things which are spoken sophistically in a mythological manner.

But it is requisite to inquire of those who speak from demonstration, why, if things are from the same principles, some are naturally eternal, but others are corrupted. However, as they do not assign the cause of this, and as it is not rational that this should be the case, it is evident that there are neither the same principles nor causes of these. For Empedocles, who, it might be thought, the same thing: for he places strife as a certain principle and cause of corruption. Yet it would seem that this no less than friendship is generated from the one; for all other things are produced from this (viz. strife) except divinity. He says, therefore, “From which all things that were, that are, and that shall hereafter be, originated; from which trees also germinated, men and women, wild beasts and birds, fishes nourished in the water, and the long-lived gods.” It is also evident, that all things subsist without these: for, if strife was not inherent in things, all things (as he says) would be one: since, when they come together, then strife stands at the extremity of things. Hence it happens to him, that the most blessed divinity is less wise than other beings: for he does not know all the elements, because he does not possess contention. But knowledge is a conjunction of similar with the similar. For he says, “By earth we behold earth, and by water, water; by ether, divine ether, and by fire, pernicious fire. By friendship we perceive friendship, and by strife, baneful strife.” But, to return whence we digressed: this is evident, that it happens to him that strife is no less the cause of corruption than of being; and, in like manner, that friendship is not more the cause of the being than of the corruption of things; for, collecting them into one, it corrupts other things. And, at the same time, he does not mention any cause of the transmutation, but that it is naturally adapted to subsist in this manner. “For” (says he) “when mighty contention was nourished in the members, it ascended to the honours of perfect time, which being vicissitudinary to them preceded the ample earth.” As if it were necessary, indeed, that a change should take place. But at the same time he evinces no cause from necessity, asserting only thus much conformably to his own doctrine, that he does not make some things corruptible and others incorruptible, but makes everything corruptible except the elements. But the doubt which is now mentioned is this: why, if all things are from the same principles, have some things a subsistence, and others not? Thus much, however, may suffice to show that they are not from the same principles. But, if the principles of things are different, one doubt is, whether they also will be incorruptible or corruptible. For, if they are corruptible, it is evident that they also must necessarily originate from certain other things: for all things are corrupted into those things from which they derive their being: so that, on this hypothesis, it happens that there are other principles prior to principles. But this is impossible, whether the progression stops, or advances to infinity. Further still: if principles are taken away, how will things corruptible subsist? But, if principles are incorruptible, why, from these being incorruptible, do things corruptible subsist, but from other things incorruptible? For this is not rational; but is either impossible, or requires a multitude of arguments.

Again: no one has endeavoured to show that these are different; but they say that these are the same principles of all things; and they pass by that which was first doubted by us, as if they apprehended this to be a thing of a trifling nature. But this is of all things the most difficult to contemplate, and, in order to know the truth, the most necessary, whether being and the one are the effects of things, and each of them is not anything else, but this is the one, and that is being? Or, whether it is requisite to inquire what the one is, and what being is, as if there was another nature subject to these? For some think that the nature of the one subsists in that, and others in this manner. For Plato, indeed, and the Pythagoreans, do not think that being differs from the one, but that this is the nature of them, as if the essence was the same, to be one, and to be a certain being. But those who are conversant with Physis accord with Empedocles, who, as if bringing us back to that which is more known, says that the one is less. For he may appear to assert that this is friendship; since this is the case for all things of their being one. But others say that fire, and others again that air, is this one and being, from which beings subsist and are generated. And, in like manner, those who establish more elements than these; for it is necessary for these also to assert, that being and the one are as numerous as they say principles are. But it happens, if anyone does not admit it, that the one and being are a certain essence, that neither can any one of other universals have a subsistence; for these are, of all things, especially universal. But, if neither the one itself nor being itself is some particular thing, much less will anything else have a subsistence, except such things as are called particulars. Further still: if the one is not essence, it is evident that neither will number have a subsistence as a certain nature separate from beings; for number is monads; but the monad is a certain one. But if the one itself is some particular thing, and likewise being itself, it is necessary that the essence of them should be being and the one; for nothing else is universally predicated of them but these very things. But, indeed, if being itself and the one itself have a subsistence, a great doubt will arise how anything besides these subsists. I mean, how there will be more beings than one: for, that which is different from being is not being; so that, according to the reasoning of Parmenides, it necessarily happens that all beings are one, and that this is being. But in both cases a difficulty ensues; for, whether the one itself is not essence, or whether it has a subsistence, it is impossible that number can be essence. But why it cannot, if the one is not, has been shown by us before. And if the one is, the same doubt as that respecting being remains; for, that from which there will be another one, besides the one itself, must necessarily be itself not one. But all beings are either one or many, each of which many is one.

Further still: if the one is indivisible, according to the axiom of Zeno, it will be nothing; for that which neither when added nor when taken away makes anything to be greater, according to him, does not rank among beings; because being is magnitude, and, if magnitude, corporeal; for this is in every respect being. But other things, when added, in a certain respect make that which is greater, and in a certain respect, nothing. Thus, a superficies and a line make that which is greater; but this is by no means true of a point and a monad. But, as he [Zeno] sees thus importantly, and it happens that there is something indivisible, the following arguments may be urged against him: The addition of a thing of this kind does not make that which is greater, but that which is more. But how will magnitude be composed from one, or more than one, of this kind? For it is just as if it should be said, that a line consists of points. But if anyone should apprehend, according to the assertion or function, that from the one itself, and another certain nature which is not the one, number is composed; yet we must, nevertheless, investigate on what account, and how, that which is generated is at one time number, and at another magnitude, if that which is not the one and in equality are of the same nature? For it does not appear how, from the one and this nature, nor how from a certain one and this nature, magnitudes can be produced.

Aristotle, Metaphysics. Book 3, Chapter 5.

But, consequent to these things, it is dubious, whether numbers and bodies, superficies and points, are certain essences or not. For, if they are not, we shall not be able to apprehend what being is, and what are the essences of things. For participated properties and motions, relatives, dispositions, and ratios, do not appear to signify the essence of anything. For all these are predicated of a certain subject, and no one of them can be said to be this or that particular thing. But those things which especially appear to signify essence, are water, and earth, and fire, from which composite bodies consist: but the heat and cold of these, and things of this kind, are passions, and not essences; while body alone, which is passive to these things, sustains them as a certain being and essence. But indeed body is less essence than superficies, and superficies than line, and line than unity and a point; for by these body is defined. And these indeed appear capable of subsisting without body, but it is impossible that body can subsist without these. Hence the many think, and the ancients thought, that essence and being are body, but that other things are the participated properties of body; so that the principles of bodies are also the principles of beings: but the moderns, and those who are considered as wiser than these, think that essence and being are numbers. As we have said, therefore, if these things are not essence, there will not, in short, be anything that is essence, nor anything that is being. For it is not worthwhile to call the accidents belonging to these, beings. But indeed, if this should be granted, that lengths and points are more essence than bodies, yet we do not see the kind of bodies to which these must belong; (for it is impossible that they can subsist among sensibles). 

Again: all these appear to be the divisions of body; one into breadth, another into depth, and another into length. And besides this, in a similar manner, every kind of figure is in a solid: so that, if neither mercury is in a stone, nor the bed of a cube in a cube, as it is defined, neither therefore is superficies in body. For, if this were the case with anyone, it would indeed be that which separates the halves. But there is the same reasoning respecting a line, a point, and a monad. So that, if body is eminently essence, and these are more essence than body, but at the same time these neither are, nor are certain essences; what being is, and what is the essence of things, will fly from our pursuit. For, in addition to what has been said, the irrational consequences respecting generation and corruption will take place. For essence, when it formerly was not, but now is; or when it formerly was, but afterwards is not, appears to suffer these things, viz. to be generated and corrupted. But points, lines, and superficies, do not admit either of generation or corruption, though they sometimes have a subsistence, and sometimes not. For, when bodies mutually touch or divide each other, by touching these become one; but, when they are divided, they become two. So that points, lines, and superficies, have no subsistence when bodies are conjoined, but are then corrupted; and when bodies are divided they have a subsistence, though prior to this they had not a being. For a point which is indivisible is not divided into two; and if they are generated and corrupted, they are made from something. The like takes place also respecting the now in time. For neither does this admit of generation and corruption: but at the same time it always appears to be something else, though it is not a particular essence. But it is evident that the like consequences also ensue respecting points, lines, and superficies; for the same reasoning takes place. For all these, in a similar manner, are either bounds or divisions.

Aristotle, Metaphysics. Book 3, Chapter 6

In short, someone may doubt why it is requisite to investigate certain other natures besides sensibles, and such as have a middle subsistence, as, for instance, the forms which we establish. For, if mathematical species differ from things which are here in some other respect, yet they do not at all differ in this, that many are of the same species; so that the principles of them will not be bounded by number, as neither, of the lines which are here, are all the principles bounded by number, but by species; unless someone takes the principle of this particular syllable, or of this particular voice. For the principles of these will also be bounded by number. And in a similar manner with respect to the natures which have a middle subsistence: for there those things which are of a similar species are infinite. So that, if there are not certain other things besides sensible and mathematical natures, such as some assert forms to be, there will not be an essence one in number and species; nor will certain principles of beings be so many in number, but in species. If, therefore, this is necessary, it is also necessary, on this account, that forms should have a subsistence; for, although those who assert these things do not express their meaning distinctly, yet this is what they wish to say; and they must necessarily affirm that every form is a certain essence, and that no one of them subsists according to accident. Indeed, if we admit that forms are, and that principles are one in number but not in species, we shall assert those impossibilities which must necessarily happen.

But a doubt which is near to this is, whether elements subsist in capacity or in some other manner. For, if in some other manner, there will, in a certain respect, be something else prior to principles. For capacity is prior to that cause. But it is not necessary that everything which is in capacity should subsist in that manner. But, if elements are in capacity, it will happen that no one being will have a subsistence; for it is possible for that to be which as yet is not; for non-being is generated: but nothing of things impossible is generated. It is necessary, therefore, that these doubts should arise concerning principles, and whether universals, or, as we say, particulars, have a subsistence. For, if there are universals, they will not be essences; for nothing of things common signifies a certain subject, but quality. But essence is a subject. But if that which is predicated, and may be exhibited in common, is a subject, Socrates himself will be many animals, and man and animal, if each signifies a subject, and that which is one. If therefore principles are universals, these things will happen; but if they are not universals, but such as particulars, there will not be objects of scientific knowledge. For all science respects things universal: so that there will be other principles universally predicated, prior to principles, in order that there may be a science of them.

Aristotle, Metaphysics. Book 4, Chapter 1.

There is a certain science which speculates being so far as being, and the things which are essentially inherent in it. But this science is not the same with any one of those which are called partial sciences. For no one of the others considers being universally so far as being; but, cutting off a certain part of it, they speculate that which is accidental to this part, as is the case with the mathematical sciences. But, since we investigate principles and the highest causes, it is necessary that they should be essentially principles and causes of a certain nature. If, therefore, those also who have investigated the elements of beings, have investigated these very principles, it is also necessary that the elements of being should not subsist according to accident, but should subsist so far as they are beings. On which account, we also must take into consideration the first causes of being, so far as being.

Aristotle, Metaphysics. Book 4, Chapter 2.

But being is, indeed, predicated variously, but with reference to one, and to one certain nature; and not equivocally, but in the same manner as everything salubrious is referred to health, partly from preserving, partly from producing, partly from indicating, and partly from being susceptible of health. This likewise takes place, in the same manner as that which is medicinal is referred to health: for one thing is called medicinal, because it has a medicinal power; but another, because it is naturally adapted to promote health; and another, because it is the work of the medicinal art. And, in a similar manner, we admit the predication of other things. Thus, too, being is indeed predicated variously, but the whole of it with reference to one principle. For some things are called beings because they are essences; others, because they are the passions of essence; and others, because they are the way to essence, or are corruptions, or privations, or qualities, or effective or generative of essence, or of things predicated with reference to essence, or to the negations of some one of these, or of essence. On this account also we say that non-being is non-being. As, therefore, there is one science of all things, the like also takes place in other things. For it is the province of one science to speculate, not only concerning things which are predicated according to one, but also concerning things which are predicated with reference to one nature. For these, likewise, in a certain respect, are predicated according to one. It is evident, therefore, that it is the province of one science to speculate beings so far as they are beings.

But everywhere science is properly of that which is first, and from which other things are suspended, and through which they are predicated. If, therefore, this is essence, it will be proper that a philosopher should possess the principles and causes of essences. For, of every genus, there is one sense, and one science; as, for instance, since there is one grammatical science, it speculates all vocal sounds. On which account also, to speculate such things as are the species of being, and such as are the species of species, is the province of one science in kind. But, if being and the one are the same and one nature, because they follow each other, in the same manner as principle and cause, but not as being signified by one definition, it is of no consequence, if we consider them in a similar manner, but is indeed more conducive to our purpose: for, one man, and existing man, and man are the same. Nor does it signify anything different, according to a repeated diction, to say, man is, and man, and one man. But it is evident that being is not separated, neither in generation nor corruption. And, in like manner with respect to the one; so that it is evident that addition in these signifies the same thing, and that the one is nothing else besides being. Further still: the essence of everything is one, not according to accident. And in a similar manner that which is some particular being: so that, as many as are the species of the one, so many also are species of being, concerning which to speculate the formal cause is the province of the same science in kind: but, I say, as for instance, concerning the same, and similar, and other things of this kind, and things opposed to these. But nearly all contraries are referred to this principle. These things, however, are considered by us in the election of contraries; and so many are the parts of philosophy as there are essences. So that it is necessary, that one kind of philosophy should be first, and another secondary. For, being and the one are things which immediately possess genera; on which account sciences also are consequent to these. For, a philosopher is similar to a mathematician; since mathematics also has parts, containing a first and second science, and another consequent to these.

But, since it is the province of one science to speculate opposites, and multitude is opposed to the one, it is the business of one science to speculate negation and privation, because the one is speculated both ways, of which there is negation or privation. For we either simply say negation is not present, or that it is not present to a certain genus. Hence, there, difference is present to the one, except that which is in negation (for negation is the absence of it). But in privation there is a certain subject nature, of which privation is predicated; and multitude is opposed to the one. So that it is the province of the aforesaid science to know the opposites to the things which we have mentioned, viz. the different, the dissimilar, the unequal, and such other things as are predicated, either according to the same, or according to multitude and the one; among the number of which is contrariety. For contrariety is a certain difference; but difference is diversity. So that, since the one is multifariously predicated, these also are predicated in various ways: but, at the same time, it is the business of one science to know all these. For it does not follow that, if they are multifariously predicated, the speculation of them belongs to another science. But if the reasons are referred, neither according to one, nor to one, then it is the business of another science. But, since all things are referred to that which is first, as, for instance, such things as are called one are referred to a first one, we must say, that the like also happens respecting same, and different, and contraries. So that by dividing, as often as any particular is predicated, we must refer it to that which is first in each category, that we may know how it is predicated with respect to that first. For some things are predicated from possessing that first; others, from making; and others are predicated according to other such like modes. It is evident, therefore, as we said in the doubts which we enumerated, that it is the province of one science to speculate both concerning these and essence. But this was one of the things which we mentioned among the doubts. And it is the business of a philosopher to be able to speculate about all things. For, if not of the philosopher, who will he be who considers whether Socrates, and Socrates sitting, are the same, or if one is contrary to one, or, what contrary is, or, in how many ways contrary and opposite are predicated? And in a similar manner respecting other things of this kind. Since, therefore, these things are the essential properties of the one so far as one, and of being so far as being, but not so far as the one and being are numbers, or lines, or fire, it is evident that it is the business of that science both to know what they are, and the things which are accidental to them. And those who consider these things, do not err in this respect as not philosophizing, but because essence, of which they understand nothing, has a prior subsistence. For, as of number so far as number there are peculiar properties; such as imparity, parity, commensurability, equality, excess, and defect; and these things subsist in numbers both considered by themselves and with relation to each other; and in a similar manner as there are other peculiar properties belonging to that which is solid and immovable, to that which is moved, to the light and the heavy; so also there are certain peculiar properties belonging to being so far as being. And these are the things the truth concerning which it is the business of the philosopher to consider; of which this is a token, that those who are skilled in dialectic, and sophists, assume the same figure as the philosopher: (for the sophistic art is only apparent wisdom, and those who are skilled in dialectic discourse concerning all things,) but being is common to all things. They discourse, however, concerning these things, because they properly belong to philosophy. For the sophistic and the dialectic arts are employed about the same genus with philosophy; but philosophy differs from one in the mode of power, and from the other, in the choice of life. For the dialectic art is praxic respecting those things of which philosophy possesses the knowledge: but the sophistic is apparently an art, but is not really so.

Further still of contraries, the other coordination, is privation; and all things are referred to being and non-being, and to the one, and multitude; as for instance, rest partakes of the one, but motion of multitude. But almost all men acknowledge that beings and essence consist from contraries. For all assert that principles are contraries: according to some, the principles of things being the even and the odd; according to others, the hot and the cold; according to some, bound and infinity; and according to others, friendship and strife. All other things, too, appear to be referred to the one and multitude. But reduction is assumed by us in the second book concerning the good. Principles however, both considered absolutely and as admitted by others, fall into these as into genera. From hence therefore also it is evident that it is the province of one science to speculate being so far as being. For all things are either contraries, or consist from contraries. But the principles of contraries themselves are the one and multitude: and these belong to one science, whether they are predicated according to one or not; which perhaps is the truth. But at the same time, though the one is predicated in various ways, yet other things are referred to the first, and in a similar manner contraries. On this account, though being and the one are not universal and the same in all things, or separate, as perhaps they are not, yet some things are referred to the one, and others are placed in a consequent order; and, on this account, it is not the business of a geometrician to speculate what contrary, or the perfect, or the one, or being, or same, or different, may be, unless from hypotheses. That it is therefore the business of one science to speculate being so far as being, together with the things which subsist in it so far as being, is evident: and also, that the same science is contemplative not only of essences, but of things subsisting in essences, together with such particulars as have been mentioned; and likewise of prior and posterior, of genus and species, of whole and part, and other things of this kind.

Aristotle, Metaphysics. Book 4, Chapter 3.

It must be declared whether it is the business of one or of a different science to speculate concerning those things which are called axioms in the mathematical disciplines, and concerning essence. But it is evident that it is the province of one science, and that the science of the philosopher, to consider these things. For they are present with all beings, but not to any particular genus separate from others. And all sciences indeed use these because they pertain to being so far as being; but every genus is being. They use them, however, so far as is sufficient to their purpose; i.e., so far as they contain the genus respecting which they bring demonstrations. So that, since it is evident that they are present to all things so far as they are beings (for this is common to them), the speculation of these also is the province of that science which knows being so far as being. On which account, no one of those who consider things according to a part, endeavours to say anything concerning them, whether they are true or not. For neither the geometrician nor the arithmetician does this, but certain natural philosophers, who in so doing act properly. For they alone think they should speculate concerning the whole of nature, and concerning being.

But, since there is yet something above that which is physical (for nature is one particular genus of being), the consideration of these things also will pertain to that which is universal, and to him who contemplates the first essence.

The natural science, indeed, is a certain wisdom, but not the first. But those who endeavour to speak concerning the truth of axioms, and to show how it ought to be admitted, do this through their ignorance of analytics. For it is requisite to enter on these things with previous knowledge, and not while hearing them mentioned begin to investigate. Hence, then, that it is the business of the philosopher, and of him who speculates the whole of essence, so far as it is naturally such, to consider likewise syllogistic principles, is evident. But it becomes him who especially knows what pertains to every genus to declare the most stable principles of a thing. Wherefore it also pertains to him to assign the most firm principles of all things, who speculates beings so far as they are beings. And he who does this is the philosopher. But that is the most stable principle of all things, concerning which it is not possible to be deceived. For it is necessary that a principle of this kind should be most known (for all men are deceived respecting things which they do not know); and, likewise, that it should be unhypothetical. For that is not hypothesis which it is necessary for him to possess who understands anything whatever which ranks among beings. But that which it is necessary for him to know who knows anything, must necessarily be possessed by him who knows anything. That a principle, therefore, of this kind is the most stable of all things, is evident.

What this principle, however, is, must in the next place be declared. For it is impossible that the same thing can at the same time be present and not be present with the same thing, according to the same; and all such things as we have already discussed for the purpose of removing the difficulties which result from logical inquiries. But this is the most stable of all principles: for it has the above-mentioned condition. For it is impossible to apprehend that anything can be the same and yet not the same, as some think Heraclitus asserted; since it is not necessary to think that a thing is, because it is asserted by someone to be. But if it does not happen that contraries are present with the same thing (but the usual actions have been made by us to this proposition), and opinions are contrary, which are adverse in a contradictory manner, it is evident that it is impossible to conceive the same thing, at the same time, to be and not to be. For he who is deceived about this thing would at the same time possess contrary opinions. I know, all who demonstrate reduce their demonstrations to this last opinion: for this is naturally the principle of all other axioms.

Aristotle, Metaphysics. Book 4, Chapter 4.

There are, however, certain persons who, as we have observed, assert that the same thing may be and may not be, and think conformably to what they assert. Many of those, too, who discourse concerning nature use the same assertion. But we now assume that it is impossible for the same thing to be and not to be; and through this we have shown that this is the most stable of all principles. Some, however, through want of erudition, have thought it worthwhile to demonstrate this axiom. For it is want of erudition not to know what are the things of which it is proper to seek demonstration, and what the particulars of which a demonstration is not requisite. For, in short, it is impossible that there should be a demonstration of all things. For, if this were admitted, there must be an infinite progression: so that neither thus would there be any demonstration. But if it is not proper to seek demonstration of certain things, yet those men are not able to assign what that is which they consider as rather deserving to be called a principle of this kind. It may, however, be demonstrated dialectically that this is impossible, if only he who doubts says anything. But, if he says nothing, it is ridiculous to inquire a reason of him who does not speak, so far as he does not speak. For such a one, so far as he is such, is similar to a plant. But I say that to demonstrate dialectically differs from demonstration, because he who demonstrates seems to inquire that which is sought after in the beginning; but when there is another cause of this kind, it will be confutation, and not demonstration. But the beginning of discourse to anyone of these should be, not to require him to assert that anything is or is not (for perhaps someone may think that this is the thing which was required from the beginning), but to desire him to signify something both to himself and another. For this is necessary, if he says anything: but if he does not, it is impossible there should be any discourse with such a one, either from himself, to himself, or to another. But if anyone admits this, there will be demonstration: for now there will be something defined. Yet, not he who demonstrates, but he who sustains, is the cause of this; for, taking away discourse, he sustains discourse.

In the first place, therefore, it is evident that a name signifies this particular thing, either to be, or not to be: so that not everything will subsist in this particular manner, and yet not in this manner. Further still: if man signifies one thing, let it be this, a biped animal. But I say this signifies one thing, when if this thing is a man, whatever is a man is a biped animal. But it is of no consequence, though someone should say that it signifies more than one thing, if they are only definite; for he may give to each definition another name. I say, for instance, if he should assert that man does not signify one thing, but many things, one definition of one of which is a biped animal. There are also many others, but the number of them is definite; for the proper name may be placed in each of the definitions. However, if someone should not place it, but should say that it signifies infinite particulars, it is evident there could be no definition of it, nor any discourse about it. For, not to signify one thing is to signify nothing. But when names have no signification, then in reality the discourse of men with each other, and of a man with himself, can no longer subsist.

For it is not possible to understand anything when not understanding one thing; since, if it were possible, one name must be imposed on this thing. Do it therefore, as was said at first, that a name signifies something, and that it signifies one thing. Hence, that man exists, will not signify the same thing as that man does not exist; if man signifies not only that which is asserted of one thing, but one thing itself. For we do not think that to signify one thing, is to predicate of one thing; since, if this were admitted, a musician, that which is white, and a man, would signify one thing: so that all things will be one, for they will be synonymous: and it will not be possible for the same thing to be and yet not be, unless so far as equivocally considered. Just as if that which we call man, should be denominated by others not man. However, that which is doubted is not this, whether it is possible that the same thing can be a man and yet not a man in name, but whether this can take place in reality. But if man and not man do not signify that which is different, it is evident that to be will be the same as not to be a man; for they will be one thing; since this signifies that they are one thing, as a tunic and a garment, if there is one definition of each. But if they are one, to be and not to be a man signify one thing. It has been shown, however, that they signify that which is different. It is necessary therefore, if anything is truly called a man, that it must be a biped animal: for this is that which man signifies. But, if this is necessary, it is not possible that this very thing should not be a biped animal. For this is what is signified by existing necessarily, viz. that it is impossible it should not be a man. It is not therefore possible that it could be true to say, at the same time, that the same thing is both a man and not a man. The same reasoning, too, takes place with respect to the not being a man. For the being of a man signifies something different from the being of that which is not a man; since to be white, and to be a man, signify things different. For that is much more opposed; so that it signifies something different. But, if anyone should say that white signifies one and the same thing with man, again we say that which was said before, that all things, and not only opposites, will be one. And, if this is not possible, that which has been said will happen, if an answer is given to the interrogation. But, if he who is simply interrogated adds also negations, he will not answer to the interrogation: for nothing hinders, but that the same thing may be man and white, and other things infinite in multitude. Nevertheless, when interrogated, if it is true to say that this is a man or not, he must answer by that which signifies one thing, and must not add, that it is both white and blue. For it is impossible to pass through accidents, because they are infinite. Either therefore, he must pass through all, or no one of them. In a similar manner, therefore, if the same man and non-man subsisted infinitely, if we are interrogated if man is, we ought not to answer, that at the same time non-man also is; unless in our answer we likewise include such things as happen, if man is, or is not. But he who does not do this will not discourse.

In short, those who make this assertion submit essence, and the formal cause: for it is necessary they should say that all things are accidental, and that there is not anything which is essentially man or animal, and to which the being of man or animal belongs. For, if there should be such a thing as that which it is for a man to be, this will not be for a man not to be, or to be not a man; although these are negations of this. For that which is signified was one, and this was the essence of a certain thing. But to signify essence is the same as to assert that the being of a thing is nothing else. But, if the being of a man belongs to a thing, it is impossible that it should not be man, or that it should be that which is not man; for it would be something else. So that they must necessarily say that a formal and essential definition of this kind, and which is always adapted to the subject, is of a non-entity, and that all things pertain to it accidentally; for in this very thing, essence and accident are separated from each other. For, whiteness on that account happens to man, because he is indeed white, but not whiteness itself. But, if all things are predicated according to accident, there will not be any first universal. And if accident always signifies a predication pertaining to a certain subject, a progression ad infinitum must necessarily ensue. But this is impossible; for they are not connected with more than two. For accident is not an accident to accident, unless because both happen to the same thing. I say, for instance, as in that which is white, and a musician; for here the musician is white, because both happen to a man: but Socrates is not on that account a musician, because both happen to a certain other thing. Since, therefore, some things are called accidents in this, and some in that way, those things which are called accidental, in the same way as white to Socrates, cannot be predicated infinitely, so as, for instance, that to Socrates who is white something else should happen. For one thing is not produced from all, nor is anything else an accident to that which is white, as, for instance, a musician; since this does not more happen to that than that to this. And at the same time we have distinguished with respect to accidents, that some things happen in this manner, but others as a musician to Socrates. Such things, however, as happen in this manner do not happen as accident to accident; but this is the case with such as happen after the other manner. So that all things are not asserted according to accident. There will, therefore, be something which signifies as essence: but if this be the case, it is shown that things contradictory cannot be predicated at the same time. Again: if all contradictions are at the same time true of the same thing, it is evident that all things will be one. The same thing, therefore, will be a trireme, and a wall, and man, if it so happens that something can be affirmed or denied of everything, as must necessarily be the case with those who speak according to the doctrine of Protagoras. For, if to anyone a man appears not to be a trireme, it is evident that he will not be a trireme; he is, however, if contradiction be true. And hence, that which Anaxagoras asserted, takes place, viz. that all things subsist together, so that nothing is truly one thing. They appear, therefore, to assert that which is indefinite, and, thinking to speak of being, they speak concerning non-being: for that which is being in capacity, and not in energy, is the indefinite. Nevertheless, we must say to the authors of this hypothesis that, of everything, either affirmation or negation must be predicated. For it is indeed absurd that the negation of a thing should be true, but that the negations of other things which are different from it should not also be true. I say, for instance, if it be true to affirm of a man, that he is not man, it is evident that he is also not a trireme. If, therefore, affirmation is true respecting him, negation is also necessarily true. But, if affirmation is not true, the negation of a trireme will more pertain to him than the negation of himself. If, therefore, that be true, the negation of a trireme is also true; and if the negation, affirmation likewise. These things, therefore, happen to those who make this assertion, and also, that it is not necessary to employ either affirmation or negation. For, if it be true that the same person is a man and not a man, it is evident that he will neither be a man nor yet not a man: for of those two things there are two negations. And, if that is one composed from both, the one so composed will be opposite.

Further still: either this will be the case respecting all things, and a thing will be white and not white, being and not being, and in a similar manner with respect to other affirmations and negations; or this will not be the case, but it will be true of some things, and not of others. And, indeed, if it be not true with respect to all things, those will be firm and definite. But if it be true with respect to all things, again, either of such things as there is affirmation there will also be negation, and of such things as there is negation there will be affirmation; or, of such things as there is affirmation there will also be negation; but of all such things as there is negation there will not be affirmation. And if this be the case, there will be something which is firmly non-being, and this will be a stable opinion. However, if not to be is something firm and known, the opposite affirmation will be more firm. But if it be necessary to affirm in a similar manner whatever is denied, it is either true to say, by dividing, that a thing is white, and again that it is not white, or it is not true. And, if it be not true to assert this by dividing, neither does he assert these things, nor has anything a subsistence. But how can anyone speak of non-entities, or understand anything with respect to them? And, as we before observed, all things will be one; and man, and god, and trireme, and the contradictories of these, will be the same. But if, in a similar manner, every contradiction is true of particulars, one thing will in no respect differ from another. For, if it should differ, this will be true, and its peculiarity. In like manner, that which we have asserted will take place, if it should happen that he who makes the division affirms that which is true. To which we may add that all men will speak the truth, and all men will assert that which is false, and everyone will acknowledge that himself speaks falsely. At the same time, too, it is evident that such an one speculates a nonentity: for he says nothing. For he neither speaks in this manner, nor in that; but in this manner, and yet not in this manner. And, again, with respect to these, he makes a negation of both, by asserting that they are neither in this manner, neither not in this manner, but in this manner, and not in this manner: for, if this were not the case, there would now be something definite.

Further still: if when affirmation is true negation is false, and when this is true affirmation is false, it will not be possible at the same time truly to affirm and deny the same thing. But someone perhaps may say, this is that which was advanced in the beginning. Again, therefore, does he who apprehends that a thing either is, or is not, in a certain respect, think falsely? but he who apprehends that a thing is both, conceives truly? For, if his conception be true, what else is asserted but this, that such is the nature of things? But if his conception be not true, but rather the conception of him who thinks after that manner, then things will be in a certain respect, and this will be true, and not at the same time not true. But if all men in a similar manner speak falsely and truly, it is not possible for him who makes this assertion, either to speak or assert anything: for, at the same time, he must assert the same things, and not the same. And if he apprehends nothing, but in a similar manner thinks and does not think, what difference will there be between such an one and a plant? Whence, also, it is sufficiently evident that no one is thus affected, neither of others, nor of those who make this assertion. For, why does he walk to Megara, and not remain quiet, thinking to ask? nor immediately at break of day proceed to some well, or to a precipice? But he appears to act cautiously, as not similarly thinking it is not good, and good, to fall. It is evident, therefore, that he apprehends that the one is better, and the other not better. But, if this be the case, it is also necessary he should think that this is a man, but that not a man; and that this thing is sweet, but that not sweet. For he does not equally investigate and form an opinion of all things, since he thinks it is better to drink water, and to see a certain person, and afterwards searches for these very things. Though it would be requisite that he should equally investigate all things, if man and not man, water and not water were similarly the same. But, as we have before observed, there is no man who does not appear cautiously to avoid the one, and not the other. So that, as it seems, all men are persuaded, that both contraries are not expedient, if not with respect to all things, yet with respect to the better and the worse. But if they thus think, not from scientific knowledge, but opinion, much more should they be studious of truth, just as the sick should pay greater attention to health than those who are healthy. For he who energizes according to opinion, when compared with him who energizes according to science, is not sanely disposed with respect to truth.

Further still: though all things should especially subsist in this manner, and yet not in this manner, yet the more and the less are inherent in the nature of things. For we do not say that two things and three things are similarly even; nor does he similarly assert an untruth, who says, that four things are five, as he who affirms that a thousand things are five. If, therefore, not similarly, it is evident that one violates the truth less than the other, and therefore says that which is more true. If, therefore that which is more true is nearer to the truth, there will indeed be something true, to which that which is more true is nearer. And, although nothing should be true, yet at least, as it appears, there is something which is more firm and more true: and thus we shall be liberated from that intemperate assertion, which prevents us from defining anything by our dianoetic part.

Aristotle, Metaphysics. Book 4, Chapter 5.

The doctrine of Protagoras originates also from the same opinion; and, in a similar manner, it is necessary that both these should either be, or should not be. For, if all things of which we form an opinion, and which appear to be, are true, it is necessary that all things, at the same time, should be both true and false. For many apprehend things contrary to each other, and think that those who do not entertain the same opinions with themselves are deceived. So that it is necessary that the same thing should both be and not be. And if this be the case, it is necessary that every thing which is the subject of opinion should be true: for, both those who assert that which is false, and those who speak the truth, opine things opposite to each other. If, therefore, things subsist in this manner, the assertions of all men will be true. That both these doctrines, therefore, originate from the same conceptions is evident. But the same mode of reply must not be adopted to all such; for some require persuasion, but others force: for the ignorance of those who think in this manner, in consequence of doubting, may be easily cured; since here the reply is not directed to their discourse, but to their dianoetic part. But the cure of such as speak in this manner for the sake of disputation, is the confutation of that discourse which consists in voice, and of that which consists in names.

This opinion, however, in those that doubt, originated from sensibles; I mean, that contradictories and contraries subsist together; and this, in consequence of perceiving contraries generated from the same thing. If, therefore, it is impossible for that which is not, to be generated, a thing according to them will pre-exist as both contraries at once. Just as Anaxagoras and Democritus say that every thing was mingled in every thing. For Democritus also asserts that there is a vacuum and a plenum in every part, and that one of these is being and the other non-being. To those, therefore, who from these things form this opinion, we say that in one respect they speak rightly, and in another ignorantly. For being is predicated in a two-fold respect; so that it is partly possible for something to be generated from non-being, and partly not; and for the same thing to be at the same time being and non-being, yet not according to the same: for it is possible that contraries may at the same time be the same thing in capacity, but not in energy. Further still: it is requisite they should consider that there is another essence of things to which neither motion, nor corruption, nor, in short, generation belongs. In a similar manner too, the truth respecting the phenomena was obtained by some from sensibles. However, they ought not to think it fit that truth should be judged either by multitude or paucity. But the same thing to the taste of some appears to be sweet, but to that of others bitter. So that if all men were diseased, or all men were insane, except two or three who were well, and in possession of intellect, these two or three might appear to be diseased and to be insane, but this would not be the case with the others. Again: to many other animals, as well as to us, contraries appear to take place respecting the same things; and to each of us, with respect to himself, things do not always appear the same, according to sense. It is, therefore, immanifest which of these is true or false: for no one of these is more true than the other, but, with respect to truth, they are similarly affected. Hence Democritus says that either nothing is true, or that it is to us immanifest. In short, because they are of opinion that prudence is sense, and that this is alteration, they say that whatever is sensibly apparent is necessarily true. For, from hence, Empedocles, Democritus, and, as I may say, each of the rest, became obnoxious to such like opinions. For Empedocles says, that in consequence of habit being changed, prudence also is changed.

“Man’s counsel varies with the present time.”

And in another place he says,

“Men, as their bodies change, in wisdom change.”

Parmenides also speaks after the same manner: “As is the temperament of the flexible members in every one, such also is the intellect which is present to men. For the nature of the members is entirely the same with that which energizes prudentially in all mankind. For that which is more than this is an intellectual conception.” Anaxagoras also is reported by some of his associates to have said that things were such to men, as they apprehended them to be. They say, too, that Homer appears to have been of this opinion, who affirms of Hector, when he was insane through a wound, “that he was wise in an unusual manner;” as if those that are insane were prudent, but not in the same manner as those that possess a sound mind. It is evident, therefore, that if both the mentally sane and the insane are wise, things also subsist in this manner, and yet not in this manner. But that which results from this conclusion is most grievous: for, if those who in the highest degree perceive that truth, which it is possible to perceive (but these are they who in the highest degree investigate and love truth), if these entertain such opinions, and assert such things respecting truth, must not those despond who endeavour to philosophize? For to investigate truth will be to pursue things volant. But this opinion was produced in them by speculating the truth of beings; and they apprehended that beings were alone things sensible. In these, however, much of the nature of the indefinite is inherent, and of that which is indefinitely being, as we have already observed. Hence they speak probably, but do not assert the truth; for thus it is more becoming to speak, than as Epicharmus speaks when writing against Xenophanes.

Further still: when they perceived that the whole of this visible nature was moved, and that nothing could be verified of that which is changed, they concluded that it was impossible to assert any thing with truth of that which is in every respect changed. For from this conception that opinion originated, which stands at the summit of those we have mentioned, viz. the opinion of those who profess to Heraclitize, and which was adopted by Cratylus, who at length thought that it was not proper to speak, but only moved his finger, and reproved Heraclitus for asserting that it was not possible to enter twice into the same river. For he thought it was not possible to do this once. But to this assertion we say, that to be of opinion that a thing which is changed is not when it changes, possesses some truth, although it is attended with ambiguity. For that which casts away, possesses something of that which it casts away; and of that which is in generation, or becoming to be, it is necessary that something should now be. In short, if it be corrupted, something will subsist; and if it be generated, it is necessary that the thing from which it is made, and by which it was generated, should subsist, and that this should not be the case ad infinitum. However, omitting these things, we say that it is not the same thing to be transmuted according to quantity and according to quality. Let it, therefore, be granted, that a thing does not abide according to quantity, yet we know that all things abide according to form. Again: it is proper to reprove those who think in this manner, because, though they perceived this flux and mutation but in the smaller number of sensibles, yet they entertained similar opinions respecting all heaven. For that with which we are surrounded, or the place of generation, alone subsists in continual generation and corruption; but this place, on account of its exility, is, as I may say, no part of the universe. So that it would have been more equitable to have drawn a conclusion from the greater number respecting the fewer, than to have condemned the former on account of the latter. Further still: it is evident that we may urge the same things against these men, as were formerly urged by us. For we must demonstrate, and persuade them, that there is a certain immoveable nature; though it happens to those who assert that a thing is and is not at the same time, that they must rather say that all things are at rest than in motion. For, on this hypothesis, there will not be any thing into which a thing may be changed; for all things will subsist in all.

But, with respect to truth, we must evince that not every thing which is apparent is true. For, in the first place, it does not follow, that, if sense is not deceived in the proper objects of its perception, this is also true of the phantasy; for phantasy is not the same with sense. In the next place, it is worthy of admiration, if they doubt whether magnitudes are so great and colours such as they appear to those who are at a distance, or so great and such as they appear to those who are near; and whether they are such as they appear to those in health, or such as they appear to the diseased: and with respect to weight, whether those things are heavier which are judged to be so by the weak, or those which appear to be so to the strong; and lastly, with respect to truth, whether such things are true as appear to those who are asleep, or such as appear to those who are awake; for it is evident they do not think that things are such as they appear to the former of these. For no one, if when in Libya he should dream that he was at Athens, would when he awoke go to the Odeon. Further still: with respect to the future, as Plato also observes, the opinion of a physician and one unskilled in medicine is not similarly certain, as to one who hereafter will or will not be well.

Again: with respect to the senses themselves, the perception of a foreign is not equally certain with that of a proper object, nor of that which is remote with that which is near. But with respect to colour, the sight judges, and not the taste; and of juices the taste, and not the sight; none of which senses affirms that any circumstance subsists in a particular manner, and yet does not so subsist, at the same time, about the same thing. But neither do the senses doubt respecting things to which they are passive, at a different time, but respecting that to which the passion happens. I say, for instance, the same wine may to the same person at one time appear to be sweet, and at another time not sweet, either because the wine itself is changed, or the organ of taste. But that which is sweet, when it is so, is never changed, but sweetness is always truly affirmed of it: and that which will be sweet, necessarily subsists in this manner, though this conclusion is subverted by all these assertions. For, as they affirm that there is no essence of any thing, they also take away the necessary subsistence of any thing. For that which is necessary does not admit of a various subsistence. So that, if any thing subsists from necessity, it will not subsist thus, and yet not thus. And, in short, if that which is sensible alone subsists, nothing will be, if animated natures have no existence; for sense will not be. And if sense is not, it is perhaps true that there are no such things as sensible objects, nor perceptions of sense; for sense is a passion of a sentient nature. But that the subjects themselves should not subsist which produce sense, even though sense were not, is impossible. For sense itself is not of itself; but there is something else besides sense, which necessarily is prior to sense. For that which moves is by nature prior to that which is moved; nor will this be less the case, though these same things are referred to each other.

Aristotle, Metaphysics. Book 4, Chapter 6.

There are some, however, who doubt, both among those who are persuaded of the truth of these assertions, and among those who are alone the authors of such assertions. For they inquire who it is that judges of a man in health, and, in short, who it is that judges rightly respecting every particular. Doubts of this kind are, however, similar to the doubt whether we now sleep, or are awake: for all such doubts as these amount to the same thing. For the authors of them think fit to investigate the reason and cause of all things; since they explore the principle, and expect to obtain it through demonstration. However, that they are not persuaded is evident from their actions: but, as we have said, this is the error of these men; for they investigate the principle of things of which there is no principle. For the principle of demonstration is not demonstration. These men, therefore, may easily be persuaded of this; for it is not difficult to apprehend. But those who alone investigate force in words, investigate that which is impossible: for, at the same time, they directly assert things contrary, deeming it fit to affirm the contrary. However, if all things are not relatives, but some subsist themselves by themselves, every thing which appears will not be true: for every thing which appears is apparent to some one. So that he who asserts that all appearances are true, makes all beings to be relatives. On which account it is requisite to observe to those who search for force in argument, and with this view engage in disputation, that not that which appears is true, but, it should be added, that it is true to him to whom it appears to be so, and when it appears, and so far as it appears, and according to the manner in which it appears. But if they dispute, indeed, yet not in this way, it happens that they rapidly assert things contrary. For the same thing may indeed to the sight appear to be honey, but not to the taste: and, as we have two eyes, if they happen to be dissimilar, the same things will not appear to be the same to each sight. As to those who, for the reasons formerly adduced, contend for the truth of that which appears, and on this account affirm that all things are similarly false and true, it is easy to reply, that neither do the same things appear to all men, nor do the same things always appear the same to the same person, but frequently contraries appear at the same time. For that which appears to the sight to be one, to the touch appears to be many, when different fingers are placed on it in succession. Nor yet do the same things appear to the same sense, and according to the same, and in a similar manner, and in the same time. So that this will be true. But, perhaps in consequence of this, it is necessary to say to those who speak, not through doubting, but for the sake of discourse, that this is not simply true, but true to this or that person. And, as it was before observed, it is necessary to make all things relatives, and refer them to opinion and sense; so that neither was any thing, nor will there be any thing, if there were no antecedent opinion of things. But if there was, or will be any thing, it is evident that all things will not be referred to opinion.

Again: if a thing has a relative subsistence, it is either predicated as one to one, or with relation to that which is definite; and if the same thing is both half and equal, it is referred to these, but the equal is not referred to the double. And with respect to opinion, if man is the same with that which is the object of opinion, that which opines is not man, but that which is the object of opinion. But, if every thing subsists with relation to that which opines, that which opines will be infinite in species. That the opinion, therefore, is the most firm of all things, viz. that opposite assertions are not at the same time true, and what happens to those who contend that they are true, and why they speak in this manner, has been sufficiently shown by us. But, since it is impossible that contradiction should at the same time be true respecting the same thing, it is evident that neither can contraries subsist at the same time in the same thing. For the other of contraries is no less privation: but the privation of essence is a negation from a certain definite genus. If, therefore, that it is impossible at the same time to affirm and deny is true, it is also impossible that contraries can at the same time be inherent in a subject; but either both must be inherent partially, or the one partially and the other simply.

Aristotle, Metaphysics. Book 4, Chapter 7.

But neither is it possible that any thing can subsist between contradictories; for it is necessary either to affirm or deny one thing of every thing which is one. This, however, will be manifest, by first of all defining what the true is, and what the false. For to say that being is not, or that that which is not is, is false: but to affirm that being is, and that non-being is not, is true. So that he who asserts that this medium is or is not, asserts that which is true, or that which is false; but he neither asserts of being, nor of non-being, that it is not or is. Again, if there is something between contradictories, it will either be, as is a dark colour between black and white, or as that which is neither man nor horse, between man and horse. If, therefore, it subsists in this manner, it will not be changed: for it will either be changed from that which is not good into good, or from this into not good. But now it always appears to take place: for there is no mutation except to things opposite, and those which subsist between. But if there be a medium, thus also there will be some mutation or generation into white, not from that which is not white. But this does not appear to be the case.

Further still: the dianoetic power of the soul either affirms or denies every thing dianoetic and intelligible. But this is evident from definition, when it asserts that which is true, or that which is false: for, when it composes in this particular manner, affirming or denying, it asserts the truth; but when in that, it asserts that which is false. Besides, this medium ought to be in all contradictions, unless it is introduced for the sake of argument. So that neither will any one assert that which is true, nor yet that which is not true: and there will be something besides being and non-being. Hence there will be a certain mutation besides generation and corruption. Further still: this medium will also be in those genera, in which negation introduces its contrary. As, for instance, in numbers there will be that which is neither an even nor an odd number; but that this is impossible, is evident from definition. Again: there will be a progression to infinity, and beings will not only be sesquialter, but even more than this: for, again, something will be found, of which it will be possible to deny the affirmation and negation of the medium of the former contradiction: for the essence of it will be something else.

Further still: when any one, being asked if a thing is white, says it is not, he denies nothing else than being; but not to be is negation. But this originated from the same source as the other paradoxical opinions: for some, when they are not able to solve the contentious arguments, yielding to reason, they say that the syllogistic conclusion is true. Some, therefore, speak in this manner through this cause; but others, because they investigate the reason of all things. But the principle to all these is to be assumed from definition; and definition is produced in consequence of its being necessary that they should signify something: for a sentence, the name of which is a sign or signification, is the definition of a thing. The doctrine of Heraclitus, indeed, when he asserts that all things both are and are not, seems to make all things true. But Anaxagoras, when he asserts that there is a certain medium in contradictions, makes all things to be false. For, when they are mingled, the mixture is neither good, nor yet not good; so that it is not possible to speak truly of any thing.

Aristotle, Metaphysics. Book 4, Chapter 8.

These things being determined, it is evident that things which are predicated in one way only, and also that those which are predicated of all things, cannot subsist as some say they subsist. For some assert that nothing is true: for, say they, nothing hinders but that all things may subsist in such a manner, as that the diameter of a square may be commensurable with its side. But, according to others, all things are true. For their assertions are nearly the same as those of Heraclitus; since he who says that all things are true, and that all things are false, separately makes each of these assertions: so that if those are impossible, these also must be impossible.

Further still: it is evident that they are contradictions, which cannot possibly be at the same time true, or at the same time false, though, from what has been said, it would rather appear that both are false. But in all such assertions it is necessary to require, as we have before observed, not that a thing should be, or should not be, but that it should signify something; so that we must dispute from definition, by assuming what the true or the false signifies. But, if the true is nothing else than to say that a thing which thus subsists, does thus subsist, and the false is nothing else than to deny that a thing subsists in a certain manner, when it does thus subsist, it is impossible that all things should be false: for it is necessary that the other part of the contradiction should be true. Further still: if affirmation or negation must necessarily take place respecting every thing, it is impossible that both should be false: for the other part of the contradiction is false. But the common saying applies to all such assertions as these, viz. that they subvert themselves. For he who says that all things are true, makes also the contrary assertion true; so that he makes his own assertion not to be true. For the contrary assertion says that it is not true. But he who says that all things are false, says also that his own assertion is false. But, if they make an exception, the one of the contrary assertion as alone not true, but the other of his own as alone not false, nevertheless it happens that they must demand infinite true and false assertions. For he who says that a true assertion is true, assents to this, that it is true; but this will proceed to infinity. It is, however, evident, that neither those who say that all things are quiescent assert the truth; nor those who say that all things are in motion. For, if all things are at rest, the same things will always be true and false: but this appears to be changed. For he who says this, once was not, and again will not be. But if all things are moved, nothing will be true. All things, therefore, will be false: but it has been demonstrated that this is impossible. Again: it is necessary that being should be changed: for mutation is from something into something. But neither are all things sometimes at rest and sometimes in motion; so that there is not that which is always moved, and that which is always immoveable. For there is something which always moves things that are moved; and the first mover is itself immoveable.

Aristotle, Metaphysics. Book 5, Chapter 1.

With respect to principle, one kind is said to be that whence something is first moved; as, for instance, the principle of length, and of a way; for the principle is from hence. On the contrary, another principle is that whence any thing becomes the best; as, for instance, with respect to discipline, we must sometimes begin, not from the first, and the principle of a thing, but whence learning may be most easily acquired. Another principle is that whence, from being inherent, a thing is first produced; as of a ship the keel, of a house the foundation; and of animals, according to some the heart, according to others the brain, and according to others something else of this kind. But another principle is that whence, not being inherent, a thing is first produced, and whence motion and mutation are first naturally adapted to originate; as an offspring from father and mother, and war from defamation. Another principle is that according to the free-will of which things in motion are moved, and mutable natures are changed, as principalities, dynasties, kingdoms, and tyrannies in a city. Arts also are called principles; and, of these especially the master building arts. Further still: that whence a thing is first known, is said to be the principle of that thing; as, for instance, hypotheses of demonstrations. Causes too, are denominated in as many ways as principles; for all causes are principles. It is common, therefore, to every principle to be the first whence a thing is either produced or known. But, of these, some have an internal, but others an external subsistence. Hence nature is a principle, as is also an element, the dianoetic power, free-will, essence, and that for the sake of which a thing subsists. For good and the beautiful are to many things the principle both of knowledge and motion.

Aristotle, Metaphysics. Book 5, Chapter 2.

Cause, in one respect, is said to be that from which, when inherent, any thing is produced, as, for instance, brass of a statue, silver of a bowl, and the kinds of these. In another respect, form and paradigm are causes; but in this case they are formal causes, and the kinds of these. Thus, for instance, the ratio of two to one, is the cause of the diapason: and, in short, number, and the parts in a ratio, belong to this order of cause. Further still: cause is that whence the first principle of mutation or rest originates: thus, for instance, he who consults is a cause, and a father of his offspring; and, in short, he who makes of that which is made; and that which has the power of changing of that which is changed.

Again: cause is as the end. But this ranks as that for the sake of which other things subsist; as, for instance, health of walking. For, on what account does a man walk? We say, That he may obtain health: and, thus saying, we think that we have assigned the cause. Such things also are causes, as subsist between another thing which moves, and the end. Thus, for instance, the cause of health is either attenuation, or purgation, or medicine, or instruments. For all these are for the sake of the end. But they differ from each other in this, that some of them are as instruments, but others as works. Causes, therefore, are nearly denominated in so many ways. But, since causes are predicated multifariously, it happens that there are many causes of the same thing, not according to accident; as, of a statue, both the statuary’s art, and the brass, and this, not from any thing else, but so far as it is a statue: yet this does not take place after the same manner, but the brass is as matter, and art as that whence motion originates. Some things also are mutually causes with respect to each other; as labor is the cause of a good habit of body, and a good habit of body, of labor; not, however, after the same manner, but the one is as the end, and the other as the principle, of motion.

Further still: the same thing is sometimes the cause of contraries: for that which when present is the cause of some particular thing, the same when absent, is, we say, sometimes the cause of the contrary. Thus, the absence of the pilot is the cause of the destruction of the ship, whose presence was the cause of its preservation. But both the presence and the absence of the pilot are as moving causes. All the causes, however, that we have now enumerated fall into four most manifest modes. For the elements of syllables, and the matter of things fashioned by art, also fire and earth, and every thing else of this kind belonging to bodies, together with the parts of a whole, and the hypotheses of a conclusion, are causes, as things from which others are produced. But of these, some are as a subject, as, for instance, parts; but others, as the formal cause, such as the whole, composition, and form. But seed, the physician, he who consults, and, in short, the maker of any thing, are all of them causes, whence the principle of mutation or stability originates; but the rest are as the end, and the good of other things. For that for the sake of which other things subsist, wills to be the best, and the end of others. But there is no difference, whether it be called real or apparent good. There are, therefore so many species of causes. But the modes of causes are many in number. They may, however, be summed up into a less numerous multitude: for causes are predicated in a manifold respect; and of those which are of the same species, one is prior and another posterior; as, for instance, of health, the physician, and the artificer; and, of the diapason, the double, and number; and always those things which comprehend any thing of particulars.

Further still: cause is predicated as accident, and the genera of these; as, for instance, of a statue, Polycletus is in one respect the cause, and in another respect the statuary, because it happens to the statuary to be Polycletus: and things which comprehend accident; as man is the cause of a statue, or in short animal, because Polycletus is a man, and man is an animal. Of accidents also, one is more remote and more proximate than another; as, for instance, if that which is white, and a musician, should be said to be the cause of a statue, and not only Polycletus, or a man. But, besides all those which are properly predicated, and those which are predicated according to accident, some causes are denominated as endued with capacity, but others as energetic: thus the builder is the cause of erecting the house, or the builder considered as building. The like takes place also in effects; as, for instance, of this statue, or of a statue simply, or in short of an image; or of this brass, or brass simply, or universally of matter: and in a similar manner with respect to accidents. Further still: both these and those are predicated conjointly; as, for instance, not Polycletus, nor the statuary, but Polycletus the statuary. At the same time, all these with respect to multitude are six; but they are predicated in a twofold respect: for they are predicated either as that which is particular, or as genus, or as accident, or as the genus of accident, or as these conjoined, or according to capacity, or simply considered, or, lastly, as energizing. But they so far differ, that causes in energy, particulars, and those things of which they are the causes, subsist together and together cease to be; as, for instance, this physician with this convalescent, and this builder with this building. But this is not always the case with causes in capacity: for the house and the builder are not corrupted together.

Aristotle, Metaphysics. Book 5, Chapter 3.

Element is said to be that from which, being primarily inherent and indivisible in species, something is composed. Thus, for instance, the elements of speech are those things from which speech is composed, and into which it is ultimately divided: but these elements are no longer divided into other words different from themselves in species; but, if it were possible for them to be divided, the parts would be of a similar species. Thus the parts of water are water, but the parts of a syllable are not syllables. In like manner the antients called those the elements of bodies, into which bodies themselves are ultimately divided, but which are no longer divisible into other bodies specifically different: and whether there is one, or many of this kind, they call these elements. The elements of diagrams and demonstrations are denominated in a similar manner. For first demonstrations, and those which are inherent in many demonstrations, are said to be the elements of demonstrations. But such as these are first syllogisms composed of three terms through one medium. Hence also, metaphorically speaking, they call that an element, which, being one and small, is useful for many purposes. On which account, the simple, the small, and the indivisible, are said to be elements. Hence it comes to pass that things eminently universal are elements; because each of them being one and simple, it is inherent in many things, or in all things, or in the greater part of all things. The one also and a point to some appear to be principles. Since, therefore, those things which are called genera are universals and indivisibles (for there is one definition of them), some denominate genera themselves elements, and more so than difference, because genus is more universal. For genus follows that to which difference is present; but that to which genus is present is not always attended with difference. But it is common to all things, for that to be the element of any thing, which first subsists in that thing.

Aristotle, Metaphysics. Book 5, Chapter 4.

Nature, in one respect, is said to be the generation of things rising into being; as if any one, extending his voice, should pronounce the letter u. But, in another respect, that from which, when primarily inexistent, that which is generated is generated. Further still: nature is that whence the first motion arises, in each of the things which subsist naturally, so far as a thing is that which it is. But things are said to be rising into being, which receive increase through another thing by contact, or being connascent with it; as embryos. The being connascent, however, differs from contact: for in the latter nothing besides contact is necessary; but in things connascent, there is a certain one the same in both, which makes them grow together, instead of merely touching each other, and causes them to be one according to continuity and quantity, but not according to quality. Again: Nature is said to be that from the power of which, when it is primarily inordinate and immutable, something of natural productions either is, or is generated: as brass is said to be the nature of a statue, and of brazen furniture; wood, of such things as are wooden; and in a similar manner with respect to other things. For each is from these, the first matter remaining unchanged: for, after this manner, they say that the elements of things which subsist naturally, are nature; some asserting that this is fire, others that it is earth, others that it is air, others again, that is water, and others that it is something else of this kind. There are also those who assert that nature is some of these; and there are others who contend that it is all these.

Further still: in another respect, nature is said to be the essence of things which subsist naturally; and in this sense it is understood by those who assert that nature is the first composition, and by Empedocles, when he says that there is not any nature of beings, but that there is a mixture alone, and permutation of things mingled, and that this mingling is denominated nature by men. So that such things, as either are, or are generated by nature (that already subsisting from which they are naturally adapted to be generated, or to be), are not yet said by us to possess nature, unless they have species and form. Hence that subsists from nature which is composed from both these, such as animals, and the parts of animals. But nature is the first matter; and this in a twofold respect: for it is either that which is first with relation to a thing, or that which is simply the first. Thus, for instance, of brazen works, the brass is first with respect to those works; but water perhaps is simply the first, if every thing which is capable of being liquefied is water. Also form and essence: but form is the end of generation. Hence, by a metaphor, every essence, in short, is called nature, because nature is a certain essence. From what has been said, therefore, the first nature, and that which is properly so denominated, is the essence of those things which possess in themselves the principle of motion, so far as they are such things. For matter, from being the recipient of this, is called nature. Generations also, and to be born, are called nature, because motions are from these. Nature also is the principle of the motion of things which have a natural subsistence, this principle being in a certain respect inherent either in capacity or energy.

Aristotle, Metaphysics. Book 5, Chapter 5.

That is called necessary, without which as a concause it is not possible to live. Thus, for instance, respiration and nutriment are necessary to an animal: for it is impossible that an animal can subsist without these. Also that is necessary, without which good cannot either be, or be produced, or a certain evil repelled and exterminated. Thus, to drink a medical potion is necessary to the prevention of disease; and to sail to Ægina, to receive a sum of money. To the necessary also belong the violent and violence. But this is that which opposes and impedes contrary to impulse and free-will. For the violent is called necessary; on which account it is painful; as Evenus also says—“For every thing necessary is grievous.” And violence is a certain necessity, as Sophocles also asserts— “But thus I act, by violence compelled.” Indeed, necessity very properly seems to be something which cannot be persuaded: for it is contrary to the motion of free-will, and to the motion of the reasoning power.

Again: we say that a thing is necessarily so, which cannot subsist in any other manner: and, according to this acceptation of the necessary, every thing else which is necessary, in a certain respect, derives its appellation. For the violent is called necessary, because he who is under the influence of violence cannot either act or suffer from impulse, on account of a compelling power; that being as it were necessary, through which a thing cannot subsist in any other manner. The like also takes place in the concauses of living and good. For, when it is not possible, either to obtain good, or to live without certain things, then those things are necessary, and this cause is a certain necessity. Further still: demonstration is of things necessary, because that which is demonstrated, if it is simply demonstrated, cannot have a different subsistence. But the causes of this, are things first, which cannot subsist in any other manner, and from which the demonstrative syllogism is composed. Some things, therefore, are necessary from a cause different from themselves; but others are necessary from no cause, since other things subsist from necessity through these: so that the first and proper necessary is that which is simple: for this cannot have a manifold subsistence; and therefore cannot subsist variously. For, if this were admitted, it would subsist manifoldly. If, therefore, there are certain eternal and immoveable natures, there is nothing in them violent, nothing contrary to nature.

Aristotle, Metaphysics. Book 5, Chapter 6.

One, is partly denominated according to accident, and partly essentially. According to accident, indeed, as Coriscus and a musician, and Coriscus the musician. For it is the same thing to say that Coriscus and the musician are one, as to say, Coriscus the musician: also to say, the musician and the just, and the just musician Coriscus. For all these are called one, according to accident: the just, indeed, and the musician, because they happen to belong to one essence; but the musician and Coriscus, because the one happens to the other. In like manner, too, in a certain respect, the musician Coriscus is one with Coriscus; because in this sentence, one part of the whole sentence happens to the other; as, for instance, the musician to Coriscus, and the musician Coriscus to the just Coriscus, because no one part of each happens to the same one. For there is no difference whether the musician happens to Coriscus, or Coriscus the just to the musician Coriscus. In a similar manner, one will be denominated according to accident, though it should be predicated of genus, or some one of universal appellations; as if, for instance man, and man the musician should be said to be the same. For these are one, either because to man who is one essence, the being a musician is accidental, or because both happen to some one among the number of particulars, as, for instance, to Coriscus. Yet both are not inherent after the same manner, but the one perhaps as genus and as in essence, but the other as habit, or the participated property of essence. Such things, therefore, as are called one according to accident, are after this manner so denominated.

But of things which are denominated one essentially, some are so called from their continuity, as a faggot, which is held together by a bond, and pieces of wood by glue. A line also, though it be curved, if it possesses continuity, is called one; as likewise each of the parts of the body, such as a leg and an arm. But of these, those things are more one, which are continuous by nature, than those which are continuous by art. But that is called continuous, the motion of which is essentially one, and which cannot be otherwise. And the motion is one which is indivisible, and indivisible according to time. But those things are essentially continuous which are not one by contact. For, if you place pieces of wood so as to touch each other, you will not say that these are one piece of wood, nor one body, nor any thing else continuous. In short, therefore, those things which are continuous are called one, although they may be curved, and still more such things as do not possess curvature. Thus the leg or the thigh is more one than the leg and foot together, because it is possible that there may not be one motion of the leg and foot. And a straight is more one than a curved line. But we say that a line which is curved, and has an angle, is both one and not one, because it is possible that a part of it may be moved, without the whole being at the same time moved. But of a right line, a part and the whole are always moved together; and it is not possible that one part of such a magnitude should be at rest, while another part is moved.

Further still: after another manner a thing is said to be one, viz. from having its subject indifferent with respect to form. But the subject of those things is indifferent, the form of which is indivisible according to sense. And the subject is either the first or the last. For wine is called one, and water one, so far as each is indivisible according to form. And all liquors are called one, as oil, wine, and such things as are fusible, because the ultimate subject of all these is the same; for all these are water and air. Those things also are called one, the genus of which is one differing by opposite differences. And all these are called one, because the genus is one which is the subject of the differences. Thus, for instance, horse, man, and dog, are one certain thing, because all of them are animals, and after a certain similar manner one, as is the case with things of which the matter is one. But these things are at one time thus called one, but another time they are called the same, from the superior genus, when they are not the proximate, but the last species of genus. Thus the isosceles and equilateral triangle possess one and the same figure, because both are triangles, but not the same triangles. Again: those things are called one, the definition of one of which is indivisible with respect to the definition of another: for every definition is itself essentially divisible. Thus, that which is increased, and that which is diminished, are one, because the definition is one: just as of superficies which have length and breadth, the definition of the form is one. In short, those things are especially one, the intellectual apprehension of the form of which is indivisible, and which can neither be separated by time, nor place, nor definition. For, universally, such things as have not division, so far as they have not, are called one. Thus, for instance, if man, so far as man, is without division, man is one; and if animal, so far as animal, is indivisible, animal is one: but if magnitude, so far as magnitude, is indivisible, magnitude is one. Most things, therefore, are called one, because they either effect, or possess, or suffer some other one thing.

But those things are primarily called one, of which the essence is one, and which are one either by continuity, or species, or definition. For we numerate as many, either those things which are without continuity, or those things of which the form is not one.

Again: we sometimes say that a thing is one by continuity, if it possesses quantity, and is continuous; and we sometimes say that a thing is not one, when it is not a certain whole, that is, if it has not one form. For we do not similarly say there is one, when we see the parts of a shoe placed any how together, although there may be continuity; but when it is so continuous, as to be a shoe, and to possess a certain form, then it is one. Hence, a circular line is more than all other lines one, because it is a whole and perfect. But the very essence of the one consists in this, that it is the principle of number. For the first measure is the principle of every genus; and that by which we first know a thing is the first measure of every genus. The principle, therefore, of that which is knowable, is in every genus the one. But there is not the same one in all genera. For here it is diesis, but there a vowel, or a mute. Moreover, of gravity there is one principle, and of motion another. But every where the one is indivisible, either in species or in quantity. Of those things, therefore, which are indivisible according to quantity, and so far as quantity, that which is every way indivisible and without position is called the monad: but that which is every way indivisible, and has position, is a point. That which is only divisible one way is a line; that which is capable of a two-fold division is a superficies; and that which is every way and triply divisible according to quantity, is a body. And, conversely, that which is divisible in a twofold respect is a superficies; that which is divisible only one way is a line; and that which is every way divisible is a body. But that which is no way divisible according to quantity is a point and the monad; without position, indeed, the monad; but with position, the point. Again: some things are one according to number, others according to species, others according to genus, and others according to analogy. Those things, indeed, are one according to number, of which the matter is one; but according to species, of which the definition is one; and according to genus, of which there is the same figure of predication; but things are one according to analogy, which subsist as one thing with relation to another. The posterior, however, always follow the anterior. Thus, for instance, such things as are one in number, are also one in species; but such things as are one in species, are not all of them one in number: but all things that are one in species, are also one in genus. Such things, however, as are one in genus, are not all of them one in species, but are one according to analogy. But such things as are one according to analogy, are not all of them one according to genus. It is, however, evident, that the many is predicated in a manner contrary to the one. For some things are called many from not being continuous; some things from possessing matter, divisible according to species, such matter being either the first or the last; and some from possessing many of those reasons which declare the essence of a thing.

Aristotle, Metaphysics. Book 5, Chapter 7.

Being is distributed into the accidental and the essential. Into the accidental indeed, as when we say that a just man is a musician, and, in a similar manner, the musician is a man. Thus too, we say that the musician builds, because it happens that the builder is a musician, or that the musician is a builder. For, to affirm this thing to be that, signifies that this thing happens to that. Hence, with respect to what has been asserted, when we say that man is a musician, and a musician man, or that something white is a musician, or a musician white, we say this, because both happen to the same thing, but that because it happens to being. But we say that a musician is a man, because the being a musician is accidental to him. In like manner, something white is said to be a man, because that is a man to which the being white is accidental. Things, therefore, which are said to be according to accident, are said to be after this manner, either because both are inherent in the same thing, or because the predicate is present to the subject, or because it is the thing itself to which accident is present, of which the thing itself is predicated.

But things are said to subsist essentially, which signify the figures of predication. For, as often as they are predicated, so often do they signify being. Since, therefore, of things predicated, some signify the essence of a thing, others the quality, others the quantity, some the relation, others the action or passion, others the situation, and others the time, being signifies the same to each of these. For it is the same thing, to say the man is convalescent, as to say the man convalesces, and the man is walking, or is cutting, as the man walks or cuts. And in a similar manner with respect to other things.

Again: the words to be and it is, signify that a thing is true; but the words not to be, that it is not true, but false. In like manner with respect to affirmation and negation. Thus, he who says that Socrates is a musician, says that he is, because this is true; or asserts that Socrates is not white, asserts this because it is true: but he who says that the diameter of a square is not incommensurable with its side, says this because it is false. Further still: to be and being partly signify that which is in capacity, and partly that which is in energy. Thus, we say that both he who is endued with sight in capacity sees, and he who possesses it in energy. And, in like manner with respect to scientific knowledge, we say that both he is endued with science who is able to use it, and he who does use it: and that, both a thing which is now at rest, and a thing which is capable of being at rest, are quiescent. We are also accustomed to speak in a similar manner with respect to essences. For we say that Mercury is in the stone, and we speak of the half of the line in capacity, and call that corn which is not yet ripe. But when a thing is possible, and when it is not so, must be elsewhere determined.

Aristotle, Metaphysics. Book 5, Chapter 8.

With respect to essence, simple bodies, such as earth, fire, water, and the like, are called essences; and, in short, bodies, together with animals and dæmoniacal natures consisting from these, and the parts of these, are thus denominated. But all these are called essences, because they are not predicated of a subject, but other things are predicated of these. After another manner, too, that is called essence which is the cause of being, and which is inherent in such things as are not predicated of a subject, such as soul in an animal. Further still: such parts as are inherent in things of this kind, defining and signifying a certain sensible thing, and which being taken away, the whole is also taken away. Thus, if superficies is taken away, body also, according to some, is destroyed; and superficies is destroyed, by taking away line. And, in short, to some number appears to be a thing of this kind; for, according to them, nothing can subsist if it is taken away, and it is that which bounds all things. Again: the formal cause, of which definition is the reason, is called the essence of any thing. But it happens that essence is predicated according to two modes, viz. according to the ultimate subject, which is no longer predicated of another thing, and according to that which is a certain definite particular, and is separable: but of this latter kind are the form and species of every thing.

Aristotle, Metaphysics. Book 5, Chapter 9.

Of things which are said to be the same, some are so denominated according to accident, but others essentially. Thus that which is white and the musician are the same, because they happen to the same thing; and man and musician are the same, because the one happens to the other, viz. the being a musician happens to man. But this is the same with either, and either of these is the same with this. For man and the musician are the same as man the musician; and this is the same with those. Hence all these are not predicated universally. For it is not true, to say that every man and a musician are the same: for universals subsist essentially, but accidents have not an essential subsistence, but are simply predicated of particulars. Thus Socrates and Socrates the musician appear to be the same. For Socrates is not predicated of many things. Hence we do not say every Socrates, as we say every man. Some things, therefore, are after this manner said to be the same according to accident.

But some things are said to be the same essentially, in the same manner as things which are essentially one. For things of which the matter is one, either in species or number, are said to be the same: and also things of which the essence is one. So that it is evident that sameness is a certain unity of essence, either of many things, or when any thing is considered as many, as when any one says that a thing is the same with itself; for then he considers that thing as two.

But things are called different, of which either the species, or the matter, or definition of the essence is many: and, in short, different is predicated in a manner opposite to same. But things are said to be different which are diverse and yet in a certain respect the same, with this exception alone, that they are not the same in number, but either in species, or genus, or analogy. Again: those things are different, of which the genus is different, also things contrary, and such things as possess diversity in their essence.

Things are said to be similar which are passive to the same thing, and which are passive to a greater number of things same than different; and also of which the quality is one. That also which possesses more, or the principal of those contraries by which another thing may be altered, is similar to that thing. But dissimilars are predicated in a manner opposite to similars.

Aristotle, Metaphysics. Book 5, Chapter 10.

Opposites are contradictories, contraries, relatives, privation, and habit, and those things from which such things as are last originate, and into which they are resolved; such, for instance, as generations and corruptions: likewise things which cannot be at the same time present to that which is the receptacle of both;—these things are either themselves said to be opposed, or the natures from which they consist. For a dark and a white colour cannot be present at the same time to the same thing; and hence the things from which these colours consist are opposed to these.

Those things are called contraries which, differing in genus from each other, cannot at the same time be present to the same thing; also things which among those in the same genus have the greatest difference between themselves; and things which being in the same recipient differ very much from each other. Things, too, are called contraries, which differ the most of all others under the same power; and things of which the difference is the greatest, either simply, or according to genus, or according to species. But, of other things which are called contraries, some are so denominated because they possess, and some because they are recipients of, things of this kind. Some, again, are so called, because they are effective, or passive, agents, or patients, rejections or assumptions, habits or privations of these and the like. But since the one and being are manifoldly predicated, it is necessary that other things also should follow which are predicated according to these. So that there will be a distribution of same, different, and contrary through the several predicaments.

But things are said to be different in species, which, being of the same genus are not placed under each other, and also such things as being in the same genus possess difference, together with such as have contrariety in their essence. Either all contraries too, or those which are primarily so denominated, are different in species. Also those things are different in species, the definitions of which in the ultimate species of genus are different, as man and horse, which are individuals in genus, but their definitions are different. This is likewise the case with such things which, being in the same essence, possess diversity. But things are the same in species, which are predicated in a mode opposite to these.

Aristotle, Metaphysics. Book 5, Chapter 11.

With respect to prior and posterior, some things are so called because there is a certain first and a principle in every genus; for that is prior which is nearer to a certain principle, defined either simply and by nature, or relatively, or according to situation, or by certain things. Thus, for instance, some things are prior and posterior according to place; prior, indeed, because they are nearer to a certain place definite by nature, as to the middle, or the extremity, or because they are nearer to any thing which is casually definite. But that which is more remote is posterior.

Again: some things are prior and posterior according to time. For some things are called prior, because they are more remote from the present time, as with respect to things which have been already transacted. Thus the Trojan are prior to the Median transactions, because they are more distant from the present time. But other things are prior, because they are nearer to the present time, as is the case with things future. Thus the Nemean are prior to the Pythian games, because they are nearer to the present time, which present time we use as the beginning, and as that which is first. Some things, again, are prior and posterior according to motion. For that which is nearer to the first mover of a thing, is prior; and, in this sense, a boy is prior to a man. But this is a certain principle simply considered. Some things, too, are prior according to power; for that which transcends in power and that which is more powerful, are prior. But of this kind is that nature whose free-will something else which is posterior necessarily follows; so that, the former not moving, the latter is not moved, and when the former moves the latter is moved. But free-will is a principle.

Again: some things are prior according to order: and these are such things as are proportionally distant from one certain definite thing. Thus, in a dance, he who obtains the second place is prior to the third in rank; and, in a musical instrument, the paranete is prior to the nete: for in the former the Coryphæus, but in the latter the middle, is the principle. After this manner, therefore, these things, are said to be prior.

But, according to another mode, that is said to be prior which antecedes in knowledge, as being simply prior. But, of these, some are prior according to reason, and others according to sense. For, according to reason, universals are prior, but according to sense, particulars. And, according to reason, accident is prior to the whole; as, for instance, the musician, to man the musician. For the whole reason or definition will not be without the part; though it is not possible that a musician can be, unless there be a certain, or some particular musician. Further still: the participated properties of things prior are called prior, as, for instance, rectitude is prior to smoothness. For the former is an essential property of a line, but the latter of a superficies. Some things, therefore, are after this manner called prior and posterior. But some things are so denominated according to nature and essence; and these are such things as are able to subsist without others, but others cannot subsist without them: which division is used by Plato.

But since to be is manifold, in the first place, the subject is prior, through which essence is prior. In the next place, things in capacity are prior in a different manner from those which are in energy. For some things are prior according to capacity, but others according to energy. Thus the half is in capacity prior to the whole, and the part to the whole, and matter to essence. But these are posterior in energy; for the whole being dissolved, they will be in energy. But after a certain manner all things which are called prior and posterior are so called according to these. For some things according to generation may be without others; and after this manner the whole is prior to its parts. But some things may subsist without others according to corruption; and after this manner the part is prior to the whole. And the like takes place in other things.

Aristotle, Metaphysics. Book 5, Chapter 12.

Capacity is called, in the first place, the principle of motion or mutation in another thing, or so far as it is another. Thus the architectural art is a capacity which does not subsist in the structure raised by that art: but the medical art being a capacity, will subsist in him who is healed, but not so far as he is healed. In short, therefore, one thing which is the principle of mutation or motion, is said to be capacity in another thing, so far as it is another. But another thing is so denominated from another, or so far as it is another: for so far as it is passive, it becomes passive to something. Sometimes, therefore, when it is possible for any thing to be passive, we say that it is capable of being passive; but sometimes we assert this, not according to every passion, but if a thing is capable of being passive with reference to that which is better. Again: benefiting another, or freely doing good, is called capacity. For sometimes we say that those who have alone walked or discoursed, but not well, or as they wished to do, are not capable of speaking or walking. And in a similar manner with respect to being passive.

Further still: all habits, through which the possessors are altogether void of passion, or are immutable, or not easily changed to a worse condition, are called capacities. For some are broken, and bruised, and bent, and in short corrupted, not from being capable, but from not being capable, and from being in something deficient. But others are impassive to things of this kind; and these are such things as scarcely and in a small degree are passive, through capacity, and the being capable, and from subsisting in a certain manner. But since capacity is predicated in so many ways, the capable or possible also, after one manner is said to be that which has the principle of motion or mutation. For that from which a permanent condition or rest may proceed, is something capable in another, or so far as it is another. In the second place, that is capable which can be passive to something else. In the third place, that which has a capacity of this kind of being changed to any thing, whether to that which is better, or to that which is worse. For that which is corrupted appears to be capable of being corrupted, or it would not have been corrupted, if this was impossible. But now it has a certain disposition, cause, and principle of a passion of this kind. For sometimes it appears to be such because it possesses something, and at other times because it is deprived of something. But if privation is in a certain respect habit, all possibles from possessing something will, indeed, be possibles: and if privation is not a certain habit, possibles will be denominated equivocally. So that a thing is possible, partly because it possesses a certain habit and principle, and partly because it possesses a privation of this, if it be possible that privation can be possessed. In the fourth place, a thing is capable or possible because it has not a capacity, or principle in another, so far as another, by which it can be corrupted. But further still: all these are called possibles, because they alone happen to be generated, or not to be generated, or to be generated in a becoming manner. For in inanimate natures a capacity of this kind is inherent, as in instruments. Thus they say that one lyre is capable of sounding and another not, if it is not a well-sounding lyre.

But incapacity is the privation of capacity, and a certain ablation of such a principle, as we have related, or an entire ablation of it; or it is an ablation of naturally possessing a thing, or of possessing when it is naturally adapted to possess. For they do not say that a boy and an eunuch are similarly incapable of generating. Further still: incapacity is opposite as well to that capacity which is alone motive, as to that which is motive in a becoming manner. And, with respect to impossibles, some are so denominated according to these modes of incapacity, but others, after a different manner, as, for instance, the possible and impossible. That is impossible indeed, the contrary of which is necessarily true. Thus, it is impossible for the diameter of a square to be commensurable with its side, because a thing of this kind is false. And the contrary of this is not only true, but necessary, viz. that the diameter is incommensurable with the side. That the diameter, therefore, is commensurable, is not only false, but is necessarily false. But the contrary to this is the possible, when it is not necessary that the contrary is false. Thus, it is possible for a man to sit; for that he does not sit, is not necessarily false. The possible, therefore, after one manner, as we have said, signifies that which is not necessarily false. But after another manner, it signifies that which is true; and according to another acceptation, that which may be true. But the capacity which is spoken of in geometry, is metaphorically called capacity. These possibles, however, are not so called according to capacity. But all those which are denominated according to capacity, are all of them so called with reference to one first capacity: and this is the principle of mutation in another so far as it is another. For, with respect to other things that are called possibles, some are so called, because something else pertaining to them possesses a capacity of this kind; others, because something belonging to them does not possess it; and others, because they possess this capacity themselves. And in a similar manner with respect to impossibles. So that the proper definition of the first capacity will be this, a principle effective of mutation in another, so far as it is another.

Aristotle, Metaphysics. Book 5, Chapter 13.

Quantity is called that which is divisible into things inherent, either or each of which is one thing, and is naturally adapted to be this definite particular. Multitude, therefore, is a certain quantity, if it be numerable; but magnitude, if it be measurable. But multitude is called that which is divisible in capacity into parts non-continuous; and magnitude that which is divisible into parts continuous. Again: of magnitude, that which is continuous one way is length; that which is continuous two ways, breadth; and that which is continuous three ways, depth. But of these, the multitude which is finite is number; length is a line; breadth superficies; and depth body.

Further still: some things are called certain quantities essentially, but others according to accident. Thus, for instance, a line is a certain quantity essentially, but a musician accidentally. But, of quantities which have an essential subsistence, some are according to essence; as, for instance, a line is a certain quantity. For, in the definition explaining what it is, a certain quantity is inherent. But others are passions and habits of an essence of this kind; as, for instance, the much and the few, the long and the short, the broad and the narrow, the high and the low, the heavy and the light, and other things of this kind. But the great and the small, the greater and the lesser, are the essential passions of quantity, considered as well essentially, as with reference to each other. These appellations also are transferred to other things.

But of those things which are called quantities according to accident, some are so called in the way we have already mentioned; for, because that in which a musician and white are inherent is a certain quantity, those also are called quantities. But others are so called as motion and time. For these are denominated certain continued quantities, because those things are divisible, of which these are passions. And here I do not mean that which is moved, but that in which motion is effected. For, because that is a quantity, motion also is a quantity. Time also is quantity, because motion is such.

Aristotle, Metaphysics. Book 5, Chapter 14.

Quality is called after one manner the difference of essence. Thus, for instance, when it is asked what kind of an animal is man (or what is the quality by which he is distinguished from other animals), we answer that he is a biped: when the same question is asked of a horse, the answer is that he is a quadruped; and when it is asked what kind of figure a circle is, we reply, a figure without angles; by which it appears that difference according to essence is quality. After one manner, therefore, quality is called difference of essence. But after another manner, as things immoveable, and mathematical entities. Thus, for instance, numbers are certain qualities, I mean such as are composite, and which are not alone referred to one, but of which a superficies and a solid are imitations. But these are plane, square, and cube numbers; and, in short, whatever besides a certain quantity is contained in the essence of number: for the essence of every number consists in being assumed once. Thus, for instance, the essence of six does not consist in twice three, or thrice two, but in being taken once: for once six is six.

Again: such things are called qualities as are the passions of essences that are moved; as, for instance, heat and cold, whiteness and blackness, gravity and levity, and things of this kind, according to which bodies are said to be internally changed. Further still: virtue and vice; and, in short, good and evil, are qualities. Quality, therefore, may be nearly denominated according to two modes; and of these one is the principal. For the first quality is difference of essence: but of this the quality which is in numbers is a certain part. For it is a certain difference of essence, but either not of those things which are moved, or not so far as they are moved. But these are the passions of things which are moved, so far as they are moved, and the differences of motions. But virtue and vice are certain parts of passions: for they manifest the differences of motion and energy, according to which those beings that are in motion, do or suffer well or ill. For that which is able to be moved, or to energise, in this particular manner, is good; but that which is moved, or energises, in that particular manner, is depraved. But especially good and evil signify quality in animated natures, and of these, particularly in such as possess a free will.

Aristotle, Metaphysics. Book 5, Chapter 15.

With respect to relatives, some things are so denominated, as the double to the half, and the triple to the third, and, in short, the multiple to the submultiple, and the surpassing to that which is surpassed. But others are so called, as that which heats to that which is heated; that which cuts to that which may be cut; and, in short, as that which is active to that which is passive. Others, again, are as that which is measurable to measure, that which is the object of science to science, and that which is sensible to sense.

But the first among these are indeed denominated according to number, either simply, or definitely with respect to each other, or to one. Thus, the double to one is a definite number: but multiple is the relation according to number to one, but not definite; as, for instance, this or that. But sesquialter to subsesquialter is the relation according to number to a definite number. Superpartient to subsuperpartient is according to the indefinite, in the same manner as multiple to one. But the exceeding to that which is exceeded, is entirely indefinite according to number. For number is commensurable; but the exceeding and that which is exceeded are denominated according to incommensurable number. For the former is to the latter so much, and something still beyond. But this is indefinite: for whatsoever takes place, it is either equal or not equal. All these relatives, therefore, are denominated according to number, and are the properties of number: and still further, the equal, the similar, and the same, according to another mode. For they are all denominated according to the one. Thus, things are same of which the essence is one; but similar of which the quality is one; and equal of which the quantity is one. But the one is the principle and measure of number. So that all these are called relatives according to number, but not after the same manner.

But things active and passive are relatives according to an active and passive power, and the energies of powers; as, for instance, that which is capable of heating to that which may be heated, because they are endued with power; and, again, that which heats to that which is heated, and that which cuts to that which is cut, are relatives as things energising. But of those things which are relatives according to number, there are not energies, unless after the manner we have elsewhere mentioned: for energies according to motion do not belong to numbers. Besides, of those things which are called relatives according to power or capacity, some are so denominated according to time; as, for instance, that which makes to that which is made, and that which will make to that which will be made. Thus, also, a father is called a father of a son; for the former makes, but the latter has been something passive.

Again: some things are called relatives according to a privation of power, as the impossible, and such things as are so denominated, as the invisible. Things, therefore, which are called relatives according to number and power, are all of them so called because each derives that which it is from reference to another, and not because something else is denominated with reference to it. But that which may be measured, that which is the object of science, and that which is the object of the dianoetic power, are called relatives, because something else is denominated with reference to these. For that which is the object of the dianoetic power signifies that the dianoetic power subsists with reference to it: but the dianoetic power does not subsist with reference to him to whom it belongs; for the same thing would be twice said. In like manner, sight is the sight of something, and not of him to whom it belongs, although to assert this is true, but it is referred to colour, or something else of this kind. But after that manner, the same thing would be twice said, I mean, that sight is the sight of him of whom it is the sight. Of things, therefore, which are essentially relatives, some are so called after this manner, but others if their genera are things of this kind. Thus, for instance, the medicinal art ranks among relatives, because the science which is the genus of it appears to belong to relatives. Add, too, those things, by which such as possess them are called relatives. Thus, equality is a relative, because the equal is a relative; and similitude, because the similar is a relative. But some things are called relatives according to accident. Thus, man is a relative, because it happens to him to be double; and this belongs to relatives: white, too, is a relative according to accident, if it happens to the same thing to be double and to be white.

Aristotle, Metaphysics. Book 5, Chapter 16.

The perfect is denominated that of which no part can be externally assumed. Thus, for instance, the time of any thing is perfect, beyond which no time can be assumed which is a part of this time. The perfect also is that which, according to virtue and well-being, has not a transcendency with respect to a certain genus. Thus, a physician is a perfect physician, and a piper a perfect piper, when they are in no respect deficient according to the species of their proper virtue. Thus, too, metaphorically speaking, in things evil, we say a perfect sycophant, and a perfect thief; since we also call these characters good; as, for instance, a good thief, and a good sycophant. Virtue also is a certain perfection: for a thing is then perfect, and every essence is then perfect, when no part of its natural magnitude, according to the species of its proper virtue, is wanting.

Further still: those things are called perfect to which a worthy end is present: for they are perfect from possessing an end. So that, since the end is something belonging to extremes, transferring it also to things depraved, we say that a thing is perfectly destroyed, and is perfectly corrupted, when nothing of corruption or evil is deficient, but it has arrived at the very extremity of these. Hence death, also, according to a metaphor, is called the end, because both are extremes. Things, therefore, essentially called perfect are in so many ways thus denominated; some, because according to well-being, they are in no respect deficient, nor have transcendency in each genus, nor any thing belonging to them external. But other things are called perfect according to these, because they either effect or possess something of this kind, or are adapted to this, or in some other way are denominated with reference to things called primarily perfect.

Aristotle, Metaphysics. Book 5, Chapter 17.

Bound is called that which is the last of any thing beyond which nothing can be assumed, as the first thing which may be assumed, and within which primarily all things are placed; also, that which is the form of magnitude, or of that which possesses magnitude, and which is the end of every thing. But that to which motion and action tend, is a thing of this kind, and not that from which they begin. Sometimes, however, it is both that from which motion and action proceed, and that to which they tend; also that for the sake of which other things operate, and the essence of every thing, and the formal cause to every thing. For this is the bound of knowledge; and if of knowledge, also of a thing. So that it is evident, that in as many ways as principle is predicated, in so many ways bound also is predicated, and still more multifariously. For principle is a certain bound; but it is evident that not every bound is a principle.

Aristotle, Metaphysics. Book 5, Chapter 18.

According to which is predicated multifariously. Considered in one way, it is the form and the essence of every thing. Thus, for instance, the good itself is that according to which a thing is good. But considered in another way, it is that in which primarily a thing is naturally adapted to be produced, as, for instance, colour in superficies. Hence, that which is primarily called according to which is form; but that which is secondarily thus denominated, is as the matter, and the first subject of every thing. In short, according to which is predicated in as many ways as cause. For to ask, according to which did a man arrive? is the same thing as to ask, for the sake of which did he arrive? And to inquire according to which a man paralogises, or syllogises, is the same thing as to inquire the cause of his paralogism, or syllogism.

Again: according to which signifies according to position; as, for instance, according to which does he stand? or according to which does he walk? For all these signify position and place. So that according to itself, or the essential, is also necessarily predicated multifariously. For, in the first place, it signifies the formal cause of a thing, or the proper form and definition explaining its essence; as, for instance, Callias, and the proper form of Callias. In the second place, it signifies such things as are inherent in definition; as, for instance, Callias is essentially an animal. For, in the definition of Callias, animal is contained: for Callias is a certain animal. In the third place, it signifies that which primarily receives any thing in itself, or in a certain part of itself. Thus, for instance, superficies is essentially white, and man is essentially an animal. For soul is a certain part of man, in which life is primarily inherent. In the fourth place, it signifies that of which there is not any other cause. For of man there are many causes, such as animal, biped; but, at the same time, man is man essentially. And, in the fifth place, it signifies such things as are inherent in some particular thing alone, and so far as it is alone. Hence, that which has a separate, has also an essential, subsistence. 

Aristotle, Metaphysics. Book 5, Chapter 19.

Disposition is called the order of that which has parts, either according to place, or according to capacity, or according to form. For it is requisite that it should be a certain position, as the name also, viz. disposition, evinces.

Aristotle, Metaphysics. Book 5, Chapter 20.

Habit is denominated, according to one mode, a certain energy, as it were, of that which possesses and that which is possessed; being, as it were, a certain action or motion. For, when any thing makes, and another thing is made, the making subsists between. In like manner, habit subsists between him who possesses a garment, and the garment which is possessed. It is evident, therefore, that there cannot be another habit of this habit. For there would be a progression to infinity, if there was a habit of the habit which is possessed. But, according to another mode, habit is called disposition, conformably to which that which is disposed is well or ill disposed, and this either essentially, or with relation to another. Thus, health is a certain habit; for it is a disposition of this kind. Further still: it is called habit, if it is a portion of a disposition of this kind. Hence also the virtue of parts is a certain habit.

Aristotle, Metaphysics. Book 5, Chapter 21.

Passion is called in the first place quality, according to which any thing may be altered; as, for instance, white and black, sweet and bitter, gravity and levity, and other things of this kind. But, in the second place, it signifies the energies and internal changes of these. And, still more than these, noxious internal changes and motions, and especially such changes as are not only noxious but painful. Lastly, calamities and sorrows of great magnitude are called passions.

Aristotle, Metaphysics. Book 5, Chapter 22.

Privation is said to take place according to one mode, when a thing does not possess something which is naturally adapted to be possessed, although it is itself not naturally adapted to possess it. Thus, for instance, a plant is said to be deprived of eyes. But according to another mode, when either a thing itself, or the genus of it, does not possess a thing which it is naturally adapted to possess. Thus, a blind man is deprived of sight in one way, and a mole in another; the latter according to genus, but the former essentially. Further still: privation takes place, if a thing is naturally adapted to possess, yet does not possess when it is so adapted. For blindness is a certain privation: but an animal is blind, not according to every age, but in that only in which, when it is naturally adapted to see, it does not see. In like manner, privation takes place when a thing does not possess in which, according to which, to which, and so far as it is naturally adapted to possess. Further still: a violent ablation of any thing is called privation. And, as often as negations are denominated from a, so often also are privations denominated. For a thing is called anison, unequal, because, though naturally adapted to possess equality, it does not possess it; and aoroton, invisible, because it is entirely without colour, and because it possesses it defectively. In like manner, an animal is called apous, without feet, when it is entirely deprived of feet, and when it has them attended with some defect. Again: privation takes place when a thing possesses but a little, as any fruit with a small kernel, viz. in this case it subsists in a certain respect defectively. Also, when a thing cannot be effected with facility, or in a proper manner. Thus, a thing is insecable, not only because it is not cut, but because it cannot be easily or well cut. Further still: privation takes place when a thing is not in any respect possessed. For he is not called blind who has only one eye, but he who is deprived of sight in both. Hence, not every man is good, or bad, or just, or unjust, but there is also an intermediate character.

Aristotle, Metaphysics. Book 5, Chapter 23.

To have is predicated multifariously. After one manner it is denominated when any being acts according to its own nature, or according to its own impulse. Hence, a fever is said to have a man, and tyrants cities, and those who are clothed a garment. But after another manner, that in which any thing subsists as a recipient. Thus, for instance, the brass has the form of the statue, and the body the disease. In the third place, as that which contains things contained. For a thing is said to be had by that in which it is contained. Thus we say, that the vessel has that which is humid, the city men, and the ship sailors. Thus also the whole has the parts. Further still: that which prevents any thing from being moved or acting according to its own impulse, is said to have this very thing. Thus, pillars have the imposed weights, and poets make Atlas to have the heavens, in order to prevent them from falling on the earth, as certain physiologists say. After this manner too, that which connects is said to have that which it connects, as if every thing according to its own impulse would be separated and dispersed. And to be in any thing is predicated similarly, and in a manner consequent to to have.

Aristotle, Metaphysics. Book 5, Chapter 24.

To be from a certain thing, is after one manner predicated from which, as from matter: and this in a two-fold respect, either according to the first genus, or according to the last form. Thus, all liquids are from water, and the statue is from brass. But after another manner, it is predicated as from the first moving principle. Thus, for instance, from what did battle arise? From defamation, because this is the principle of the battle. In the third place, it is denominated from that which is a composite from matter and form, as the parts from the whole, the verse from the Iliad, and the stones from the house. For form is the end; and that which has the end is perfect. In the fourth place, as species from a part. Thus, man is from biped, and a syllable from a letter. For these are from those, in a manner different from that in which the statue is from brass. For a composite essence is from sensible matter; but form also itself consists from the matter of form. Some things, therefore, are predicated after this manner, and some, if a thing subsists according to a certain part of these modes. Thus, the offspring is from father and mother, and plants from the earth, because they are from a certain part of these. In the fifth place, that which subsists after any thing according to time. Thus, night is said to be from the day, and a storm from fair weather, because the former are posterior to the latter. But of these, some are thus denominated from having a mutation into each other, as the particulars which have been just mentioned; but others because they are alone consequent according to time. Thus, a navigation was made from the equinoctial, because it was made after the equinoctial: and the Thargelia are from the mysteries of Bacchus, because they are posterior to these mysteries.

Aristotle, Metaphysics. Book 5, Chapter 25.

Part is denominated according to one mode, that into which quantity, so far as quantity, can be divided. For, always that which is taken away from quantity, so far as quantity, is called a part of it. Thus, two is after a manner said to be a part of three. But, according to another mode, that alone is called a part of quantity which measures it. Hence in a certain respect two, as we have said, is a part of three, but in another respect is not. Again: those things into which form can be divided without quantity are called the parts of form. Hence they say that species are parts of genus. Further still: those things are called parts, into which any thing is divided, or from which the whole is composed, or form, or that which possesses form. Thus, the brass is a part of a brazen sphere, or of a brazen cube. But this is the matter in which form is received. An angle also is a part. Again: those things which are contained in the definition of a thing are also parts of the whole. Hence genus is called a part of species; but species is in a different manner a part of genus.

Aristotle, Metaphysics. Book 5, Chapter 26.

Whole is called that of which no part is wanting of those things from which the whole is said naturally to consist. Also, whole is that which contains things contained so as to form one thing. But this in a twofold respect: for either in such a manner that each may be one, or so that one thing may emerge from these. For universal, and, in short, that which is denominated as being a certain whole, are universal and a whole because they contain many things, are predicated of particulars, and all are one according to the predicate. Thus man, horse, and god are all of them one, because each of them is an animal. But the continuous and the finite are a whole, when one thing is produced from many things which are inherent, especially when this multitude is inherent in capacity, and not in energy. But of these, things which have a natural subsistence are more wholes than things which are formed by art, as we have said in the division of things denominated one. For totality is a certain unity. Again: since quantity has a beginning, middle, and end, of those quantities in which position does not make a difference, the all is predicated; but of those in which it does make a difference, the whole is predicated. And of those things which admit both, the whole and the all are predicated. But there are things of which the same nature remains in transposition, but not the same form; as, for instance, wax and a garment. For they are called whole and all, in consequence of possessing both. But water, such things as are moist, and number, are denominated all. For we do not say the whole number, and the whole water, except metaphorically. But of those things of which all is predicated as a certain one, all things is likewise predicated. Thus, of things divided, we say all the number, all these monads.

Aristotle, Metaphysics. Book 5, Chapter 27.

The diminished or mutilated is predicated, not of every quantity which may casually occur, but it is requisite that it should be divisible and a whole. For two things are not mutilated, when one of them is taken away (for a thing mutilated, and that by the ablation of which it was mutilated, can never be equal); nor, in short, is any number mutilated: for it is necessary that its essence should remain. Thus, if a cup is mutilated, still it is necessary that it should be a cup; but a number is no longer the same when a part is taken away. Besides, neither can all those things be called mutilated, which consist of dissimilar parts. For number is that which has dissimilar parts, as, for instance, the duad and triad: but, in short, none of those things are mutilated, of which the position makes no difference; as water, or fire, and the like. But it is necessary that mutilated natures should be such things as have an essential position.

Again: it is requisite that they should be continuous. For harmony consists from dissimilar parts, and has position, but it does not become mutilated. Besides this, neither are such things as are wholes mutilated by the privation of any part indifferently. For the principal parts of essence, or any parts indifferently, being taken away, will not make that which remains mutilated. Thus, if a cup is perforated, it is not diminished or mutilated; but this happens when its handle, or some one of its extremities, is taken away. A man also is mutilated, not when his flesh or spleen, but when some extreme part, is taken away, and this not any part indifferently, but which, when wholly taken away, cannot be again generated. Hence men that are bald are not mutilated.

Aristotle, Metaphysics. Book 5, Chapter 28.

Genus is predicated, when the generation of things possessing the same species is continuous. Thus, for instance, it is said, as long as the genus (i.e. race) of men may be, i. e. as long as the generation of them is continuous. It is also predicated as that from which things derive their existence as the first mover. Thus, according to genus, some are called Greeks, and others Ionians, because the former descended from Helenus and the latter from Ion, as the first generators. But genus is rather denominated from the generator than from the matter. For genus is also denominated from the female, as, for instance, from Pyrrha. Again: superficies is called the genus of superficial figures, and solid of such as are solid: for, of every figure, this is such a superficies, and that is such a solid. But genus is that which is the subject of differences.

Again: genus also is that which is first inherent in definitions signifying the essence of a thing, the differences of which are called qualities. In so many ways, therefore, is genus predicated: for it is either denominated according to a continued generation of the same species, or according to the first mover of the same species; or it is predicated as matter. For that of which there is difference and quality, is that subject which we call matter. But things are called different in genus, of which the first subject is different, and one is not resolved into the other, nor both into the same. Thus, form and matter are different in genus, and such things as are denominated according to a different figure of the predication of being. For, of beings, some things signify what a thing is, others what kind of a thing it is, and others signify conformably to the division we have previously made. For neither are these resolved into each other, nor into one certain thing.

Aristotle, Metaphysics. Book 5, Chapter 29.

The false is denominated after one manner, as a thing false: and this in the first place, because it is not composed, or because it is impossible for it to be composed; as when it is said that the diameter of a square is commensurable with its side, or that you sit. For, of these, the former is always false, but the latter sometimes; so that these are non-entities. But other things are false, which are indeed entities, but are naturally adapted to appear either not such as they are, or things which are not, as, for instance, pictures and dreams. For these are indeed something, but not the things of which they cause the imagination. Things, therefore, are thus said to be false, either because they are not, or because the imagination which emerges from them is the imagination of that which is not.

But discourse is false, which is of non-entities, so far as it is false. On this account every false discourse is employed about something different from that respecting which it would be a true discourse. Thus, the discourse respecting a circle is false when applied to a triangle. But the discourse about any thing which explains its essence, is partly one and partly many, since a thing itself, and itself considered as the recipient of something else, are in a certain respect the same; as, for instance, Socrates, and Socrates the musician. But a false discourse is simply considered as a discourse about nothing. On this account Antisthenes entertained a stupid opinion when he thought that nothing could be said, except one thing of one thing, by a proper discourse; the consequence of which opinion must be, that there can be no contradiction, and it will be scarcely possible to make a false assertion. Any thing, however, may be asserted, not only by a discourse peculiar to that thing, but also by that which belongs to another thing; and this so as to be perfectly false, and yet in a certain respect true. After this manner, the number 8 is double from the definition of the duad. Some things, therefore, are after this manner denominated false. But a man is false who readily and voluntarily admits false assertions, not for the sake of any thing else, but merely because they are false, and who is the cause of others adopting such like assertions. Just as we say that things are false which produce a false phantasy. Hence the reasoning in the lesser Hippias of Plato deceives, which endeavours to show that the same man is both false and true: for he considers him as false who is capable of deceiving; but such a one possesses both knowledge and prudence. Besides, it also says that he who is voluntarily depraved is the better man. But the false here is collected by induction. For he who is voluntarily lame is better than him who is involuntarily so: for here voluntary lameness is considered as the same with an imitation of lameness. Since, if he were voluntarily lame, he would perhaps be worse; just as this would also be the case in moral conduct.

Aristotle, Metaphysics. Book 5, Chapter 30.

Accident is called that which is inherent in something, and of which something may be truly asserted, yet neither necessarily, nor for the most part; as, for instance, if any one digging for a plant in a ditch should find a treasure, the finding the treasure would be an accident to him who digs in the ditch. For neither does the one follow from the other, nor after it. Nor, if any one plants, will he for the most part find a treasure. A musician also may be white; but since this takes place neither from necessity, nor for the most part, we call it an accident. Since, therefore, there is something which has a subsistence, and a subsistence in something, and some of these are in a certain place, and at a certain time, whatever has a subsistence indeed, but not because it is this particular thing, or because it is now, or here, will be an accident. Nor is there any definite cause of accident, but the cause of it is casual; and this is indefinite. Thus, some one may have accidentally come to Ægina, if it was not his design to go to that place, but he was driven thither by a storm, or taken by robbers. Accident, therefore, was generated and is, but not so far as itself is, but so far as something else is. For the storm was the cause of his going to that place, to which he did not sail: but this was Ægina. Accident is also after another manner denominated that which essentially belongs to a thing, but yet is not contained in the essence of that thing; as, for instance, the possession of angles equal to two right in a triangle. And it happens, indeed, that accidents of this kind are eternal: but this is not the case with any of the others; the reason of which we have elsewhere assigned.

Aristotle, Metaphysics. Book 6, Chapter 1.

The principles and causes of beings are investigated; and it is evident that they are investigated of beings so far as beings. For there is a certain cause of health and a good habit of body. Of mathematical entities, too, there are principles, elements, and causes. And, in short, every dianoetic science, or which participates any thing of the dianoetic power, is conversant with causes and principles, which are either more accurate or more simple. But all these circumscribing one particular thing, and a particular genus, are employed about this, but not about being simply, nor so far as it is being, nor do they pay any attention to the inquiry what a thing is: but from this, some making it manifest from sense, but others assuming it from hypothesis, thus demonstrate in a more necessary or more remiss manner things essentially present with the genus, about which they subsist. On which account it is evident that there are not demonstrations of essence, nor of definition from an induction of this kind, but there is some other mode of rendering these apparent. In like manner, they are entirely silent as to the genus with which they are conversant, whether it is, or is not, because it belongs to the same dianoetic power, to make manifest what a thing is, and if it is this thing.

But since the physical science is conversant with a certain genus of being (for it is conversant with such an essence as contains in itself the principle of motion and rest) it is evident that it is neither practical nor effective. For of things which are effective, the principle, whether it is intellect, or art, or a certain power, is in the efficient; but of things practical the principle, viz., free-will, is in the agent. For the same thing is practicable, and the object of free-will. So that if every dianoetic energy is either practic, or effective, or theoretic, the physical dianoetic energy will be a certain theoretic science; but it will speculate being of such a kind as is capable of being moved, and an essence which is for the most part known through definition, and has not alone a separate subsistence.

It is, however, requisite to understand in what manner the formal cause and definition subsist. For, to investigate without this knowledge is to do nothing. But of things defined, and to which the inquiry what they are belongs, some subsist in the same manner as the flat nose, and some as the hollow. But these differ, because the flat nose is conceived together with matter: for a flat nose is a hollow nose; but hollowness is without sensible matter. If, therefore, all physical things are predicated in a manner similar to a flat nose; as, for instance, nose, eye, face, flesh, bone, and, in short, animal, leaf, root, bark, and plant (for the definition of no one of these is without motion, but it always possesses matter), it is evident in what manner in physical inquiries it is requisite to investigate and define the essence of a thing, and why it belongs to the natural philosopher to speculate respecting a certain soul, viz. such a soul as is not unconnected with matter. That the physical dianoetic energy, therefore, is theoretic, is from what has been said evident.

But the mathematical science also is theoretic. Whether, however, it contemplates things immoveable, and which have a subsistence separate from sensibles, is at present immanifest. But that there are some mathematical disciplines which contemplate things so far as they are immoveable, and so far as they have separate subsistence, is evident. If, indeed, there is something immoveable, eternal, and separate from sensibles, it is manifest that it is the province of the contemplative science to know it, and not of the physical (for the physical science is conversant with certain moveable natures) nor of the mathematical, but of a science prior to both these. For the physical science is conversant with things inseparable indeed, but not immoveable: but of the mathematical sciences, some are conversant with things immoveable indeed, yet not separate perhaps, but subsisting as in matter. The first of sciences, however, is employed in the speculation of things separate and immoveable. But it is necessary that all causes, indeed, should be eternal, and especially these: for these are the causes to the phenomena of things divine. So that there will be three contemplative philosophies, viz. the mathematical, the physical, and the theological. For it is not immanifest, that if a divine nature any where subsists, it subsists in a nature of this kind. And it is requisite that the most honorable science should be conversant with the most honorable genus of things. The theoretic sciences, therefore, are more eligible than other sciences; but this (or the theological science) is more eligible than the theoretic.

But some one may doubt whether the first philosophy is universal, or conversant with a certain genus and one nature. For neither in the mathematical sciences is there the same mode of speculation; but geometry and astronomy are conversant with a certain peculiar nature, while the mathematical science itself is, in short, common to all the branches of that science. If, therefore, there is not any other essence besides things which have a natural subsistence, the physical will be the first science. But if there is a certain immoveable essence, this will be prior, and will be the first philosophy. It will thus also be universal, because it is the first of sciences: and it will be the province of this science to speculate respecting being so far as being, and to contemplate what it is, and what, in short, are the things inherent in it so far as being.

Aristotle, Metaphysics. Book 6, Chapter 2.

Since, however, being, simply so called, is multifariously predicated, of which predication one is according to accident, but another as that which is true, to which non-being is opposed, as that which is false. But besides these there are the figures of the categories, as, for instance, substance, quality, quantity, where, when, and whatever else there may be of this kind. Again: besides all these, there is that which subsists in capacity, and that which subsists in energy. But, since being is predicated multifariously, we must in the first place say, respecting that which subsists according to accident, that there is no speculation concerning it; of which this is a token, that no science is attentive to accident, neither the practic, nor the effective, nor the theoretic. For neither does he who makes a house, at the same time make such things as happen to the house when built (for these are infinite); since nothing hinders but that the house may be to some pleasant, to others noxious, and to others beneficial, and, as I may say, different from all things, of none of which the building art is effective. After the same manner, neither does the geometrician speculate things which thus happen to figures, nor whether a wooden triangle and a triangle which has angles equal to two right are different from each other. And this happens rationally; for accident itself is only as it were a name. Hence, Plato after a certain manner does not improperly dispose non-being about the sophistic art. For the arguments of sophists are, as I may say, the most of all things employed about accident. For they ask, Whether a musician and a grammarian are a different or the same person; whether the musician Coriscus and Coriscus are the same; and if every thing which is, but is not always, is generated. So that if he is a musician he is made a grammarian, and if he is a grammarian he is made a musician, and whatever other arguments there are of this kind. For accident appears to be something near to non-entity. And this is evident from what has been just now said. For, of things which subsist in a different manner from accident, there is generation and corruption; but this is not the case with things which subsist according to accident.

But at the same time let us speak still further about accident, as much as possible showing what the nature of it is, and through what cause it subsists. For, at the same time, perhaps it will be evident why there is not any science of accident. Since, therefore, in beings some things always subsist in a similar manner, and from necessity (not from that necessity which is denominated according to the violent, but from that by which we say a thing cannot subsist otherwise), but others, though they are not necessarily, nor always, yet they are for the most part, this is the principle, and this is the cause of the subsistence of accident. For whatever is neither always, nor for the most part, this we say is accident. Thus, for instance, if, when the sun is in Canis, stormy and cold weather should be produced, we should say that this happened; but we should not speak in this manner if suffocation and heat were produced; because the latter is always, or for the most part, but this is not the case with the former. That man is white is also an accident; for this is neither always the case, nor for the most part: but that man is an animal is not from accident. Likewise that a builder should give health, is an accident, because a builder is not naturally adapted to effect this, but a physician: but here it happens that a builder is a physician. A cook, also, intent upon giving pleasure, may make something salubrious, but not from the art of cooking. Hence, we say that this happens, and in a certain respect he makes something salubrious, but simply considered he does not. For of others’ things the powers are sometimes effective; but of these no art nor power is definite. For, of things which either are, or are generated according to accident, the cause is also according to accident. So that, since all things are not from necessity, nor either always are entities, nor are in generation (i. e. becoming to be, or tending to being), but most things have a subsistence for the most part, it is necessary that there should be something which subsists according to accident, and that it should be such as is a white musician, who is neither always so, nor for the most part. But, since it is sometimes effected, there will be a subsistence according to accident: for, if not, all things will be from necessity. So that matter will be the contingent cause of accident, which subsists differently from that which has a subsistence for the most part, or which seldom fails of subsisting. But this should be the beginning of the inquiry, Whether there is nothing which neither subsists always, nor for the most part, or whether this is impossible. There is, therefore, something besides these things which have a casual subsistence, and a subsistence according to accident. But shall we admit that there is such a thing as that which subsists for the most part, but that there is not in the nature of things that which has a perpetual subsistence? or are there certain eternal entities? These things, therefore, will be the subject of a posterior consideration. But that there is not a science of accident is evident: for every science is of that which is always, or of that which is for the most part. How, otherwise, can a man learn any thing, or teach another? For it is necessary that the object of science should be defined either by the perpetual, or by a subsistence for the most part; as, for instance, that, to a person in a fever, mead is, for the most part, beneficial. But no one will say that mead administered during the new moon is beneficial in a fever: for during the new moon this is efficacious, either always, or for the most part. But accident is something different from these. We have, therefore, declared what accident is, and through what cause it is, and that there is not a science of it.

Aristotle, Metaphysics. Book 6, Chapter 3.

That there are principles and causes which rise into existence and perish without being generated and corrupted is evident. For, if this were not the case, all things would be from necessity, if it is necessary that, of that which is generated and corrupted, there should be a certain cause which does not subsist from accident. For, whether will this thing take place or not? If this is done, it will; but if not, it will not take place. But this will take place, if something else is effected. And thus, by always taking away time from a definite time, you will at length arrive at the now. So that this man will die either by disease or violence, if he goes out of the city: but this will take place, if he should be thirsty; and this will happen, if something else happens: and so we shall arrive at that which now is, or at something which is past. As, for instance, if he should be thirsty; but this will happen, if he has eaten salt meat; and this either is or is not. So that, from necessity, he will either die or not. In like manner, if any one directs his attention to past transactions, the same reasoning will take place. For now this will subsist in something; I mean that which has been effected. All future events, therefore, will be from necessity; as, for instance, death to that which has life. For now something has been effected; as, for instance, contraries in the same body. But if from disease or violence, this will not yet be the case, but if this shall have been effected. It is evident, therefore, that this reduction tends to a certain principle; but this principle does not tend to any thing else. This, then, will be the principle of that which is casual, and there will not be any cause of its generation. But it must be especially considered to what kind of a principle, and to what kind of a cause, a reduction of this kind tends, whether as to matter, or as to that for the sake of which a thing subsists, or as to that which moves. But we shall omit the further speculation of that which subsists according to accident; for it has been sufficiently discussed by us.

But that which subsists as true is being, and that which subsists as false is non-being, because they are employed about composition and division, and entirely about the division of contradiction. For the true has affirmation in composition, but negation in division; but the false has the contradiction of this division. But in what manner things which subsist together, or which have a separate subsistence, are to be understood, is another question. But I mean things which subsist together, and which subsist apart, not in a consequent order, but so as to become one thing. For the false and the true are not in things (as, for instance, to say that the good is true, but the evil false); but they subsist in the dianoetic part. But the truth and falsehood respecting things simple, and essences, are not in the dianoetic part. Such things, therefore, as it is requisite to speculate concerning that which is thus being and non-being, we shall afterwards consider. But since composition and division are in the dianoetic part, and not in things, and that which is after this manner being is different from those things which are properly beings (for the dianoetic part conjoins or divides either substance, or quality, or quantity, or something else), that which is as accident, and that which is as true being, are to be omitted. For the cause of the one is indefinite, but of the other a certain affection of the dianoetic part; and both are conversant with the remaining genus of being, and do not render manifest a certain nature which surpasses being; on which account these are to be omitted. But the causes and principles of being itself are to be considered, so far as it is being. And it is evident, from what we have said respecting the multifarious predication of every thing, that being is multifariously predicated.

Aristotle, Metaphysics. Book 7, Chapter 1.

Being is multifariously predicated, as we have before evinced in what we have said respecting multifarious predication. For one signification of being is what a thing is, and this particular thing; another, quality, or quantity, or each of the other things which are thus predicated. But since being is in so many ways predicated, it is evident that the first being among these is, what a thing is, which signifies essence. For when we say, what kind of a thing is this particular thing? we either say it is good or bad, but we do not say it is of three cubits, or that it is a man. But when we say, what it is, we do not assert that it is white, or hot, or of three cubits, but that it is a man or a god. But other things are called beings, because, as belonging to true being, some of them are quantities and others qualities, some are participated properties, and others something else of this kind. Whence some one may doubt, whether to walk, to be in health, and to sit, are being or non-being. And in a similar manner with respect to other things of this kind. For no one of these is naturally adapted to subsist by itself, nor can be separated from essence; but this ought rather to be said of that which walks, and of that which sits, and of that which is in health. For these rather than those appear to be beings, because they have a certain definite subject. But this is essence, and that which is particular, which appears in a predication of this kind. For the good, or that which sits, is not asserted without this. It is evident, therefore, that each of those subsists through this. So that, that which is primarily being, and not some particular being, but being simply, will be essence.

That which is first, indeed, is multifariously predicated; but at the same time essence is the first of all things, in definition, knowledge, time, and nature. For no one of the other predicates has a separate subsistence, but this alone. This also is first in definition. For it is necessary in the definition of every thing, that the definition of essence should be inherent; since we then think that we especially know any particular, when we know what man is, or fire is, rather than when we know the quality, or quantity, or situation of a thing. For we then think that we know each of these things themselves, when we know what the quantity or the quality is. Indeed, that which formerly has been, and which now is, continually investigated and continually doubted, viz. what being is, is an inquiry what essence is. For this is by some said to be one, but by others more than one; by some it is called things finite, and by others infinite. Whence we also must especially, and in the first place, and only, as I may say, speculate respecting that which is thus being.

Aristotle, Metaphysics. Book 7, Chapter 2.

But essence appears to subsist most manifestly in bodies. On which account we say that animals and plants, and the parts of these, are essences, as likewise natural bodies, viz. fire, water, and earth, and every thing of this kind; and such things as are parts of these, or are composed from these, either partly or entirely; such as heaven and its parts, the stars, sun, and moon. But whether these alone are essences, or likewise other things, or whether none of these, but certain other things, must be considered. To some, indeed, the boundaries of body, as for instance superficies, line, point, and monad, appear to be essences, and to be more so than body and solid. Again, some are of opinion that nothing has any subsistence besides sensibles; but others assert that there are many kinds of essences, and particularly eternal entities. Among these is Plato, who established two kinds of essences, viz. forms and mathematical species; and a third, the essence of sensible bodies. But, according to Speusippus, there are many essences beginning from the one, and principles of every essence, one of numbers, another of magnitudes, and another of soul; and after this manner he extends essences. Some again say that forms and numbers have the same nature, but that things in a following order, viz. lines and superficies, as far as to the essence of the heavens and sensibles, [are second essences]. But with respect to these things we must consider what has been well or ill said, what essences there are, and whether there are certain essences besides sensibles or not, and, if there are, in what manner they subsist; also, whether there is any separate essence, and why there is, and how it subsists; or whether there is no essence besides sensibles, having first of all summarily described what essence is.

Aristotle, Metaphysics. Book 7, Chapter 3.

Essence then, if not multifariously, yet at least is predicated according to four modes. For the formal cause, universal, and genus, appear to be essence to every thing; and the fourth of these is the subject. But the subject is that of which the rest are predicated, while itself is no longer predicated of any other thing. Hence this must be the first object of our inquiry. For essence appears to be especially the first subject. Such also matter is said to be, after a certain manner; form, in another respect; and the third, that which is composed from these. But I mean by matter, for instance, brass; by form, the figure of the idea; and by that which is composed from these, the whole statue. So that, if form is prior to matter, and is more being, that also which is composed from both will be prior for the same reason. Now, therefore, we have, by a rude delineation, as it were, said what essence is, viz. that it is not predicated of a subject, but is that of which other things are predicated. It is, however, necessary not only to speak of it in this manner, for it is not sufficient. For this definition is obscure; and, besides this, matter is essence. For, if matter is not essence, what else is will escape detection: since, other things being taken away, nothing else appears to remain. For other things are the participated properties, productions, and powers of bodies; but length, breadth, and depth, are certain quantities, and not essences. For quantity is not essence, but rather that in which these very things are primarily inherent, that is, essence. But, indeed, length, breadth, and depth, being taken away, we see that nothing remains except that which is defined by these. So that, to those who thus consider the affair, matter alone must necessarily appear to be essence. But I mean by matter, that which of itself is neither called essence nor quantity, nor any one of those things by which being is defined. For there is something of which each of these is predicated, and from which being and each of the predications are different. For the rest are predicated of essence; but this of matter. So that the last of all things is of itself neither essence, nor quantity, nor any thing else; nor yet negations: for these also subsist according to accident. From these considerations, therefore, matter appears to be essence. It is, however, impossible: for a separate subsistence, and subsisting as this particular thing, appear especially to belong to essence. Hence form, and that which subsists from both, appear to be more essence than matter. That essence, therefore, which subsists from both (I mean from matter and form) must be omitted: for it is posterior and manifest. Matter also is in a certain respect manifest. But let us consider respecting the third; for this is most dubious: and as it is acknowledged that there are certain essences of sensibles, let us make our first inquiry in these.

Aristotle, Metaphysics. Book 7, Chapter 4.

Since, then, in the beginning of this book, we have shown in how many ways we divide essence, and one of these is the very nature of a thing, let us contemplate this. For it is very advantageous to pass on to that which is more known. For thus all men acquire discipline, by proceeding through things less known to nature, to such as are more known. And as in practical affairs it is requisite from those things which are good to some one to effect such as are altogether good, and the good of every one; so, from things more known to every one, those things which are known to nature and to some one are to be made known. But things which are known to individuals, and such things as are first to these, are often but little known, and have little or nothing of being. At the same time, however, from things which are known in a depraved manner, but are known to some individual, we should endeavour to know things which are altogether known, proceeding as we have before said through these very things themselves.

And in the first place, we shall say something respecting them logically. The very nature of a thing, therefore, is that which a thing is said to be essentially. For your essence does not consist in being a musician; since you are not a musician according to yourself. Yet, not every thing which is essentially present to a thing is the very nature of that thing. For this is not the case with that which is so essentially present as a white superficies, because the being of a superficies is not the same as the being of whiteness. But neither is that which is composed from both, viz. the essence of a white superficies, the same as the essence of superficies. Should it be asked, Why is it not? we reply, Because superficies is contained in the definition of a white superficies. Hence, that is a definition signifying the very nature of a thing, in which the thing defined is not inherent. So that, if the being of a white superficies is the being of a smooth superficies, the being of white and smooth is one and the same. But since there are also composites according to the other categories (for there is a certain subject to each, as, for instance, to quality, to quantity, to when, where, and to motion), let us consider whether there is a definition of the very nature of each of them, and whether the very nature of a thing is present with these; as, for instance, what the very nature is of a white man. But let his name be garment. What then is the being of a garment? But, indeed, neither is this among the number of things which are predicated essentially. Or shall we say that a thing which is not essential is predicated in a twofold respect? and that of this, one thing is from addition, but another not? For one thing is said to be that which is defined, because it is added to another thing; as, if any one defining the being white should assume the definition of man: but another thing is so denominated, because something else is not added to it; as, if a garment signifies a white man, but some one should define the garment as white. A white man, therefore, in this case is something white, yet his very nature does not consist in being white, but in being a garment.

Is there then, in short, such a thing as the very nature of beings, or not? For the very nature of a thing is the essence of that thing. But, when one thing is predicated of another, it is not properly this particular thing; as, a white man is not this particular thing, if the being this particular thing belongs to essences only. So that the very nature of a thing pertains to those things the discourse respecting which is a definition. But not every discursus which signifies the same thing as a name is a definition (since if this were the case all discourses would be definitions: for name will be the same with any discourse whatever; so that the word Iliad will be a definition): but a discourse is then a definition when it is of some first thing. But things of this kind are such as are denominated, not from one thing being predicated of another. The very nature of a thing, therefore, does not belong to any thing besides the species of genus, but to these alone. For these appear to be predicated, not through participation, and passion, nor as accident, but there will be a discourse of each thing; and it will signify something of other things, if it is a name; I mean, that this thing is inherent in this, or, instead of a simple assertion, is more accurate: but it will not be definition, nor the very nature of a thing. Or shall we say that definition, as well as the essence of a thing, is predicated multifariously? For the inquiry what a thing is, in one way, signifies essence, and this particular thing; but, in another, each of the categories, viz. quantity and quality, and the rest of this kind. For, as the inquiry what a thing is, belongs to all things, though not in a similar manner, but to one thing primarily, and to others in a consequent order; in like manner definition, simply indeed, pertains to essence, but in a certain respect to other things. For we may ask what quality is; so that quality is of things to which the inquiry what they are, belongs; yet not simply, but just as of non-entity: some, logically arguing, say that it is non-entity, yet do not simply assert that it is, but that it is non-entity: so also with respect to quality.

It is requisite, therefore, to consider how we ought to speak respecting each, yet not more than in what manner each subsists. Hence, now also, since that which is asserted is manifest, the very nature of a thing in a similar manner will be primarily and simply inherent in essence, and afterwards in other things, just as in the inquiry what a thing is. So that the very nature of a thing will subsist with the addition of quality or quantity. For it is requisite to assert, that these things are beings, either equivocally, or with addition and ablation, in the same manner as that which is not the object of scientific knowledge, is scientifically known; since it is right neither to speak of these equivocally, nor after the same manner: just as with respect to the medicinal art, which is predicated with relation to one and the same thing, without being one and the same, and yet is not equivocally predicated. For no medicinal body is called a work and an apparatus, neither equivocally, nor according to one thing; but with relation to one thing. With respect to these things, however, it is of no consequence in what manner any one may be willing to speak of them. This, indeed, is evident, that definition primarily and simply considered, and the very nature of a thing, belong to essences; and in a similar manner they also belong to other things, though not primarily. For, though it should be admitted that any name has the same signification with a discourse, yet it does not necessarily follow, that a discourse about that which the name signifies is a definition; but this will take place when a name has the same signification with a certain discourse. This, however, happens, if it is of one thing, not by continuation as the Iliad, or such things as are one by conjunction, but if it is multifariously predicated as one thing. But unity is predicated in as many ways as being; and being partly signifies substance, partly quantity, and partly quality. Hence there will be a certain discourse about, and definition of, a white man; and after another manner, of that also which is white, and of essence.

Aristotle, Metaphysics. Book 7, Chapter 5.

A doubt, however, arises, If any one should deny that definition is a discourse subsisting from addition, of what will the definition be of things not simple but conjoined? For it is necessary that they should be rendered manifest from addition. But, I say, for instance, there is nose, and concavity, and flatness, and that which is denominated from both, because this is inherent in that, and neither concavity nor flatness is an accidental, but an essential, property of the nose; nor do they subsist as whiteness in Callias or man, because Callias is white who happens to be a man; but they subsist as the male in animal, and the equal in quantity, and in the same manner as all such things as are said to be essentially inherent. But these are things in which either the definition or the name of which this is the property is inherent, and which cannot be manifested separately, in the same manner as whiteness can be manifested without man; but the feminine cannot be rendered apparent without animal. So that the very nature and definition of these are either of nothing, or, if there is a definition of these, it is in the manner we have previously related.

There is also another doubt respecting these things: for, if a flat nose and a concave nose are the same, the flat and the concave will be the same; but if not, because it is impossible to use the word flat-nose, without the thing of which it is an essential property, and flatness of nose is a hollowness in the nose, either it is not possible to say a flat nose, or the same thing will be said twice, i. e. nose, concave nose: for a flat nose will be a concave nose. Hence, it is absurd, that the essential should be inherent in things of this kind: for, if it were, there would be a progression to infinity; since in nose, concave nose, something else essential would be inherent. It is evident, therefore, that definition is of essence alone. For, if it were also of the other categories, it must necessarily be from addition, as, for instance, in the definitions of quality and the odd. For it is not framed without number; nor the definition of feminine without animal. But I say, that those definitions are composed from addition, in which the same thing happens to be said twice, as in these: but if this be true, neither will there be definitions of things conjoined, as, for instance, of an odd number. However, they do not perceive that the definitions of these things are not accurately assigned by them. But if there are also definitions of these things, they are either after a different manner, or, as we have said, definition and the very nature of a thing have a manifold subsistence. So that in one respect definition and essence will not be inherent in any one of these except essences, and in another respect they will be inherent. That definition, therefore, is a description of the very nature of a thing, and that the very nature of a thing either alone belongs to essences, or especially, both primarily and simply, is evident.

Aristotle, Metaphysics. Book 7, Chapter 6.

Let us now consider, whether the very nature of a thing is the same with each individual thing, or different from it. For this will very much contribute to the speculation respecting essence; since each particular thing does not appear to be different from its own essence; and the very nature of a thing is said to be the essence of that thing. But in things which are predicated according to accident, these two may appear to be different; as, for instance, a white man, and the being of a white man. For if a white man and the being of a white man were the same (for man and a white man are, as they say, the same), then, the being of a white man would be the same with the being of man separately considered. Or is it necessary, that things which subsist according to accident should be the same [as those things which have an essential subsistence]? For the extremes do not become similarly the same. But perhaps it may appear to happen, that the extremes will become the same according to accident; as, for instance, the being of white and the being of a musician. This, however, does not appear to be the case: but in things which are essentially predicated, it is always necessary that they should be the same, as must be the case with certain essences, if there are such, to which there are no other essences, nor natures prior, such as some assert ideas to be. For, if the good itself were different from the being of good, animal from the being of animal, and being from the essence of being, there would be other essences and ideas besides those which are said to be, and those would be prior essences, if there is an essence of essence itself. And if, indeed, they are unconnected with each other, of these there will not be science, and those will not be beings. But I mean by being unconnected with each other, if neither the being of good is inherent in good itself, nor to be good pertains to this. For a scientific knowledge of a thing is a knowledge of the very nature of that thing: and the like takes place with respect to good and other things. So that, if neither the being of good is good, neither will the essence of being be being, nor of the one be one; and in a similar manner, all or none of the essences of ideas have a subsistence. So that if the essence of being is not being, neither will the essence of any one of the rest.

Further still: that in which the essence of good is not inherent is not good. It is necessary, therefore, that good and the essence of good should be one; also the beautiful and the essence of the beautiful, and so of all such things as are not predicated through another, but are first natures, and have an essential subsistence. For this is sufficient if it takes place, though forms should have no subsistence, though perhaps it is more so if they do subsist. At the same time it is evident, that if ideas are such things as some say they are, essence will not be as a subject to them. For it is necessary that these should be essences, and that they should not be predicated of a subject; for, if they were, they would subsist according to participation. From these reasons, therefore, it is evident that each particular itself, and the very nature of a thing, are one and the same, not according to accident; and that to have a scientific knowledge of any thing, is to know scientifically the very nature of that thing. So that, from induction it is necessary that both should be one thing. But it is not true to affirm, that a thing which is predicated according to accident, as a musician, or that which is white, is the same as the very nature of a thing itself, because that to which it happens, and the accident itself, have a twofold signification. So that in a certain respect a thing itself is the same, and in another respect is not the same, with the very nature of a thing. For the being of man is not the same thing with that of a white man; but so far as the essence of man is passive to whiteness, or is whitened, it is the same. But it may appear to be absurd also, if some one should call an individual the very nature of a thing; for there will be another very nature of a thing besides that, as, besides the essence or very nature of a horse, there will be another very nature of a horse. Though what hinders but that now certain essences themselves in continued succession may be the same as the things of which they are the very natures, if the very nature of a thing is essence? They are, however, not only one, but the definition also of them is the same, as is evident from what has been said. For to be one, or the being of one, and one, are not one according to accident. Again: if they are different, there will be a progression to infinity. For the one, being as it were the essence of one thing, will be the very nature of that thing, but the other will be that one thing itself. So that there will be the same definition of them. That in things first, therefore, and such as are essentially predicated, the essence of a thing, and the thing itself, are one and the same, is evident. But it is also evident, that sophistic arguments against this position are solved by the same solution. For the sophists inquire, Whether Socrates is the same with the essence of Socrates? For there is no difference with respect to the things from which the interrogation may be made, nor those which may be employed by him who solves the question. We have, therefore, shown, after what manner the very nature of a thing is the same, and in what respect it is not the same with any particular thing.

Aristotle, Metaphysics. Book 7, Chapter 7.

Of things which are generated, some are produced by nature, others by art, and others by chance: but all things which are generated are generated by something, and from something, and become something. But I mean that they become something according to each of the categories: for they either become substance, or quantity, or quality, or where. But natural generations are those the generation of which is from nature: and that from which they are generated is that which we call matter. That by which they are generated is some one of the things which have a natural subsistence. And that which is some particular thing, is man or plant, or some one of such like things which we say are especially essences. All things, indeed, which are generated either by nature or art, have matter: for it is possible for each of them to be and not to be; which capability is the matter in each. And, in short, nature is that from which, and that according to which. For that which is generated has matter, as, for instance, a plant or animal: and also that from which, viz. Nature herself, which is predicated according to form, and is, indeed, of a similar species. But this subsists in another: for man generates man. After this manner, therefore, are things generated through nature. But other generations are called makings. All makings, however, are, either from art, or from power, or the dianoetic part. But of these some are also generated from chance and fortune, just as in things which are generated by nature. For there, also, some things are generated the same, both from seed, and without seed. Concerning these things, however, we shall consider hereafter. But things are produced from art, the form of which is in the soul. But I mean by form the very nature of every thing and the first essence. For after a manner there is the same form of contraries. Thus, an opposite essence is the essence of privation, as, for instance, health of disease. For the absence of health manifests disease. But health is reason in the soul and in science. Health, therefore, is produced, when the physician thus reasons:—If this is health, it is necessary that the inequality of things hot and cold should pass into equality. And if this is to be effected, it is necessary that heat should arise. In this manner he perpetually reasons, until he arrives at that which at last he is able to effect. Afterwards, that motion which now begins from this, is called the making which leads to health. So that it happens after a manner, that health is produced from health, and a house from a house, viz. that which possesses matter is produced from that which is without matter. For the medicinal art is the form of health, and the building art of the house. But I call essence without matter, the very nature of a thing.

Moreover, of generations and motions this is called intellection, and that making. That, indeed, which begins from the principle and form is intellection; but that which commences from the end of intellection is making. In like manner, each particular thing is produced in other things which subsist as mediums. I say, for instance, if health is to be restored, it is necessary that a reduction to equality should take place. And this will be effected if heat is introduced. And what is this? It is this particular thing. But this particular thing subsists in capacity. And this is now placed in the power of the physician. That which makes, therefore, and that whence the motion of restoring health begins, if it is from art, is form in the soul; but if from chance, it begins from that which is finally the principle of making to him who makes according to art: as also in healing, the principle perhaps is from imparting heat; but this is accomplished by friction. Heat, therefore, in the body, is either a part of health, or some such thing which is a part of health follows it either immediately, or through many mediums. But this which makes is the last, and is in such a manner a part of health, as stones are parts of a house, or other things of something else. So that, as it is said, it is impossible for any thing to be generated, if nothing pre-exists. That a part, therefore, exists from necessity is evident: for matter is a part, since it has an inherent subsistence, and is itself generated. But does it rank among things which belong to definition? Indeed, in both respects, we assert what many circles are; and speaking of the matter, we say it is brass; and of the form, that it is such a figure: and this is the genus in which it is first placed. But a circle of brass contains matter in its definition. Some things, however, when they are produced, are not called that from which they are produced as from matter, but are called something of that kind; as a statue is not called a stone, but stony. But a man who is recovering his health is not called that from which he recovers his health. But the cause of this is, that they are generated from privation, and a subject which we call matter. Thus, for instance, both man and he who is sick are made well. Yet, health is rather said to be produced from privation, as, for instance, from him who is sick, than from man. Hence, he who is healthy is not said to be tending to sickness; but this is said of man, and man in health. But with respect to things of which the privation is uncertain and nameless, as in the brass of any figure, or in the tiles or wood of a house, those things appear to be generated from these, as, in the former instance, from him who is tending to sickness. Hence, as, there, that which is produced is not called by the name of that from which it is produced; so neither here is the statue called wood, but derivatively wooden; brazen, and not brass; stony, and not stone. The house also is not called tiles (plinthoi), but plinthine. For, if any one attentively considers, he will not simply say that the statue is made from wood, or the house from tiles; because it is requisite that whatever is generated from any thing should be changed from that from which it is generated, and should no longer remain that which it was before. On this account, therefore, it is thus denominated.

Aristotle, Metaphysics. Book 7, Chapter 8.

Since that which is generated is generated by something (but I call this that whence the principle of generation is derived) and from something; let this not be privation but matter (for the manner in which we denominate this has been already defined). There is also that which is generated; but this is either a sphere or circle, or whatever else may casually present itself. [Moreover, as that whence the principle of motion is derived] neither makes the subject, I mean the brass itself, so neither does it make the sphere, unless from accident, i.e. because a brazen sphere is a sphere; but the sphere itself it does not make. For, to make this particular thing, is to make it this particular thing from the whole subject. I say, for instance, that to make the brass round, is not to make the round, or the sphere, but something else, viz. this form in another thing. For, if it makes, it will make from something else: for this was supposed; as, for instance, to make a brazen sphere. But this he thus makes, because, from this which is brass, he makes this which is a sphere. If, therefore, he also makes this very thing itself, it is evident that he makes in a similar manner, and the generations will proceed to infinity. It is evident, therefore, that neither is species (or by whatever other name it may be proper to call the form in sensibles) generated, nor is it that which is the very nature of a thing. For it is generated in another, either from art, or from nature, or from capacity. But the efficient cause makes the sphere to be brazen: for it makes from brass and sphere. For in this it makes this form: and this is a brazen sphere.

But, in short, if there is a generation of the essence of a sphere, it will be from a certain something. For it will be requisite that that which is generated should always be divisible, and that this should be one thing, and that another; I mean, that this should be matter, and that form. But, if a sphere is a figure equal from the middle, of this, one part will be that in which the production of the efficient will be inherent; but the other, that which will be inherent in this part; but the whole will be that which is effected, as, for instance, the brazen sphere. It is evident, therefore, from what has been said, that that which is denominated as form, or as essence, is not generated; but that the concourse which is said to take place according to this, is generated: also, that in every thing which is generated matter is inherent; and that one part is matter, but the other form. Is there, then, any sphere besides these, or house, besides tiles? Or shall we say that, if this were the case, this particular thing would never have been generated, but because it signifies such a particular thing. This, however, is not definite, but makes and generates such a particular kind of thing from this particular; and when it is generated it is this thing with such a particular quality. But the whole of this is Callias or Socrates, just as this is a brazen sphere. But man and animal are altogether as a brazen sphere. It is evident, therefore, that forms themselves (as some are accustomed to speak of forms), if there are certain natures of this kind besides particulars, are of no use with respect to generations and essences, nor will essences essentially subsist through these. Indeed, in some things it is evident that the generator is such as the thing generated, yet is not one and the same in number, but in species, as is manifest in things physical: for man generates man, and horse horse, unless when something contrary to nature is generated, as when a horse begets a mule. And these also are similarly affected. For that which is common to a horse and an ass, viz. the most proximate genus, is not named: but both, perhaps, will be as a mule. So that it is evident, that it is not by any means necessary to introduce form as a paradigm (for, in sensibles, forms should be especially investigated, since these are especially essences), but that which generates is sufficient to make, and to be the cause of form in matter. But now the whole of such a form in these flesh and bones is Callias and Socrates; who are, indeed, different, on account of the matter (for the matter in each is different), but the same in species: for species or form is indivisible.

Aristotle, Metaphysics. Book 7, Chapter 9.

But some one may doubt why some things are produced both by art and chance, as health; but others are not so produced, as a house. The reason, however, is this: that matter, which is the principle of generation, in making and generating something of things artificial, in which a certain part of the thing is inherent, is partly of such a nature as to be moved by itself, and partly not; and of this, one part is capable of being moved in this particular manner, but another part is incapable of being so moved. For many things are capable of being moved by themselves, but not in this manner; as, for instance, to leap. It is impossible, therefore, for things, the matter of which is of this kind, as, for instance, stones, and fire, to be thus moved, unless by something else. Hence, some things will not be, but others will be, without that which possesses art. For they will be moved by those things which do not indeed possess art, but which are able to be moved themselves, either by other things which do not possess art, or from a part. But it is evident from what has been said, that all things are after a manner generated from equivocals, as things which have a natural subsistence, or from an equivocal part; as, for instance, a house from a house, or from intellect. For art is form, either from a part, or from that which possesses a certain part, if it is not produced according to accident. For the cause of making is the first essential part: for the heat which is in motion produces heat in the body. But this is either health, or a part of health; or some part of health, or health itself, follows it. Hence it is said to make, because that which follows, and to which heat happens, produces health. So that, as in syllogisms essence is the principle of all things (for syllogisms are from the what), so here generations. Things also which are constituted by nature subsist in a manner similar to these. For seed makes just as the artist operates; for he possesses form in capacity, and that from which seed originates is in a certain respect univocal, unless an injury happens to take place: for it is not proper to investigate all things, as man from man; for woman is from man; and hence mule does not originate from mule. But those things are produced by chance, the matter of which, as there, is capable of being moved by itself with that motion with which seed moves. And those things the matter of which is not capable of being so moved cannot be produced in any other way than from generations. But this reasoning not only shows, respecting essence, that form is not generated, but it also in a similar manner evinces this in common of all first natures, as of quality, quantity, and the other predicaments. For, as a brazen sphere is that which is generated, and not the form of the sphere, nor the brass; for it is always necessary that matter and form should preexist; the like must be understood respecting essence, quality, quantity, and the other predicaments. For quality is not generated, but such like wood; nor quantity, but wood, or an animal of a certain dimension. However, from these things the peculiarity of essence may be apprehended, viz. that another essence which makes, having a subsistence in energy, must necessarily always preexist; as, for instance, an animal must preexist, if an animal is generated: but it is not necessary that this should be the case with quality, or quantity, except in capacity alone.

Aristotle, Metaphysics. Book 7, Chapter 10.

Moreover, since definition is a sentence, but every sentence has parts, and as a sentence is to a thing, so is a part of a sentence to a part of a thing, it is now doubted, whether it is necessary or not that the parts should be inherent in the definition of the whole. For in some things they appear to be inherent, and in others not. Thus, the definition of a circle does not contain the sections of the circle defined: but the definition of a syllable contains the parts of a syllable; though a circle is divided into sections, as a syllable into the elements of speech. Further still: if parts are prior to the whole, but, an acute is a part of a right angle, and a finger of an animal, the acute will be prior to the right angle, and the finger to man. These, however, do not appear to be prior: for wholes are introduced in the definition of parts; and they are prior because they can subsist without parts. Or shall we say, that part is multifariously predicated? Of which one mode is that which measures according to quantity. The consideration of this, however, must be omitted: but our attention must be directed to the speculation of what those things are from which essence consists as parts. If, therefore, one thing is matter, another form, and a third that which is composed from these, and essence is matter and form, and that which consists from these, matter also is in one respect said to be a part of something, and in another is not said to be a part; but this is true of those things from which the definition of form consists. Thus, for instance, flesh is not a part of concavity (for this is matter in which concavity is generated), but it is a certain part of flatness of nose. And the brass, indeed, is a part of the whole statue; but by no means of the statue which is denominated as form. For form is predicated in every thing, and every thing is to be denominated so far as it has form. But that which is material is never to be essentially predicated. Hence, the definition of the circle does not contain the definition of its sections; but the definition of a syllable contains that of the elements from which it is composed. For the elements of speech are parts, and not the matter of form; but the sections of a circle are parts, as the matter in which the circle is produced; yet they are more proximate to form than the brass, when roundness is ingenerated in the brass. But in a certain respect neither will all the elements be contained in the definition of a syllable; as, for instance, these waxen letters, or those which are in the air. For now these also are a part of a syllable, as sensible matter. For it does not follow, that because a line is corrupted, when divided into equal parts, or a man when divided into bones, and nerves, and flesh, that they are so composed from these as parts of essence; but it follows, that they are composed from them, as matter only. And they are, indeed, parts of the whole; but they are not parts of form, and of that which is the subject of definition: and, therefore, neither are they introduced in definitions. In some definitions, therefore, a definition of parts of this kind will be inherent; but, in others, it is necessary that it should not be inherent, unless it is the definition of both taken together. For, on this account, some things consist from these as principles, into which they are corrupted, but others do not consist from these. Such things, therefore, as are taken together, are form and matter; as a flat nose, or a brazen circle: for those, indeed, are corrupted into these, and matter is a part of them. But such things as are not assumed in conjunction with matter, but without matter, as the definitions of form alone, these are either altogether not corrupted, or at least not after this manner. So that the things which they contain, are indeed the principles and parts of them; but, of form, these are neither principles nor parts. Hence, a statue of clay is corrupted into clay, and a sphere into brass, and Callias into flesh and bones: and further still, a circle is corrupted into sections. For there is something which is assumed together with matter. For the circle is predicated equivocally, both that which is simply predicated, and those which are taken severally, because those that are taken severally have not a proper name.

We have now, therefore, unfolded the truth; but at the same time it is necessary that, by making a repetition, we should speak more clearly. For such things as are the parts of a definition, and into which definition is divided, these are prior, either all or some of them. But the definition of a right angle is not divided into the definition of an acute angle, but the definition of an acute into that of a right angle. For he who defines an acute, uses a right angle; since an acute is less than a right angle. The like takes place with respect to a circle and semicircle. For the semicircle is defined by the circle; and the finger by the whole. For a finger is such a part of the man. So that such parts as have, indeed, the relation of matter, and into which, as into matter, the whole is divided, these are, indeed, posterior; but such as have the relation of definition, and of essence according to definition, are prior, either all or some of them.

But since the soul of animals is their form (for this is the essence of the animated nature, an essence according to definition and form, and the very nature of such a body; for a part of any thing, if it is well defined, is not defined without its proper employment, and which here does not subsist without sense)—this being the case, the parts of soul are prior, either all or some of them, to the whole animal. And the like takes place in other things. But the body and its parts are posterior to this essence, and are divided into these as into matter. This is not the case with essence, indeed, but with the entire whole. These, therefore, are partly prior, and partly not prior, to the whole. For, when separated, they are not able to subsist. For neither is a finger according to every mode of subsistence the finger of an animal; but a dead finger is only equivocally so called. But some things perish together with the whole itself; and these, indeed, are principal parts, in which definition and essence are primarily inherent; such, for instance, as the heart, if it is this principal part, or the brain. For it is of no consequence which of these is of this kind. But man and horse, and the like, are in particulars: and universal essence does not subsist separate from the particulars to which it belongs, but a certain whole consisting from this definition and this matter subsists as universal. But a particular, consisting from ultimate matter, is now Socrates; and in a similar manner with respect to other things.

Definition, therefore, is a part of form (but I mean by form the very nature or essence of a thing), and of the whole which is composed from form and matter. But the parts of definition are alone the parts of form; and definition is of that which is universal. For the essence of a circle and a circle are the same, and in like manner the essence of soul and soul are the same. But of that which is now a whole, as, for instance, of this circle, and, in short, of that which is a particular, or sensible, or intelligible whole (but I mean by intelligibles such things as mathematical entities, but by sensibles, such things as are composed of brass and wood); of these I say there is no definition, but they are known by intellection or sense. But when the energy ceases by which they were visible, it is not manifest whether they are or are not; nevertheless, they are always predicated and known by universal reason: but matter is of itself unknown. With respect to matter, however, one kind is sensible, and another intelligible. And sensible matter, indeed, is such as brass and wood, and whatever matter is moveable: but intelligible matter is that which subsists in sensibles, yet not so far as they are sensibles, as, for instance, mathematical entities. We have, therefore, shown in what manner this takes place respecting whole and part, and also respecting prior and posterior. But it is necessary to answer the interrogation, when any one asks, Whether a right angle, a circle, and an animal, are prior to the parts into which they may be divided, or whether the parts from which these are composed are prior to their wholes? And we must reply, That part is not simply predicated. For, if soul is the animal, or that which is animated, or every animal is its own soul; and in like manner, if the circle is the essence of the circle, and the right angle of the right angle, what part is each of these, and to what whole must we say it is posterior? For instance, of those parts which are in a definition, which should we say is posterior to the whole, viz. to the whole of a certain right angle? For both the angle of brass which subsists in conjunction with matter is a right angle, and that also contained in lines which subsist as particulars. But the right angle which is without matter, is posterior to the parts which are contained in definition, but is prior to the parts which subsist as particulars. It must not, however, be said that this is true of part simply considered. But if soul is something else, and not the animal, thus also some parts must be said to be prior, and others not prior, as we have already observed.

Aristotle, Metaphysics. Book 7, Chapter 11.

It may justly be doubted what the quality is of the parts of form, and also of the parts of that which is a composite; since, this not being manifest, it is not possible to define every particular. For definition is of that which is universal, and of form. If, therefore, it is not apparent which of the parts have the relation of matter, and which have not, neither will the definition of the thing be manifest. Such things, therefore, as are ingenerated in different species, as, for instance, a circle in brass, in stone, and in wood, these appear indeed to be manifest, since neither the brass nor the stone is any thing of the essence of the circle, because it is separated from them. But such things as are not perceived to be separated are not in any respect prevented from subsisting similar to these; just as, if all circles were of brass, brass would appear to be of the essence of the circle, yet, nevertheless, brass would not then be a part of form. Nevertheless it is difficult to separate this in our dianoetic part. For the form of man always appears in flesh and bones, and such-like parts. Whether, therefore, are these parts of form and definition? or, are they by no means parts, but matter? However, as the form of man is not ingenerated in another, it is impossible to separate it. But since this appears to happen, and it is immanifest when, some also have taken occasion to doubt respecting the circle and triangle, as if it did not pertain to lines and to continued quantity to be defined; but all these were similarly predicated, as the flesh or bones of a man, and brass and stone of a circle. They likewise refer all things to number, and say that the definition of a line is that of the duad. Of those also who assert that there are ideas, some say, that line itself is the duad, but others the form of line. For, in some things, say they, form and that of which it is the form are the same, as, for instance, the duad and the form of the duad. But this is not the case in a line. It happens, therefore, that there is one form of many things of which the species appears to be different; which thing likewise happens to the Pythagoreans. The consequence also will be that there will be one form only of all things, and that other things will not be forms; though, after this manner, all things will be one. We have shown, therefore, that the particulars respecting definition are connected with a certain doubt, and likewise through what cause this takes place. Hence, to refer all things after this manner, and to take away matter, is superfluous. For in some things, perhaps, this is in that, or this thing thus subsisting. And that is not a good comparison respecting an animal, which the junior Socrates was accustomed to adduce. For it leads us from the truth, and causes us to apprehend that it may be possible for man to subsist without parts, in the same manner as the circle without brass. The latter instance, however, is not similar to the former: for animal, perhaps, is something sensible, and cannot be defined without motion; and therefore neither without its parts subsisting after a certain manner. For the hand is not in every respect a part of man, but that which is able to accomplish the proper office of the hand. So that it is a part when animated; but, when not animated, it is not a part.

But, with respect to mathematical entities, why are not definitions parts of definitions? For instance, why are not semicircles parts of the definition of a circle? For these are not sensibles. Shall we say this is of no consequence? for they will be the matter of certain things, and of such as are not sensible, and of every thing which is not the very nature of a thing. These, therefore, will not be parts of universal circle, but of particulars, as we have before said. For, of matter, one kind is sensible, and another intelligible. But it is manifest that soul is the first essence, but body, matter; and man or animal is that which is composed from both as universal. But Socrates or Coriscus, if soul is the form of each, is two-fold. For some call Socrates as soul, but others as a whole. But if simply this soul, and this body, they will have the relation of universal and particular. Whether, however, besides the matter of such like essences, there is some other essence, and whether it is proper to investigate a certain other essence of these, as, for instance, number, or something of this kind, must be a posterior consideration. Indeed, for the sake of this we endeavour to define respecting sensible essences; since, after a manner, the speculation of sensible essences is the business of natural and the second philosophy. For the natural philosopher ought not only to have a knowledge of matter, but much more of that essence which subsists according to definition. However, with respect to definitions, how those things are parts which are assumed in definition, and why definition is one reason (for it is evident that the thing is one, and a thing possessing parts is one definite particular); this must be considered afterwards. We have, therefore, shown what the very nature of a thing is universally, and how itself subsists by itself: likewise on what account the definition of the very nature of some things contains the parts of that which is defined; but in other things this is not the case: and also that, in the definition of essence, those parts which subsist as matter are not inherent; for they are not parts of that essence, but the whole. But of this in a certain respect there both is and is not definition. For with matter there is not a definition (since it is indefinite); but according to the first essence there is. Thus, the definition of man is the definition of soul. For essence is the inherent form, from which and matter the whole essence is denominated; as, for instance, concavity. For, from this and nose, a flat nose and flatness of nose are composed. For nose is twice inherent in these. But in the whole essence, as in a flat nose, or Callias, matter also is inherent. We have also shown that the very nature of a thing, and each particular thing, are in some things the same, as in first essences. Thus, for instance, curvature is the same with the essence of curvature, if it is the first. But I mean by first, that which is not denominated, because one thing is inherent in another, and is in a subject as matter. But in things which subsist as matter, or as assumed together with matter, these are not the same; nor in things which are one according to accident, as Socrates and a musician; for these are the same according to accident.

Aristotle, Metaphysics. Book 7, Chapter 12.

It is now requisite, in the first place, that we should discuss what we have omitted in our Analytics respecting definition. For a doubt which was not there dissolved will conduce to the discourse respecting essence. But the doubt is this: Why that which is defined, of which we say the reason is definition, is one thing? For instance, if the definition of man is a biped animal (for let this be his definition), why is this one thing, and not many, animal and biped? For man and white are indeed many things, when the one is not inherent in the other. But when the one is inherent in the other, and the subject, viz. man, is affected with something, they are one. For then a white man becomes and is one thing. But here the one does not participate of the other. For genus does not appear to participate of differences; since, at the same time, the same thing would participate of contraries. For differences are contraries, in which the genus is different. But if it does participate, the same reasoning will take place, if the differences are many, as capable of walking, biped, and without wings. For, why are these one, and not many? [It cannot be, that they are one because they are inherent]. For thus there will be one from all. But such things as are contained in definition ought to be one. For definition is one particular reason and essence; so that it is necessary that it should be the definition of one certain thing. For essence, as we say, signifies one particular thing, and this definite thing.

It is requisite, however, in the first place, to consider respecting those definitions which subsist through divisions. For there is nothing else in definition than the genus which is called first, and difference. But other things are genera, both that which is so, and together with it the assumed differences. Thus, for instance, the first genus is animal; but that which is consequent to this is animal biped; and again animal biped, and without wings. And the like consequence will ensue, if there is a greater multitude in the definition. And, in short, there is no difference, whether it subsists through many things, or through few things, or through two things. But if through two things, the one will be genus, and the other difference. Thus, for instance, of biped animal, animal is the genus, but the other is difference. If, therefore, genus, simply considered, is not any thing separate from its own species, or if it is, indeed, yet it is as matter (for voice is genus and matter; but differences make forms and elements from this). This being the case, it is evident that definition is a sentence composed from differences. But it is also requisite that difference should be divided into its differences. Thus, for instance, the difference of animal is the possession of feet. Again: it is requisite to know the difference of animal possessing feet, so far as possessing feet. So that we must not say of things possessing feet, one is winged, and another without wings, if we wish to speak accurately; but he will do this who is unable to divide properly: but we should say, that one has fissured feet, and another feet without a fissure. For these are the differences of feet, since the fissure of the feet is a difference of feet. And thus we must always divide, till we arrive at things without difference. But then there will be as many species of foot as there are differences, and the number of animals with feet will be equal to their differences. If, therefore, this be the case, it is evident that the last difference will be the essence and definition of a thing, if it is not necessary often to assert the same things in definitions; for it is superfluous. Nevertheless, this sometimes happens. For, when any one says an animal having feet, and a biped, he says nothing else than this, an animal having feet, and having two feet. And if he divides this by a proper division, he will often say the same thing, and as often as the number of differences. If, therefore, a difference is produced of difference, one, which is the last, will be form and essence. But if the division is made according to accident, as, if in a division of things having feet, it should be said, one is white and another black, there will be as many differences as there are divisions. So that it is evident that definition is a sentence composed from things different, and from the last of these, when it is properly framed. But this will be manifest if any one transposes such definitions, as, for instance, the definition of a man, and says, animal biped, having feet. For, having said he is biped, renders the addition of having feet superfluous. But there is no order in essence. For in what manner is it requisite to understand this as posterior, and that as prior? Thus much, therefore, we have in the first place said respecting the quality of definitions which subsist through division.

Aristotle, Metaphysics. Book 7, Chapter 13.

Since, however, our speculation is respecting essence, let us again return to this. As, therefore, a subject, the very nature of a thing, and that which is composed from these, are each of them said to be essence, in like manner that which is universal is called essence. Concerning two of them, therefore, we have already spoken. For we have spoken respecting the very nature of a thing, and also of a subject, which we have said is subjected in a twofold manner, either as this particular thing, as an animal to passions (i. e. participated properties), or as matter to energy. Universal also to some appears to be especially a cause and principle. On which account it is necessary that we should also make this the subject of discussion. For it seems to be impossible that essence should be any thing of universals: for the first essence of every thing is that which does not belong to another thing; but that which is universal is common. For that is called universal which is naturally adapted to be inherent in many things. Of what, therefore, will this be the essence? For it will either be the essence of all things, or of nothing. But it is not possible that it can be the essence of all things: and if it should be the essence of one thing, other things also will be this. For things of which the essence and very nature are one, are themselves also one. Further still: essence is said to be that which is not predicated of a subject; but universal is always predicated of a certain subject. Shall we say, therefore, that it cannot subsist, indeed, in the same manner as the very nature of a thing, but that it is inherent in it, as animal in man and horse? It is evident, therefore, that there will be a certain definition of it. But it is of no consequence if there is not a definition of every thing which essence contains. For, nevertheless, this will be an essence of something, as man of man, in which he is inherent. So that the same thing will again happen. For essence will be the essence of man, as animal of that species in which it is inherent as peculiar.

Again: it is impossible and absurd, that this particular individual thing, and essence, if they are composed from certain things, should not be composed from essences, nor from a particular individual thing, but from quality. For that which is not essence, and also quality, will be prior to essence, and this particular individual; which is impossible. For it is not possible that participated properties can be prior to essence, either in definition, or time, or generation; since they would thus have a separate subsistence. Further still: in Socrates, who is essence, essence will be inherent; so that Socrates will be an essence in two essences. And, in short, if man is essence, and such things as are thus denominated, it will happen that nothing contained in definitions is the essence of any thing, and that it has not a subsistence separate from them, and does not subsist in another. I say, for instance, that there is not any animal besides those which rank as particulars, nor any thing else of the things contained in definitions. From these considerations, therefore, it is evident that nothing which has an universal subsistence is essence, and that nothing of things predicated in common signifies this particular individual, but a particular quality. For, if this be not admitted, many other things will happen, and, among the rest, that there will be a third man.

This, too, will be evident from the following consideration: It is impossible that essence can be composed from essences, which are inherent in such a manner as to be in energy. For, two things thus subsisting in energy are never one in energy. But, if they are two things in capacity, they will be one. Thus, the double is composed from two halves in capacity; for energy separates them. So that, if essence is one thing, it will not be composed from inherent essences, and after that manner which Democritus rightly asserts. For he says it is impossible that one atom should be generated from two, or two from one: for he makes indivisible magnitudes to be essences. It is evident, therefore, that the like will take place in number, if number is a composition of monads, as it is said to be by some. For, either the duad is not one, or it does not contain the monad in energy. But that which happens is attended with a doubt: for, if it is neither possible that any essence can subsist from universals, because universal does not signify this particular individual, but a thing with a particular quality, nor possible for any composite essence to consist from essences in energy, every essence will be incomposite. So that neither will there be definition of any essence. However, it appears to all men, and we have formerly asserted, that definition is either alone or principally of essence. But now it is concluded, that neither is there a definition of essence. There will not, therefore, be a definition of any one thing. Or shall we say that after a certain manner there will be, and after a certain manner there will not be, a definition of essences? But what we have now said will be more manifest hereafter.

Aristotle, Metaphysics. Book 7, Chapter 14.

From these very things, that which happens to those who assert that ideas are separate essences, and who at the same time make form to consist from genus and differences, is manifest. For, if forms and animal are in man and horse, there is either one and the same, or a different animal in number. For by definition it is manifest that there is one and the same; since he who says that it is in each will assign the same reason. If, therefore, there is some man, itself subsisting by itself, this particular individual, and separate, it is necessary also, that those things from which it consists, as, for instance, animal and biped, should signify this particular individual, and should be separate, and essences: so that this will likewise be the case with animal. If, therefore, animal is the same in man and in horse, as you in yourself, how will it be one in things which are separate, and why will not this animal also subsist separate from itself? In the next place, if it participates of biped and multiped, it will be impossible that any thing should happen. For contraries will be at the same time inherent in the same thing, subsisting as one, and as this definite particular. But if it does not participate, what is the mode, when any one says an animal is biped, or capable of walking? But, perhaps they form a composite, and touch, or are mingled. All these modes, however, are absurd. Shall we say that that which is different in number is in each? There will, therefore, be infinite particulars, as I may say, of which the essence is animal: for man is not from animal according to accident. Further still: animal itself will be many things. For animal, which is in every individual, is essence; since it is not predicated according to any thing else. But if this be not the case, man will subsist from that, and that will be the genus of man. And again, all things from which man consists will be ideas. Idea, therefore, will not be of one thing and essence of another: for this is impossible. Hence each of those things contained in animals will be animal itself. Besides, this will subsist from a certain particular, and how will animal subsist from it? Or how is it possible that there should be animal, which is itself essence, besides animal itself? Further still: these things will happen in sensibles, and things still more absurd than these. But if it is impossible that this can be the case, it is evident that there is not idea of them, in such a manner as some assert there is.

Aristotle, Metaphysics. Book 7, Chapter 15.

Since, therefore, the whole and form are of a different essence (but I say, that the former is essence as matter assumed together with form, but the latter is entirely form), hence, of such things as are denominated according to the former of these, there is corruption; for there is also generation. But of form there is not corruption; for neither is there generation. For the being or form of house is not generated, but of this particular house. But forms are and are not, without generation and corruption; for it has been shown that these are neither generated nor made by any one. Hence there is neither definition nor demonstration of sensible particular essences, because they have matter, the nature of which is such, that it is possible for it both to be and not be. On this account all the individuals of sensibles are corruptible. If, therefore, demonstration is of things necessary, and also scientific definition, and it is not possible that science can be at one time science, and at another time ignorance, but a thing of this kind is opinion; in like manner demonstration and definition cannot pertain to things which may subsist differently, but such as these are the objects of opinion. It is evident, therefore, that things which may subsist differently at different times, are not the objects of either demonstration or definition. For things corruptible are not manifest to those who possess science, when they are not present to sense. And though the same reasons are preserved in the soul, there will no longer be either definition or demonstration. Hence he who defines any thing which ranks among particulars, ought not to be ignorant that a definition of this kind may always be subverted. For it is not possible that such things can be defined.

Neither is it possible to define any idea: for idea ranks, as they say, among the number of particulars, and has a separate subsistence. It is also necessary that definition should consist from names. But he who defines does not make a name; for it will be unknown: but the things which are admitted are common to all things. It is necessary, therefore, that these should also subsist in other things: just as, if any one should define you, he would say that you are a slender animal, or white, or some thing else which also belongs to another. If some one, however, should say, Nothing hinders but that all these may separately belong to many persons, but that all collectively only belong to this individual, we must say, in the first place, that animal biped pertains to both, viz. to animal and to biped. And this, indeed, must necessarily take place in things perpetual, since they have a prior subsistence, and are parts of a composite. But they are also separate, if man is separate; for either nothing will be separate, or both. If, therefore, nothing, there will not be genus besides species; but if both are separate, there will also be difference. In the next place, because they are prior in essence; these, on the contrary, will not be taken away. And, besides this, ideas are from ideas; for those things from which others consist are more incomposite. Further still: it is requisite that those things from which idea consists, should be predicated of many things; as, for instance, animal and biped. For, if not, how can it be known? For there will be a certain idea which cannot be predicated of more things than one. This, however, does not seem to be the case; but every idea appears to be participable. As we have, therefore, said, they are ignorant that it is impossible for definition to take place in things eternal, and especially in such as are single, as the sun and moon. For they not only err in adding things of this kind, which being taken away the sun will still remain, such as is that of revolving round the earth, or being concealed by night; for if the sun should stop in his course, or become apparent by night, he will be no longer sun; but it will be absurd if, in this case, he should not be sun: for the sun signifies a certain essence. Besides, they assume those particulars which may also be asserted of another thing. Thus, for instance, if something else should become a thing of this kind, it is evident that it will be sun. The definition, therefore, is common. But the sun ranks among particulars, in the same manner as Cleon or Socrates. In short, why has no one of them given a definition of idea? For the truth of what we have now said will become apparent to him who shall make the attempt.

Aristotle, Metaphysics. Book 7, Chapter 16.

That it is evident that most of those things which appear to be essences, as the parts of animals, are only so in capacity; for none of them has a separate subsistence. But, when they are separated, then they are all of them as matter, as earth, and fire, and air. For none of them is one thing, but each is as it were a heap, before they are digested, and one thing is produced from their conjunction. But some one may especially apprehend that the parts of animated natures and of the soul very nearly approach to a subsistence both in energy and capacity, because they possess the principles of motion from something in their flexures. Hence some animals live when divided. But at the same time all of them will subsist in capacity, when they are one continued thing by nature, and not by force, or coalescence. For a thing of this kind is mutation. But, since the one is denominated as being, and the essence of the one is one thing, and those things of which the essence is one in number are one in number, it is evident that neither the one nor being can be the essence of things, as neither the essence of element or principle is the essence of all things. But we inquire, what, therefore, the principle is, that we may proceed to that which is more known. Of these, then, that which is being and one, is more essence than either principle is, or element, or cause. But yet neither are these essences, if nothing else which is common is essence. For essence is not inherent in any thing but itself, and that by which it is possessed, of which it is the essence.

Further still: the one will not be in many places at the same time; but that which is common is at the same time present with all things in many places. So that no universal can have a subsistence separate from particulars. But those who say that there are forms in one respect speak rightly, in giving them a separate subsistence, if they are essences; but in another respect not rightly, because they say there is one form in many. But the reason of this is their inability to assign what such like essences are which are incorruptible, and which have a subsistence independent of particulars and sensibles. They, therefore, make them to be the same in species with corruptible natures (for these we know), viz. man itself, and horse itself, adding the word itself to sensibles. Though, even if we did not see the stars, yet I think there would no less be eternal essences besides those of which we have a knowledge. So that also now, though we are not able to see what eternal essences are, yet perhaps it is necessary that certain eternal essences should have a subsistence. It is, therefore, evident, that none of those things which are called universals is essence, and that no essence is composed from essences.

Aristotle, Metaphysics. Book 7, Chapter 17.

But, again, as if making another beginning, let us say what, and what kind of a thing we ought to call essence. For, perhaps, from these things, the particulars respecting that essence which is separate from sensible essences will also be apparent. Since, therefore, essence is a certain principle and cause, it is requisite that we should proceed from hence in our inquiry. But the investigation, on what account a thing subsists, always proceeds as follows, viz. on what account one thing is inherent in a certain other thing. For to inquire on what account a musical man is a musical man, is either to inquire, as we have said, on what account a man is a musician, or to inquire something else. To inquire, therefore, on what account a thing is that thing which it is, is to inquire nothing. For it is requisite that to be inherent in something, and to be, should subsist as manifest. I say, for instance, that the moon is eclipsed: but of the inquiry, Why a thing is that thing which it is? there is one reason, and one cause in all things; as, on what account a man is a man, or a musician a musician, unless some one should say that every thing is indivisible with respect to itself. But this is to be one; and this is common to all things, and is concise. Some one, however, may inquire, On what account man is that kind of animal which he is? This, therefore, is evident, that such a one does not inquire on what account he who is a man, is a man? He, therefore, inquires, Why a certain thing subsists in a certain thing? But that it is inherent ought to be manifest: for if not, he investigates nothing. Thus, for instance, on what account does it thunder? Because a sound is produced in the clouds: for thus one thing is inquired respecting another. And, on what account are these things, as, for instance, tiles, and stones, a house? It is evident, therefore, that he investigates the cause. But this is, as I may say, speaking logically, the very nature of a thing; which in some things is that for the sake of which, as, perhaps, in a house, or a bed. But in other things it is that which first moves: for this also is a cause. A cause, however, of this kind is investigated, when a thing is generated or corrupted; but the other cause is investigated when a thing already is. But that which is investigated, is especially latent in things not conveniently predicated; as, for instance, in the inquiry, What man is? because it is simply asserted, and not definitely, that he is this or that. It is, however, requisite to investigate definitely, otherwise it will come to pass that something and nothing will be investigated in common. But, since it is requisite that essence should be possessed and should subsist, it is evident that the inquiry will be on what account the matter is. As, for instance, these particulars are a house: But on what account? Because there are that which a house is. Thus, too, in the inquiry, Why man is this particular thing, or why this body possesses this particular thing? the like inquiry is made. So that the cause of the matter is investigated: but this is the form by which any thing is; and this is essence. It is evident, therefore, that there is not any investigation nor discipline respecting things which have a simple subsistence, but that there is another mode of investigating things of this kind.

But, because that which is composed from something is so composed as that the whole is one thing, and not as a heap, but as a syllable; but a syllable is not the elements of speech, nor is it the same as b and a, nor is flesh, fire, and earth; for when a dissolution takes place, flesh and syllable no longer remain, but the elements, fire and earth, continue to subsist;—this being the case, syllable is something besides the elements, viz. besides vowel and mute: and flesh is not only fire and earth, or the hot and the cold, but also something else. If, therefore, it is necessary, that flesh should either be an element, or that which is composed from elements; if it is an element, the same reasoning will again take place. For from this fire and earth will consist, or flesh, and still further, something else; so that a progression will take place to infinity. But, if it is composed from element, it is evident that it will not consist from one but from many, or it will be that very element itself. So that, again, the same reasoning must take place in this as in flesh or syllable. But it should seem that there is a thing of this kind, and that it is not an element, but the cause that this thing is flesh and that a syllable: and in a similar manner with respect to other things. But this is the essence of every thing: for this is the first cause of subsistence. However, since some things are not the essences of things, but this is the case with those alone which are naturally essences and which are constituted by nature, it may appear to some that this nature also, which is not an element but a principle, is essence. But an element is that into which, being inherent as matter, a thing is divided, as, of the syllable ab, a and b.

Aristotle, Metaphysics. Book 8, Chapter 1.

From what has been said, it is requisite to syllogise, and, by a summary collection, form a conclusion. But we have said that the causes, principles, and elements of essences are investigated. And, with respect to essences, some are granted to have a subsistence by all men; but concerning others, some have entertained peculiar opinions. Natural essences, indeed, have been granted to subsist; such as fire, earth, water, and other simple bodies; in the next place, plants, and the parts of these; animals also, and the parts of animals; and, lastly, heaven, and the parts of heaven. But those who have entertained peculiar opinions respecting essences, say that forms and the mathematical species are essences. However, it happens, from the reasonings about things, that the very nature of a thing, and that which ranks as a subject, are essences. Again: in another respect, genus is more essence than species, and universal than particulars. Ideas also are conjoined with universal and genus; for, according to the same reasoning, they appear to be essences. But since the very nature of a thing is essence, and the reason of this is definition, hence we have unfolded the particulars respecting definition, and the essential. And, since definition is a sentence, and a sentence has parts, it was also necessary to perceive respecting a part, what are the parts of essence, and what are not; and, likewise, whether it is necessary that these should be the same with the parts of definition.

Further still: neither is universal nor genus, essence. But we shall afterwards speak concerning ideas, and mathematical entities: for some say that these have a subsistence besides sensible essences. At present, however, we shall discourse respecting those essences which are acknowledged to have a subsistence. But these are sensible: and all sensible essences have matter. But essence is that which ranks as a subject; and this is in one respect matter, but in another definition. And I call matter that which is not this definite particular in energy, but in capacity. But definition and form are subject in a different respect, which are definite particulars, and are separable by reason. But the third is that which consists from these, of which alone there is generation and corruption, and which is simply separable. For of those essences which subsist according to reason, some are separated, and others not. But that matter is essence is manifest: for in all opposite mutations, there is something which is as a subject to those mutations; as, for instance, according to place, that which is now here, is again elsewhere. Thus, too, according to increase, he who is now so much, is again less or more; and according to internal change, he who is now well, is again ill. In like manner also, according to essence, that which is now in generation, is again in corruption: and that which is now a subject as this definite particular, is again a subject as according to privation. And other mutations follow this; but this does not follow one or two of the rest. For it is not necessary, that if any thing has local matter, it should also have this matter generable and corruptible. What the difference, however, is between the being simply and not simply generated, we have declared in our Physics.

Aristotle, Metaphysics. Book 8, Chapter 2.

But, since the existence of that essence which is as a subject, and as matter, is acknowledged by all men, but this is that which subsists in capacity, it now remains that we should declare what that essence is amongst sensibles which subsists as energy. Democritus, therefore, appears to have thought that there are three differences. For he considered the subject body and matter to be one and the same; but that it differed either by rhusis, which is figure; or by trope which is position; or diathesis which is order. But there appear to be many differences. Thus, some things are said to be from the composition of matter, and these are such things as are mingled, as for instance mead; but others from a nail, as a little coffer; others again from a bond, as a bundle; others from glue, as a book; and others again from many of these things. Some too, are said to be from position, as a threshold, and the lintel of a door. For these in a certain respect differ from position. Others again derive their being from time, as supper and dinner: others from place as winds; others from the passions of sensibles, as from hardness and softness, density and rarity, dryness and moisture: and some things are from some of, but others, from all these. And, in short, some things are from transcendency, others from deficiency. So that is is predicated in so many ways. For a threshold is, because it is so situated; and its essence signifies that it has this position: and to be ice, is to be thus condensed. But the being of some things is defined by all these, and this because some things are mingled, and others consist from temperament; some are bound, and others are condensed; and others use other differences, as the hand, or the foot. The genera of differences therefore are to be taken into consideration: for these will be the principles of being; as, for instance, things which have their subsistence in the more and the less, or the dense and the rare, and other things of this kind. For all these belong to transcendency and deficiency. But, if any thing has its subsistence in figure or smoothness and roughness, every thing of this kind is such through the right-lined and the curved. The essence likewise of some things consists in being mingled, and their non-existence in the opposite.

But it is manifest from these things that if essence is the cause of being to every thing, in these we must investigate what the cause of the being of each of these is. Essence, therefore, is none of these, nor is it these combined; but at the same time it subsists analogously in each. And, as in essences that which is predicated of matter is energy itself, this is especially the case in other definitions; as, for instance, if it were requisite to define a threshold, we should say that it is wood or stone thus placed; and if a house, that it is tiles and wood placed in this particular manner. Or shall we say that in some things there is that for the sake of which they are fashioned? But, if we should define ice, we should say that it is water congealed or condensed in this manner: and if symphony, that it is such a mixture of the sharp and the flat. And after the same manner also in other things. It is evident therefore, from these things, that energy and form are different from matter. For of some things composition is the energy and form, of others mixture, and of others something else of the above mentioned particulars. Hence, of such as define, those who say that a house is stones, tiles, and wood, define a house in capacity. For these are matter. But those who say that a vessel is that which preserves possessions and bodies, or add something else of this kind, define energy. And those who add both these define a third essence, and an essence consisting from capacity and energy. For the definition which subsists through differences appears to be that of form and energy; but that which is from things inherent appears to be rather the definition of matter. The like also takes place with respect to those definitions which Archytas admitted: for they are composed from both. Thus, for instance, What is serenity? Quietness (according to him) in an abundance of air. For air is matter, but quietness, energy and essence. What is tranquillity? Smoothness of the sea. The subject indeed, as matter, is the sea; but energy and form, smoothness. It is evident, therefore, from what has been said, what a sensible essence is, and how it subsists. For one thing is as matter, another as form, because it is energy; but the third is that which is composed from these.

Aristotle, Metaphysics. Book 8, Chapter 3.

But, it is necessary not to be ignorant that it is sometimes concealed from us whether a name signifies a composite essence, or energy and form; as for instance whether a house is the sign of that which is common, viz. of a covering from tiles and wood and stones thus placed; or whether it is a sign of energy and form, because it is a covering. Likewise, with respect to a line, whether it is a duad in length or the duad. And, with respect to animal, whether it is soul in body, or soul. For soul is an essence, and the energy of a certain body; but animal will be in both, not as predicated in one definition, but as with relation to one thing. These things however contribute to something else, but do not at all contribute to the investigation of a sensible essence. For the very nature of a thing belongs to form and to energy. For soul, and the being of soul are the same. But the being of man and man are not the same, unless the soul is called man. So that man, and the essence of man, will be the same in one respect, and not the same in another.

From investigation, therefore, it does not appear that a syllable consists from letters and composition, nor that a house is tiles and composition: and this rightly: for neither the composition nor mixture of any thing is with those things of which it is the composition or mixture. And in a similar manner, neither is this the case with any thing else. Thus, for instance, if a threshold is from position, position is not from a threshold, but rather this is from that. Nor is man animal and biped; but it is necessary that there should be something which is besides these, if these are matter, and which is neither an element, nor from an element, but which they call essence, separating it from matter. If therefore this is the cause of being, and essence, they will say that this is essence itself.

But it is necessary that this should be either eternal, or corruptible without being generated, and generated without generation. We have however elsewhere shown and rendered manifest that form is not made by any one, nor generated, but that it becomes this particular form and that which consists from these. But whether there are separate essences of things corruptible, is not yet manifest; except that it is evident that there cannot be of some corruptible natures, which are not able to subsist independently of sensibles, as a house, or a vessel. Perhaps, therefore, neither are these essences, nor is any thing else essence which has not a natural subsistence: for some one may consider nature, as alone that essence which subsists in things corruptible.

So that the doubt entertained by the followers of Antisthenes, and those similarly unlearned, viz. that essence cannot be defined, may now be opportunely solved; for, say they, definition is a long sentence; but it is possible to instruct others in the particular quality of a thing, though it cannot be defined: for you cannot say what silver is, but you may say that it resembles tin; so that of a certain essence, as, for instance, of that which is a composite, whether it be sensible or intelligible, there may be a definition and reason; but there cannot be of those things from which these first consist, if definitive reason signifies something of something; and it is requisite that this should be as matter, but that as form. It is also evident why, if in a certain respect numbers are essences, they are so after this manner, and not because they are a multitude of monads; for definition is a certain number: (for it is divisible and may be resolved into indivisibles, since reasons are not infinite) and number is a thing of this kind. And as, when any one of those things from which number consists is subtracted from, or added to a number, there is no longer the same, but a different number, though that which is the least should be subtracted or added; in like manner, neither will definition nor the very nature of a thing, be any longer the same, if any thing be taken away or added. Besides, it is requisite that there should be something through which number itself is one, and which now they cannot assign, if number is one thing; for either it is not one thing, but is as it were a heap, or, if it is, it must be said what that is which makes it to be one from many things. Definition also is one thing composed from the many; but neither can they assign a reason why this is one; and this very properly happens on the same account. Essence also is after this manner one, and not according to some, who assert that it is as it were a certain monad, or point, but each is energy and a certain nature; and as number has neither more nor less, so neither has that essence which subsists according to form; but if there is any essence which has the more and the less, it is that which subsists according to matter. Concerning the generation therefore and corruption of the above mentioned essences, how each may be admitted to take place, and in what respect each is impossible, and also concerning the reduction of definition to number, let it be thus far determined.

Aristotle, Metaphysics. Book 8, Chapter 4.

Concerning a material essence we ought not to be ignorant that though all things are from the same first nature, or from the same things as those which are first, and though the same matter is as a principle to generated natures, yet at the same time there is something which is proper or domestic to every thing. Thus, for instance, the first matter of phlegm is the sweet or the fat; but of bile the bitter or something else: and these things also, are perhaps from the same thing; but many matters of the same thing are generated when one thing is the matter of another: thus phlegm is from the fat and the sweet, if the fat is from the sweet; and it is also from bile, because it is analysed into bile, as into the first matter: for one thing is from another in a twofold respect, viz. either by progression, or analyzation into its principle; but, one matter existing, it happens that different things are generated, through the moving cause. Thus, from wood a chest and bed are formed. Of some things, however, which are different, the matter is necessarily different. Thus a saw can never be made from wood, nor is it in the power of the moving cause to effect this; for it can never make a saw from wool or from wood. But, if it is possible for the same thing to be made from different matter, it is evident that art, and the principle as moving are the same: for if matter and that which moves are different, that also which is generated will be different.

When therefore any one investigates the cause of a thing (since causes are predicated multifariously) it is requisite to enumerate all the contingent causes. Thus, for instance, what is the cause of man as matter? is it not the menstrual blood? But what is the cause as that which moves? is it not seed? What is the cause as form? that which is the very nature of a thing. What is the cause as that for the sake of which he subsists? the end; but perhaps both these are the same. It is requisite however to enumerate the most proximate causes: What is the matter of man? not fire or earth, but that which is proper or domestic.

With respect to physical and generated essences, therefore, it is necessary that he should proceed in this manner, who proceeds rightly, if there are these causes, and they are so many in number, and a knowledge of causes is necessary. In physical essences however, but which are perpetual, a different mode of proceeding must be adopted; for some of them perhaps are without matter, or have not a matter of this kind, but such only as is moveable according to place. Nor does matter belong to such things as have indeed a natural subsistence but are not essences, but that which is the subject to these is essence. Thus, for instance, what is the cause of an eclipse? what the matter of it? No matter however can be assigned, but the moon is that which suffers; but what is the cause as that which moves, and corrupts the light? the earth. An eclipse however, has not perhaps that cause for the sake of which it subsists; but the cause which is as form is definition. This however is immanifest, unless it subsists together with cause: as, for instance, what is an eclipse? a privation of light; but if it is added that this privation of light is occasioned by the intervention of the earth, this will be a definition together with the cause. Moreover with respect to sleep it is immanifest what that is which is first passive: shall we say that it is the animal? be it so. But according to what is this passive? and what is first passive? the heart, or something else? and in the next place, to what is it passive? likewise what is its passion, and which is not the passion of the whole? Shall we say it is such a particular kind of immobility? be it so. But this is because there is something which is first passive.

Aristotle, Metaphysics. Book 8, Chapter 5.

But, since some things both are and are not without generation and corruption, as points, if they have a subsistence, and, in short, forms (for whiteness is not generated, but the white wood, if every thing which is generated is generated from something, and is generated something); this being the case, all contraries are not generated from each other, but a white man is in one way generated from a black man, and in another way whiteness from blackness. Nor of every thing is there matter; but of those things of which there is generation and mutation into each other. But such things as either are or are not without mutation, these are without matter. It is, however, dubious, how the matter of every thing subsists with respect to contraries. Thus, for instance, if the body is well in capacity, but disease is contrary to health, shall we say that both are in capacity? Shall we also say that water is both vinegar and wine in capacity? Or shall we say that the body is the matter of health, according to habit and according to form, but that it is the matter of disease according to privation, and unnatural corruption? But there is a certain doubt why wine is not the matter of vinegar, nor vinegar in capacity, although vinegar is produced from it. Also, with respect to that which has life, it may be doubted, whether it is a dead body in capacity or not. The doubt, however, may be solved, by saying that corruptions subsist from accident. But the matter itself of an animal is, according to corruption, the capacity and matter of dead body, and water also of vinegar. For they are generated from these, in the same manner as night from day. And it is requisite that such things as thus change into each other, should return into matter. Thus, in order to the generation of an animal from a dead body, it is requisite that the dead body should first be resolved into matter, and, that thus an animal should afterwards be generated from it. In like manner, vinegar must be resolved into water, and thus from it wine will afterwards be produced.

Aristotle, Metaphysics. Book 8, Chapter 6.

With respect to the abovementioned doubt concerning definitions and numbers, what is the cause of their being one? For, of all such things as have many parts, and where the whole is not as it were a heap, but is something besides the parts, there is a certain cause. For in some bodies contact is the cause of their being one, in others viscosity, or some other passion of this kind. But definition is one discourse, not by a bond, as the Iliad, but because it is of one thing. What then is it which makes man to be one, and why is he one, and not many things, such as, for instance, animal and biped, especially if, as some say, animal itself and biped itself have a subsistence? For why is not man those very things? And will men subsist, not by the participation of one man, but by the participation of two things, animal and biped? In short, man will not be one thing but many things, animal and biped. It is manifest, therefore, that those who are thus accustomed to define and speak, cannot assign the reason of this, and solve the doubt. But if it is as we have said, that one thing is matter and another form; and again, one thing is in capacity and another in energy, the doubt which is investigated will no longer appear to exist. For the doubt is the same as if the definition of a garment were round brass. For this name would be a sign of the definition. So that the object of investigation is, what the cause is that the round and the brass are one. The doubt, therefore, appears no longer to remain, because this is matter, and that form. What else then causes that which was in capacity, in things in which there is generation, to subsist in energy, except the efficient cause? For there is no other cause of the sphere in capacity becoming a sphere in energy; since this is the very nature to both. But with respect to matter, one kind is intelligible and another sensible: and always with respect to definition, one thing is matter and another energy, as, a circle is a plane figure. But such things as have neither intelligible nor sensible matter, of these each is immediately one particular thing, as that which is this particular being (i.e. substance), also quantity and quality. Hence, in definitions there is neither being nor the one, and the very nature of a thing is immediately one particular thing, as also a particular being. Hence, too, there is no other cause that each of these is one, nor that each of these is a particular being. For immediately each is a certain being, and a certain one; yet neither being nor the one is the genus of these, nor have they a subsistence separate from particulars. But in consequence of this doubt, some say that participation is the cause; but they are dubious what the cause of participation is, and how it is effected. Some assign the copula of the soul as the cause, as Lycophron, who says that science is the copula of scientific knowledge and the soul; but others assert that life consists in the composition or conjunction of the soul with the body; though the same reason may be assigned in all things. For to be well, will either be a copula, or conjunction, or composition of the soul and health. And for brass to be a triangle, will be a composition of brass and triangle: and for a thing to be white, will be a composition of superficies and whiteness. But they speak in this manner, because they investigate the uniting reason and difference of capacity and energy. However, as we have before said, the last matter and form are the same, the one being in capacity, and the other in energy. So that to investigate the cause of unity, is similar to an investigation of the cause of a thing being one. For every thing is one particular thing; and that which is in capacity, as also that which is in energy, is in a certain respect one thing. So that there is no other cause except that which subsists as moving from capacity into energy. But of such things as are without matter, each is simply and properly one and being.

Aristotle, Metaphysics. Book 9, Chapter 1.

We have, therefore, discoursed concerning essence which is primarily being, and to which all the other predicaments of being are referred. For other things, viz. quantity, quality, and the rest which are thus denominated, are denominated according to the definition of essence: for all these have the definition of essence, as we have before observed. But, since being is denominated either substance, or quantity, or quality, and is either in capacity or energy, it is requisite that we should now speak concerning capacity and energy. And in the first place respecting that capacity which is most properly so denominated, it does not contribute to our present design. For capacity and energy are more extended than those things which are alone predicated according to motion. But, when we speak concerning this in our explanations of energy, we shall also render manifest the particulars respecting the rest. That capacity or power, therefore, and to be able, are predicated multifariously, we have elsewhere shown. But, of these, such as are equivocally called powers are omitted. For some are denominated by a certain similitude, as, in geometry, we speak of powers, or things possible, also of things impossible, because in a certain respect they are, or are not. But such things as are referred to the same form, are all of them certain principles, and are predicated with relation to one first, which is the principle of mutation in another, so far as it is another. For there is a capacity of suffering, which in the patient itself is the principle of passive mutation from another, so far as it is another. But there is a habit of impassiivity and corruption into that which is worse, which proceeds from another transmuting principle, so far as it is another. For, in all these definitions, there is the definition of the first capacity.

Again: these are alone called either the capacities of acting or suffering, or of acting or suffering in a becoming manner. So that, in the definitions of these, the definitions of the former capacities are in a certain respect inherent. It is evident, therefore, that in a certain respect there is one power of acting and suffering (for a thing is able, both because it has a capacity of suffering, and because something else may suffer from it), and that in another respect there is a different power: for there is one power in the patient. For, because it has a certain principle, and matter is a certain principle, the patient suffers, and one thing suffers from another. Thus, that which is fat is combustible, and that which yields after this manner may be pressed; and in a similar manner with respect to other things. But there is another power in the agent; as, for instance, the hot and the power of building: the former in that which is able to give heat, and the latter in the builder. Hence, nothing which naturally possesses unity and continuity is itself passive to itself; for it is one thing, and not another: but impotency, which is contrary to such a power, is privation. So that all power and impotency are of the same thing, and subsist according to the same. But privation is predicated multifariously: for we say that a thing has privation which does not possess a certain thing, and which is naturally adapted to possess, if it does not possess, either altogether, or when it is naturally adapted; and after this manner we say that it either entirely, or in a certain respect, has privation. We also say of some things which through violence do not possess that which they are naturally adapted to possess, that they suffer a privation of such things.

Aristotle, Metaphysics. Book 9, Chapter 2.

But since such-like principles of capacities subsist in inanimate natures, and some of them in animated natures, in soul, and in that part of the soul which possesses reason, it is evident, that of capacities or powers also, some will be irrational, but others accompanied with reason. Hence all arts, both such as are effective, and such as are sciences, are powers; for they are the principles of mutation in another thing, so far as it is another. And all those powers which are accompanied with reason are effective of contraries; but each of those which are irrational, is alone effective of one thing. Thus, for instance, the hot is alone effective of heat; but the medicinal art is effective both of disease and health. But the cause of this is, that science is reason: and the same reason manifests both a thing and its privation, though not after the same manner. In a certain respect, indeed, reason knows both, but also in a certain respect it has a greater knowledge of the thing, than of its privation. So that it is necessary that such sciences should possess a knowledge of contraries, but of the one essentially, and of the other not essentially. For reason knows the one essentially, but the other after a manner accidentally; since by negation and ablation it manifests the contrary. For first privation is that which is contrary; but this is an ablation of the other. But since contraries are not ingenerated in the same thing (and science is a power from the possession of reason, and the soul also has the principle of motion), hence that which is salubrious alone produces health, and that which is calefactive heat, and that which is frigefactive cold; but he who possesses scientific knowledge produces both. For reason has a knowledge of both, though not similarly; and this reason subsists in soul which possesses the principle of motion. So that soul will move both from the same principle, conjoining them with the same thing. Hence natures which are endued with power according to reason, effect things contrary to the productions of those endued with power without reason. For one principle is comprehended in reason.

But it is evident that the power of alone acting or suffering follows that power which is the principle of acting or suffering well; but the latter does not always follow the former. For it is necessary that he who acts well should act; but it is not necessary that he who alone acts should also act well.

Aristotle, Metaphysics. Book 9, Chapter 3.

There are, however, some, as the Megaric philosophers, who say that a thing when it energises is then alone endued with power, but that when it does not energise, it does not possess power; as, for instance, that he who does not build has not the power of building; but that he who builds possesses this power when he builds; and in a similar manner with respect to other things. But it is not difficult to perceive the absurdities which attend this opinion. For it is evident that he who does not build will not be a builder. For the very essence of a builder consists in the power or capacity of building; and in a similar manner also in other arts. If, therefore, it is impossible that any one can possess arts of this kind, unless he has once learned and received them; and again, that he should be without the possession of them, unless he some time or other loses them, viz. either through oblivion, or a certain disease, or time (for he will not lose the thing itself, because it is perpetual), this being the case, when such a one ceases to operate, he will not be in possession of art. But how will he again immediately build on resuming the art which he had lost? The like also happens with respect to things inanimate. For neither will there be any thing hot or cold, or sweet, or, in short, any thing sensible, when they are not perceived by us. So that it happens to them, that they assert the same thing as Protagoras. But, indeed, neither will a man have any sense, if he neither perceives nor energises. If, therefore, that animal is blind which does not see, though naturally adapted to see, and when it is naturally adapted, and further as it is naturally adapted, the same animals will often in the same day be blind, and in like manner deaf.

Again: if that is impossible which is deprived of power, it will be impossible for that which is not generated to be generated: but he who says that a thing which cannot be generated, either is, or will be, will speak falsely. For this will signify that which is impossible. So that those assertions subvert both motion and generation. For that which stands will always stand, and that which sits will always sit. For a man will not rise if he sits; since it will be impossible for that to rise which is not able to rise. If, therefore, these assertions cannot be admitted, it is evident that capacity and energy are different from each other. But those assertions make capacity and energy to be the same. Hence it is not a small thing which they endeavour to subvert. So that it happens, that it may be possible for a thing to be, and yet it may not be; and that it is possible for a thing not to be, which yet may be. In a similar manner too, in the other predicaments, that which is able to walk may not walk, and that which does not walk may be able to walk. But that is possible, to which, when the energy is present of which it is said to have the capacity, nothing will be impossible. My meaning is this, if, for instance, it is possible for any one to sit, and it happens that such an one sits, nothing impossible will take place when he sits: and in a similar manner, if it is possible for any thing to be moved or to move, to stand, or to be stopped, to be, or to be generated, not to be, or not to be generated. But the name energy, which accords with entelecheia, and also with other things, is principally derived from motions. For motion especially appears to be energy. Hence, to things which are not, motion is not attributed, but other predications. Thus, for instance, things which are not, are dianoetic and desirable objects, but are not moved. But this is, because not being in energy, they may be in energy. For, of things which are not, some are in capacity, but yet are not, because they are not in entelecheia.

Aristotle, Metaphysics. Book 9, Chapter 4.

If, therefore, the possible is that which we have said it is, to which energy is consequent, it is evident that it cannot be true to say that this thing is possible, and yet will not be. For if this were admitted, things which are possible would elude our search. I say, for instance, as if some one should assert that it is possible for the diameter of a square to be commensurate with the side, but that it never will be commensurate, not considering that this is impossible, and, therefore, conceiving that nothing hinders but that a thing which is possible to be, or to be generated, neither is, nor will be. However, from what has been laid down, this is necessary. For, if we suppose that a thing may be, or may be generated, which is not indeed, but which is possible, there will be nothing impossible in such a supposition. But if it is admitted that the diameter is commensurable with the side, it will follow that even are equal to odd numbers, which is impossible. For the false is not the same with the impossible. For, that you now stand is false indeed, but not impossible. At the same time also, it is manifest, that if, in consequence of the existence of a, it is necessary that b should exist, if it is possible for a to be, it necessarily follows that it is also possible for b to be. For if it is not necessarily possible for it to be, nothing hinders but that it may not be possible for it to be. Let it, therefore, be possible for a to be: since, then, it is possible for a to be, nothing impossible will happen from considering a as existing. It is also necessary that b should exist; but it was impossible. Let it, therefore, be impossible. But if it is impossible that b should exist, it is necessary that it should also be impossible for a to exist. But the first is, and therefore the second is. Hence, if a is possible, b also will be possible, if they subsist in such a manner, as that in consequence of the existence of a it is necessary that b should exist. If, therefore, a and b thus subsisting, it is not possible for this to take place with respect to b, neither will a, b, subsist in the manner in which they are supposed to subsist. And if a being possible, it is also necessary that b should be possible; if a is, it is necessary that b also should exist. For, that it is possible from necessity for b to exist, if it is possible for a to exist, signifies this, that if a is, and when it is, and as it is possible to be, then this is also necessary with respect to b.

Aristotle, Metaphysics. Book 9, Chapter 5.

But since of all powers some are connate as those of the senses, but others are from custom, as the power of playing on the pipe, and others again are from discipline, as those of the arts, it is necessary that those powers which are derived from custom and reason should be acquired through antecedent energies. But it is not necessary that those which are not of this kind, and which are passive powers, should subsist after this manner. Since, however, that which possesses power is able to effect something, it is necessary to add in the definition at a certain time, and after a certain manner, and such other particulars as are consequent to these. And some things, indeed, are able to move according to reason, and their powers are accompanied with reason; but others are irrational, and their powers also are irrational. And it is also necessary that those should subsist in that which is animated, but these in both. This being the case, it is necessary with respect to such like powers, that when the active and passive approximate as far as they are able, the one should act and the other suffer. But in the rational powers this is not necessary: for with respect to all these, each is effective of one thing; but those are effective of contraries. It is, however, impossible that the rational powers should at the same time produce contraries. It is necessary, therefore, that something else should be that which has dominion. But I call this appetite, or free-will: for whatever it desires, this it will principally effect when it approximates as far as it is able to that which is passive. So that every thing which is endued with power according to reason, must necessarily accomplish this, when it desires that of which it possesses the power, and as it possesses. But it has the power of acting, that which is passive being present, and subsisting in this manner; for if not, it will not be able to act. For there is no longer occasion to add the words, nothing external impeding; since, as it is a power of acting, it possesses power. It does not, however, possess this power universally, but when it subsists in such a manner that external impediments are removed. For thus certain things in the definition are taken away. Hence, the efficient will neither at the same time effect two things or contraries, though he should at the same time wish or desire to effect them. For he will not thus possess the power of them at the same time; nor is power capable of effecting contraries at once. For he will thus effect things of which he has the power.

Aristotle, Metaphysics. Book 9, Chapter 6.

Since then we have spoken concerning the power which is denominated according to motion, let us now consider what energy is, and what the quality which it possesses. For by division the nature of that which is endued with power will at the same time be manifest; because we not only say that a thing is endued with power which is naturally adapted to move another, or to be moved by another, either simply or after a certain manner, but we also say this in another respect. Hence in our inquiry we shall also discuss these particulars. But for a thing to subsist in energy, is not such a subsistence as when we say a thing subsists in capacity. But we say a thing is in capacity, as Mercury in the wood, and the half in the whole, because it can be taken away from the whole; and we call him scientifically knowing in capacity, although he does not contemplate, who is able to contemplate. However, by an induction of particulars, what we wish to say will be manifest. For it is not necessary to investigate the definition of every thing, but it is sufficient to perceive the analogous, viz. that as building is to the architect, he who is awake to him who is asleep, he who sees to him whose eyes are closed, but who possesses sight, and as that which is separated from matter is to matter, and that which is effected by art to that which is uneffected, so is energy to that which is endued with power or capacity. But all things are not similarly said to be in energy, but analogously, as this thing in this, or with relation to this; but that in that, or with relation to that. For some things are as motion with respect to power, but others as essence with respect to a certain matter. But the infinite and the void, and such-like things, are after one manner said to be in energy and capacity, and after another manner many other things; as, for instance, that which sees, that which walks, and that which is seen. For it sometimes happens that these are simply verified. Thus, one thing is said to be seen, because it is seen; but another, because it has the power of being seen. But the infinite does not so subsist in capacity, as that it will at length become separate in energy, but in knowledge. However, that this energy subsists in capacity is owing to a division which never fails; but this never-failing division will not cause it to become separate in energy. With respect, therefore, to a subsistence in energy, what it is, and what the quality which it possesses, let it be manifest to us from these and such-like particulars.

Aristotle, Metaphysics. Book 9, Chapter 7.

It is now requisite to determine when a thing is in capacity, and when it is not. For a thing is not in capacity at any time. Thus, for instance, is earth man in capacity or not? Or is not this rather the case when seed is generated? Nor even then, perhaps. As neither is every thing healed by the medicinal art, nor by fortune; but there is something which is capable of being healed, and this is sane in capacity. But the definition of that which from a subsistence in capacity acquires through the dianoetic part a subsistence in energy, is this: that which is reduced into energy, when he by whom it is so reduced is willing, nothing external impeding. But this takes place in him who is healed, when nothing within him impedes. In like manner, a house also is in capacity, if nothing in this, and in the matter of it, prevents the house from being constructed, and when there is nothing which ought to be added, or taken away, or changed: for this is a house in capacity. And in a similar manner with respect to other things, the principle of the generation of which is external, and with respect to those which contain this principle within themselves, and which, when nothing external impedes, energise from themselves. Thus, seed is not yet in capacity: for it is requisite that it should subsist in another, and be changed. But when it is now a thing of this kind through its own principle, then this is in capacity; but that requires another principle. Just as earth is not yet a statue in capacity; for when changed it will be brass. But it appears that this is not what we now say, but the following, viz. that a chest is not wood, but wooden, nor wood earth, but earthly. Again, if earth is after this manner not any thing else, but is considered denominatively, that which is always simply in capacity, is that which is posterior. Thus, for instance, the chest is neither earthly, nor earth, but wooden. For this is the chest in capacity, and this is the matter of the chest; simply, indeed, of that which is simply, but of this particular chest, this particular wood. Indeed, if there is something which is first, and which is no longer denominated from another, this is the first matter. Thus, if earth is aerial, but air not fire, but fiery, fire in this case is the first matter, as that which is this particular thing, and which is essence. For in this that which is universal and a subject differ, that the one is this particular thing, and the other not. Thus man, body, and soul, are each the subject of passions; but passion is the being a musician, and the being white. However, when music is ingenerated, that is not called music, but a musician; and man is not called whiteness, but white; nor walking or motion, but that which walks or is moved. In things, therefore, which are thus denominated that which is the last is essence. But in things which are not so denominated, but of which a certain form and this particular thing are predicated, that which is last is matter, and a material essence. And, indeed, it very properly happens that the one is predicated of the other, both according to matter and passions; for both are indefinite. And thus we have shown when a thing may be said to be in capacity, and when not.

Aristotle, Metaphysics. Book 9, Chapter 8.

But since we have shown in how many ways the prior is predicated, it is evident that energy is prior to capacity. I mean not only that definite capacity which is called the principle of mutation in another so far as another, but in short every principle of motion and rest. For nature is in the same genus with capacity; since it is a motive principle, yet not in another, but in itself, so far as it is itself. But energy is prior to every thing of this kind, both in definition and essence. It is also in a certain respect prior, and in a certain respect not prior, in time. That it is therefore prior in definition is evident. For that which primarily possesses power, on that account possesses it, because it is capable of energising. Thus, that is fabricative which is able to build; that is visive which is able to see; and that is visible which is capable of being seen. The same reasoning also applies to other things. So that it is necessary that the definition and knowledge of energy should precede the definition and knowledge of capacity.

Energy is also prior in time to capacity in the same species. For that antecedes in time which effects the same thing in species, but not in number. But my meaning is this, that of this particular man who is now in energy, and of this corn, and this horse, and of that which sees, the matter, and the seed, and the visive power, are prior in time; these being in capacity, man, corn, and that which sees, but are not yet these in energy. But other things which are in energy, and from which these are generated, are prior to these in time. For always, from that which is in capacity, that which is in energy is generated, through that which is in energy. Thus, from man man is generated, from a musician a musician, something first always moving. But that which moves is now in energy. However, in what we have said concerning essence, we have shown that every thing which is generated is generated from something, and by something, and that this is the same in species. Hence it appears to be impossible that there should be a builder who has never built any thing, or a harper who has never played on the harp. For he who learns to play on the harp learns to play by playing on the harp; and the rest in a similar manner. Hence that sophistic argument originates, that some one not possessing science will produce a scientific effect. For he who learns does not possess science. But in answer to this we reply, that, of that which is in generation, or passing into existence, something is already generated; and, in short, of that which is in motion, something is moved, as we have demonstrated in our books concerning Motion. This being the case, it is perhaps also necessary that he who learns should possess something of science. And from this also it is evident that energy is thus prior to capacity, both according to generation and time.

It is likewise prior in essence. In the first place, because those things which are posterior in generation are prior in form and essence; as a man is prior both to a boy and seed: for the one now possesses form, but the other does not. And in the next place, because every thing which is generated proceeds to a principle and an end. For, that for the sake of which a thing subsists is the principle; but generation is for the sake of the end. And the end is energy; and power or capacity is received for the sake of this. For animals do not see in order that they may have sight; but they have sight in order that they may see. In like manner, men possess the capacity of building that they may build, and of contemplating that they may contemplate; but they do not contemplate that they may possess the power of contemplating, except those who meditate. These, however, do not perfectly contemplate; but they either contemplate in a certain respect, or they have no occasion for contemplation. Further still: matter is in capacity, because it may arrive at form. But when it is in energy, then it is in form; and a similar reasoning takes place in other things, and of which the end is motion. Hence, as teachers, when they exhibit their disciple energising, think that they have accomplished the end of teaching, this is also the case with nature. For, if it were not so, a circumstance like the Hermes of Paiso would take place; since it would be immanifest, whether science is internal or external, as was the case with his Hermes: for a work is the end, and energy is a work. Hence the word energy is denominated from work, and tends to entelecheia. But since the last of some things is the use, as of sight seeing, and no other work besides this is produced by the sight, but by certain things something else is produced, as by the building art, besides building, a house is produced; yet, nevertheless, energy will be the end of capacity in both these instances, though it is more the end of it in the latter than the former. For building is in that which is built, and at the same time is generated, and is with the house. Of such things, therefore, of which that which is generated is something besides the use, of these energy is in that which is made. Thus, for instance, building is in that which is built, and weaving in that which is woven; and in a similar manner in other things. And, in short, motion is in that which is in motion. But with respect to things of which there is no other work besides energy, in the things themselves energy subsists. Thus, seeing is in him who sees, and contemplation in him who contemplates, and life is in the soul. Hence felicity also is in the soul; for it is a certain life. So that it is evident that essence and form are each of them a certain energy. And according to this reasoning, it is also manifest that energy is prior in essence to capacity: and, as we have said, one energy always precedes another in time, as far as to the energy of that which first eternally moves.

Energy, indeed, is prior to capacity in a more principal and excellent manner. For things eternal are prior in essence to things corruptible; but nothing eternal is in capacity. The reason of which is as follows: Every power or capacity is at the same time a capacity of contradiction: for that which is not capable of subsisting will not subsist in any thing. But it is possible that every thing endued with capacity may not energise. Hence, that which is capable of being may both be and not be. The same thing, therefore, is capable both of subsisting and not subsisting. But that which is capable of not subsisting may not subsist. And that which may not subsist is corruptible, either simply, or it is not this very thing which it is said to be, either according to place, or according to quantity, or according to quality; but it is simply corruptible according to essence. No one, therefore, of things simply incorruptible is simply being in capacity. Nothing, however, hinders but that it may be so in a certain respect, either according to quality or place. Neither, therefore, things which are simply, nor things which have a necessary subsistence, are in capacity, but all these are in energy; and these are first natures: for, if these were not, nothing would be. Nor, again, if there is a certain motion which is perpetual, is such a motion in capacity. Nor, if that which is moved is perpetual, is it moved according to capacity, unless so far as it proceeds from this to that boundary. Nothing, however, hinders but that it may possess a capacity of this kind. Hence, if the sun, and stars, and all heaven, perpetually energise, there is no occasion to fear, as certain natural philosophers have feared, that they will ever stand still. For they are not wearied in accomplishing this; since their motion does not subsist about the capacity of contradiction (as is the case with corruptible natures), so as to render the continuity of their motion laborious. For an essence which is matter and capacity, and which does not subsist in energy, is the cause of this. But those natures which subsist in mutation, as, for instance, earth and fire, imitate incorruptible natures. For these too always energise; since they possess motion essentially, and in themselves. But all the other powers about which we have discoursed are conversant with contradiction. For that which is able to move in this particular manner is also able not so to move. I mean by the other powers, such as are rational: but the irrational powers will be conversant with contradiction, through being present, and not being present. If, therefore, there are certain natures or essences of such a kind as those who are skilled in disciplines assert ideas to be, some one will be much more knowing than science itself; and something will be much more moved than motion itself. For the former will be rather energies, but the latter are the capacities of the former. It is evident, therefore, that energy is prior both to capacity and to every mutable principle.

Aristotle, Metaphysics. Book 9, Chapter 9.

Frome hence also it is evident that energy is better and more truly excellent than capacity which is excellent. For, such things as are said to be capable are also capable of contraries. Thus, it is the same thing which is said to be capable of health and sickness, and at the same time. For there is the same capacity of acquiring health and sickness, rest and motion, and of building and destroying a house; and it is also the same capacity, by which a house may be built, and may be thrown down. The capacity, therefore, of effecting contraries subsists at the same time, but to effect contraries at the same time is impossible. It is also impossible that contrary energies should be present at one and the same time, as, for instance, to be well, and to be ill. So that it is necessary that one of these should be good. But to be capable is equally accommodated to both, or to neither. Energy, therefore, is the more excellent of the two.

In things evil, however, it is necessary that the end and energy should be worse than capacity: for it is the same thing which is capable of effecting both contraries.

It is evident, therefore, that evil is not any thing besides things themselves. For evil is by nature posterior to capacity. Hence, in things which subsist from the principle, and in eternal natures, there is neither evil, nor error, nor corruption. For corruption belongs to things evil. Diagrams also are found to be in energy; but they are found to be so by division. For if they were divided they would be manifest. But now they are inherent in capacity. Why has a triangle angles equal to two right? Because the angles which are about one point are equal to two right. If, therefore, the line about the side is produced, this will immediately become evident. Why universally is the angle in a semicircle a right angle? Because there are three equal lines; two into which the base is divided, and that which is raised upon it from the middle point. When this construction is seen by him who previously knew it, he will also immediately perceive that which follows from it. It is evident, therefore, that mathematical entities are in capacity, and that they are discovered when reduced into energy. But the cause of their being reduced into energy is this, that intellection is energy. So that capacity proceeds from energy: and on this account those who act know. For energy according to number is posterior in generation.

Aristotle, Metaphysics. Book 9, Chapter 10.

Since, therefore, being and also non-being are partly denominated according to the figures of the categories, and partly according to the capacity or energy of these, or contraries; and since that which is most principally being is true or false, and this in things themselves consists in composition or division; so that he asserts the truth, who is of opinion that a thing which is divided is divided, and that a thing which is a composite is a composite; but he speaks falsely who, either when things are, or when they are not, speaks of them in a manner contrary to that in which they subsist;—this being the case, let us consider what that is which is called true or false. For it is not that you are white because we truly think that you are white; but, because you are white, we who assert this, assert the truth. If, therefore, certain things are always composites, and cannot be divided, others are perpetually divided, and can never become composites, and some become the recipients of contraries: to be, indeed, is to be a composite and to be one thing; but not to be, is not to be a composite, and to be more than one. About things contingent, therefore, the same opinion and the same discourse become false and true; and it happens that at one time they are true and at another false. But about things which cannot subsist differently, the true is not at one time generated, and at another time the false, but these are always true and false.

With respect to incomposite natures, therefore, what is the being or non-being, what the true and the false of these?—For it is not any thing composite, so as to be, when it is joined together, and not to be, when it is divided; just as white wood, or the diameter of a square which is incommensurable with its side: nor will the true and the false be similarly inherent in things incomposite. Or shall we say, that as neither the true in these is the same, so neither is their being the same? But the one indeed is true, and the other false. For in these truth is obtained by contact and assertion. For affirmation and assertion are not the same. But not to pass into contact with them, is to be ignorant. For we cannot be deceived about the essence of a thing, unless by accident. And in a similar manner with respect to incomposite essences: for we cannot be deceived about these. All of them too are in energy, and not in capacity. For, if they were in capacity, they would be generated and corrupted: but now being itself is not subject either to generation or corruption. For it would be generated from something. But with respect to such things as are beings and in energy, about these it is not possible to be deceived, but they are either intellectually apprehended or not. But concerning these essence is investigated, whether it is, of such a kind or not.

Moreover, after one manner being is considered as true, and non-being as false; if it is a composite, as true, but if not a composite, false. But after another manner, if it thus subsists, it is; but if not thus, it is not. Truth consists in the intellectual apprehension of these; but the false is not deception but ignorance, though not an ignorance which resembles blindness. For blindness is just as if some one should be wholly deprived of the intellective power. It is evident also, that there will not be occasionally deception concerning things immoveable, if they are considered as immoveable. Thus, he who does not consider a triangle as mutable, will not think that at one time it has angles equal to two right, and that at another time it has not. For if this were the case it would be changed. But he may entertain this opinion of one thing, and not of another. Thus, for instance, he may think that no even number is a first number, or that some numbers are first numbers, and others are not. But he cannot entertain this opinion about one thing in number. For he will no longer think that it is now this thing, and at another time will be something else: but he will either assert that which is true or false concerning it, as of a thing which always subsists after this manner.

Aristotle, Metaphysics. Book 10, Chapter 1.

That the one is predicated multifariously was before observed by us, when we explained in how many ways every thing is denominated. But since it is manifoldly predicated, the modes of things primarily and essentially denominated one, are, when collected into one sum, four. For that which is continued either simply, or especially by nature, and not by contact, nor by a bond, is one. And that is more one and in a manner prior to these, of which the motion is more indivisible, and more simple. Further still: that is a thing of this kind and more so, which is a whole, and has a certain form and species; especially if there is a thing of this kind by nature and not by violence, (as things which are one through glue, or a nail, or a bond,) and which contains in itself the cause of its continuity. But it is a thing of this kind, through its motion being one, and indivisible in place and time. So that it is evident that, if any thing naturally possesses the principle of the first motion, it is the first magnitude; I mean, for instance, a circular motion; for this is the first of motions. Some things, therefore, are after this manner one, either as continued, or as a whole.

But some things are called one of which the definition is one. And things of this kind are those of which the intellection is one. But the intellection of that is indivisible, which is indivisible in species or number. That which ranks among particulars, therefore, is indivisible in number; but that is indivisible in species, which is indivisible in that which is known, and in science. Hence that will be the first one, which is the cause to essences of unity. In so many ways, therefore, is the one predicated, viz. that which is continuous by nature, a whole, particular, and universal. But all these are one; because of some the motion is indivisible, but of others the intellection, or the definition.

This, however, ought to be considered, that it is not the same thing to inquire what things are one, and what the essence and definition are of the one. For the one is predicated in so many ways, and each of these will be one, in which any one of these modes is inherent. But the essence of the one will sometimes accord with one of these, and sometimes with another, which is also nearer to the name: but those are one in capacity. Just as, if it were requisite to speak of element and cause, it would be necessary to distinguish the things, and to assign the definition of the name. For fire perhaps, or the infinite itself, or something else of this kind, in a certain respect is, and in a certain respect is not, an essential element. For there is not the same essence of fire and of an element; but so far as fire is a certain thing and nature, it is an element. But the name signifies that this particular thing happens to it, because something subsists from this, as that which is primarily existent. And the like takes place with respect to cause and the one, and every thing else of this kind. Hence the essence of the one consists in being indivisible, viz. in being this particular thing, and inseparable either in place, or species, or the dianoetic part, or in that which is a whole and definite.

But the essence of the one especially consists in this, that it is the first measure of every genus, and principally of quantity. Hence also it appears to have acceded to other things. For that is a measure by which quantity is known. But quantity, so far as quantity, is known by the one, or number. And every number is known by the one. So, that every quantity, so far as quantity, is known by the one, and that by which it is first known is the one itself. And hence the one is the principle of number so far as number. Hence also, in other things, that is called a measure by which each particular is first known, and the measure of every thing is one, in length, in breadth, in depth, in gravity, and in celerity. For gravity and celerity are common in contraries: for each of these is twofold. Thus, for instance, that is heavy, which has any momentum whatever, and that which has an excess of momentum. That also is swift which has any motion whatever, and that which has an excess of motion. For there is a certain celerity of that which is slow, and gravity of that which is light. But in all these, that which is the measure and the principle is a certain one, and something indivisible. Thus, in lines, the measure of a foot is used as indivisible. For every where one certain measure and that which is indivisible are investigated. But this is the simple either in quantity or quality. Hence, where it appears that nothing is to be taken away or added, this is accurately the measure. Hence, too, the measure of number is the most accurate of all measures: for the monad is considered as every way indivisible. But in other things a measure of this kind is imitated. For, from a stadium and a talent, and always from that which is greater, more may be taken away than from that which is lesser. Wherefore that among sensibles which is first considered as indivisible, is by all men made the measure of things moist and dry, of weight and magnitude: and they then think that they know the quantity, when they know through this measure. Motion, too, is measured by a simple and the most rapid motion. For this has the shortest time. Hence, in astronomy, a one of this kind is the principle and the measure. For the motion of heaven is supposed to be equal and most swift, by which other motions are determined. In music, likewise, diesis is the measure, because it is the least sensible sound: and in voice a letter. And all these are a certain one; yet not so as that the one is something common to them, but in such a manner as we have before shown.

A measure, however, is not always one in number, but is sometimes more than one; as, for instance, two dieses, which are not understood according to the hearing, but in definitions. Voices also are many by which we measure; and a diameter is also measured by two things; and this is the case with a side, and with all magnitudes. And thus the measure of all things is the one; because we know those things from which essence consists, by making a division either according to quantity, or according to form. Hence the one is indivisible, because the first of every thing is indivisible; but every thing is not similarly indivisible, as, for instance, a foot and the monad. But the latter is in every respect indivisible, while the former is assumed indivisible with respect to sense, as we just now observed. For, perhaps every thing continued is divisible; but measure is always of a kindred nature. For magnitude is the measure of magnitudes and of individuals, length of length, breadth of breadth, sound of sounds, weight of weight, and monad of monads. For in this manner it is requisite to speak, and not to call number the measure of numbers. Though this would be necessary if measure is to be similarly assigned. But he who entertains this opinion does not think similarly, but just as if he should think that monads are the measure of monads, and not the monad. However, number is a multitude of monads: and on the same account we say that science is the measure of things, and also sense, because we know something through these; for they are measured rather than they measure. But it happens to us just as if, another measuring us, we should know the quantity we contain, because he so many times applies to us a cubital measure. But Protagoras says that man is the measure of all things, just as if he had said that he who possesses scientific knowledge, or sensible perception, is a measure; and this because the one possesses sense and the other science, which we say are the measures of their subjects. Hence, though asserting nothing excellent, he appears to say something pertinent. That the essence of the one, therefore, consists in being a certain measure, and the most principal measure of quantity, and especially according to the nature by which it is distinguished from other things, and that it is, in the next place, the measure of quality, is evident. But a measure will be of one kind, which is indivisible according to quantity, and of another, which is indivisible according to quality. So that the one is indivisible either simply, or so far as it is one.

Aristotle, Metaphysics. Book 10, Chapter 2.

It is now requisite to inquire in what manner the one subsists with respect to its essence and nature, as in the doubts which we formerly made we discussed what the one is, and how we ought to conceive respecting it; whether the one itself is a certain essence, as the Pythagoreans formerly said, and Plato afterwards, or rather a certain nature is subjected to it; and how it ought to be considered after a manner more known, and whether the conceptions of natural philosophers concerning it are to be admitted. For, of these, one asserts that fire is the one, another air, and another the infinite. But if nothing of universals can be essence, as we have asserted in our discourse concerning essence and being, nor this very thing essence can be one certain thing separate from the many (for a thing of this kind is something common, and alone subsists as a predicate)—this being the case, it is evident that the one is not essence. For being and the one are the most of all things universally predicated. So that neither are genera certain natures and essences separable from other things; nor can the one be genus, through the same causes by which neither being nor essence is genus.

Further still: it is necessary that the like should take place in all things. But being and the one are predicated equally. Wherefore, since in qualities there is a certain one, and a certain nature, and in a similar manner in quantities, it is evident that what the one is, must, in short, be investigated, as also what being is; so that it is not sufficient to assert that this very thing is the nature of it. In colours also there is one colour, as, for instance, the white; afterwards, other colours appear to be generated from this and black. But black is a privation of white, in the same manner as darkness of light; for this is a privation of light. So that, if beings were colours, beings would be a certain number. But of what? Evidently of colours. And the one would be a certain one, as, for instance, the white. In like manner, if beings were melodies, they would indeed be a number, but out of diesis; but the essence of them would not be number; and the one would be something, the essence of which would not be the one, but diesis. In a similar manner too, with respect to sounds, if all beings were sounds, they would be the number of the elements, and the one would be a vocal element. And if beings were right-lined figures, they would be the number of figures, and the one would be a triangle: and there will be the same reasoning in the other genera. So that if in participated properties, in qualities, in quantities, and in motion, there are numbers, and there is a certain one in all these, number being the number of certain things, and the one a certain one, but this is not the essence of the one, it is necessary that the like should take place in essences. For this will similarly happen in all things. That the one, therefore, is a certain nature in every genus, and that this very thing the one is not the nature of any thing, is evident. But, as in colours we investigate one colour as the one, so in essence we investigate one essence as the one itself. Moreover, that in a certain respect the one and being signify the same is evident, from this, that the one equally follows the categories, and is not in any of them; as, for instance, it is neither in substance nor in quality, but subsists in a manner similar to being. It also follows from this, that in predication one man does not add any thing else besides man, as neither is being any thing besides substance, or quality, or quantity: and the being of the one is the same as the being of some individual thing.

Aristotle, Metaphysics. Book 10, Chapter 3.

The one and the many are opposed multifariously; according to one of which modes the one and multitude are opposed as indivisible and divisible. For that which is either divided or is divisible is called a certain multitude; but that which is indivisible or is not divided is called one. Since, therefore, oppositions are fourfold, and one of these is denominated according to privation, these indeed will be contraries, and will neither be denominated as contradiction nor as relatives. But the one is denominated and rendered apparent from its contrary, viz. the indivisible from the divisible, because multitude and the divisible are more manifest to sense than the indivisible. So that, through sense, multitude is prior in definition to the indivisible. But the same, the similar, and the equal are of the one, as we have shown in the division of contraries; but the different, the dissimilar, and the unequal, are of multitude. But since same is predicated multifariously, it is predicated in one way according to number, which we sometimes call itself; but in another way, if a thing is one in definition and number. Thus, for instance, you are one with yourself, both in form and matter.

Further still: those things are said to be the same, of the first essence of which there is one definition. Thus, equal right lines are the same, and equal and equal-angled quadrangular figures, though they are many in number; for in these equality is unity. But things are said to be similar, which are not indeed simply the same, nor without difference according to their subject essence, but yet are the same according to form. Thus, a greater square is similar to a lesser, and also unequal right lines. For these are indeed similar, but are not simply the same. But some things are called similar, if they have the same form, and in which though the more and the less are ingenerated, yet the things themselves are neither more nor less. Other things are so denominated, if there is the same passion and one in species. Thus, that which is very white and that which is less white are said to be similar, because the form of them is one. But some things are called similar, if they have more of the same things than of such as are different, either simply, or which are more obvious to sense. Thus, tin is more similar to silver than to gold; but gold is similar to fire, so far as it is yellow and ruddy. So that it is evident that the different and the dissimilar are denominated multifariously.

The different also and the same have an opposite mode of subsistence. Hence, every thing with relation to every thing is either the same or different. But that is said to take place, if the matter and definition are not one. Hence, you, and that which is next to you, are different. But the third signification of the similar is when things subsist as in mathematical species. All such things, therefore, as are denominated one and being, are, with reference to each other, different or the same. For there is not any contradiction of the same. Hence, it is not asserted of non-entities, but of all beings; but not the same is also predicated of beings. For same and different are naturally either one, or not one, which non-one is both being and one. Different, therefore, and same, are after this manner opposed. But difference is not the same with diversity. For it is not necessary that a thing which is another, and that with relation to which it is another, should be another by a common something. For every thing whatever which is a being is either the same or different. But that which is different from something is different by something. So that it is necessary that there should be something the same by which they differ. But this something the same is either genus or species: for every thing which differs, differs either in genus or species. And those things, indeed, differ in genus, of which neither the matter is common, nor the mutual generation; as, for instance, those things of which there is another figure of predication; but those things are different in species, of which there is the same genus. But genus is said to be that by which both the things that differ are called the same according to essence. So that contraries are things different, and contrariety is a certain difference. But that this is well asserted by us is evident from induction. For all things appear to differ, and not only to be diverse; but some are diverse in genus, and others in the same co-ordination of predication. So that they are in the same genus, and are the same in genus. But we have elsewhere shown what kind of things are the same or different in genus.

Aristotle, Metaphysics. Book 10, Chapter 4.

But since it happens that things which differ from each other differ more or less, there is a certain greatest difference, and this I call contrariety. And, that this is the greatest difference, is evident from induction. For things which differ in genus have not a way to each other, but are much distant, and cannot be compared together. But to things which differ in species the generations are from contraries, as from extremes. And the last interval is the greatest: so that the interval of contraries is the greatest. But the greatest in every genus is the perfect: for that is greatest which cannot be transcended; and that is perfect beyond which nothing can be assumed. For perfect difference has an end, just as other things from having an end are called perfect. But nothing is beyond the end: for this is the last in every thing, and comprehends that of which it is the end. Hence, nothing is beyond the end, nor is the perfect indigent of any thing. That contrariety, therefore, is perfect difference, is from hence evident.

But, since contraries are predicated multifariously, the perfect will follow in such a manner as accords with their subsistence as contraries. But, this being the case, it is evident that there cannot be many contraries to one thing. For neither will there be any thing more extreme than that which is last, nor of one interval will there be more than two extremes. And, in short, if contrariety is difference, but difference is the difference of two things, this will also be the case with perfect difference. But it is necessary that the other definitions also of contraries should be true: for perfect difference differs in the greatest degree. For we have shown that of things which differ in genus and species, nothing external can be assumed, since there is no difference with respect to things beyond genus; but of these this is the greatest. And things which being in the same genus differ in the greatest degree, are contraries. For the greatest difference of these is that which is perfect. Things also which being in the same recipient differ in the greatest degree, are contraries: for the same matter is the subject of contraries. And, likewise, those things are contraries, which differ in the greatest degree under the same power. For one science is conversant with one genus of things in which perfect difference is the greatest. But the first contrariety is habit and privation; yet not every privation (for privation is predicated multifariously), but such as is perfect. But other contraries are denominated according to these; some from possessing; some from acting, or being effective; and some, because they receive or reject these or other contrarieties. But if contradiction, privation, contrariety, and relatives are opposed; but of these contradiction is the first, and of contradiction there is no medium, but there is of contraries, it is evident that contradiction and contrariety are not the same. But privation is a certain contradiction: for, either there is a privation of that which cannot by any means be possessed, or of that which, when it is naturally adapted to be possessed, is not possessed; and this either altogether, or in some definite manner. For we speak of this multifariously, as we have elsewhere shown. So that privation is a certain contradiction, or a definite impotency, or comprehended together with its recipient. Hence there is no medium of contradiction, but there is a certain medium of privation. For every thing is either equal or not equal, but not every thing is equal or unequal, except alone in that which is the recipient of the equal. If, therefore, generations are in matter from contraries, but they are produced from form and the habit of form, or from a certain privation of species and form, it is evident that every contrariety will be a certain privation, but not every privation perhaps is contrariety. But the cause of this is, that whatever suffers a privation of any thing, may suffer this privation in a manifold respect. For those things are contraries from the extremities of which mutations are produced. This also is evident from induction. For every contrariety has a privation of the other of contraries; but not all things in a similar manner. For inequality is a privation of equality, dissimilitude of similitude, and virtue of vice. But there is a difference, as we have already observed: for one thing is said to suffer privation, if it is alone deprived of something; but another, if it does not possess when it is naturally adapted to possess, as in a certain age, or in that which is principal, or altogether. Hence, of some contraries there is a medium, and a man is neither good nor bad; but of others there is not a medium, but it is necessary that a number should be even or odd. Further still: some things have a definite subject, and others have not. So that it is evident that the other of contraries is always denominated according to privation. But it is sufficient if first natures and the genera of contraries, as, for instance, the one and the many, are so denominated. For other things are referred to these.

Aristotle, Metaphysics. Book 10, Chapter 5.

But since one thing is contrary to one, it may be doubted how the one and the many are opposed, and how the equal is opposed to the great and the small. For we always speak of the whether in opposition; as, for instance, whether a thing is white or black; and whether it is white or not white. But we do not say whether it is man or white, unless from hypothesis, and when investigating, as, whether Cleon came or Socrates. This inquiry, however, is not necessary in any genus. For opposites alone cannot subsist together, as is evident in this inquiry which of the two came. For, if it were possible for both to have come, the interrogation would be ridiculous. But if this were possible, he who makes the inquiry falls into opposition, viz. into the one and the many; as, for instance, whether both came, or one of the two. But if the inquiry respecting the whether is always in opposites (but it is said whether a thing is greater, or lesser, or equal)—what is the opposition with respect to these of the equal? For it is not alone contrary to one of them, nor to both. For why is it rather contrary to the greater than the lesser? Further still: the equal is contrary to the unequal; so that it will be contrary to more than one. But, if the unequal signifies the same thing with both these together, it will indeed be opposite to both; and the doubt will assist those who say that the unequal is the duad. It happens, however, that one will be contrary to two; which is impossible.

Again: the equal appears to be a medium between the great and the small; but contrariety neither appears to be a medium, nor, from the definition of it, is it possible that it should. For it would not be perfect, if it was the medium of any thing, but rather it always has some medium with respect to itself. It remains, therefore, that the equal must either be opposed as negation or as privation. But it is not possible that it can be alone opposed to the great or to the small. For why should it be rather opposed to the great than to the small? Negation, therefore, is privative of both. Hence, the whether is predicated with respect to both, but not with respect to either. Thus we do not say, whether is it equal or greater? or, whether is it equal or less? But the whether is always asserted with reference to three things. It is not, however, privation from necessity: for it does not follow that every thing is equal which is not greater or lesser; but this takes place in things in which the greater and the lesser are naturally inherent. The equal, therefore, is that which is neither great nor small, but which is naturally adapted to become great or small; and it is opposed to both, as negative privation. Hence it is a medium. That also which is neither evil nor good is opposed to both, but is nameless. For each is predicated multifariously; and that which is the recipient is not one thing, but rather that which is neither white nor black; though neither is this called one thing. But colours are in a certain respect definite, of which this negation is privatively predicated. For it is necessary that this negation should be brown, or pallid, or something else of this kind. Hence, they are not rightly reproved who think that all things are similarly denominated; so that, between a shoe and a hand, the medium is that which is neither a shoe nor a hand, since also that which is neither good nor evil is the medium between good and evil, as if, with respect to all things, there would be a certain medium. It is not, however, necessary that this should happen. For this co-negation of opposites is of things which are naturally adapted to have a certain medium, and a certain interval. But with respect to these there is no difference: for those things are in another genus, of which these were co-negations; so that the subject of them is not one.

Aristotle, Metaphysics. Book 10, Chapter 6.

In a similar manner, also, some one may doubt respecting the one and the many. For, if the many are simply opposed to the one, certain impossible consequences will happen; for it will either be a small multitude, or small multitudes, since the many is also opposed to the few. Besides, two things are many, since the double is multiplex; and thus also two is called double. So that the one is few. For, with relation to what are two things many, unless with relation to the one and the few? For nothing else appears to be less. Further still: what the long and the short are in length, that the much and the few are in multitude, and whatever is much is also many, and the many is much. Unless, therefore, something intervenes in continued indefinite quantity, the few will be a certain multitude. So that the one is a certain multitude, if it is the few. But this is necessary if two things are many. Perhaps, however, the many is denominated in the same manner as the much, yet as differing, as water which is much, but not many. But with respect to such things as are divisible, in these the many subsists, according to one mode, if the multitude has a transcendency either simply or relatively; and in a similar manner the few, when the multitude is deficient. But, according to another mode, the many subsists as number, which is alone opposed to the one. For thus we speak of the one or the many; just as if some one should say one and ones, or white and things white, and things measured with respect to measure, and that which is measured. Thus, also, things which are manifold are called many: for every number is many, because it is one many, and because each is measurable by one, and is as that which is opposed to the one, and not to the few. After this manner, therefore, two things also are many; but as having transcendent multitude, or as relatives, or simply considered, they are not many; but two is the first multitude in numbers. Two is, however, simply few; for it is the first multitude having a defect. Hence, Anaxagoras did not speak rightly in asserting, that all things subsisted together, and were infinite in multitude and smallness: for, instead of smallness, he ought to have said in fewness. For the few is not infinite; since it does not subsist through the one, as some say, but through two. They are, therefore, after this manner opposed. But the one and the many are opposed in numbers, and the one is opposed to the many, as measure to that which is measured. And these are opposed as relatives, which have not an essential subsistence. But we have elsewhere shown that relatives are denominated in a twofold respect. For some things are so called as contraries, others as science to the object of science, because something else is predicated with respect to it. Nothing, however, hinders but that the one may be less than a certain thing; as, for instance, than two. For it does not follow, that if it is less, it is also few. But multitude is as it were the genus of number. For number is multitude, which may be measured by the one. And the one and number are in a certain respect opposed, not as contraries, but, as we have said, in the same manner as certain relatives. For, so far as the one is a measure, but number measurable, so far they are opposed to each other. Hence, not every thing which is one is number, as, for instance, if there is any thing indivisible. But, though science is in a similar manner denominated with respect to the object of science, yet it is not similarly attributed: for science may appear to be a measure, but the object of science that which is measured. But it happens that every science is the object of scientific knowledge, though not every thing which may be scientifically known is science, because in a certain respect science is measured by the object of scientific knowledge. Moreover, neither is multitude contrary to the few; but to this the much is opposed, in the same manner as multitude which transcends is opposed to the multitude which is transcended; nor is multitude altogether contrary to the one. But with respect to the one, as we have said, one kind is divisible, and another indivisible, which subsists as a relative, just as science with respect to the object of science, if science were number: but the one is a measure.

Aristotle, Metaphysics. Book 10, Chapter 7.

But since it happens that between contraries there is a certain medium, it is necessary that the media should derive their subsistence from contraries. For all media, and the things of which they are media, are in the same genus. For we call those things media into which that which is changed is necessarily first changed. Thus, he who passes from the hypate to the nete, if the transition is made in a short time, will first arrive at the sounds which subsist between. And in colours, if any one passes from white to black, he will arrive at the red and the brown before he arrives at the black. And in a similar manner in other things. But a transmutation from one genus to another cannot take place, except from accident; as, for instance, from colour to figure. It is necessary, therefore, that media and the things of which they are media should be in the same genus. But all media are the media of certain opposites; for, from these alone essential mutation subsists. Hence, it is impossible that there should be any medium between things which are not opposites; for otherwise there would be a mutation from things not opposed. But in opposites there is no medium of contradiction. For contradiction is antithesis, and an opposition of which one of the parts is present, without having any medium. But, of the rest, some are relatives, others are privation, and others are contraries. And of those which are relatives, such as are not contraries have not a medium; and this because they are not in the same genus. For, what is there between science and the object of science? There is, however, a medium between the great and the small. But if media are in the same genus, as we have shown, and are media of contraries, it is necessary that they also should be composed from these contraries. For, either there is a certain genus of them, or none. And if there is a genus, and it subsists in such a manner that something will be prior to contraries, those contrary differences will be prior which make contraries as species of genus; for species subsist from genus and differences. Thus, if white and black are contraries, and the one is a segregative but the other a congregative colour, these very differences themselves, the segregative and the congregative, will have a prior subsistence. So that these contraries are prior to each other. But contraries which are differences are more contraries. The rest also, and the media, will consist from genus and differences. Thus, it is requisite that whatever colours are between white and black should be said to consist from genus (but colour is a genus) and certain differences. But these will not be the first contraries; for otherwise each will be black or white. There are, therefore, other colours. And hence these colours will be the media of first contraries. But the first differences are the segregative and the congregative. So that the first thing to be investigated with respect to such contraries as are not in genus is this, from what the media of them consist. For it is necessary that things in the same genus should be either composed from things incomposite in genus, or should be incomposites. Contraries, therefore, are not composed from each other; and hence they are principles. But media are either all things or nothing. From contraries, too, something is generated. So that, before there is a mutation into contraries, there will be a mutation into this: for of each there will be the more and the less. There will therefore be a medium, and this will be the medium of contraries. Hence, all other media are composites. For that which is more than one thing and less than another, is in a certain respect composed from those things of which it is said to be more and less. But since of contraries other things which are prior are not of the same kind, all media will be from contraries. So that all inferiors, and contraries, and media will be from first contraries. That all media, therefore, are in the same genus, and that they are media of contraries, and are composed from contraries, is evident.

Aristotle, Metaphysics. Book 10, Chapter 8.

But that which is different in species is different from something, and it is necessary that this should subsist in both differentes. Thus, if animal is different in species, both will be animals. It is necessary, therefore, that things which are different in species should be in the same genus. But I mean a genus of that kind, by which both are called one and the same, not possessing difference from accident, whether it subsists as matter, or as something different from matter. For it is not only requisite that a common something should be present, as, for instance, that both should be animals, but, that this very animal itself should be different from either, as that the one should be horse, and the other man. Hence, this something common belongs to things different from each other in species. And hence, too, this will be such a particular animal essentially, and that an animal essentially different; as, for instance, that will be a horse, and this a man. It is necessary, therefore, that this difference should be a diversity of genus. But I call that difference of genus diversity, which makes this very thing to be different. Hence this will be contrariety. And this is evident from induction: for all things are divided by opposites; and it has been shown that contraries are in the same genus. For contrariety is perfect difference. But every difference which is in species is something belonging to a certain thing. So that this is the same, and is genus in both. Hence all contraries are in the same co-ordination of predication, which differ in species and not in genus, and are especially different from each other. For the difference between them is perfect, and they are not at the same time generated together. Difference, therefore, is contrariety. For this is to be different in species, viz. for things which are individuals, when they are in the same genus, to possess contrariety. But things are the same in species, which subsisting as individuals have not contrariety. For in division and in media contrarieties are produced, before we arrive at individuals. So that it is evident that none of those things which accord as species of genus, is, with respect to that which is called genus, either the same, or different in species. For matter is rendered manifest by negation; and genus is the matter of that of which it is said to be the genus; not, however, as the genus of the Heraclidae, but as that which subsists in nature. Nor is genus denominated from things which are not in the same genus, but which differ in genus from them. But things differing in species differ from those in the same genus. For it is necessary that contrariety should be the difference of that from which it differs in species. But contrariety alone subsists in things which are in the same genus.

Aristotle, Metaphysics. Book 10, Chapter 9.

Some one, however, may doubt why woman does not differ in species from man, since the male and female are contraries, and contrariety is difference. But neither are male and female animals different in species, though these are the essential differences of animal, and are not as whiteness or blackness, but are inherent in animal so far as it is animal. The following doubt likewise is nearly the same with this, viz. Why, with respect to contrariety, one kind makes things different in species, and another does not: as, for instance, why it makes that which is capable of walking and that which is winged, but does not make whiteness and blackness. Shall we say it is because some things are the proper passions of genus, but others are not? And since one thing is reason or form, but another matter, such contrarieties as are in form produce difference in species; but such as are in that which is assumed together with matter do not produce specific difference. Hence, neither whiteness nor blackness makes man, because these are not the specific differences of a white and black man, though one name should be assigned to both. For man is as matter; but matter does not produce difference: for man is not man from the matter, but from the form of man. Hence, though the flesh and bones from which this and that man consist are different, yet the entire whole is different indeed, but is not different in species, because there is no contrariety in reason or form. But this entire whole is an individual; and Callias is form in conjunction with matter. This is likewise the case with a white man, because Callias is white. Man, therefore, is white according to accident. Nor do a brazen and wooden circle, nor a brazen triangle and wooden circle, differ in species through matter, but because there is contrariety in the form. But whether shall we say, that matter does not make things different in species, though in a certain respect it is itself different, or that it partly does? For, why is this horse different in species from this man, since the forms of these subsist together with matter? Shall we say it is because contrariety is inherent in form? for there is a specific difference between a white man and a black horse, but not so far as the one is white and the other black; since, even if both were white, they would in a similar manner be specifically different. But the masculine and the feminine are the proper passions of animal, yet not according to essence, but in matter and body. Hence the same seed, in consequence of suffering a certain passion, becomes either female or male. And thus we have shown what it is to be different in species, and why some things are specifically different, and others are not.

Aristotle, Metaphysics. Book 10, Chapter 10.

But since contraries are different in species, and the corruptible and the incorruptible are contraries (for privation is definite impotency), hence the corruptible and incorruptible must necessarily be generically different from each other. We have now, therefore, already spoken concerning these universal appellations. In consequence of this, it may seem not to be necessary that the corruptible and incorruptible should be different in species, as neither are white and black. For it would happen that the same thing would be both corruptible and incorruptible, if any thing of universals subsists, just as man will be black and white; and after the same manner as it happens in particulars, that one and the same man is white and black successively, and not at once; though white is contrary to black. But, of contraries, some are inherent in certain things according to accident, such, for instance, as the particulars which have been just now mentioned, and many others; but in other things this is impossible, among which are the corruptible and incorruptible. For nothing is corruptible according to accident. For accident may happen not to be; but the corruptible is of things which necessarily subsist in the particulars in which it is inherent. Or the corruptible and incorruptible will be one and the same, if it is possible that the corruptible may not subsist. It is necessary, therefore, that the corruptible must subsist in each of the things which are corruptible, either essentially or in the essence of each. The same reasoning also applies to that which is incorruptible: for both are of things which have a necessary subsistence. So far, therefore, as one is primarily corruptible and the other primarily incorruptible, so far they are opposed to each other; so that they are necessarily generically different. Hence it is evident that there cannot be such forms as some assert there are. For, with respect to man, one will be corruptible and another incorruptible, though forms are said to be the same in species with particulars, and not with respect to them equivocal. But things generically different are more distant from each other than such as are specifically different.

Aristotle, Metaphysics. Book 11, Chapter 1.

That wisdom, therefore, is a certain science concerning principles, is evident from the first books, in which we doubted against the assertions of others respecting principles. But some one may doubt whether it is requisite to consider wisdom as one science, or as many sciences. For, if it is one science, there is always one science of contraries. But principles are not contraries. And if there is not one, of what kind are these many sciences? Further still: is it the province of one, or of many sciences, to contemplate demonstrative principles? For, if of one, why is it the province of this more than of any other? And if of many, of what kind are these many? Again: whether is there one science of all essences, or not? For, if not of all, it will be difficult to show what kind of essences those are of which there is one science. But if there is one science of all, it is immanifest how it happens that there is the same science of many essences. And further still: whether is demonstration conversant with essences alone, or also with accidents? For, if with accidents, it is not conversant with essences. But if there is one science of essences and another of accidents, what is the characteristic of each, and which of the two is wisdom? For demonstrative wisdom is conversant with accidents; but the wisdom which considers first principles is conversant with essences. But neither must the science which we investigate be established about the causes which we have mentioned in our Physics; nor about that cause for the sake of which other things subsist. For a thing of this kind is the good; but this subsists in practical things, and in things which are in motion. And this first moves: for the end is a thing of this kind. But in things immoveable there is not that which first moves. And, in short, it is dubious whether the science which is now investigated is conversant with sensible essences, or not with these, but with certain others. For, if with certain others, it will either be conversant with forms or mathematical species. But that forms are not is manifest. And at the same time, though any one should admit that they do subsist, it will be dubious why the like does not take place in other things of which there are forms, as in mathematical entities. But I say, that they place mathematical entities between forms and sensibles, as certain third natures, besides forms, and things which are here. However, there is not a third man, nor a third horse, besides man itself and horse itself and particulars. But if they are not as they say, about what kind of things must the mathematician be considered as conversant? For it cannot be with things which are here; since none of these are such as the mathematical sciences investigate; nor, indeed, is the science which we now investigate conversant with mathematical entities. For none of these has a separate subsistence. Nor yet is it conversant with sensible essences; for these are corruptible. And, in short, it is dubious to what kind of science it belongs to doubt concerning the matter of mathematical entities. For neither can it be the physical science, because the whole employment of physics is about those things which contain in themselves the principle of motion and rest. Nor yet that which is conversant with demonstration and science; for it makes this very genus itself the object of its investigation. It remains, therefore, that the first philosophy must make these the object of its speculation. Some one, however, may doubt whether it is requisite to establish the science which we now investigate, as conversant with those principles which are called by some elements. But these are considered by all men as inherent in composite natures. However, it will rather appear that the science which we investigate, ought to be conversant with universals. For every reason and every science are employed about universals, and not about the last of things; so that thus this science will be conversant with first genera. But these will be being and the one. For these are especially considered as comprehending all beings, and as in the most eminent degree assimilated to principles, because they rank as things first by nature. For, these being corrupted, other things also are at the same time destroyed: for every thing is being and one. But so far as it is necessary that differences should participate of these, if any one admits the subsistence of these genera, since no difference participates of genus, so far it will not appear necessary to establish these either as genera or principles. Further still: if that which is more simple is more a principle than that which is less simple; but the last of things which proceed from genus are more simple than genera; for they are indivisibles; but genera are divided into many species and differences;—hence species will appear to be more principles than genera. But so far as species are taken away together with genera, genera will appear to be more similar to principles. For that is a principle which takes away other things together with itself. These, therefore, and other such-like particulars, are the things which are dubious.

Aristotle, Metaphysics. Book 11, Chapter 2.

Further still: it may be doubted whether it is necessary that something besides particulars should be admitted or not, since the science which we now investigate is conversant with these. These, however, are infinite: and things which have a subsistence besides particulars, are either genera or species. But the science which is at present investigated is not the science of either of these. And why this is impossible we have already shown. For, in short, it is dubious, whether a certain essence separate from sensible essences, and things which are here, ought to be admitted or not. Or shall we say that sensibles are beings, and that wisdom is conversant with these? We appear, however, to investigate a different essence; and this essence is the object of our present investigation. I say, it seems that we inquire, if there is any thing essentially separate, and which does not subsist in any sensible nature.

Again: if there is another certain essence besides sensible essences, what kind of sensibles are they, besides which it is requisite to establish this essence? For, why should any one admit that it subsists besides men, rather than besides horses, or other animals, or, in short, than things inanimate? But, indeed, he who devises other eternal natures equal to sensible and corruptible essences would appear to fall beyond the boundaries of reason. However, if the principle which is now investigated is not separate from bodies, what else can any one admit rather than matter? But this has not a subsistence in energy, but in capacity. Species, therefore, and forms will appear rather than this to be the most proper and powerful principle. But this also is corruptible: so that, in short, there is not an eternal essence separate, and subsisting by itself. This, however, is absurd: for it appears that there is such an essence; and a certain principle and essence of this kind is investigated by men of the most elegant minds. For, how will there be order, if nothing eternal, separate, and permanent subsists? Again: if there is a certain essence and principle, naturally such, as we are now investigating, and this is one principle of all things, and the same is the principle of things eternal and corruptible, it is dubious why, since there is the same principle, some things under this principle are eternal, and others are not eternal. For this is absurd: but if there is one principle of things corruptible, and another of things eternal, if the principle of things corruptible is also eternal, a similar doubt will arise. For why, since the principle is eternal, are not the things which subsist under this principle eternal? But, this principle being corruptible, there will be some other principle of this principle, and again another of this, and this will be the case ad infinitum. If, again, any one admits the subsistence of being and the one, which especially appear to be immoveable principles, in the first place, unless each of them signifies this particular definite thing and essence, how will they be separate, and have an essential subsistence? But we investigate such-like eternal and first principles; and if each of them signifies this particular thing and essence, all things will be essences: for being is predicated of all things, and of some things the one. But that all things are essences is false.

Again: how can that which is asserted by some be true, viz. that the first principle is the one, and that this is essence, and that from the one and matter the first number is generated, which is essence? For, in what manner is it requisite to understand as one, the duad, and each of the other composite numbers? For they neither say any thing, nor indeed is it easy to speak concerning this. But if any one establishes lines as first principles, or the things consequent to these (I mean superficies), these are not separate essences, but are sections and divisions, the former of superficies, and the latter of bodies; but points are sections and divisions of lines: and besides this, they are the boundaries of these very same things. But all these have a subsistence in others, and no one of them is separate. Further still: in what manner ought we to conceive the essence of the one, and of a point? For, of every essence there is a generation, but there is not of a point. For a point is division. This also is an occasion of doubt, that every science is of things universal, and of that which is of this kind; but essence is not of universals, but is rather this particular definite thing, and has a separate subsistence. So that if science is conversant with principles, in what manner ought we to conceive that essence is the principle of things?

Again: whether is there any thing besides the whole, or not? But I mean matter, and that which subsists together with this. For, if there is not, every thing in matter is corruptible. But if there is any thing besides, it will be species and form. It is difficult, therefore, to determine in what things this subsists, and in what it does not. For, in some things it is evident that there is not a separate form, as, for instance, in a house. Likewise, whether are principles the same in species, or in number? For, if they are one in number, all things will be the same.

Aristotle, Metaphysics. Book 11, Chapter 3.

Since, however, the science of the philosopher is conversant with being so far as being, and this universally, and not according to a part, but being is predicated multifariously, and not according to one mode;—this being the case, if being is predicated equivocally, and not according to any thing common, it is not under one science. For there is not one genus of things of this kind. But if it is predicated according to any thing common, it will be under one science. It seems, therefore, that it is predicated after the same manner as that which is medicinal, and that which is salubrious. For each of these is predicated multifariously. But each of them is predicated after this manner, because this is in a certain respect referred to the medicinal art, but that to health; and again something else is referred in a different respect, but each is referred to the same. For a medicinal discourse and a little knife are predicated; the former because it proceeds from the medicinal science, and the latter, because it is useful to this science. The salubrious, too, in a similar manner is partly so denominated because it is significant, and partly because it is effective of health. And there is the same mode with respect to the rest. After the same manner, likewise, all beings are predicated: for each of them is called being, because it is either a passion, or habit, or disposition, or motion, or something else of this kind, of being so far as being.

But as there is a reduction of every being to a certain one, and something common, so of contraries each is reduced to the first differences and contrarieties of being, whether multitude and the one, or similitude and dissimilitude are the first differences of being, or certain other things: for let these be the subject of future speculation. There is, however, no difference, whether the reduction of being is made to being or to the one. For, if they are not the same but different, yet they are converted: for the one is also in a certain respect being; and being is the one. But since it is the province of one and the same science to speculate all contraries, and each of these is predicated according to privation (though respecting some things of which there is a certain medium, as of the unjust and the just, it may be doubted how they are predicated according to privation), this being the case, about all these, it is requisite to place privation, not of the whole definition, but of the last species; as, if he is a just man who obeys the laws according to habit, he who is unjust will not be altogether deprived of the definition of the just man. However, as he is in a certain respect deficient as to obedience to the laws, in this respect a privation of this definition will be inherent in him. And the like reasoning will take place in other things. But, as the mathematician speculates from abstraction (for he contemplates by abstracting all sensible natures, as, for instance, gravity and levity, hardness and its contrary, and, besides these, heat and cold, and other sensible contrarieties), but alone leaves quantity and the continuous, of which some pertain to one, others to two, and others to three, and the participated properties of these so far as they are quantities and continuous, and does not speculate them according to any thing else: and of some, indeed, he contemplates the natures and positions with reference to each other, and the things which are inherent in these, but of others the commensurations and incommensurations, and of others again the ratios, yet at the same time we establish one and the same geometrical science of all these,—the like also takes place with respect to being; since, to contemplate the accidents to this so far as it is being, and its contrarieties so far as it is being, is the business of no other science than philosophy. For some one may attribute to the physical science the speculation of these, not so far as they are beings, but rather so far as they participate of motion. But the dialectic and sophistic sciences are conversant indeed with the accidents of beings, but not so far as they are beings, nor do they speculate being so far as being. It remains, therefore, that the philosopher contemplates the things we have just mentioned, so far as they are beings. But since every being is predicated according to a certain one, and something common which is multifariously denominated, and after the same manner contraries (for they are referred to the first contrarieties and differences of being); and also, since it is possible that things of this kind may be under one science, hence the doubt which was mentioned in the beginning is solved: I mean the doubt, how there will be one science of many things which are generically different.

Aristotle, Metaphysics. Book 11, Chapter 4.

But since the mathematician uses things common in an accommodated manner, to speculate also the principles of these things will be the business of the first philosophy. For that, when equal things are taken away from things equal, the remainders are equal, is common to all quantities. But the mathematical science receiving this speculates about a certain part of its proper matter; as, for instance, about lines, or angles, or numbers, or something pertaining to other quantities; not, however, so far as they are beings, but so far as each of them is continuous in one, or two, or three dimensions. Philosophy, however, does not make particulars the objects of its speculation so far as something is accidental to each of these; but it contemplates every thing of this kind about being, so far as it is being. And after the same manner the first philosophy speculates about the physical science: for the physical science contemplates accidents, and the principles of beings, so far as they are in motion, and not so far as they are beings. But we have said, that the first science is employed about these, so far as the subjects of them are beings, and not so far as they are any thing else. Hence this and the mathematical science must be considered as parts of wisdom.

Aristotle, Metaphysics. Book 11, Chapter 5.

There is, however, in beings a certain principle, about which we cannot speak falsely; but it is always necessary to do the contrary to this, I mean, to speak conformably to truth; as, for instance, that it is not possible for the same thing, at one and the same time, to be and not to be, and so of other things which are after this manner opposed. And concerning things of this kind, there is not indeed simply demonstration [but it is possible to confute him who affirms that contradiction can be at the same time true]. For it is not possible to syllogise concerning it from any principle more worthy of belief than this, which, however, would be necessary if it could simply be demonstrated. But to him who shows it is false, that opposite assertions are at the same time true, something of such a kind must be assumed, which, though it will be the same with that which cannot be and not be the same at one and the same time, yet will not appear to be the same with it. For thus alone a demonstration can be effected against him who contends that opposite assertions may be verified respecting the same thing. In the next place it must be assumed, that those who are about to discourse together ought to understand each other; for, unless this is effected, how will there be a mutual communication of discourse? It is requisite, therefore, that each of the appellations should be known, and should manifest one thing alone, and not many things; because, if it signifies many things, it is evident that the sense in which it is used must be explained. He, therefore, who says that this thing both is and is not, asserts that this is not, which he says is; so that he asserts that the name does not signify that which it does signify. But this is impossible. Hence, if there is any meaning in asserting that this thing signifies this thing, it is impossible that contradiction concerning the same thing can be verified. Again: if a name signifies any thing, and this is verified, it is requisite that this should be from necessity: but that which is from necessity cannot then not be. Opposite affirmations therefore and negations cannot be verified concerning the same thing. Further still: if affirmation is not more verified than negation, he who asserts that any one is a man, will not speak more truly than if he asserts that he is not a man. But it will appear that he who says man is not horse, speaks either more or not less truly than if he asserted that man is not man: so that he will speak truly in asserting that the same is a horse; because, according to this doctrine, opposite assertions are similarly true. It happens, therefore, that the same thing is man and horse, or some other animal. Hence, there is simply no demonstration of these things; but against him who makes these positions there is demonstration. Any one likewise may easily compel Heraclitus himself, if interrogated after this manner, to confess that opposite assertions cannot by any means be verified concerning the same thing: but now, not being conscious of what he said, he entertained this opinion. In short, if that which is asserted by him is true, neither will this be true, that it is possible for the same thing, at one and the same time, to be and not to be. For as when these assertions are divided, affirmation is not more true than negation, after the same manner when they are conjoined and united, and affirmation is considered as one thing, negation will not be more true than the whole assumed in affirmation. Further still: if nothing can be truly affirmed, this also will be false, to say that no affirmation is true. But if any affirmation is true, the assertion of those who oppose things of this kind, and who entirely subvert discourse, will be dissolved.

Aristotle, Metaphysics. Book 11, Chapter 6.

Similar also to what has been said is the assertion of Protagoras. For he said that man is the measure of all things; signifying by this nothing else than that whatever appears to every one is firmly that which it appears. If this however be admitted, it will happen that the same thing will both be and not be, and will be good and evil, and whatever else is said according to opposite assertions; because frequently this thing appears to some to be beautiful, and to others the contrary: but that which appears to every one is a measure. This doubt, however, will be solved, by contemplating whence this opinion derived its origin. For to some, indeed, it appears to have originated from physiologists; but to others, from all men not possessing the same knowledge about the same things: but to some this thing appears pleasant, and to others the contrary. For that nothing is generated from non-entity, but every thing from being, is nearly the common dogma of all physiologists. Since, therefore, from that which is perfectly white and by no means not white, that which is not white is generated; if now that which is not white is generated from that which is not white, according to their doctrine, it will be generated from non-entity; unless that which is not white and that which is white were the same.

It is not however difficult to dissolve this doubt. For it has been said by us in our Physics, how things which are generated are generated from non-entity; and how they are generated from being. And, indeed, to attend similarly to both the opinions and phantasies of those who oppose each other, is stupid: for it is evident that one of them must necessarily assert that which is false. This also is evident from the things which are effected according to sense: for the same thing never at any time appears to some to be sweet, and to others the contrary, when that organ which has the power of perceiving and judging the above-mentioned tastes is not corrupted and injured in the other of these. This being the case, some of these must be considered as a measure, and the others as not a measure. I also assert this in a similar manner of good and evil, of the beautiful and the base, and of other things of this kind. For to admit nothing but appearances does not in any respect differ from those who, by placing the finger under the eye, and causing two things to appear from one, should think that there are two, because there appears to be so many, and again, that there is one: for to those who do not move their sight, one thing appears to be one. In short, it is absurd, because things which are here appear to be changeable, and never abide in the same state, to form from this circumstance a judgment of truth: for it is requisite to investigate truth from things which always subsist according to the same, and never change. But of this kind are the natures which the world contains. For these do not appear to be different at different times, but they are always the same, and participate of no mutation.

Again: if there is motion, and something which is moved, but every thing which is moved is moved from something, and into something, it is necessary that a thing which is moved should still be in that from which it is moved, and yet should not be in it; and that it should be moved in this particular thing, and yet not be in it, or according to these men contradiction will not be verified. And if things which are here continually flow, and are moved according to quantity, and this is admitted by some one, although it is not true, why are they not permanent according to quality? For these men appear in no small degree to predicate contradictions of the same thing, in consequence of conceiving that quantity is not permanent in bodies. Hence, according to them, the same thing is and is not of four cubits. But essence is according to quality: for this is of a definite nature. But quantity partakes of the indefinite. Again: why, when the physician orders this particular food, do they take it? For why is this rather bread than not? So that it will be just the same thing to eat as not to eat. But now, because the physician asserts the truth respecting it, and this which they are ordered to take is food, they take it: they ought not, however, since no nature whatever among sensibles firmly abides, but all things are perpetually in motion, and perpetually flowing.

Further still: if we are perpetually changing, and never abide the same, is it wonderful, if things should never appear the same to us, in the same manner as it happens to the diseased? For to these, because their habit is not similarly disposed as when they are in health, things which present themselves to the senses do not appear in a similar manner; the sensible things themselves not partaking through this of any mutation, but producing different and not the same sensations in the diseased. It is therefore perhaps necessary that the same consequences should be produced in us, if the above-mentioned mutation takes place: but if we are not changed, but continue the same, there will be something permanent. Hence, it is not easy to confute the assertions of those who entertain these doubts from reasoning, when they do not admit something, and no longer require a reason to be given for these things: for after this manner all reasoning and demonstration subsist: for, by admitting nothing, they, in short, subvert disputation and discourse; so that no reasoning can be addressed to men of this kind. But, from the above-mentioned doubts, it is easy to reply to those who are dubious, and to dissolve the particulars which occasion them to doubt, as is evident from what has been said: so that from these things it is manifest that opposite assertions cannot be verified at one and the same time about the same thing, nor yet contraries; because these are denominated according to privation. But this will be evident, by analysing the definitions of contraries to their principle. And in a similar manner, neither can any medium be predicated of one and the same thing: for, if the subject is something white, by saying that it is neither black nor white we shall speak falsely; for it happens that it is, and yet is not white: for the other of the extremes will be verified concerning it; but this is a contradiction of the white. Neither, therefore, shall we assert that which is true, by speaking either like Heraclitus, or Anaxagoras; for, otherwise, it would happen that contraries would be predicated of the same thing: for, when Anaxagoras says that a part of every thing is in every thing, he says that a thing is not more sweet than bitter, or any one of the other contraries; if all things subsist in all, not only in capacity, but in energy, and separate from each other. In like manner, neither is it possible that all assertions can be false, nor all true; as well on account of many other difficulties which attend this position, as because, all assertions being false, neither when any one asserts that they are all false, will he speak the truth: and all assertions being true, he who says all are false will not speak falsely.

Aristotle, Metaphysics. Book 11, Chapter 7.

But every science investigates certain principles and causes about the respective objects of its knowledge; as, for instance, the medicinal and gymnastic, and each of the remaining effective or mathematical sciences. For each of these, circumscribing for itself a certain genus, is conversant with this as subsisting, and as being, yet not so far as it is being, but this is the province of another science, different from these sciences. But each of the above-mentioned sciences, receiving in a certain respect definition in each genus, endeavours to demonstrate what remains more negligently or more accurately: and they receive definition, some of them through sense, and others from hypothesis. Hence, from an induction of this kind, it is evident that there is no demonstration of essence and definition. Since, however, there is a certain science concerning nature, it is evident that it is different from the practic and effective sciences: for the principle of motion of the effective science is in that which makes, and not in that which is made; and this is either a certain art, or some other power. And in a similar manner in the practic science; motion is not in the thing which is done, but rather in the agents. But the physical science is conversant with things which contain in themselves the principle of motion. That the physical science, therefore, is neither practic nor effective, but is necessarily theoretic, is from these things evident: for it must necessarily fall into one of these genera.

Moreover, since it is necessary that each of the sciences should, in a certain respect, have a knowledge of definition, it is requisite not to be ignorant how the physical science is to be defined, and how the definition of essence is to be assumed; whether as the flat nose, or rather as the concave: for of these, in the definition of the flat nose, the matter of the thing is assumed; but the definition of the concave is without matter: for flatness is generated in the nose. Hence, the definition of it is contemplated together with this: for the flat nose is a hollow nose. It is evident, therefore, that the definition of flesh, of the eye, and of the other parts of the body, must always be assigned in conjunction with matter. But since there is a certain science of being so far as being, and so far as it is separate, we must consider whether it is to be admitted as the same with the physical science, or rather as different from it. The physical science, therefore, is conversant with those things which contain in themselves the principle of motion: but the mathematical science is speculative indeed, and about things which are permanent; but not separate from sensibles. There is therefore another science besides both these, which is conversant with separate and immoveable being, if an essence of this kind subsists: I say an essence separate and immoveable, the subsistence of which we shall endeavour to evince: and if there is an essence of this kind in beings, there also divinity will reside; and this will be the first and most powerful principle. It is evident, therefore, that there are three genera of contemplative sciences, the physical, the mathematical, and the theological. Hence, too, the genus of the contemplative sciences is the most excellent; and of these, that which was mentioned in the last place; for it is conversant with the most honorable of beings: for every science is called better or worse, according to the proper object of its knowledge. Some one, however, may doubt whether it is requisite to establish universally the science of being, so far as it is being, or not. For each of the mathematical sciences is employed about one certain definite genus; but the universal science speculates in common about all things. If, therefore, physical essences are the first of beings, the physical science also will be the first of sciences: but if there is another nature and essence separate and immoveable, it is also necessary that there should be another science of it, and that this should both be prior to the physical science, and universal because prior.

Aristotle, Metaphysics. Book 11, Chapter 8.

Since, however, being, simply considered, is predicated according to many modes, of which one is that which is said to subsist according to accident, let us in the first place speculate concerning being which thus subsists. That none of the sciences, therefore, which are delivered to us is conversant with accident is evident. For neither does the architectural art consider what will happen to those who are to use the house; as, for instance, whether they will inhabit it painfully, or the contrary: nor is accident the object of attention to the weaving, shoe-making, and cooking arts; but each of the sciences alone considers that which is essentially peculiar to itself; and this is its proper end. Nor does it consider any one so far as he is a musician and grammarian; nor assert that he who is a musician, if he should become a grammarian, will at the same time be both, though he was not before. But that which is not always, was generated; so that at the same time he becomes a musician and grammarian. This, however, none of those which are acknowledged to be sciences investigates, except the sophistic science; for this alone is conversant with accident. Hence, Plato does not speak badly when he says that the sophistic art is employed about non-entity. But, that it is not possible there can be a science of accident will be evident, if we endeavour to perceive what accident is. With respect to all things, therefore, some things are always, and from necessity; (I do not mean a necessity which is denominated according to violence, but that which we use in demonstrations) but others subsist as for the most part; and others neither subsist as for the most part, nor always, and from necessity, but as it happens. Thus, cold may be produced under the dog-star; but this will neither be produced as always from necessity, nor as for the most part. And thus we have shown what accident is.

But why there is not science of a thing of this kind is evident: for every science is of that which always is, or which is for the most part; but accident does not rank among either of these. It is also evident that there are not such like causes and principles of being according to accident, as there are of that which is essentially being: for, if this were the case, all things would be from necessity: for, if this thing is in consequence of that, and that in consequence of this, and this thing is not contingent, but from necessity, that also will be from necessity of which this was the cause, as far as to that which is called the last effect: but this was according to accident. Hence, all things will be from necessity; and to subsist casually after this or that manner, to be contingent, and to be generated, and not to be generated, will be taken away from generated natures. And although cause is supposed not to be being, but that which subsists in generation, or becoming to be, the same things will happen. For every thing will be generated from necessity. For to-morrow there will be an eclipse, if this particular thing takes place; but this will be effected if something else takes place, and this last if something else. And after this manner, if time is taken away from that definite time which is from the present instant till to-morrow, we shall at length arrive at that which exists. So that, since this is the case, all things after this will be generated from necessity; so that all things will be generated from necessity.

But, with respect to that which is truly being, and which does not subsist according to accident, one kind is that which subsists in the comprehension of the dianoetic power, and is a passion in this; and hence, causes are not investigated about that which is after this manner being, but about that which is being external to this, and has a separate subsistence. That, however, which subsists according to accident is not necessary, but indefinite. But of a thing of this kind the causes are inordinate and infinite; but that which subsists for the sake of something ranks among things generated by nature, or proceeds from the dianoetic power. And fortune then subsists when some one of these is produced according to accident: for, as with respect to being, one kind is essential, and another according to accident, so also with respect to cause. But fortune is a cause from accident in things which are produced according to free-will for the sake of something. Hence, fortune and the dianoetic power are conversant with the same thing: for free-will is not without the dianoetic power. But the causes are indefinite by which the things proceeding from fortune are produced. Hence, fortune is a thing immanifest to human reasoning, and a cause according to accident; but, simply, it is not the cause of any thing. Fortune, likewise, is good or evil, when any thing good or evil happens; but prosperous and adverse fortune subsist about the magnitude of these. But, since nothing which subsists according to accident is prior to things which have an essential subsistence, neither are accidental prior to essential causes. If, therefore, fortune, or that which is casual, is the cause of the universe, intellect and nature will be a prior cause.

Aristotle, Metaphysics. Book 11, Chapter 9.

Of things, some are in energy only, others in capacity, and others both in energy and capacity. And of these, one is substance, another quantity, and another some one of the rest. But there is not any motion besides things themselves: for that which is changed is always changed according to the categories of being. But in these there is nothing common in any predication. But every thing subsists in a twofold relation in all things. Thus, with respect to this particular thing, this is the form of it, and that its privation: and, according to quality, this is white and that black. Thus, too, according to quantity, this is perfect and that imperfect; and according to lation, this is upwards and that downwards, or this is light and that heavy. So that there are as many species of motion and mutation as there are of being. But since in every genus there is a division into capacity and energy, I call motion the energy of that which is in capacity, so far as it is in capacity. And that our assertion is true, is evident from hence: for, when there is that which may be built so far as it is a thing of this kind, we say that it is itself in energy so far as it is built; and this is building. In a similar manner with respect to mathesis, healing, rolling, walking, leaping, growing old, and becoming thick. But a thing happens to be moved when there is entelecheia itself, and when it is neither prior nor posterior to this. But the entelecheia of that which is in capacity, when being in entelecheia it energises, not so far as it is that which it is, but so far as it is moveable, is motion. My meaning is this: Brass is the statue in capacity; but at the same time the entelecheia of the brass, so far as brass, is not motion. For the essence of brass is not the same as the essence of a certain capacity; since, if it were simply the same according to definition, the entelecheia of the brass would be a certain motion. But it is not the same as is evident in contraries: for the capacity of becoming well, and the capacity of becoming ill, are not the same; for, if this were the case, to be well would be the same as to be ill. But the subject which is capable of being made well and ill, whether it be moisture, or whether it be blood, is one and the same. Since, therefore, the essence of a thing is not the same with the essence of a certain capacity, as neither is colour the same with that which is visible, motion is the entelecheia of that which is capable so far as it is capable. For that motion is, and that a thing happens to be moved, when it is itself entelecheia, and neither prior nor posterior to this, is evident. For it happens that every thing at one time energises, and at another time does not, as in that which is capable of being built, so far as it is capable of being built; and the energy of that which may be built, so far as it possesses this capacity, is building: for the energy of it is either building or the house. But when the house is the energy, it will no longer be capable of being built; and that which is capable of being built is built. Building, therefore, is necessarily an energy, and building is also a certain motion. There is likewise the same reasoning respecting other motions.

But the propriety of what we have now said is evident from the assertions of others concerning motion, and from its not being easy to define it in a different manner. For, neither can it be placed in any other genus. And this is evident from their assertions: for some of these say, that it is diversity and inequality, and non-being, none of which is necessarily moved. But, neither is mutation a change into these, nor from things of this kind rather than from their contraries. The reason, however, why they placed motion in these, is because motion appears to be something indefinite. But the principles of the other co-ordination, in consequence of being privative, are indefinite. For no one of them is either this particular thing, or a thing with a certain quality, or any one of the other predicaments. And motion appearing to be something indefinite, is the cause that it can neither be placed in the capacity nor in the energy of beings: for neither that which is capable of being quantity is moved from necessity, nor that which is quantity in energy. Motion, however, appears to be a certain energy, though this energy is imperfect. But the cause of this is, that the capable of which it is the energy is imperfect; and on this account it is difficult to comprehend what it is: For it is either necessary to place it in privation, or in capacity, or in simple energy. But it does not appear that it can be any one of these. It remains, therefore, that it must be what we have said, viz. both energy, and yet not simply energy; which is indeed a thing difficult to perceive, but yet is capable of subsisting. That motion also is in that which is moved is evident: for the entelecheia of this is from that which is motive; and the energy of that which is motive is no other than this. For it is necessary that there should be entelecheia in both: for that which is motive is motive from possessing the capacity of moving; and that which moves moves from energising: but it is energetic of that which is in motion. So that, in a similar manner, there is one energy of both, just as there is the same interval of one to two, and of two to one, and of ascent and descent, but the essence is not one. And the like takes place in the mover and the thing moved.

Aristotle, Metaphysics. Book 11, Chapter 10.

Infinite is either that which it is impossible to pass over, because it is not naturally adapted to be permeated, in the same manner as voice is invisible; or it is that which has a boundless passage, or that which scarcely, or which is naturally adapted to have, but has not, a passage or an end. Again: it either subsists from addition, or ablation, or from both. And, indeed, that infinite should be something separate and sensible is impossible. For, if it is neither magnitude nor multitude, but the infinite is the essence of it and not an accident, it will be indivisible. For that which is divisible is either magnitude or multitude. But if it is indivisible, it is not infinite, except in the same manner as voice is invisible. Neither, however, do they thus speak, nor do we thus investigate, but we consider it as impermeable. Further still: how is it possible how there can be the essentially infinite, if there is neither essential number nor magnitude, of which the infinite is a passion?

Again: if the infinite subsists according to accident, it will not be so far as infinite an element of things, as neither is the invisible an element of speech, though voice is invisible. And that the infinite is not in energy is evident: for any part whatever of it which is assumed will be infinite; since the essence of the infinite and the infinite are the same, if the infinite is essence, and does not subsist in a subject. So that it is either indivisible or divisible into infinites, if possible. But it is impossible that the same thing can be many infinites: for, as a part of air is air, so infinite is a part of infinite, if it is essence and a principle. It is, therefore, impartible and indivisible. But it is impossible that a thing which is in entelecheia should be infinite; for it must necessarily be quantity. Hence it subsists according to accident. But thus subsisting, we have shown that it cannot be a principle, but this must be asserted of that to which it happens, viz. number or the even. This inquiry, therefore, is universal.

But that the infinite is not in sensibles is evident from hence: for, if the definition of body is, that which is bounded by superficies, there will not be an infinite body either sensible or intelligible. But neither will it be number as separate and infinite: for number, or that which possesses number, is numerable. But, that the infinite is not in sensibles will be physically manifest from the following considerations: It can neither be any thing composite nor simple: for, if a composite, it will not be a body, if the elements are finite in multitude. For it is requisite that contraries should be equalised, and that one of them should not be infinite. For, if the power of the other body fails in any respect whatever, the finite will be corrupted by the infinite body. But that each of the elements should be infinite is impossible: for that is body which every way possesses interval; but that is infinite which has interval without end. So that, if there is an infinite body, it will be every way infinite. Nor yet is it possible that there can be one infinite simple body, nor, as some say, different from the elements, which according to them it generates. For there is not besides the elements a body of this kind; since all things are resolved into the natures from which they originate. But this does not appear to be, besides the simple bodies, either fire, or any other of the elements: for it is impossible, if it be admitted that the universe is finite, that the infinite can either be, or be generated from, some one of the elements, as Heraclitus said that all things were once fire. There is also the same reasoning respecting that one thing which the natural philosophers introduce besides the elements. For every thing changes from a contrary, as, for instance, from the hot into the cold.

Again: a sensible body is in a certain place; and there is the same place of the whole and the part, as, for instance, of the whole earth and one clod. So that, if the infinite is of similar parts, it will either be immoveable, or will always be impelled forward. But this is impossible: for, why should it be rather impelled downwards than upwards, or in any other direction? Thus, for instance, if it is a clod of earth, where will it be moved, or where will it abide? For the place naturally adapted to this body is infinite. It will, therefore, occupy the whole place. But after what manner? What, therefore, will be its rest, and what its motion? Shall we say that it will be every where at rest? It will not, therefore, be moved. Or shall we say that it is every where moved? It will not, therefore, abide. But if the universe is dissimilar, places also will be dissimilar, and in the first place the body of the universe will not be one, except by contact alone. In the next place, these things will either be finite or infinite in species. But that they should be finite is impossible. For some things will be infinite, and others not, if the universe is infinite; as, for instance, fire or water. But a thing of this kind is corruption to contraries. But if they are infinite and simple, places also will be infinite, and the elements will be infinite. However, if this is impossible, and places are finite, the universe also is necessarily finite. In short, it is impossible that there can be an infinite body, and at the same time a place for bodies, if every sensible body has either gravity or levity: for it will either be impelled to the middle, or upwards. But it is impossible that either the whole or the half, or any part whatever, of the infinite should be passive to any thing. For, how will you make a division? Or how of the infinite can one part be upwards and another downwards, or this the extremity, and that the middle?

Further still: every sensible body is in place; and of place there are six species: but it is impossible that these should subsist in an infinite body. And in short, if it is impossible that place can be infinite, it is also impossible that body can be infinite: for that which is in place is somewhere; but this signifies either upwards or downwards, or some one of the other differences of place: and each of these is a certain boundary. But the infinite is not the same in magnitude, motion, and time, as if it were one particular nature; but the posterior is denominated according to the prior. Thus, motion is denominated infinite, according to the magnitude upon which a thing is moved, or changed, or increased: but time is denominated according to motion.

Aristotle, Metaphysics. Book 11, Chapter 11.

Of things which are changed, one thing is changed according to accident; as when we say that the musician walks; but another thing is simply said to be changed, because something belonging to it is changed; as, for instance, such things as are changed according to parts: for the body is healed, because the eye is healed. There is also something which is of itself said to be moved; and this is that which is moveable from itself. There is a like distinction too in that which moves: for one thing moves according to accident; another thing according to a part; and another from itself, or essentially. There is also that which first moves; and there is something which is moved. There is besides the time in which, and from which, and with reference to which, a thing is moved: but the forms and passions, and place to which things in motion are moved, are immoveable; as, for instance, science and heat. Likewise not heat but calefaction is motion. But mutation, which is not according to accident, is not in all things, but is in contraries, and media, and in contradiction: and the credibility of this is derived from induction. That also which is changed, is either changed from a subject into a subject, or from a non-subject into a non-subject, or from a subject into a non-subject, [or from a non-subject into a subject]. But I mean by a subject, that which is manifested by affirmation. So that there are necessarily three mutations: for that which is from a non-subject into a non-subject is not mutation. For it is not between contraries, nor between contradictions, because, in passing from a non-subject to a non-subject, there is not opposition. Mutation, therefore, from a non-subject into a subject according to contradiction, is generation; and such a mutation when it is simple is a simple, but when partial a partial generation. But the mutation from a subject into a non-subject is corruption; which when it is simple is a simple, but when partial a partial corruption. If, therefore, non-being is predicated multifariously, and that which subsists according to composition or division cannot be moved, neither can that which subsists according to capacity, which is opposite to that which simply is; for non-white or non-good can be moved according to accident, since that which is not white may be a man; but this can by no means be the case with that which is not simply this: for it is impossible that non-being can be moved. But if this be the case, it is impossible that generation can be motion: for, if it were, non-being would be generated. For though it should be especially generated according to accident, yet at the same time it would be true to assert of that which is simply generated, that it is non-being. And in a similar manner with respect to being at rest. Such are the absurdities, therefore, which attend this hypothesis. And again: if every thing which is moved is in place, but non-being is not in place; for it would be somewhere;—hence, neither is corruption motion: for motion or rest is contrary to motion, but corruption to generation. But since every motion is a certain mutation, and there are three mutations as above enumerated, and since of these the mutations according to generation and corruption are not motions (but these subsist according to contradiction)—hence it necessarily follows, that mutation from a subject into a subject is alone motion. But subjects are either contraries or media: for privation is admitted to be a contrary, and is manifested by affirmation; as, for instance, the naked, the toothless, and the black.

Aristotle, Metaphysics. Book 11, Chapter 12.

If, therefore, the categories are divided by substance, quality, place, action and passion, relation and quantity, it is necessary that there should be three motions, viz. of quality, of quantity, and of place. But there is not any motion according to substance, because nothing is contrary to substance. Nor is there any motion of relation: for it is possible that, one of the relatives being changed, it may be truly said of the other that it is not at all changed; so that the motion of them is according to accident. Nor is there any motion of agent and patient, or of that which moves and that which is moved, because there is not motion of motion, nor generation of generation, nor, in short, mutation of mutation. For it happens that there is motion of motion in a twofold respect; viz. either as of a subject, as man is moved, because he changes from white into black; so that thus also motion is either made hot or cold, or is changed in place, or is increased. This, however, is impossible; for mutation is not any subject. Or, there is motion of motion, because some other subject is changed from mutation into another form. Thus, man is changed from disease into health. But neither is this possible except according to accident: for every motion is a mutation from one thing into another, and in a similar manner generation and corruption; except that mutations from opposites are in this or that manner; but this is not the case with motions. Man is, therefore, at the same time changed from health to sickness, and from this very mutation into another. But it is evident that, when he becomes sick, he will be changed into a certain disease: for it is possible to rest. It is likewise evident that he will not always be changed into whatever may casually take place; and that will be a mutation from a certain thing into something else. So that convalescence will be an opposite motion, but from accident; just as if he should be changed from reminiscence into oblivion, because that in which oblivion is inherent is sometimes changed into science, and sometimes into health.

Further still: there will be a progression ad infinitum if there is a mutation of mutation, and generation of generation. But it is necessary that there should be the former, if there is the latter. Thus, if simple generation is at any time generated, that also which is simply in generation, or becoming to be, will be generated, so that a thing which is simply in generation will not yet be: but there was something which was in generation, and that something was formerly generated, and this again was once in generation or becoming to be; so that what was then in generation was not yet. But since there is not any thing first in things infinite, there will not be that which is first generated; so that neither will that which is consequent be. Neither, therefore, will it be possible for any thing to be generated, nor to be moved, nor to be changed. Again: contrary motion, and rest, and generation and corruption are of the same thing. So that a thing which is generated, when it becomes that which is generated, will then be corrupted. For it is not immediately corrupted as soon as it is becoming to be, nor posterior to this: for that must necessarily be which is corrupted. Further still: it is requisite that matter should be subject to that which is in generation and mutation. What, therefore, will it be? As that, indeed, which is variable is either body or soul, so that which subsists in becoming to be is either motion or generation. And, again, what is that into which it is moved? For it is requisite that there should be motion and generation of this thing from this into this. After what manner, therefore? For the generation of discipline is not discipline; so that neither is there generation of generation.

But, since there is neither any motion of substance, nor of relation, nor of action and passion, it remains that there can be alone motion according to quality, and quantity, and place; for in each of these there is contrariety. But I do not mean by quality, that which is in substance (since difference also is quality); but I mean passive quality, by which a thing is said either to suffer, or to be impassive.

With respect to the immoveable, that which is wholly impossible to be moved is immoveable; and that which is scarcely moved in a long time, or which slowly begins to be moved; and that which is naturally adapted to be moved, but yet is not able when it is naturally adapted, and where, and as it is naturally adapted, which alone among things immoveable, I denominate that which rests. For rest is contrary to motion; so that it will be a privation of that which is capable of motion.

Again: things are said to subsist together according to place, which are in one first place; and those are said to subsist separately, which are in a different place. But things are said to touch each other, the extremities of which subsist together. A medium is that into which a thing which is changed is naturally adapted to proceed, before it arrives at that into which it is ultimately changed, when it is continually changed according to nature. That is contrary according to place which is very much distant according to a right line. But that is successive, between which and that to which it is consequent nothing of the same kind intervenes; when it is after the principle, either by position alone, or form, or some other mode thus defined. Thus, lines succeed or are consequent to a line, monads the monad, and houses a house. Nothing, however, hinders but that something else may subsist between them. For that which is successive is successive to something, and is something posterior: for one is not successive to two, nor the Calends to the Nones. That is coherent which being successive touches. But, since every mutation is in things opposite, and these are contraries and contradiction, and there is no medium of contradiction, it is evident that there is a medium in contraries. But the continuous has something of the nature of the coherent, or of the tangent. And things are called continuous, when the boundaries of each by which they touch and are continued are one and the same. So that it is evident that the continued is in those things, from which one thing is naturally adapted to be produced according to contact. And it is also evident that the successive ranks as the first: for it is necessary that whatever touches should be successive, but not every thing which is successive touches. Likewise, if a thing is continuous, it is necessary that it should touch; but if it touches it is not yet continuous. But in those things in which there is not contact there is not natural coherence. So that a point is not the same with the monad; for with points there is contact, but this is not the case with monads: for these are successive to each other; and something subsists between points, but not between monads.

Aristotle, Metaphysics. Book 12, Chapter 1.

The present speculation is concerning essence; for the principles and causes of essences are here investigated. For, if the universe is as one whole, essence will be its first part; or, if things subsist in a consequent order, after this manner also essence will be first, and afterwards quality or quantity. But at the same time, in short, neither are these beings, but qualities and motions, in the same manner as that which is not white, and that which is not straight. For, we also say that these are, as for instance, that such a thing is not white. Further still: no one of the rest has a separate subsistence. And the truth of this is in reality testified by the ancients: for they investigated the principles, elements, and causes, of essence. Those, indeed, of the present time rather consider universals as essences: for genera are universals, which they say are rather principles and essences, because they investigate logically. But the ancients called particular essences, such as fire and earth, but not a common body. But there are three essences: one, sensible; of which one part is eternal, and another corruptible, as all men acknowledge, such as plants and animals. Of this sensible essence it is necessary to admit the elements, whether one or many. But another essence is immoveable, which, according to some, has a separate subsistence. Others, again, give it a twofold division; others place in one nature forms, and mathematical entities; and others consider mathematical entities alone. The sensible essence, therefore, belongs to the physical science (for it subsists with motion): but the immoveable essence, to another science, if they have no principle in common.

Aristotle, Metaphysics. Book 12, Chapter 2.

But sensible essence is mutable. If, therefore, mutation is from opposites, or from things subsisting between opposites, but not from all opposites (for a white colour is not from voice), but from that which is contrary, it is necessary there should be something which may be changed into contrariety; for contraries are not changed. Besides, this abides, but that which is contrary does not abide. Hence there is a certain third thing besides contraries, viz. matter. If, therefore, mutations are four in number, viz. either in substance or in quantity, in quality or in place, and simple generation as also corruption is a mutation according to substance, but augmentation and diminution according to quantity, alteration according to passion, and lation according to place; if this be the case, the several mutations will be into contrarieties. It is necessary, therefore, that matter should be changed, which is able to pass into both. But, since being is twofold, every thing which is changed is changed from that which is in capacity into that which is in energy: as, from white in capacity, into white in energy; and in a similar manner with respect to augmentation and diminution:—hence, not only all things may be generated accidentally from non-entity, but likewise from being; from being indeed in capacity, but from non-being in energy. And this is the one of Anaxagoras. For it is better to assert this, than that all things subsisted together: it is likewise preferable to the mixture of Empedocles and Anaximander; and, as Democritus says, all things were together in capacity, but not in energy: so that these men touched upon matter. But all such things as are changed have matter, though in some things it is of a different kind from that of others: for the matter of those perpetual natures which are not generable, but moveable according to local motion, is itself not generable, but is only moved from one place to another. But it may be doubted from what kind of non-being generation subsists: for non-being is threefold. If, therefore, any thing is in capacity, from this generation will subsist, yet not from any thing indiscriminately, but one thing will be generated from another. Nor is it sufficient to say that all things subsisted together; for things differ in matter. For why were things infinite in number produced, and not one thing, since intellect is one? So that, if matter is one, that would have been generated in energy of which the matter is in capacity. There are, therefore, three causes and three principles; two indeed contrariety, of which one kind is reason and form, but the other privation: and the third principle is matter.

Aristotle, Metaphysics. Book 12, Chapter 3.

In the next place it is requisite to know that neither matter nor form is generated; I mean that matter and that form which subsist at the extremity of things: for every thing which is changed is changed by something, and into something. By something, indeed, viz. the first mover; but that in which it is changed is matter; and that into which it is changed is form. An infinite progression, therefore, must take place, if not only the brass is made round, but the roundness also, or the brass, is generated. It is therefore necessary to stop. After this, it must be shown that every essence is generated from that which has the same appellation with itself: for those things which are generated by nature, and also other things, are essences. For things are generated either by art, or nature, or fortune, or chance. Art, therefore, is a principle which subsists in another; but nature is a principle subsisting in the thing itself: for man generates man. But the remaining causes are the privations of these. Essences, too, are three in number: and one of these indeed is matter, which is some particular thing in consequence of that which it appears to be: for such things as are one by contact, and not by cohesion, are matter and a subject. But another of these is nature, which is some particular thing, and a certain habit, subsisting as a boundary. Further still: the third essence is that which consists from these, and ranks among particulars; such as Socrates or Callias. In certain things, therefore, that which is some particular thing has not any subsistence independent of a composite essence; as for instance, the form of a house, unless art is this form: nor is there any generation and corruption of these: but the house itself, which is without matter, likewise health, and every thing effected by art, both are and are not after a different manner: for if forms have any subsistence they are in things produced by nature. Hence, it is not badly said by Plato that forms are such things as have a natural subsistence, if there are forms different from these, such as fire, flesh, the head, and the like: for all these are matter, and especially belong to that essence which is the last of things. Moving causes, therefore, are antecedent to productions: but causes which subsist as reason, are consubsistent with productions. For, when a man is well, then health is present; and the form of the brazen sphere subsists together with the brazen sphere itself. But whether forms remain after separation must be considered; for nothing hinders this from taking place with some forms: as, for instance, if soul should be a thing of this kind, not indeed every soul, but intellect; for perhaps it is impossible that this should be the case with every soul. It is evident, therefore, that ideas are not requisite on account of these things; for man generates man, some particular, some certain man. And in a similar manner with respect to arts: for the medicinal art is the reason of health.

Aristotle, Metaphysics. Book 12, Chapter 4.

The causes and principles of all things are partly the same and partly different; for, if any one speaks universally, and according to analogy, the causes and principles of all things are the same. But it may be doubted whether the principles and elements of essences, and of things which subsist as relatives, are different or the same; and in like manner with respect to each of the predicaments. But an absurdity will ensue, if there are the same principles and elements of all things. For relatives and essence will subsist from the same things. What, then, will this be? For, besides essence and the other predicaments, there will be nothing common. But an element is prior to the things of which it is the element. Nor yet is essence the element of relatives, nor is any one of these the element of essence. Further still: how can there be the same elements of all things? For no element can be the same with that which is composed from elements; as, for instance, neither b nor a can be the same with ba. Nor is it possible that any one of the intelligible elements, viz. the one or being, can be the element of all things: for these are present with every composite nature. No composite nature, therefore, will have any subsistence, nor yet essence, nor relatives. It is, however, necessary that these should subsist. There are not, therefore, the same elements of all things. Or, as we have said, are there partly the same causes and principles of things, and partly not? As, with respect to sensible bodies, the hot is as form, and after another manner the cold, as privation; but matter is that which is first essentially both these in capacity. But essences are as well these as the things which consist from these, and of which these are the principles. Or if any thing becomes one from the hot and the cold, as flesh, or bone, still that which is thence generated must be different from these. Of these things, therefore, there are the same, but of other things different elements and principles. We cannot, however, say that the principles of all things are after this manner the same; but we may assert that this is the case according to analogy: just as if any one should say that there are three principles, form, privation, and matter. But each of these is different about every genus; as in colours, white, black, superficies, light, darkness, and air; but from these day emerges, and the night. However, since not only things inherent are causes, but, of things external, such as that which moves is a cause, it is evident that principle is different from element. Yet both are causes; and into these principle is divided: but that which moves or stops is a certain principle and essence. So that there are three elements according to analogy, but four causes and principles; which four are different in different things. And the first cause, as that which moves, is different in different things. Thus, health is as form, disease as privation, body as matter, the medicinal art as that which moves. Again: a house is as form, a certain confusion as privation, the bricks as matter, and the builder’s art as that which moves. And, indeed, into these things is principle divided. But, since that which moves is indeed in natural men man, but, in things proceeding from the dianoetic power, form, or the contrary, in one respect there will be three causes, but in another four. For the medicinal art is in a certain respect health; and the builder’s art the form of the house; and man generates man. Further still: besides these, as that which is the first of all things, there will be the mover of all things.

Aristotle, Metaphysics. Book 12, Chapter 5.

But since some things are separable and others inseparable, the former are essences, and on this account are the causes of all things; because, without essences passions and motions have no subsistence. In the next place, these will be perhaps soul and body, or intellect, appetite, and body. Further still: principles are the same after another manner by analogy, such as energy and capacity: but these also are different in different things, and in a different manner. For, in some things, indeed, the same thing is at one time in energy and at another time in capacity; as, for instance, wine, or flesh, or man. But these also fall into the above-mentioned causes. For form is energy, if it is separable, as also that which consists from both; but privation is as darkness, or as one that is sick, and matter is in capacity: for this is that which is able to become both. But those things which have not the same matter, and of which there is not the same, but a different form, differ in another manner in energy and capacity. Thus, the causes of man are the elements fire and earth as matter; his proper form; and if there is any thing else external, such as his father; and, besides these, the sun and the oblique circle, which are neither matter, nor form, nor privation, nor of the same species, but are motive natures. Further still: it is requisite to perceive, that of causes, some may be called universal and others not. The first principles of all things, therefore, are that which is in energy this first thing, and something else which is in capacity. But those things which are universal have no subsistence. For that which is particular is the principle, as one man is the principle of another; but there is no universal man. For Peleus is the cause of Achilles, and your father of you; and this letter b is the cause of the syllable ba; and, in short, b is the cause of ba simply considered. In the next place, the forms of essences are principles: but, as we have said, of different things there are different causes and elements. Thus, the causes of those things which are not in the same genus, such as colours, sounds, essences, quantity, are not the same except according to analogy. The causes also of those things which are in the same species are different, but they are not different in species; but because of particulars, your matter, form, and that which moves, differ in number from mine, though according to universal reason they are the same. But in an inquiry, what are the principles and elements of essences, of relatives, and qualities, whether they are the same or different, it is evident that, if they are predicated multifariously, there are the same principles and elements of every essence; but if they are divided, there are not the same but different principles, except that there are the same in a certain respect; for, according to analogy, there are the same; because there is matter, form, privation, and that which moves. So that, after this manner, the causes of essences are as the causes of all things; because, essences being taken away, all things are taken away. Further still: that which is last is in energy. Hence, contraries are in a different manner things first, as they are neither predicated as genera, nor as things multifarious. And, again, different kinds of matter are called causes: and thus we have shown what are the principles of sensibles, how many there are, and in what respect they are the same, and yet different from each other.

Aristotle, Metaphysics. Book 12, Chapter 6.

Since it has appeared there are three essences, two indeed physical, but one immoveable, respecting this we must say, that it is necessary there should be a certain eternal and immoveable essence. For essences are the first of things; and if all essences are corruptible, all things will be corruptible. It is, however, impossible for motion either to be generated or corrupted; for it always was. This is likewise true respecting time: for it is not possible that there can be prior and posterior, time not existing. There is the same continuity, therefore, of motion, as of time: for time is either the same as motion, or a certain passion of motion. But there is not any continued motion, except that which is local; and local continued motion is that which is circular. If, however, there is something motive or effective, but not energetic, motion is not. For it is possible for that which has capacity not to energise. No utility, therefore, will ensue, though we should make eternal essences, in the same manner as those who make forms or ideas, unless a certain principle is inherent which has the power of producing mutation. Neither, therefore, will this be sufficient, nor any other essence different from forms: for, if it does not energise, there will not be motion. Nor yet will this be the case if it energises, but the essence of it is capacity: for there will not be perpetual motion: for that which is in capacity may happen not to be. It is requisite, therefore, that there should be such a principle, the essence of which is energy. Further still: it is requisite that these essences should be without matter: for it is necessary they should be eternal, if there is any thing else eternal. They are, therefore, in energy. A doubt, however, here arises: for every thing which energises appears to have the capacity of energising; but every thing endued with capacity does not energise; so that capacity will be prior to energy. But, indeed, if this were the case, nothing will have any subsistence; for it will happen, that a thing will have the capacity to be, but will not yet be.

But, if the case is as theologists assert, who generate all things from night, or if as the natural philosophers, who say that all things subsisted together, the same impossible consequence will ensue. For how could matter be moved if there was no cause in energy? For the matter of a house does not move itself, but the builder’s art: nor does the menstrual blood move itself, nor earth, but seeds, and human seed. On which account some have recourse to a perpetual energy, as Leucippus and Plato; for they say that motion always is, but they do not say why and what it is, nor why some things are moved differently from others; nor do they assign the cause of this perpetuity of motion. For nothing is casually moved: but it is requisite that something should always have subsisted; as at present, one thing is moved naturally after this manner, and another is moved by force, either by intellect or something else after a different manner. In the next place, what is the nature of the first motion? for this makes an immense difference. But, neither is it possible for Plato to call that a principle which moves itself, and which sometimes he considers as a principle. For, soul, as he says, is posterior to, and at the same time consubsistent with, the heavens. To consider, therefore, capacity as prior to energy, is partly right and partly not. But in what respect it is right we have already declared. However, that energy is prior to capacity Anaxagoras testifies; for intellect is energy. Empedocles also testifies this, by introducing friendship and strife; and this is confirmed by those who assert that motion is perpetual, as Leucippus. So that chaos or night did not subsist in an infinite time, but the same things always were which now are, either by circulation or otherwise, if energy is prior to capacity. But if things are always the same, either by circulation, or in some other way, it is requisite that something should always remain which possesses sameness of energy. But to the existence of generation and corruption it is necessary there should be something which always energises variously. It is necessary, therefore, that after this manner it should energise from itself, but in a different manner according to something else. It must, therefore, either energise according to that which is different, or according to the first. But it must necessarily energise according to this: for, again, this is the cause of energy both to the one and the other. Hence, that which is first is the better cause: for it is the cause of a perpetual sameness of energy; but something else is the cause of variable energy. And both these are the cause of an energy eternally variable. After this manner, therefore, motions subsist. Why, then, is it requisite to investigate other principles?

Aristotle, Metaphysics. Book 12, Chapter 7.

Since, therefore, this is the case (and if it were not so, things would subsist from night, from all things collectively and from non-entity), these questions may be solved; and there is something which is always moved with an unceasing motion; but this is a circular motion. And this is not only evident from reason, but from the thing itself. So that the first heaven will be eternal. There is, therefore, something which moves. But, since there is that which is moved, that which moves, and that which subsists as a medium between these, hence there is something which moves without being moved, which is eternal, and which is essence and energy. But it moves in the following manner: That which is desirable and that which is intelligible move without being moved. But the first intelligible is the same as the first desirable: for that which appears to be beautiful is desirable. But the first object of the will is that which is really beautiful. However, we rather aspire after it because it appears to be beautiful, than it appears to be beautiful because we aspire after it. For the principle is intelligence; but intellect is moved by the intelligible. And the other co-ordination is essentially intelligible. To this co-ordination also the first essence belongs, and likewise that which subsists simply, and according to energy. But the one is not the same with the simple: for the one signifies measure; but the simple, the mode of subsistence. Likewise the beautiful, and that which is eligible for its own sake, are in the same co-ordination: and that which is the first is always the best, or analogous to that which is best. But, that in immoveable natures there is that for the sake of which other things subsist, division manifests: for there is something to which that for the sake of which a thing is done belongs, of which the one is different from the other. But the first mover moves as that which is beloved; and through that which is moved it moves other things. But if there is any thing which is moved, it may subsist in a various manner. If, therefore, the first lation is energy, so far as it is moved, it may subsist differently according to place, though not according to essence. But since there is something which moves, itself at the same time being immoveable, and subsisting in energy, this cannot subsist in a various manner: for lation is the first of mutations; and of this that which is circular. But this the first mover moves. Hence, he is necessarily being; and so far as he necessarily subsists, so far he subsists according to rectitude, and is thus the principle of things: for the necessary is multifarious. For it either signifies that which is effected by violence, because contrary to the will; or that without which a thing is not well conditioned; or that which does not admit of a various, but possesses a simplicity of, subsistence. From such a principle, therefore, heaven and nature are suspended.

But the life which he lives is the most excellent, and such as we enjoy for a small portion of time; for such a life is with him perpetual. To us, indeed, this is impossible; but not to the first mover, because his energy is pleasure. And on this account vigilance, the energies of sense, and intellection, are most delightful. Hope, too, and memory are pleasing through energies. But essential intellection is the intellection of that which is essentially the most excellent; and the most essential of that which is most essential. Intellect, too, understands itself by the assumption of the intelligible: for it becomes intelligible by contact and intellection: so that intellect is the same with the intelligible. For intellect is the recipient of the intelligible, and of essence. But it energises possessing. Hence, that which intellect appears to possess as divine, belongs more eminently to the first intellect than to ours: and his contemplation is the most delightful, and the best. If, therefore, God always possesses that excellent condition of being which we sometimes possess, it is admirable; but, if he possesses it in a still higher degree, it is still more admirable. In this manner, however, he subsists.

Life also is present with him; for the energy of intellect is life; and he is energy. But essential energy is his most excellent and eternal life; and we say that God is an animal eternal, and the most excellent: so that life and duration continued and eternal are present with God. For God is this. But those who are of opinion, like the Pythagoreans and Speusippus, that the most excellent and the most beautiful are not inherent in the principle of things, because the principles of plants and animals are indeed causes, but the beautiful and the perfect are in things proceeding from these, do not think rightly: for seed is from other perfect natures which have a prior subsistence: nor is seed the first thing, but that which is perfect; just as some one may say that man is prior to seed, not indeed the man who is generated from seed, but another from whom seed flows. That, therefore, there is a certain eternal immoveable essence, and which is separated from sensibles, is evident from what has been said. It has also been shown that this essence cannot possess any magnitude, but that it is impartible and indivisible; for it moves in an infinite time. But nothing finite possesses an infinite power. Since, however, every magnitude is either infinite or finite; hence, this essence will not possess a finite magnitude: and it cannot possess an infinite magnitude, because an infinite magnitude has not any existence. It has likewise been shown that he is without passivity, and unchangeable: for all other motions are posterior to that which is local. These arguments, therefore, evince why he subsists in this manner.

Aristotle, Metaphysics. Book 12, Chapter 8.

But we ought not to be ignorant whether one essence of this kind is to be admitted, or more than one, and if more than one how many; but we should also call to mind the opinions of others, because, concerning the multitude of such like essences, they have said nothing certain and clear. For the opinion respecting ideas has not any apposite speculation, since those who assert that there are ideas call them numbers. But, respecting numbers, they sometimes speak of them as of things infinite, and sometimes as of things limited as far as the decad. Nothing, however, is asserted by them with demonstrative diligence, why there is such a multitude of numbers. This then must be declared by us, from the things pre-supposed and determined. The principle and the first of beings is immoveable both essentially and according to accident: but he moves the first, eternal, and single motion. But since that which is moved must necessarily be moved by something, and that which first moves is essentially immoveable, and an eternal motion must be moved by an eternal mover, and one by one; and since we see that besides the simple lation of the universe, which we say the first and immoveable essence moves, there are also other eternal lations of the planets—(for a body which revolves in a circle is eternal and unstable, as has been shown in the Physics)—since this is the case, it is necessary that each of these lations should be moved by an essentially immoveable and eternal essence: for the nature of the stars is a certain eternal essence, and that which moves is perpetual, and prior to that which is moved; and that which has a priority of essence is necessarily essence. It is evident, therefore, that there are NECESSARILY so many essences, naturally eternal, essentially immoveable, and without magnitude, for the reason already assigned. That there are therefore essences, and which of these is first and which second, according to the same order as that of the revolutions of the stars, is evident.

But the multitude of these lations must be considered from that philosophy of the mathematical sciences which is most peculiarly adapted to this purpose, viz. astronomy. For this contemplates an essence, sensible indeed but eternal; but the other mathematical sciences speculate no essence whatever; for this is neither effected by the science which is conversant with numbers, nor by geometry. That there are therefore many lations of the stars is evident to those who are but moderately conversant with these things: for each of the planets is borne along with more than one lation. But how many these are we shall now explain; and, that we may understand their definite number, relate what certain mathematicians assert. As to what remains, it is proper that we ourselves should investigate some things, and ask some questions of those who search into these affairs, that we may know whether any thing appears to them in addition to what we have said. Both, however, are to be believed, but assent is to be given to the more accurate.

Eudoxus, therefore, places the lation of the sun in three spheres, and also that of the moon; of which the first is that of the inerratic stars; the second is through that circle which passes through the middle signs of the zodiac; and the third through that circle which is oblique in the latitude of the signs. But that oblique circle through which the moon is carried, is in a greater latitude than that through which the sun is carried. But Eudoxus places the lation of each of the planets in four spheres; and of these he considers the first and second as the same with those of the sun and moon; but the sphere of the inerratics is, according to him, similar to that first sphere of the heavens which carries all the orbs; and that which ranks under this, and is carried through the middle of the zodiac, is common to all of them. He is also of opinion that the poles of the third sphere, which is common to all, are in that sphere which is in the middle of the signs; and that the lation of the fourth declines from the middle of the third. Likewise that the poles of the third sphere are the proper poles of the other spheres; but that Venus and Mercury have the same poles.

But Calippus gives the same position to the spheres, that is, the same order of distance, as Eudoxus: and, with respect to their multitude, he agrees with him in the number belonging to Jupiter and Saturn, but is of opinion that still two spheres require to be added to the sun and moon in order to solve the phenomena; and to each of the remaining spheres of the planets he adds one. But it is necessary, in order, when all of them are collected together, to assign the causes of the phenomena, that there should be other revolving spheres less in number by one, than those which carry the planets, and which always restore in the same position the first sphere of that star which ranks in an inferior order: for thus alone can all things be effected by the lation of the planets. Since, therefore, with respect to those spheres in which the planets are carried, some are eight, and others twenty-five; of these, those only ought not to have revolving spheres in which the lowest star is carried. And those, indeed, which revolve the spheres of the two first stars will be six; but those which revolve the spheres of the four posterior stars will be sixteen. The number, therefore, of all the spheres, that is, both of those that carry and those that revolve the stars, will be fifty-five. But, if those motions of the sun and moon which we have mentioned are not added, the number of all the spheres will be forty-seven. Let this then be the multitude of the spheres: so that it is rational to conceive that there are as many immoveable and as many sensible essences and principles as we have enumerated; for to prove that there must necessarily be this number, must be left to those who are better qualified for such an undertaking.

But if it is not possible that there can be any lation which does not contribute to the lation of a star; and if it is requisite to conceive that every nature and every essence which is impassive, and capable of subsisting from itself, is allotted the best end, there will be no other nature besides these, but this will necessarily be the number of essences. For, if there are others, they will be motive, as being the end of lation: but it is impossible that there can be any other lations than those which we have enumerated. But this may be rationally inferred from these revolving bodies themselves: for, if every thing which carries naturally subsists for the sake of that which is carried, and every lation is of something which is carried, no lation will subsist for its own sake, nor for the sake of another lation, but it will subsist for the sake of the stars. For, if lation should subsist for the sake of lation, it will also be requisite that this latter should subsist for the sake of other lations. So that, since it is impossible that there can be an infinite progression, the end of every lation will be some one of the divine bodies which revolve in the heavens. But that heaven is one is manifest: for, if there were many heavens, as there are men, the principle about each will be one in species, but many in number. But such things as are many in number are connected with matter: for there is one and the same reason of the many, as of man, but Socrates is one. But that which ranks as the first among formal causes is not connected with matter; for it subsists in energy. Hence, that which first moves immoveably is one both in reason and number; and, consequently, that which is always and continually moved is also one. There is therefore only one heaven or universe.

BUT OUR ANCESTORS AND MEN OF GREAT ANTIQUITY HAVE LEFT US A TRADITION INVOLVED IN FABLE, THAT THESE FIRST ESSENCES ARE GODS, AND THAT THE DIVINITY COMPREHENDS THE WHOLE OF NATURE. The rest indeed is fabulously introduced for the purpose of persuading the multitude, enforcing the laws, and benefiting human life. For they ascribe to the first essences a human form, and speak of them as resembling other animals, and assert other things consequent and similar to these. BUT IF AMONG THESE ASSERTIONS ANY ONE SEPARATING THE REST RETAINS ONLY THE FIRST, VIZ. THAT THEY CONSIDERED THE FIRST ESSENCES TO BE GODS, HE WILL THINK IT TO BE DIVINELY SAID; AND IT MAY BE PROBABLY INFERRED, THAT AS EVERY ART AND PHILOSOPHY HAS BEEN INVENTED AS OFTEN AS POSSIBLE, AND HAS AGAIN PERISHED, THESE OPINIONS ALSO OF THE ANCIENTS HAVE BEEN PRESERVED AS RELICS TO THE PRESENT TIME. Of the opinions of our fathers, therefore, and men of the highest antiquity, thus much only is manifest to us.

Aristotle, Metaphysics. Book 12, Chapter 9.

But there are certain doubts respecting intellect; for it seems to be the most divine of things which are apparent: yet, by what mode of subsistence it is so, it is difficult to determine. For, if it is void of intellection, and is like one sleeping, what will there be venerable in such a condition of being? But, if it possesses intellection, and yet something else has dominion over or is the author of this, then its essence will not be intelligence, but capacity, and so it will not be the most excellent essence. For that which is honorable is present with it through intellection. Further still: whether its essence is intellect or intelligence, what does it understand? For, either itself understands itself, or it understands something else. And if something else, either always the same, or a different thing. Is it, therefore, of no consequence whether it understands that which is beautiful, or any thing which may casually present itself? Or is it absurd to suppose that it cogitates about certain things? It is evident, therefore, that he understands that which is most divine and most honorable, and that he is not changed. For the mutation would be into something worse, and a thing of this kind would now be a certain motion. In the first place, therefore, if his essence is not intelligence, but capacity, it is reasonable to conclude, that continuity of intellection is laborious to him; and in the next place it is evident that there will be something else more honorable than intellect, viz. the intelligible, or the object of intellection. Besides, intellection and intelligence will be present with him when understanding the worst of things. This, therefore, must be avoided. For, not to perceive certain things is better than to perceive them. Hence, intelligence will not be that which is most excellent. He understands himself, therefore, if he is the best of all things; and intelligence is the intelligence of intelligence. But science, sense, opinion, and the dianoetic power always appear to be employed about something different from themselves; so that the principal design of each of these is not the speculation of itself. Further still: if intellection is different from that which is apprehended by intellect, according to which of these is excellence of subsistence present with him? For the being of intelligence is not the same as that of the intelligible. Or shall we say, that in some things science is the thing itself which is the object of science? In effective sciences, indeed, essence and form are without matter; but in the contemplative sciences this must be affirmed of reason, the thing, and intelligence. Hence, in things without matter, since the intelligible is not different from intellect, it is the same with it. Intelligence also is the same with the intelligible. Further still: a doubt remains, whether the intelligible is a composite nature; for, if this be the case, it will be changed in the parts of the whole. Or, shall we say that every thing without matter is indivisible? In the same manner, therefore, as the human intellect, or the intellect of composite natures, subsists for a certain time (for this intellect does not possess the excellent condition of its being in this or that portion of time, but in a certain whole), so does the first intellect subsist for ever; and thus through all eternity itself possesses the intelligence of itself.

Aristotle, Metaphysics. Book 12, Chapter 10.

It must also be considered in what manner the nature of the universe possesses the good and that which is most excellent, whether as something separate, and itself subsisting by itself, or as order, or as both these, in the same manner as an army. For the good of this consists in order, and in its commander, who is the good of the army in a still greater degree. For the commander is not on account of the order, but the order on account of the commander. But all things are in a certain respect co-ordinated, though not in a similar manner, such as aquatic and aerial animals and plants. Nor do they subsist in such a manner as that one has nothing in common with the other, but there is something in which they all agree: for all things are co-ordinated to one thing. But as, in a house, those who are free are permitted to act just as they please, in all or in most things which contribute to the common good; but this is only granted in a small degree to slaves and irrational animals, since they act for the most part casually (for the nature of each of them is a principle in them of this kind); I say, in this manner it is necessary that all things should subsist in order to effect separation. And as in a house, so in the universe, there are other things of which all participate in order to the constitution of the whole.

But we ought not to be ignorant of the impossible or absurd consequences which happen to those who speak differently, nor yet of their assertions who speak more elegantly, and whose opinions are attended with the fewest doubts. For all philosophers consider all things as produced from contraries. But neither are all things generated; nor is it rightly said that all things are from contraries; nor do they appear to have informed us how those things in which contrariety is inherent consist from contraries: for contraries are not passive to each other. But this difficulty is solved by us in a rational manner, by introducing a certain third nature. Others make one of the contraries to be matter, as those who subject the unequal to the equal, or multitude to the one. This, however, is solved after the same manner: for matter which is one is not contrary to any thing. Further still: all things will participate of evil, except the one; for evil itself is the other of the elements. But, according to others, good and evil are not principles, though in all things the good is most eminently a principle. Others, again, are right in considering the good as a principle; but they do not say how it is a principle, whether as the end, or as that which moves, or as form. Empedocles too acts absurdly; for he makes friendship to be the good. For friendship, according to him, is a principle, and that which moves (for it congregates); it is also as matter, for it is a part of that which is mixed. However, though friendship should happen to subsist as matter, as a principle, and as that which moves, yet its essence would not be the same with the essence of these. Which of these, therefore, will friendship be? But it is also absurd that strife should be incorruptible; since this very thing is the nature of evil itself.

But, according to Anaxagoras, the good is a principle so far as motive. For intellect moves; but it moves for the sake of something; so that it will be different from that for the sake of which it moves, unless it subsists as we affirm it to subsist: for the medicinal art is in a certain respect health. He has also acted absurdly, in not making a contrary to the good, and to intellect. But all those who speak of principles as contraries do not use contraries, as will be obvious to him who does not negligently consider their opinions. And no one assigns a reason why some things are corruptible, but others incorruptible: for they make all things from the same principles. Further still: some generate all things from non-entity: but others, that they may not be compelled to do this, make all things to be one. Again: no one assigns a reason why generation will perpetually exist; nor does any one say what is the cause of generation. And both those who make two principles, and those who introduce ideas, necessarily require another more powerful principle; because there is a principle more powerful than these. For why is matter participated, or why does it still continue to participate ideas? And to others, indeed, it is necessary that there should be something contrary to wisdom and the most honorable science; but this is not necessary to us. For there is not any thing contrary to that which is first; since all contraries have matter, and these are in capacity. Ignorance, too, is opposed to its contrary; but nothing is contrary to that which is first.

Further still: if there are no other natures besides sensibles, there will not be a principle and order, generation, and the celestial orbs; but there will always be a principle of a principle, as is also asserted by theologists and all natural philosophers. But if there are forms or numbers they will not be the causes of any thing. And if this is not admitted, they will not at least be the causes of motion. Again: how can magnitude and that which possesses continuity emerge from things void of magnitude? For number will not make continued quantity, either as that which moves, or as form. Indeed there will not be any one of things contrary which has the power both of making and moving; for it may happen not to be. But energy is in a certain respect posterior to capacity. There will not, therefore, be eternal beings; BUT THERE ARE. Hence some one of these hypotheses must be rejected. But we have shown in what manner capacity antecedes energy. Further still: how numbers are one, or soul and body, and, in short, form and a thing, no one informs us: nor is it possible to explain this, unless he says as we do, that the cause of this, in effecting it, operates as that which moves. But those who say that mathematical number is first, and so always suppose another essence adhering in succession and other principles of every thing—these make the essence of the universe to be adventitious; (for, thus one thing does not contribute any thing to another, whether it exists or does not exist); and besides this, they introduce many principles. But beings are unwilling to be governed ill.

The domination of many is not good; there is, therefore, one supreme.

Aristotle, Metaphysics. Book 13, Chapter 1.

Respecting the essence, therefore, of sensibles, we have shown what it is in the mode of investigation employed by us in our Physics, concerning matter, and afterwards in our inquiry concerning energy. But since our present design is to consider whether, besides sensible essences, there is a certain immoveable and eternal nature, or not, and if there is what it is, in the first place we shall take a survey of the assertions of others, that, if in any thing they have not spoken well, we may not be liable to the same accusation; and that, if there is any dogma common to us and them, we may receive it separately, and not be indignant as with a thing hostile to our design. For we must be contented if any one asserts some things better than us, and other things not worse. But there are two opinions on this subject: for they say that mathematical natures are certain essences, such, for instance, as numbers and lines, and things allied to these, and again, ideas. However, since some consider ideas and mathematical numbers as two genera; but others are of opinion that there is one nature of both; and others again assert that mathematical natures are alone essences, in the first place let us make mathematical entities the object of our consideration, without adding to them any other nature; viz. without investigating whether they are ideas or not, and whether or not they are the principles and essences of things; alone attending to this, whether mathematical entities have any subsistence or not, and if they have, in what manner they subsist.

In the next place, we shall separately speculate concerning ideas themselves, and this simply, and in a small degree, for the sake of law; for many things are divulged respecting them, even in exoteric discourses. Further still: it is requisite that greater attention should be paid to that part of our inquiry, in which we consider if the essences and principles of things are numbers and ideas: for, after ideas, this remains as the third consideration. But it is necessary, if there are such things as mathematical entities, that they should either be in sensibles, according to the assertions of some; or that they should be separated from sensibles, as is asserted by others: or, if neither of these is to be admitted, either they have no subsistence, or they subsist in some other way. So that the controversy with us will not be respecting their being, but their mode of subsistence.

Aristotle, Metaphysics. Book 13, Chapter 2.

That it is impossible, therefore, that they should subsist in sensibles, and that the reasoning adduced in defence of this mode of subsistence is at the same time fictitious, has been evinced in the doubts in which we have shown the impossibility of two solids occupying the same place. Further still: by the same reasoning, it appears that other powers and natures are in sensibles, and that no one of them has a separate subsistence. These things, therefore, have been already discussed. But, besides this, it is evident that it would be impossible for any body to be divided: for it would be divided according to a superficies, and this according to a line, and a line according to a point. So that, if it is impossible to divide a point, it is also impossible to divide a line; and if a line, it is impossible to divide the rest. What is the difference, therefore, in admitting, either that there should be such natures, or that there should not be, but that such natures should be contained in sensibles? For the same thing will happen; for, sensibles being divided, they also will be divided, or they will not be sensibles. But neither can such like natures have a separate subsistence: for if there should be other solids, besides such as are sensibles, separate from these, and prior to sensibles, it is evident that, besides superficies, there must necessarily be other superficies having a separate subsistence, and in like manner other lines and points: for this must follow from the same reasoning. And if this be admitted, again, besides the superficies, lines, and points of a mathematical solid, there will be others subsisting separately, since incompostes are prior to composites. And if bodies which are not sensible are prior to sensibles, for the same reason, those superficies which subsist by themselves will be prior to those which have their subsistence in immoveable solids: so that both these superficies and lines are different from those which have a co-subsistence in separate solids: for the latter subsist together with, but the former are prior to, mathematical solids. Again, therefore, of these superficies there will be lines, prior to which it will be requisite that there should be other lines and points, and other points prior to those contained in the lines which have a subsistence prior to sensibles; to which there will no longer be any that are prior. But this co-acervation is indeed absurd: for it will happen, that there is only one order of solids besides such as are sensible, but that there are two ranks of superficies besides sensibles; viz. those which are in the separate bodies, and those which have a subsistence separate from bodies; and again: that there are triple lines, viz. those which are in solids, those which are in superficies, and those which are separate; and, from the same reasoning, that there are quadruple points and quintuple monads. So that, about which of these will the mathematical science be employed? For it cannot be employed about superficies, lines, and points, which are in an immoveable solid; since science is always conversant with things which have a priority of subsistence. The same reasoning also will take place respecting numbers: for besides points there will be other monads, and besides beings sensibles, and afterwards intelligibles; so that there will be infinite genera of mathematical numbers.

Further still: how will it be possible to solve the doubts which we have already enumerated? For the particulars about which astronomy is conversant, are in a similar manner things different from sensibles, and this is also the case with the objects of geometric speculation. But how is it possible that heaven and the parts of it can subsist, or any thing which possesses motion? The like will take place in optics and harmonics. For there will be voice and sound, besides such as are sensible and particular. So that it is evident there will both be other senses and other sensibles. But why these more than those? And if these, there will also be other animals, since there will be other senses. Besides, some things are exhibited through universal reasons by mathematicians, besides these essences. This, therefore, will be another separate essence, subsisting between ideas and things which have a middle subsistence, and which will neither be number nor points, neither magnitude nor time. But if this is impossible, it is evidently impossible that those natures can have a subsistence separate from sensibles. In short, the very contrary to that which is usually apprehended will take place, if any one considers mathematical entities as certain separate natures. For it is necessary, if they subsist in this manner, that they should be prior to sensible magnitudes, when at the same time in reason they are posterior to them: for an imperfect magnitude is in generation prior, but in essence posterior; as, for instance, the inanimate to the animate. Further still: in what and when will these mathematical magnitudes be one? For those which are here either reside in the soul, or in a part of the soul, or in something which participates of reason. But, if this is not the case, they will be many, and will be dissolved. However, as those are divisible and quantities, what is the cause of their being one, and subsisting in conjunction? Further still: this is evinced by generations. For that which pertains to length is first produced, afterwards that which pertains to breadth, and, lastly, that which pertains to depth; and thus the end is obtained. If, therefore, that which is posterior in generation is prior in essence, body will be prior both to superficies and length; and thus will be perfect and more a whole, because it is animated. But how will a line or superficies be animated? For this will be an axiom above the reach of our senses.

Again: body indeed is a certain essence; for it already possesses in a certain respect the perfect. But how can lines be said to be essences? For they are not essences, in the same manner as a certain species and form, as if a thing of this kind were soul; nor are they essences after the same manner as matter, as if a thing of this kind were body. For it does not appear that any thing is capable of subsisting either from superficies or points. But if it were a certain material essence, it might appear capable of suffering this. Mathematical natures, therefore, are prior in definition to sensibles; yet it does not follow, that all such things as are prior in definition are also prior in essence. For, things prior in essence are such as, having a separate subsistence, transcend in being: but things prior in definition are those, the definitions of which are composed from definitions. These, however, do not subsist together: for, if passions do not subsist apart from essences, as, for instance, something moved, or something white, whiteness is prior to a white man, according to definition, but not according to essence; for it cannot have a separate subsistence, but always subsists together with the whole: but I mean by the whole, the white man. So that it is evident that neither is that prior which subsists by ablation, nor is that posterior which subsists from addition: for, by the addition of whiteness a man is denominated white. That mathematical natures, therefore, do not possess a greater degree of entity than bodies, and that they are not prior in essence, but only in definition, to sensibles; and also, that they cannot have a separate subsistence, has been sufficiently shown. Since, however, they cannot subsist in sensibles, it is evident that, either they altogether have no subsistence, or that they subsist after a certain manner, and on this account simply are not: for we speak of being multifariously.

Aristotle, Metaphysics. Book 13, Chapter 3.

As universals in the mathematics are not conversant with any other separated natures than magnitudes and numbers, but are employed about these, though not so far as they are such things as possess magnitude, or are divisible, it is evident that definitions also and demonstrations take place about sensible magnitudes, but not so far as they are sensibles, but so far as they are considered universally. For, as there are many reasons of things in motion so far as they are in motion only, without considering what the nature is of each, or what the accidents which belong to them; and yet it is not necessary on this account, that there should be any thing in motion separated from sensibles, or that in things in motion there should be any separated nature; in like manner there will be reasons and sciences about things which are moved, yet not so far as they are moved, but so far as they are bodies only: and again, so far as they are superficies only, and so far as they are lengths only, and so far as they are divisible; likewise so far as being indivisible they have position, and so far as they are indivisible only. So that, since it is simply true to say that there are not only things separable, but also things not separable, such as things in motion, and such as are mathematical: (since it is simply true to assert that there are such things as they are said to be,) and as with respect to other sciences, it is simply true to say that they are conversant with this definite particular, and not with that which is accidental; as, for instance, with that which is white, if that which is salubrious should be white, but yet so far as it is salubrious; they are not conversant, I say, with that which is accidental, but with that to which each particular belongs—if salubrious with the salubrious, if with man so far as he is man. In like manner with respect to geometry, it does not follow that, though the objects with which it is conversant are sensible, and though it is not conversant with them so far as they are sensible—it does not follow, I say, though this be admitted, that the mathematical sciences do not depend on sensibles, or that they are employed about other separate natures. But there are many essential accidents to things, so far as each has its peculiar characteristic; since, so far as an animal is feminine, and so far as it is masculine, these are its peculiar passions; although there is not any thing feminine nor any thing masculine separate from animals. So that, so far as geometry considers lengths alone, and superficies alone, and by how much the more it is employed about things which are prior in definition and more simple, by so much the more will it possess the accurate and the certain: but the accurate is that which is simple. Hence, geometry rather speculates things without magnitude, than according to magnitude, and in a particular manner it speculates things without motion. But if it contemplates motion, it especially contemplates that motion which is first; for this is most simple and regular. The same reasoning will also take place respecting the harmonic and optic science: for neither speculates so far as sight or so far as sound, but so far as the objects of speculation are lines and numbers; for these are the proper passions of those. And in a similar manner with respect to the mechanic science. So that, if any one, abstracting from accidents, considers any thing respecting these sciences so far as they are such, he will not through this be in the smallest degree deceived, as neither when he describes any thing in the earth, and calls that pedal which is not pedal: for there is nothing false in the propositions. But each particular will thus be contemplated in the best manner, if any one considers that as separate, which has not a separate subsistence, as the arithmetician does, and also the geometrician: for man is one and indivisible so far as man. But the arithmetician establishes an indivisible one; and afterwards considers, whether any thing happens to man so far as he is indivisible. On the other hand, the geometrician considers man neither as man, nor as indivisible, but as solid. So that on this account geometricians speak with rectitude, and discourse about beings: for being is twofold; one kind subsisting in energy, and the other materially. But since the good is different from the beautiful (for the one is always conversant with practical affairs, but the beautiful is also in immoveable natures), those who say that the mathematical sciences assert nothing respecting the beautiful or the good, speak falsely: for they speak about these, and especially render them manifest. For though they do not employ these names, yet when they exhibit the operations and reasons of these, do they not speak concerning them? Indeed, the greatest species of the beautiful are order, symmetry, and the definite, which the mathematical sciences especially evince. And since these appear to be the causes of many things, (I mean, for instance, order and the definite) it is evident that they speak of such a cause as is after a certain manner beautiful. But about these we shall elsewhere speak more perspicuously. Concerning mathematical natures, therefore, that they are beings, and how far they are beings, how they are not in one respect prior to sensibles, and yet how in another they are prior, thus much has been said by us.

Aristotle, Metaphysics. Book 13, Chapter 4.

With respect to ideas, in the first place that opinion concerning ideas is to be considered, which does not in the least associate it with the nature of numbers, but is that which was adopted from the beginning by those who first asserted the existence of ideas. But the opinion respecting forms was entertained by the advocates for their subsistence, in consequence of their being persuaded of the truth of the Heraclitean arguments, that all sensible things are in a perpetual flux; so that, if any thing is the object of science and intellectual prudence, there must necessarily be certain other permanent natures besides sensibles; for there is no science of things flowing. But Socrates, employing himself about moral virtues, first of all explored the manner of defining respecting these: for Democritus touched only upon physics in a small degree, and defined how the hot and the cold subsist: but the Pythagoreans prior to him invented definitions respecting a certain few particulars, the reasons of which they referred to numbers; as, for instance, what opportunity is, what the just, or what marriage is. Socrates, indeed, rationally inquired after the what: for he sought how to syllogise; but the principle of syllogisms is the what. For dialectic strength did not then exist; so that they were able without the possession of the what, to consider contraries, and whether there is the same science of contraries: for there are two things which may be justly attributed to Socrates, inductive arguments, and the definition of universal: for both these subsist about the principle of science. But Socrates did not consider universals and definitions as things which have a separate subsistence; but others separated them, and denominated things of this kind the ideas of beings. So that, for the same reason, it nearly happened to them that there are ideas of all things which are predicated universally: and this is just as if some one wishing to enumerate, should be of opinion that when there are fewer things he cannot, but when he has made more he will be able to enumerate: for, as I may say, forms are more in number than sensible particulars, from an inquiry into the causes of which, these men proceeded from sensibles to ideas: for ideas are homonymous with sensible particulars, and besides essences they are inherent in many other things, both in sensibles and things eternal.

Further still: it does not appear from any one of these, according to what modes the subsistence of forms is evinced: for from some, it is not necessary that syllogism should take place; but from others, even of things of which they do not think there are forms, forms arise. For, according to the reasons originating from the sciences, there will be forms of all things of which there are sciences; and, according to the one in the many, there will also be forms of negations; but, from our understanding something of that which is corruptible, there will be forms of things corruptible; for there is a certain phantasm of these. Again, with respect to the most accurate arguments of the advocates for ideas, some establish ideas of things relative, of which we do not say there is an essential genus; but others introduce a third man. And, in short, the assertions respecting forms subvert the very things the existence of which the advocates for forms are more willing to admit than that of ideas themselves. For it happens that the duad is not first, but number; and that, prior to this, that which is relative and the essential subsist. And this will be the case with all such particulars as, being consequent to the opinions respecting forms, are contrary to principles.

Further still: agreeably to that opinion by which they say that there are ideas, there will not only be forms of essences, but also of many other things. For there is not only one conception of essences, but also of things which are not essences; and sciences will not alone be conversant with essence; and ten thousand similar consequences will ensue. But, according to the necessary, and the opinions respecting ideas, if forms may be participated, it unavoidably follows, that there are alone ideas of essences: for they are not participated according to accident; since each is necessarily participated, so far as it is not predicated of a subject. I say, for instance, if any thing participates of the double, this also participates of the eternal, but according to accident: for it happens to the double to be eternal; so that forms will be essence: but these both here and there signify essence. Or, can we say that the one in the many is any thing besides these? If, indeed, there is the same form of ideas and their participants, there will be something common: for why, of corruptible duads, and of duads which are many indeed, but eternal, is there rather one and the same duad, than of this, and some particular duad? But if there is not the same form, it will be homonymous, and will be just as if some one should call Callias and a piece of wood a man, perceiving no communication whatever between them. But if we consider other things, i.e. common reasons, as adapted to forms, as, for instance, a plane figure to the circle itself, and the other parts of the definition of a circle, that to which it belongs being added, if this be done, it is requisite to consider whether or not this is altogether vain. For, to what is it added? to the middle, or to the plane, or to all? For all things which are in essence are ideas, as, for instance, animal and biped. Further still: it is necessary that a thing itself, as for instance a plane, should be a certain nature, which, in the same manner as genus, is inherent in all species.

Aristotle, Metaphysics. Book 13, Chapter 5.

But most of all it may be doubted what forms contribute either to things perpetual among sensibles, or to things generated and corrupted: for they are neither the cause to them of any motion, nor of any mutation whatever. Nor yet do they afford any assistance to the science of other things: for, neither are they the essence of these (since they would be in these), nor do they contribute to the being of any thing, since they are not inherent in their participants: for, if this were the case, they might thus perhaps be considered as causes, as white mingled with white. But that reason which Anaxagoras first, and Eudoxus afterwards, introduced, doubting, and likewise certain others, may be easily confuted. For, to this opinion it is easy to collect many things, and such as are impossible. But neither do other things subsist from forms according to any of the modes which are usually adduced. And to say that ideas are paradigms, and that other things participate of them, is to speak idly, and to employ poetic metaphors. For, what is that which operates looking to ideas? For it is possible that any thing may be, and may be generated, though it be not assimilated to a paradigm; so that, Socrates both existing and not existing, there will be such a person as Socrates. In a similar manner, it is evident, though Socrates should be eternal, there will be many paradigms of the same thing, and therefore also forms; as, for instance, of man, animal and biped, and man subsisting as an idea. Further still: forms will not only be paradigms of sensibles, but also of themselves; as, for instance, genus, of generic species; so that the same thing will be both paradigm and image. Again: it may seem to be impossible that essence, and that of which it is the essence, should be separate. So that, how can ideas, which are the essences of things, have a separate subsistence? But, in the Phædo, it is asserted that forms are the causes both of being and generation; and yet, notwithstanding the subsistence of forms, things will not be produced, unless there is that which moves. To which we may add, that many other things are made, as, for instance, a house and a ring, of which they do not assert there are forms. So that it is evident that other things also, of which they say there are ideas, may both be, and be generated, through such-like causes as we have just now mentioned, but not through forms. But, indeed, respecting ideas, many things similar to those already considered, may be collected, both after this manner and through arguments more logical and more accurate.

Aristotle, Metaphysics. Book 13, Chapter 6.

Since, then, we have concluded thus much concerning ideas, it will be well again to speculate the consequences respecting numbers, which happen to those who assert that they are separate essences, and the first causes of things. But it is necessary, if number is a certain nature, and there is not any other essence of it, but this very thing itself is its essence, as some assert,—if this be the case, it is necessary, either that something belonging to it should rank as first, and something as consequent which is second, and is different in form; and this either directly subsists in monads, and every monad is incapable of being compared with every monad; or all of them are directly consequent, and, each may be compared with each, as they say is the case with mathematical number; for in mathematical number no one monad differs from another: or some monads may be compared with others, and some not; just as if the first duad subsists after the one, in the next place the triad, and then another number. But the monads in each number are capable of being compared, as, for instance, those which are in the first duad, and those which are in the first triad; and in a similar manner, in other numbers. But the monads in the duad itself cannot be compared with those in the triad itself, and in a similar manner in the other following numbers. Hence, the mathematician after one numerates two, with the former one another one: and in numerating three, he adds another one to these two; and so of the rest. But Plato, after the one, considers two other unities without the first one, and the triad without the duad, and, in a similar manner, other numbers. Again, therefore, one kind of numbers must be such as that which was first mentioned, but another that which is employed by mathematicians, and a third that which we have spoken of as the last. Further still: these numbers must either be separate from things or not separate, but subsist in sensibles; yet not in such a manner as was considered by us at first, but as from numbers existing in sensibles. Or one kind of these must have a subsistence, and another not, or all of them must exist. The modes, therefore, according to which it is possible for them to be, are necessarily only these.

But those who assert that the one is the principle, essence, and element of all things, and that from this and another certain one, number subsists, each of these nearly adopts some one of these modes, excepting this, that all the monads are not comparable; and this reasonably happens. For it is not possible that numbers can have any other mode of subsistence besides those which have been enumerated. Some, therefore, assert that both are numbers, and that one of these modes which possesses the prior and the posterior accords with ideas: but that mathematical number is different from ideas and sensibles; and that both ideas and mathematical numbers are separate from sensibles. But according to others, the mathematical number alone is the first of things, and is separated from sensibles. The Pythagoreans also celebrate the mathematical one, but not as having a separate subsistence; but they say that from this sensible essences are derived. For they fabricate all heaven from numbers, only not from the monadic: but they consider monads as possessing magnitude. At the same time they seem to doubt how the first one consists, possessing magnitude. But a certain other philosopher asserts that the first number ranks among forms; and according to others, the mathematical number is the first number. In like manner with respect to lengths and superficies, and solids: for, according to some, those which subsist after ideas are different from such as are mathematical. But, of those who speak differently, some discourse of mathematical natures mathematically, and these are such as do not consider ideas to be numbers, nor assert that there are ideas. But others speak of mathematical natures not mathematically: for they contend that every magnitude cannot be cut into magnitudes, and that any kind of monads do not compose the duad. All, however, consider numbers as monadic, except such of the Pythagoreans as assert that the one is the element and principle of things. But these consider monads as endued with magnitude, as we have already observed. In how many ways, therefore, numbers are considered by these men, and that all the modes have been enumerated, is, from what has been said, manifest. All the modes, however, are impossible, though perhaps one more than another.

Aristotle, Metaphysics. Book 13, Chapter 7.

In the first place, therefore, let us consider whether monads are capable of being compared with each other, or cannot be compared: and if they cannot be mutually compared, in what way can we as it were divide them; for every kind of monad will not admit of comparison with every kind. But those monads which are in the duad, do not admit of comparison with those in the triad; and thus the monads in each prime number cannot be compared with each other. If, therefore, all the monads are capable of being compared, and are without any difference, mathematical number, and one number alone will subsist; and it will not be possible that ideas can be numbers: for what kind of number will man-itself be, or animal-itself, or any other species? For there is one idea of each, as for instance, one idea of man-itself, and another one of animal-itself. But similar monads, and such as have no difference, are infinite: so that this triad will not in any respect be more man-itself, than any thing else. But, if ideas are not numbers, it is not, in short, possible that they can have any subsistence: for from what principles will ideas be derived? For number is from the one and the indefinite duad: and these are said to be the principles and elements of number, and cannot be in order either prior or posterior to numbers. But if monads do not admit of comparison, and are in such a manner incapable of being compared that every one is different from every one, neither is it possible that this can be mathematical number, (for mathematical number consists of monads which are not different from each other, and the things manifested by it, harmonise with monads of this kind), nor yet can this number belong to forms; for the first duad will not be from one and the indefinite duad; and afterwards the following numbers, as it is said, viz. the duad, triad, and tetrad: for at the same time, the monads which are in the first duad are generated; whether they subsist from unequal monads (for from things made equal they were produced) or have a subsistence different from this.

In the next place, if one monad is prior to another, it will also be prior to the duad which subsists from these: for when of any thing, something is prior, and something posterior, then, that also which subsists from these, will be prior to this, and posterior to that. Further still: since the one itself is first, and afterwards a certain one of the rest; also, a second after this, and again, a third; there will be a second indeed, after a second, but a third after the first one: so that monads will be prior to the numbers which are composed from them. Thus, for instance, in the duad there will be a third monad, before the number three has a subsistence, and in the triad a fourth, and in the tetrad a fifth, before these numbers subsist. None of them, however, asserts that monads are after this manner incapable of comparison. But indeed, according to their principles, it is reasonable it should be so, though impossible according to truth: for it is reasonable that monads should be prior, if there is a certain first monad, and a first one; and in like manner with respect to duads, if there is a first duad: For after that which is first, it is rational and necessary that there should be a certain second: and if a second, a third; and so of the rest in a following order. But to assert at the same time, that there is a first and second monad after the one, and also a first duad, is impossible. These, however, introduce a monad and a first one, but no longer a second and a third. They also introduce a first duad, but not a second and a third. It is evident, however, that if all monads do not admit of comparison, it is impossible that there can be a duad and a triad, and other numbers: for whether monads are without any difference, or whether each differs from each, it is necessary that number should be numerated by addition; as, for instance, the duad, by the addition of one to another one; and the triad, by another one being added to two: and in a similar manner the tetrad. But this being the case, it is impossible that there should be a generation of numbers, in such a manner as they generate them from the duad and the one: for the duad becomes a part of the triad, and the triad of the tetrad. And the like consequences ensue in the following numbers. But from the first duad, and the indefinite duad, the tetrad is produced, being two duads beside the duad itself. But, if the duad itself is not a part, there will yet be another one duad, and the duad will subsist from the one itself, and another one. If this, however, is the case, it is not possible that the indefinite duad can be the other element: for it generates another monad, but not the definite duad.

Further still: besides the triad, and the duad itself, how will there be other triads and duads? And in what manner will they be composed from prior and posterior monads? For all these things are fictitious; and it is impossible that there should be a first duad, and afterwards the triad itself. It follows, however, that this must necessarily be the case, if the one, and the indefinite duad, are the elements of numbers. But if the consequences are impossible, it is also impossible that these can be principles. If, therefore, some monads differ from others, these things, and other things of this kind, necessarily happen. But if the monads in another number are different, but those in the same number are alone without any mutual difference, even in this case difficulties as numerous will arise. As, for instance, in the decad itself, there are ten monads; but it is composed both from these, and two pentads. Since, however, the decad is not a casual number (for neither is it composed from casual pentads, nor from casual monads) it is necessary that the monads in this decad should differ: for, if they do not differ, neither will the pentads differ from which the decad is composed. But, since they differ, the monads also will differ. If, therefore, they differ, whether does it follow, that there will not be other pentads, but only those two, or that there will be? For in the decad, there is not another decad besides itself. But, indeed, it is also necessary that the tetrad should not be composed from casual duads: for the indefinite duad, as they say, receiving the definite duad, produces two duads, for it causes the duad which it receives to become two.

Again: how does it happen that there is a certain nature, i.e. the duad, besides two monads, and the triad, besides three monads? For either one participates of the other, as a white man, besides white and man; (for he participates of these) or the one is a certain difference of the other, as man besides animal and biped. Further still: some things are one by contact, others by mixture, and others by position; none of which can pertain to the monads from which the duad and the triad consist. But as two men are not one certain thing besides both, the same consequence must necessarily apply to monads; nor must it be said that they differ because they are indivisible; for, on this account points also are indivisible. But at the same time the duad of two men, is not any thing else besides the two. Nor yet, ought this to be concealed, that there will be prior and posterior duads; and in like manner with respect to other numbers. For the duads in the tetrad subsist together with each other, but they are prior to those in the octad; and as the duad produces the duads in the tetrad, so these duads produce the tetrads in the octad itself. So that, if the first duad is an idea, these also will be certain ideas. The same reasoning will likewise take place with respect to monads: for the monads which are in the first duad will generate the four monads which are in the tetrad. So that all monads will be ideas, and idea will be composed from ideas. And hence, it is evident that those things also of which these are ideas will be composites. Just as, if any one should say that animals are composed from animals: if, therefore, there are ideas of these, ideas will be composed from animals. And, in short, to make monads in any respect different, is absurd and fictitious. But, I mean by fictitious, that which is forcibly introduced to an hypothesis. For we do not see that monad differs from monad either according to quantity or quality: and it is necessary that every number should be either equal or unequal, but especially monadic number. So that, if neither greater nor lesser, it must be equal. But we consider things which are equal, and altogether without difference, as the same in numbers. And, if this be not the case, neither will the duads in this decad be without difference, since they are equal: for what cause can he assign who says that they are without difference?

Further still: if every monad and another monad make two, a monad taken from the duad, and a monad from the triad will be two; and this duad will consist of monads which have no diversity. It may therefore be asked, whether this duad is prior or posterior to the triad? For there appears to be a greater necessity that it should be prior; since the one subsists together with a triad of monads, but the other with a duad. And we, in short, apprehend that one and one are two, whether they are equal or unequal; as, for instance, the good and the evil, man and horse. But, if the number of the triad is not greater than that of the duad, it is wonderful; and, if it is greater, it is evident that equal number also is inherent in the duad; and is not different from the duad itself. This, however, will not happen, if there is a certain first, and also a second number; nor will ideas be numbers: for this is rightly said by those who think it proper that monads should be different; since, as we have before observed, they will be ideas: for the species of both is one. But, with respect to monads, if they are without difference, this also will be the case with duads and triads. So that it is necessary to say to the authors of this assertion, that in enumerating one, two, that which is pre-existent must not be admitted: for neither is generation from the indefinite duad, nor is it possible that idea can subsist: for one idea would be inherent in another; and all forms would be parts of one. Hence, with respect to the hypothesis indeed, they speak rightly, but simply considered not rightly; for they subvert many things: since they say it is doubtful, whether when we enumerate and predicate one, two, three, we assume any thing, or effect this according to parts. But we do both; on which account it is ridiculous to refer this to so great a difference of essence.

Aristotle, Metaphysics. Book 13, Chapter 8.

In the first place, however, it will be well to define the particular difference, if there is any, between number and the monad. But it is necessary that this difference should be, either according to quantity, or according to quality. Neither of these, however, appears to be possible; but the difference so far as number, is according to quantity. If, therefore, monads also differ in quantity, one number will differ from another, though equal to it in the multitude of monads. Further still: whether are the first monads greater or lesser, and whether do they afterwards increase, or the contrary? For all these particulars are absurd. But neither can they differ according to quality: for no passion can be inherent in them; since they say that quality is present with numbers posterior to quantity.

Again: this will neither happen to them from the one, nor from the duad. For the one does not partake of quality, but the duad partakes both of quantity and quality: for the nature itself of the duad is the cause that beings are many. If, therefore, this subsists in a certain respect differently, it must be said that this is especially so in the principle; and we must define respecting the differences of the monad, that it is especially necessary, and why it is so, that this should be the case. But, if monads do not differ in quantity, nor yet in quality, what other difference in them can they assign? And indeed, if ideas are numbers, it is evident that in neither of these ways, can all monads be compared with each other, nor yet be mutually without comparison. Nor again, as certain others speak concerning numbers is it well said. But these are such as do not indeed admit that there are ideas, neither simply considered, nor yet as being certain numbers, but assert the subsistence of mathematical entities, and contend that numbers are the first of things, and that the principle of them is the one itself: for it is indeed absurd that the one should be something which is first of unities, as they say it is; but that the duad should not be something, which is first of duads, nor the triad of triads; since the same reasoning will apply to all of them. If, therefore, this is the case with the particulars respecting number, and some one alone admits the subsistence of mathematical number, the one is not the principle of numbers: for it is necessary that a one of this kind should differ from other monads. But if this be the case, a certain first duad also must differ from other duads: and a similar consequence must take place with respect to all following numbers. But if the one is the principle, there is a greater necessity that the particulars respecting numbers should subsist (as Plato said), and that there should be a first duad and triad, and that numbers should not admit of comparison with each other. But yet again, if any one adopts these positions, it has been said by us that many impossible consequences will ensue. It is however necessary, that either these or those positions should be adopted; so that if neither of them is true, it is not possible that number can have a separate subsistence.

But, from these things, it is evident that the third mode is the worst, I mean that which asserts that mathematical number is the same with the number belonging to forms: for it is necessary that two errors should accord in one opinion. For neither can mathematical number subsist in this manner; but it is necessary that he who lays down the peculiar hypotheses should be prolix, and that he should also necessarily enumerate the consequences which happen to those who speak of numbers as if they were forms. But the mode of the Pythagoreans has partly fewer difficulties than those which we have before mentioned, and partly has others which are peculiar. For indeed, to make number inseparable from sensibles, takes away many impossibilities; but to suppose that bodies are composed from numbers, and that this number is mathematical, is absurd: for neither is it true to say that there are indivisible magnitudes. And, in the next place, because they especially subsist in this manner, the monads do not possess magnitude. But how is it possible that magnitude can be composed from indivisibles? However, arithmetic number is monadic; but they assert that beings are number. They adapt, therefore, speculations to bodies, as if from them numbers subsisted. Further still, therefore, it is necessary, if number is something essentially belonging to beings, that some one of the above-mentioned modes should take place. But this is impossible. It is evident, therefore, that there is no such nature of number as those introduce who make number to have a separate subsistence. Further still: it may be asked, whether each monad consists from the great and the small equalised or one monad from the small, and another from the great? If then this be the case, neither is each number from all the elements, nor are the monads without difference: for, in this the great will be inherent, but in that the small, being naturally contrary. Again: how do these elements subsist in the triad itself? for one of them is superfluous. But through this perhaps they make the one itself the middle in the odd number. But if each of the monads is from both the elements equalised, how will the duad be one certain nature, composed from the great and the small? or in what will it differ from the monad? Further still: the monad is prior to the duad: for, being taken away, the duad also is taken away. It is necessary, therefore, that it should be the idea of idea, being prior to idea, and having a prior generation: for the indefinite duad was effective of duality. Further still: it is necessary that number should be either finite or infinite; for they make number separate: so that it is not possible that the other of these should not subsist. That it cannot therefore be infinite is manifest: for infinite number is neither odd nor even. But the generation of numbers is always either of the odd number or the even: for, when unity falls upon an even number, an odd number is produced; but when the duad falls upon the even, that number which is from unity is doubled; and when it falls upon the odd number an even number is produced. Again: if every idea belongs to some particular thing, but numbers are ideas, infinite number also will be the idea of something, either of sensibles or of something else; although this is neither possible according to position, nor according to reason: in this manner, however, they arrange ideas.

But if number is finite, how far does it extend? For this ought to be shown, not only that it is, but also why it is. But if, as some say, number extends as far as the decad, in the first place, forms will swiftly fail; as, for instance, if the triad is ideal man, what number will ideal horse be? For every ideal number extends as far as the decad. It is, however, necessary that certain numbers should be in these: for these are essences and ideas; but at the same time they will fail, if they exceed the species of animal. It is also evident, that if the triad is after this manner ideal man, this will also be the case with other triads: for those in the same numbers are similar; so that there will be infinite men. If, indeed, every triad is an idea, each will be ideal man; or, if this be not admitted, at least it will be men. But if the tetrad itself is the idea of any thing, as of horse, or that which is white, man will be a part of horse, if man is the duad. It is also absurd that there should be an idea of the decad, and not of the endecad, nor of the numbers consequent to the endecad.

Again: certain things both are, and are generated, of which there are no ideas: so that it may be asked on what account there are no ideas of these? Forms, therefore, are not causes. Further still: it is absurd that number, as far as the decad, should be in a greater degree a certain being, and the form of the decad itself; although of this indeed there is no generation as of the one, but there is of that. But they speak as if number as far as the decad was perfect, and therefore generate the following numbers, considering as a vacuum, analogy, the odd, and other things of this kind within the decad. For they attribute some things to principles, as, for instance, motion and rest, good and evil; but others to numbers. Hence the one is odd: for, if in the triad, how is the pentad odd? Again: how far do magnitudes and such-like things partake of quantity? as, for instance, the first indivisible line, then the duad, and afterwards these also as far as to the decad.

Further still: if number is separate, some one may doubt whether the one is prior, or the triad and the duad: for, so far as number is a composite, the one is prior; but so far as universal and form are prior, number has a priority of subsistence; for each of the monads is a part of number as matter, but that as form. And indeed the right angle is in a certain respect prior to the acute, because it is limited by its definition; but in another respect the acute angle is prior, because it is a part, and the right angle is divided into this. Indeed, as matter, the acute angle, an element, and the monad are prior; but, considered with relation to form, and an essence according to definition, the right angle, and the whole composed from matter and form are prior: for both are more proximate to form, and to that to which definition belongs, but they are posterior in generation. How, therefore, is the one a principle? Because, say they, it is not divisible, but indivisible, both that which is universal, and that which is particular, and also that which is an element; but in a different manner: the one, indeed, according to definition, but the other according to time. After what manner, therefore, is the one a principle? for, as we have said, the right appears to be prior to the acute angle, and the acute to the right angle, and each is one. But, according to both these modes, they make the one a principle. Still, however, it is impossible: for this is as form and essence, but that as a part, and as matter: for each is in a certain respect one, in reality indeed, in capacity; if, indeed, number is one certain thing, and not as a heap, but, as they say, different numbers subsist from different monads. But the monad is not each of these in energy. The cause, however, of the accidental error is this, that they investigate at the same time from mathematical natures and universal reasons; so that, from those as a point, they have placed the one and the principle: for the monad is a point without position. As, therefore, certain others have composed beings from that which is least, so also they. So that the monad becomes the matter of numbers, and at the same time prior to the duad. It is, however, again posterior, the duad subsisting as a certain whole, as one, and as form. But, in consequence of their investigating a universal predicated one, they speak of it as of a part. It is, however, impossible that there should subsist at the same time in the same thing. But if it is requisite that the one itself should alone be without position (for it differs in nothing, except that it is the principle, and that the duad is divisible, but the monad not)—if this be the case, the monad will be more similar to the one. But if the monad alone is without position, the one will be more similar to the monad than to the duad; so that in either case the monad will be prior to the duad. They do not, however, assert this; for they generate the decad the first. Lastly, if the duad itself is one certain thing, and also the triad itself, both are a duad. From what, therefore, does the duad itself consist?

Aristotle, Metaphysics. Book 13, Chapter 9.

But some one may doubt, since there is no contact in numbers, whether the first monad in the duad or triad is placed in an order consequent to the one, or not; and whether the duad is prior to the monads which are in a consequent order, or whether this is the case with any kind of monads. In like manner, these difficulties take place in the posterior genera of number, of a line, a superficies, and a body: for some make lengths from the species of the great and the small, as it were from the long and the short; but superficies from the broad and the narrow, and bulks from the profound and the low. But these are the species of the great and the small: but others differently place among things of this kind, that principle which subsists according to the one. And in these also ten thousand impossibilities, fictions, and things contrary to all rational assertions appear. For it happens that they will be liberated from any connection with each other, if the principles also do not at the same time follow; but if the principles co-exist, a line will be the same with a superficies, and a superficies with a solid.

Further still: how can angles, figures, and things of this kind be assigned? The same thing also happens to the particulars respecting number. For these are the passions of magnitude: but magnitude does not consist from these, as neither does length consist from the straight and the curved, nor solids from the smooth and the rough. To all these, however, the same doubt is common, which happens to species considered with relation to genus, when any one admits universals; viz. whether animal itself is in animal, or something different from animal itself: for this not being separate produces no doubt; but if separate, as those say who make these assertions, it is not easy to solve the doubts respecting the one and numbers. But, if not easy, it is requisite to say that it is impossible: for, when any one understands the one in the duad, and universally in number, whether does he understand some particular thing itself, or something else? Some, therefore, generate magnitudes from matter of this kind, but others from a point, (but a point appears to them not to be the one, but to possess a like quality with the one) and another matter such as is multitude; concerning which it happens that the same doubts no less arise: for, if the matter is one, line, superficies, and solid are the same; for, from the same things there will be one and the same thing: but if the matters are many, and there is one matter of a line, another of a superficies, and another of a solid, they either follow each other, or they do not. So that thus also the same things will happen: for either a superficies will not have a line, or it will be a line. Further still: no one endeavours to explain how it happens that number subsists from the one and multitude. But in whatever manner they speak, the same difficulties take place which also happen to those who assert that number consists from the one and the indefinite duad: for one generates number from predicated universal, and not from a certain multitude, but another from a certain multitude, yet that which is first; for, according to them, the duad is the first multitude. So that, as I may say, there is no difference with respect to the difficulties that take place, but the same doubts follow, whether mixture, or position, or temperament, or generation, or any thing else of this kind is adopted. But especially it may be inquired, if each monad is one, from what it subsists: for each will not be the one itself. It is necessary, however, that it should either be from the one itself, and multitude, or from a part of multitude. To say, therefore, that the monad is a certain multitude is impossible, since it is indivisible. But to say that each monad is from a part of multitude, is an assertion attended with many other difficulties; for it is necessary that each of the parts should either be indivisible, or be multitude, and that the monad should be divisible, and the one and multitude not be an element; for each monad is not from multitude and the one.

Again: he who says this, does nothing else than make another number: for multitude is a number of indivisibles. Further still: it may be inquired of those who speak in this manner, whether number is infinite or finite: for the multitude also, as it seems, was finite, from which and the one finite monads were produced; and multitude itself is different from infinite multitude. What kind of multitude, therefore, is an element and the one? In like manner, it may be inquired respecting point and element, from which they make magnitudes: for there is not only one point itself. From what, therefore, does each of the other points consist? For it does not consist from a certain interval, and the point itself. But neither does it happen that indivisible parts are the parts of interval, as they are of the multitude which consists from monads: for number is composed from indivisibles, but this is not the case with magnitudes. All these, however, and other such like particulars render it evident, that it is impossible for number and magnitudes to have a separate subsistence. Further still: since the first authors of these hypotheses disagree respecting numbers, it is a sign that these things not being true are the sources of confusion to them. For some, making mathematical species alone besides sensibles, and perceiving the difficulty and fiction respecting forms, abandoned formal, and introduced mathematical, number. But others, being willing to make forms at the same time and numbers, and not perceiving how, if any one adopts these principles, mathematical number can subsist besides the formal, made formal and mathematical number to be the same in definition. But since the mathematician is entirely withdrawn in their assertions, they introduce peculiar, and not mathematical, hypotheses. However, he who first adopts forms and numbers, rationally separates forms and mathematical entities; so that all of them in a certain respect speak rightly, but not entirely so. They likewise do not accord with, but speak contrary to, each other; the cause of which is this: that their hypotheses and principles are false. But it is difficult, according to Epicharmus, to speak well from things which are not well presupposed: for in this case, as soon as any thing is said, it immediately appears not to be well said.

But, with respect to numbers, the doubts already enumerated and the things already determined are sufficient: for he who is persuaded by what has been said, may yet be more persuaded by more numerous arguments; but nothing further can be urged to persuade him who is not yet persuaded. But with respect to first principles, and first causes, and elements, such things as are asserted by those who alone employ themselves about a sensible essence, have been partly mentioned by us in our Physics, and what further remains to be said respecting them does not belong to the present inquiry. But such things as are asserted by those who introduce other essences besides sensibles, form speculations consequent to what has been said. Since, therefore, some assert that there are such like ideas and numbers, and that the elements of these, are the elements and principles of things, let us consider what they say, and how they speak respecting these; reserving for an after speculation the opinions of those who alone introduce numbers, and these such as are mathematical. But of those who assert that there are ideas, some one may at the same time perceive the mode, and the doubts which take place respecting them: for at the same time they make ideas to be universal essences, and again they consider them as separate, and as particulars. But, that these things are not possible, we have already doubted. The cause, however, which induced those who call ideas universals, to consider both as one and the same thing, was because they did not make them to be the same essences as sensibles. Particulars, therefore, which are in sensibles, they considered as having a flowing subsistence, and that none of them had any permanent essence; but that there was universal besides these, and that it was different from them. But this, as we have before observed, excited Socrates through definitions, yet he did not abstract from particulars; and by thus not abstracting he conceived rightly. The truth of this, indeed, is evident from operations: for without universals science cannot be attained. But to separate them from sensibles is the cause of the difficulties which take place respecting ideas. But others, as if it were necessary that, if there are certain essences besides sensible and flowing natures, they should have a separate subsistence, not having any others, introduced these which are called universals. Hence it happens that universals and particulars are nearly the same natures. This, therefore, will itself be a certain essential difficulty, with which the above-mentioned particulars are attended.

Aristotle, Metaphysics. Book 13, Chapter 10.

But, as we observed in the doubts which we enumerated before, that both the assertions of those who contend that there are ideas, and of those who contend that there are not, are attended with a certain doubt, we must now also repeat the same observation. FOR HE WHO DOES NOT ADMIT THAT THERE ARE SEPARATE ESSENCES, AND THAT PARTICULARS ARE AS IT WERE AFTER THIS MANNER THE SUBJECT OF DISCOURSE—SUBVERTS, AS WE WILLINGLY ALLOW, ESSENCE ITSELF. But yet, if any one admits that there are separate essences, how will he establish the elements and principles of them? For if these are particulars, and not universals, there will be as many beings as there are elements, and the elements will not be the objects of scientific knowledge; for, let the syllables in a word be essences, but the elements of them the elements of essences: but it is necessary that ba and each of the syllables should be one, if not universally indeed, and the same in species, yet each must be one in number, and this particular thing, and not homonymous. Further still: each one is considered by them as the very thing itself: but if syllables, so likewise the things from which they are composed. There will not, therefore, be more than one letter a; and for the same reason, each of the other elements will only be one, as neither of the other syllables will the same syllable be in different words. But, indeed, if this be the case, there will be no other beings than elements, but things will be elements alone. Again: elements will not be the objects of scientific knowledge; for they are not universals, but the objects of science are universals. But this is evident from demonstrations and definitions: for the syllogism will not be, that this particular triangle has angles equal to two right, unless the same conclusion is true of every triangle; nor that this man is an animal, unless every man is an animal. But yet, if principles are universals, or if the essences which subsist from these are universals, non-essence will be prior to essence: for universal is not essence; but element and principle are universals. But element and principle are prior to the things of which they are the element and principle. All these consequences, therefore, rationally happen, both when they make ideas from elements, and when, besides ideas and essences which have the same form, they think fit that there should be a certain one which has a separate subsistence. If nothing, however, hinders, but that, as in the elements of speech, there is a multitude of the letter a, and a multitude of the letter b, and a itself and b itself are nothing besides the multitude of these, on this account there will be infinite similar syllables. But that all science is of universals, so that it is necessary the principles of things should be universals, and should not be separate essences, this is attended with a greater doubt than any thing which has yet been said. In a certain respect, however, that which is now asserted is true, and in another respect it is not true: for science as also scientific knowledge is twofold; of which one is capacity, but the other energy. Capacity, therefore, being as it were the matter of that which is universal and indefinite, is the capacity of the universal and indefinite; but energy being definite, has also a definite object, being something particular of something particular. But sight perceives accidentally universal colour; and the grammarian speculates this particular a. Since, if it is necessary that the principles should be universals, it is also necessary that the things which subsist from them should be universals, as is evinced in demonstrations. But if this be the case, nothing will have a separate subsistence, nor even essence itself. It is evident, however, that science is in a certain respect of that which is universal, and in a certain respect not.

Aristotle, Metaphysics. Book 14, Chapter 1.

And thus much, therefore, respecting this essence. But, as we observed in our Physics, that all philosophers make principles to be contraries, the like is also true concerning immoveable essences. However, if it is not possible that any thing can be prior to the principle of all things, it will be impossible that the principle being any thing else should be the principle of all. Just as if any one should say that a thing white is the principle, not so far as it is something else, but so far as it is white, which yet according to its subject is white, and at the same time something else: for that will be prior. But, indeed, all things are generated from contraries as from a certain subject. It is therefore especially necessary that this should take place in contraries. Hence, all contraries pertain to a subject, and none of them has a separate subsistence. But, as it appears, nothing is contrary to essence; and reason testifies the truth of this assertion. No one, therefore, of contraries is properly the principle of all things, but something different from these. But, according to some, the other of contraries is matter. According to others, the unequal is contrary to the one, that is to the equal, as if this were the nature of multitude. And again: according to others, multitude is contrary to the one: for numbers are generated by some from the unequal duad, viz. the great and the small, but by a certain person from multitude; by both, however, from the substance of the one: for he who calls the unequal and the one elements, but the unequal from the small and the great the duad, speaks of the unequal, the great and the small, as if they were one, nor does he clearly assert that they are so in definition, but not in number. Nor yet do they well explain the principles which they call elements. For some, introducing the great and the small together with the one, assert that these three are the elements of numbers; the two first indeed, having the relation of matter, but the one of form. But according to others, the much and the few are elements, because the great and the small are naturally more allied to magnitude. According to others, again, the elements are things more universal in these, viz. the surpassing and the surpassed. But no one of them differs, as I may say, with respect to certain things which take place, but only with respect to logical difficulties which they defend, because they also introduce logical demonstrations. Indeed an instance of this may be seen in their assertion, that principles are the surpassing and the surpassed, but not the great and the small, and that of the elements, number is prior to the duad: for both are more universal. But now they assert the one, and not the other. Others again, oppose to the one that which is different and another. But others introduce as principles, multitude and the one. But if beings are from contraries as they are willing they should be, but to the one either nothing is contrary, or, if there be, it is multitude; but the unequal is contrary to the equal, difference to sameness, and that which is another to that which is the same,—if this be the case, those who oppose the one to multitude, have something to urge in defence of their opinion: yet neither is their hypothesis sufficient: for the one will be few; since multitude is opposed to paucity, and the much to the few. But, with respect to the one, it is evident that it signifies measure. And in every thing there is a certain other thing which ranks as a subject; as for instance, in harmony, diesis; but in magnitude, a finger, or foot, or something of this kind; but in rhythms, the basis, or a syllable. In like manner, in weight, there is a certain definite measure, and so in all things. With us, too, in qualities, there is a certain definite quality, and in quantities a certain indivisible quantum: for, with respect to measure, one kind is according to form, but another according to sense; so that there is not any essence which is essentially one. And this rationally: for the one signifies that it is the measure of a certain multitude; and number, that it is multitude measured and a multitude of measures. Hence, it may be reasonably inferred that the one is not number; for neither is a measure measures, but a principle, and the measure, and the one. But it is requisite that a measure should always subsist the same in all things; as, for instance, if a horse is the measure in horses, and if a man in men. But if man, horse, god, and animal are measures, perhaps the number of them will be animals; but if man, white, and walking, there will by no means be a number of these, because all of them subsist in one and the same according to number. At the same time, however, there will be a number of their genera, or of something else which has a similar appellation. But those who make the unequal as one certain thing, but the indefinite duad from the great and the small, speak very far from the truth of things apparent and possible; for these are rather passions and accidents, than things subject to numbers and magnitudes. For the much and the few, the odd and the even, are the passions of number; and the great and the small, the smooth and the rough, the straight and the curved, are the passions of magnitude.

Further still: in addition to this error, it is also necessary that the great and the small, and things of this kind should be relatives. But of all the categories, relation is in the least degree a certain nature or essence, is posterior both to quality and quantity, and, as we have said, is a certain passion of quantity, but is not matter, or any thing else; and, in short, is something common both to the parts and species of quantity. For there is nothing, either great or small, or much or few, or, in short, which subsists as a relative, which is not much or few, great or small, or a relative, at the same time that it is something else. But that relation is in the smallest degree a certain essence, and being is apparent from hence, that of it alone there is neither generation, nor corruption, nor motion, as with respect to quantity there is increase and diminution, with respect to quality alteration, with respect to place local motion, and with respect to essence, simply generation and corruption; but this is not the case with respect to relation: for, without being moved, at one time it will be greater, and at another time lesser or equal, the other being moved according to quantity. It is also necessary that the matter of every thing should be such as the thing itself is in capacity; so that this will also be the case with the matter of essence: but relation neither in capacity nor in energy is essence. It is absurd, therefore, or rather impossible, to make non-essence to be the element of, and prior to, essence: for all the categories are posterior. Again: elements are not predicated of those things of which they are the elements: but the much and the few are predicated both separately and together of number, and the long and the short of a line, and a superficies is both broad and narrow. But if there be a certain multitude to which the few always belongs, it will be, for instance, the duad; (for, if this be much, the one will be few,) and if it be much simply, it will be much after the manner of the decad; and if this be not the case, it will be more than ten thousand. How, therefore, will number consist from the few and the much? For, either it is necessary that both should be predicated, or neither; but now one of these alone is predicated.

Aristotle, Metaphysics. Book 14, Chapter 2.

But it is requisite simply to consider whether it is possible for things eternal to be composed from the elements: for they will have matter, since every thing consisting from elements is a composite. If, therefore, it is necessary that a thing should be generated from that from which it consists (both if it always is, and if it is generated), but every thing is generated from that which is in capacity the thing generated (for it could not have been generated from the impossible, and it was not before it was generated), but that which is possible may energise, and may not energise; if this be the case, number also, although it most eminently always is, or any thing else which possesses matter, may happen not to be, just as that which possesses the space of one day, and that which has any number of years whatever. But if this be the case, it will be true also of time, when it is so extended as to be without bound. There will not, therefore, be things eternal, since that is not eternal which it is possible may not be, as we have elsewhere shown. But if that which is now said is universally true, that no one essence is eternal, unless it be in energy, and elements are the matter of essence, there will not be elements of any eternal essence, from which being inherent such essence is composed. But there are some who make the indefinite duad together with the one, the element, but are very properly unwilling to admit the unequal, on account of the impossibilities which take place; from whom, such of the difficulties only are taken away, as must necessarily happen to those who make the unequal and relation to be the elements of things. But such difficulties as take place separate from this opinion, must also necessarily happen to these, whether they produce from them ideal or mathematical number. There are, therefore, many sources of error with respect to these causes; but the opinion of the ancients is especially the occasion of doubt: for it appeared to them that all things would be one, viz. being itself, unless some one solves the doubt, and at the same time proceeds conformably to the reasoning of Parmenides: for this cannot by any means be non-being; but it is necessary to show that non-being is. For thus, from being and something else, things will subsist, if they are many; though, indeed, this will be true in the first place, if being is manifold: for this signifies that a thing is essence, that its possession of quality, this again that it is endued with quantity, and so of the other categories. What kind of one, therefore, will all things be, if non-being is not? Whether will they be essences, or passions; and in a similar manner other things? Or will they be all things? And the one will be this thing, and such-like, and so much, and such other particulars as signify one certain thing. But it is absurd, or rather impossible, that one certain nature should be a generated cause, and that of this being, and of the same being, something should be this particular thing, something else should be endued with quality, this belong to quantity, and that to situation. In the next place, from what kind of non-being and being do beings subsist? For non-entity is manifold, since this is also true of being. And, indeed, non-man signifies that which is not this particular thing; but not straight signifies that which does not possess this particular quality; and not three cubits, that which does not possess this particular quantity. From what kind, therefore, of being and non-being, does the multitude of beings subsist? This opinion, therefore, wishes to assert that which is false, and to call this nature non-being, from which, and being, the multitude of beings subsists. Hence, it is also asserted that something false ought to be supposed, in the same manner as geometricians admit as an hypothesis, that a thing is pedal which is not pedal. It is not, however, impossible, that this should be the case: for neither do geometricians suppose any thing false (since that is not the proposition in the demonstrative syllogism), nor are things generated or corrupted from that which is after this manner non-being. But since non-being, according to cases (πτώσεις), is equally predicated with the categories, and, besides this, that is called non-being which subsists as the false, and also that which subsists according to capacity, from this generation takes place from that which is not man, but man is produced from man in capacity; and a thing white, from that which is not white in energy, but in capacity. The like consequences ensue whether one thing is generated or many. But the inquiry seems to be, how being, which is predicated according to essences, is many: for numbers, and lengths, and bodies, are things which are generated. It is absurd to inquire how being, which is some particular thing, is many, and not also to inquire how it possesses quality or quantity. For neither is the indefinite duad the cause, nor yet the great and the small, that two things are white, or that there are many colours, or tastes, or figures: for these will be numbers and monads. Indeed, if they had attended to these things, they would have perceived the cause also in them. For the same thing, and the analogous, is the cause: for the deviation itself is the cause, and also the opposition of that which they investigated to being and the one, which induced them to suppose that which has a relative subsistence, and the unequal, because there is neither a contrary to, nor a negation of, these, but one nature of things, as, for instance, this particular thing, and that quality. This also ought to have been investigated, how relatives are many, and not one. But now it is inquired, how there are many monads besides the first one: but they do not also inquire how there are many unequals besides the unequal, although they employ and speak of the great and the small, the much and the few, from which numbers consist; the long and the short, from which length is composed; the broad and the narrow, which constitute superficies; and the deep and the low, from which bulks consist; and so of any other species of relatives which they may introduce. What then is the cause to these of their being many? It is necessary, therefore, as we have said, to suppose in each of these being in capacity. And this also is evinced by him who makes these assertions, viz. that this particular thing is being in capacity, and essence, but that of itself it is non-being, because it is relative. Just as if he should speak of something of such a nature, that it is neither the one nor being in capacity, nor yet a negation of the one or being,—but one certain thing, which is something belonging to beings. But much more will this be the case (as we have said) if he inquires after what manner beings are many; not by inquiring how things in the same predicament are many essences, or many things endued with quality, but how they are many beings: for some things are essences, others are passions, and others are relatives. In the other categories, therefore, the subsistence of the many is the subject of another consideration. For, because they are not separable, the subject becomes, and is many; and those things also endued with qualities and quantity are many. But though it is necessary that there should be a certain matter to every genus, yet it is impossible that it should be separate from essences. In things, however, which subsist as particulars, there is some reason in the inquiry, how this particular thing is many, if it is not something particular, and this very particular thing, and a certain nature. But this doubt rather originates from thence, how there are many essences in energy, and not one. However, if this particular thing is not the same with that which is a certain quantity, it is not said how and on what account beings are many, but how and on what account quantities are many: for every number signifies a certain quantity; and the monad is nothing else than a measure, because it is according to quantity indivisible. If, therefore, a quantity is different from that which subsists as a definite particular, it is not said from what such definite particular originates, nor how the many subsist. But if it is the same, he who asserts this sustains many contradictions. It may also be suggested with respect to numbers, whence are we to obtain conviction of their subsistence? for the doctrine of ideas introduces a certain cause to things, since every number is an idea. But idea in some way or other is the cause of being to other things: for let this be supposed by them. With respect, however, to the man who is not of this opinion, because he sees the difficulties with which the doctrine of ideas is attended, so that on this account he does not make them to be numbers, but introduces mathematical number, whence is it proper to believe that there is number of this kind, and that it is in any respect useful to other things? For, neither does he say that it is the cause of any thing, who asserts its subsistence, but such a one affirms that it is a certain nature, which has an essential subsistence; nor does it appear that it is a cause. For, as we have already said, all arithmetical theorems are conversant with sensibles.

Aristotle, Metaphysics. Book 14, Chapter 3.

Those, therefore, who assert that there are ideas, and that they are numbers, should endeavour to inform us how and why they subsist; since, according to the exposition of each, every idea is one certain thing different from the many. However, as these things are neither necessary nor possible, neither must it be said that mathematical number has a separate subsistence. But the Pythagoreans, in consequence of perceiving many passions of numbers subsisting in sensible bodies, made beings to be numbers, not however separate; but they considered beings as composed from numbers. But why? Because the passions of numbers subsist in harmony, in the heavens, and in many other things. But, to those who speak of mathematical number alone, nothing of this kind follows according to their hypotheses; but it was said by them, that of these there will not be sciences. We however say that there is, as we before asserted. And it is evident that mathematical natures have not a separate subsistence; for, if they had, the passions of them would not be inherent in bodies. The Pythagoreans, therefore, so far as relates to a thing of this kind, are not to be reprehended: but so far as they make natural bodies from numbers, from things without gravity or levity, things heavy and light, they appear to speak of another heaven and other bodies, and not of sensibles. But those who make numbers to have a separate subsistence, because axioms are not in sensibles, and the assertions of mathematicians are true, these cause a perturbation in the soul, and apprehend that numbers are, and have a separate subsistence; and in a similar manner, mathematical magnitudes. It is evident, therefore, that the adverse argument asserts contraries, and that which was just now doubted is solved by those who speak in this manner, viz. why, since these things by no means subsist in sensibles, yet the passions of them are in sensibles? But there are some, who, in consequence of the subsistence of boundaries and extremities, viz. from a point being the boundary of a line, a line of a superficies, and a superficies of a solid, are of opinion that such natures must necessarily exist. It is requisite therefore to consider, whether this opinion also is not very debile: for neither are extremities essences, but rather all these are boundaries: since both of walking, and universally of motion, there is a certain boundary. Is therefore this boundary some particular thing, and a certain essence? But to suppose this would be absurd. Admitting, however, that these were essences, all of them would be sensibles; for the assertion admits that they subsist in these. Why therefore will they be separate? 

Further still: some one who is not very easily persuaded, may inquire concerning every number, and mathematical natures, why such of these as are prior contribute nothing to those that are posterior: for, according to those who say that mathematical natures alone subsist, though number should not be, yet magnitudes would still have a subsistence; and though these were not, yet still soul would be and sensible bodies. But from the phenomena, nature does not appear to be adventitious, like a bad tragedy. This, however, escapes the notice of those who introduce ideas: for they make magnitudes from matter and number; from the duad indeed lengths; but from the triad perhaps superficies; and from the tetrad solids, or from other numbers: for it is of no consequence. But whether will these be ideas, or what is the mode of their subsistence, and what do they contribute to beings? Nothing indeed, as neither do mathematical natures contribute any thing. But neither is there any theorem of these, unless some one is willing to move mathematical entities, and to make certain peculiar opinions. But it is not difficult for those who assume any kind of hypotheses to be prolix and speak incessantly. These therefore in this manner err, by connecting mathematical entities with ideas. But the first of these making two numbers, the one of forms, and the other mathematical, by no means say, nor are they indeed able to say, how and from what a mathematician will be formed; for they place him between the formal and the sensible: for, if from the great and the small, he will be the same with him who is one among the number of ideas; but if from another small and great, he will compose magnitudes. If, however, he speaks of any thing else, he speaks of many elements. And if the principle of each is a certain one, the one will be something common in these. But then it must be investigated how these many are one; and at the same time, according to him who makes this assertion, it is impossible for number to be generated, otherwise than from the one and the indefinite duad. All these consequences, therefore, are irrational, and both oppose themselves, and those who argue rationally. In these conclusions, too, there appears to be the long discourse of Simonides: for a long discourse is like that of slaves, where nothing sane is asserted. They appear also, with respect to those elements, the great and the small, to exclaim as if they were dragged up with violence: for they cannot by any means generate number, without doubling that which proceeds from the one. But it is absurd, or rather, it is one of the things impossible, to introduce generation of these things which are eternal. With respect to the Pythagoreans, therefore, there is no occasion to hesitate, whether they introduce, or do not introduce, generation: for they clearly assert that, the one being established, immediately that which is nearest to the infinite, whether from superficies, or from colour, or from seed, or from such things as they are dubious to assert, is drawn forth, and terminated by bound. But, since they show how the world was fabricated, and are willing to speak physically, it is just that they should investigate something concerning nature, but depart from the present method: for we investigate the principles in things immoveable. So that it is requisite to consider the generation of numbers of this kind.

Aristotle, Metaphysics. Book 14, Chapter 4.

They do not, therefore, speak of the generation of the odd number, as if it were evident that generation is of the even number. But they first of all constitute the even number from unequals, i.e. the great and the small equalized. It is therefore requisite that inequality should subsist prior to the equalization of these. But, if they were always equalized, they would not have been prior to this unequal: for there is not any thing prior to the even. So that it is evident that they do not make the generation of numbers for the sake of contemplating. But the manner in which elements and principles are related to the good and the beautiful is dubious, and, to him who doubts properly, is a subject of reprehension. The doubt is this, whether some one of them is such as we wish to call the good itself, and the most excellent, or whether this is not the case, but they are of posterior generation. Indeed, by some of the present theologists this appears to be acknowledged, who say, that from the progression of the nature of things the good and the beautiful become apparent. But they do this to avoid the real difficulty which happens to those who assert (as is the case with some) that the one is the principle of things. The difficulty, however, arises, not from their attributing to the principle good as a thing present with it, but from their considering the one as a principle, and that it is a principle as an element, and that number is from the one.

Thus, too, in a similar manner antient poets assert, that Jupiter reigned and governed, and not those first principles such as Night and Heaven, or Chaos, or even Ocean. But it happens indeed to these, to assert things of this kind, in consequence of changing the rulers of the world; since those among these, who were of a mixed class, and who did not speak of these things fabulously, such as Pherecydes, and certain others, establish the first generating principle, as the best of things. This is also the case with the Magi, and among the wise of latter times, with Empedocles and Anaxagoras; the former making friendship to be the element, and the latter, intellect to be the principle, of things. But of those who assert that there are immoveable essences, some say that the one is the good itself; but nevertheless they are of opinion that the essence of the good is especially the one. In which way, therefore, is it proper to solve this doubt? But it is wonderful, if to that which is first, perpetual, and most sufficient to itself, sufficiency and the preservation of itself should not be good to it the first of all things. Indeed, it is incorruptible and sufficient to itself for no other reason than because it has an excellent condition of subsistence. So that to say that the principle of things is of this kind, may rationally be supposed to be true. That this, however, should be the one, or, if not this, the element of numbers, is impossible: for many difficulties attend this hypothesis, which some in order to avoid, acknowledge that the one is the first principle and element of things, but that this one is not the principle of mathematical number: for, if this were the case, all the monads would become a certain good, and there would be a great abundance of things good.

Further still: if forms are numbers, all forms will be a certain good. Let however, any one suppose ideas to be of whatever nature he pleases: for, if they are of things good alone, ideas will not be essences. But if of essences also, all animals and plants are good, and the participants of these. These absurdities therefore, attend this hypothesis, and the contrary element, whether it be multitude, or the unequal, and the great and the small, will be evil itself. Hence, a certain person avoids connecting the good with the one, because, on this hypothesis, since generation is from contraries, the nature of multitude must be necessarily evil. But others assert, that the unequal is the nature of evil. It so happens, therefore, that all beings participate of evil, except the one which is the one itself, and that numbers participate it more purely than magnitudes. It also follows that evil is the place of good, and that it participates and aspires after that which is corruptive of itself: for one contrary is corruptive of another. But if, as we have said, matter is every thing in capacity, as, for instance, fire in capacity of fire in energy, evil will be the good itself in capacity. All these things therefore happen, in consequence of making every principle an element,—contraries principles,—the one the principle of things,—and numbers the first essences, having a separate subsistence, and existing as forms.

Aristotle, Metaphysics. Book 14, Chapter 5.

If, therefore, not to rank the good among principles, and to rank it among them in the manner we have mentioned, is impossible, it is evident that neither principles nor the first essences are rightly assigned. Nor yet does he conceive rightly, who assimilates the principles of the universe to the principle of animals and plants; because things more perfect always proceed from such as are indefinite: on which account also, in first essences, they say, it so happens that neither is any particular being the one itself. But, in sensible things also, the principles from which sensibles originate are perfect. For man generates man, and seed is not the first thing. It is also absurd to make place together with mathematical solids: for the place of particulars is peculiar to them, on which account they are locally separable. But mathematical solids are not situated in a certain place. And to say indeed that they are situated somewhere, and at the same time not to say what place is, is absurd. But it is requisite that those who assert that beings are composed from elements, and that numbers are the first of beings, should, by dividing one thing from another, inform us after what manner number subsists from principles, and whether this is accomplished by mingling. But neither is every thing mingled which is generated.

Does number then subsist from composition, as a syllable? But, in this case, it is necessary there should be position; and he who employs his intellect on this subject will understand separately the one and multitude. Number, therefore, will be the monad and multitude, or the one and the unequal. And since that which subsists from certain things, subsists indeed partly as from things which are inherent, and partly not, in which way will number subsist? For those things which subsist as from things inherent, are no other than those of which there is generation. Does it, therefore, subsist as from seed? But it is impossible for any thing to depart from that which is indivisible. Shall we say, it is as from a contrary not abiding. But things which subsist in this manner, are also from something else which is of a permanent nature. Since, therefore, with respect to the one, this person considers it as contrary to multitude, but that as contrary to the unequal, employing the one as if it were the equal, number will subsist as from contraries. There is, therefore, something else from which, being permanent, the generation of the other is effected.

Further still: why are such other things as are from contraries, or to which there are contraries, corrupted, though they may consist from every thing, but this is not the case with number? For, respecting this nothing is said, though contrary, both when it is inherent and when it is not inherent, corrupts; as, for instance, strife that which is mixed. This, however, is not requisite; for the former is not contrary to the latter. But nothing is determined with respect to the manner in which numbers are the causes of essences, and of being, whether as boundaries in the same manner as points of magnitudes, and, according to Eurytus, as number of a certain thing; as, for instance, this number of man, and that of horse. Just as those who refer numbers to figures, the triangle and the square, thus assimilating the forms of plants to calculations. Shall we say, this is because it is either ratio, or the symphony of numbers? and in a similar manner, with respect to man and every thing else. But with respect to passions, how are they numbers, such as the white, the sweet, and the hot? However, that numbers are neither essences, nor the causes of form, is evident: for reason is essence; but number is matter, as, for instance, the number of essence of flesh or bone. Thus, too, three of fire, but two of earth; and always number, whatever it may be, is of certain things, and is either fiery, or terrene, or monadic. But essence consists in being so much with respect to so much according to mixture. But this is not number, but the ratio of the mixture of corporeal numbers, or of certain things. Number, therefore, is not a cause by making; nor is number altogether, nor monadic number, either as matter, or as reason and the form of things. Neither is it as that for the sake of which a thing subsists.

Aristotle, Metaphysics. Book 14, Chapter 6.

But some one may doubt what the good is which results from numbers; if mixture is either in rational or in the odd number: for now nothing more salubrious arises, from water and honey being thrice three times mingled: but it will be more beneficial if there be no proportion in the mixture; and it will be watery, or in number unmingled. Further still: the ratios of mixtures consist in the addition of numbers, and not in numbers themselves; as, for instance, the ratio between three and two is that of three to two, but is not thrice two: for it is requisite that there should be the same genus in multiplications; so that it is requisite that the series abg should be measured by a, and dez by d; so that all things must be measured by the same measure. There will be, therefore, of fire begz, and of water the number twice three. But if it is requisite that all things should participate of number, it is also necessary that many things which are the same should happen, and that there should be the same number to this thing and to another. Is, therefore, this the cause, and is a thing through this? Or is it immanifest, such as is a certain number of the revolutions of the sun, and again of those of the moon, and of the life and age of every animal? What, therefore, hinders, but that some of these may be squares, others cubes, and equal to each other, and others again double? Nothing, indeed, hinders; but it is necessary that they should be intimately connected with these, if all things participate of number. It will also happen that things which differ from each other will fall under the same number; so that, if the same number happens to certain things, they will be the same with each other, having the same form of number; as, for instance, the sun and moon will have the same numerical form. But through what cause have they the same form? There are, indeed, seven vowels, seven chords or harmonies, seven Pleiades: in seven years, too, some shed their teeth, and some do not; and those who led an army against Thebes were seven in number. Is it, therefore, because such a particular number is naturally adapted to the purpose, that either they were seven, or that the Pleiades consist of seven stars? Or are these, indeed, on account of the gates of Thebes, or through any other cause? But if we thus numerate and assign twelve stars to the Bear, others ascribe to it a greater number: for they say, that ξ ψ ζ are symphonies: and that, because those are three, these also are three. However, that there are ten thousand such-like things is not an object of concern to any one: for γ and ρ will be one sign; but if at one time each of the others is double, but another is not, this is, because one in each is added to σ. On this account there are three only, and not because there are three symphonies: for there are more symphonies than three; but here there cannot be more than three. These men also resemble the ancient Homerics, who perceived small similitudes, but overlooked such as are great. But some assert there are many such-like particulars, as, for instance, with respect to media, one medium is 9 and another 8; and a verse of 17 feet is equal in number to these. But in syllables they say that 9 ascends on the right hand, but 8 on the left; and that there is an equal interval in letters from α to ω, and in pipes from the most grave sound to the most acute note (nete?), the number of which is the equality in the all-various melody of the heavens. But we ought not to perceive things of this kind (for no one will make them the subject of doubt), nor speak concerning them, nor attempt to discover them in things perpetual, because they are to be found in things corruptible. But those natures in numbers which are the subject of praise, and the contraries to these, and, in short, the objects of mathematical contemplation, as they are considered by some, and made to be the causes of nature, appear to escape the attention of those who speculate in this manner. For no one of them is a cause according to any of those modes which are defined respecting principles. Yet, as they make it manifest that well being has a subsistence, and that the odd number, the straight, the equal, and powers of certain numbers, are of the co-ordination of the beautiful (for the season of the year and a particular number subsist together), and such other things as they collect from mathematical theorems,—all these possess this power; on which account they resemble casual accidents: for they are indeed accidents, but all of them accord with each other; but the analogous is one: for in each category of being there is the analogous, as, for instance, the straight in length is analogous to the even in superficies; and perhaps the odd in number, and the white in colour. Further still: the numbers which are in forms are not the causes of things harmonic and the like: for those equals in species differ from each other, for the monads also differ; so that, in consequence of these things, forms are not to be introduced. These consequences, therefore, and still more than these, may be collected; but they appear to afford an argument that the patrons of ideas fall into many errors respecting the generation of them, and that they cannot be consistent, because mathematical species are not, as some say, separated from sensibles, nor are these the principles of things.

THE END