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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.

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 thos e 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 w ill 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 period 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 there 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 of 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 then manual artificers; and the theoretic then fabricators. That wisdom, therefore, is a science about certain causes and principles, is evident.

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, two 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 odd 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, two no 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 too for man to know: for they are most remote from the senses. But the most accurate of the sciences are those which especially relate two things first period 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 period 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 then 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, two, 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 closed parenthesis 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. Four 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 this 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Book III, 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.

Book III, Chapter 4

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