Aristotle, Posterior Analytics

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We are happy to host the only online edition of Thomas Taylor’s translation of Aristotle’s Posterior Analytics. The text below is an adaptation of Thomas Taylor’s translation of Aristotle’s Posterior Analytics (1805) and is intended for use by students of the Classical Liberal Arts Academy. This text may not be copied or used in any way without written permission from Mr. William C. Michael.

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Table of contents

Aristotle, Posterior Analytics. Book I

Aristotle, Posterior Analytics. Book I, Chapter 1

All doctrine and every dianoetic discipline are produced from pre-existing knowledge. But this will be evident if all of them are surveyed. For the mathematical sciences are obtained after this manner,

and each of the other arts. The like also takes place in arguments, as well those which are formed through syllogisms, as those which are formed through induction. For both procure doctrine, through things previously known; these assuming as from the intelligent; but those demonstrating the universal, in consequence of that which is particular being manifest. In a similar manner also rhetorical arguments persuade; for they either persuade through examples, which is induction, or through enthymemes, which is syllogism. But it is necessary to know previously in a twofold respect. For with regard to some things, it is necessary to pre-assume that they are; with respect

to others, it is requisite to understand what that is which is spoken of; or what it signifies, and with respect to others both these must be known. Thus, for instance, it ought to be pre-assumed that of everything it is true to affirm or deny that it is; but of a triangle, that this is its signification; and of the monad both ought to be previously known, viz. what it signifies, and that it is; for each of these is not similarly manifest to us. It is possible, however to know, in consequence of knowing some things previously, and at the same time receiving the knowledge of others; as of things which are contained under universals, and of which the knowledge is possessed. For that every triangle has angles equal to two right, is previously known; but that this which is in a semicircle is a triangle is known as soon as it is described.  For of some things the discipline is after this manner, nor is the extreme

known through the middle; viz. such things as are now particulars, and are not predicated of any subject. Perhaps, however, it must be confessed, that knowledge may after a certain manner be · possessed prior to the description of the triangle, or the assumption of syllogism; but after a certain manner not. For how, in short, can he who is ignorant whether a thing is in existence, simply know that it has angles equal to two right? But it is evident that he thus knows, because he knows the universal, but simply does not know.  For if this be not admitted, the doubt will happen which is mentioned in Plato’s Meno; for he will either learn nothing or he will learn the things which he knows. For we must not make the interrogation of some who endeavour to solve this doubt; viz. Do you know that every duad is an even number? or not? For if some one says that he does, they adduce

a certain duad which he did not think existed, and, therefore, did not  think to be an even number. But they solve the ambiguity not by saying that he knew that every duad was even, but that he was ignorant that what they knew was a duad.  They know, however, that of which they have the demonstration, and the demonstration of which they have received. But they have received it not of everything which they know to be a triangle, or number; but simply of every number or triangle. For no proposition is assumed of such a kind as, This is the number which you know, or, This is the rectilinear figure which you know; but a proposition pertains to every number, and every rectilinear

figure. Nothing, however, I think, prevents, but that he who learns, in a certain respect knows, and in a certain respect is ignorant. For it is not absurd that he should in a certain respect know that which he learns; but it is absurd that he should thus know it, viz. as he does when he learns it, and in the same manner.

Aristotle, Posterior Analytics. Book I, Chapter 2

We think, however, that we know each thing simply, and not in a sophistical manner, from accident, when we think that we know the cause on account of which a thing is, that it is the cause of that thing, and that the thing cannot subsist otherwise.  It is evident, therefore, that scientific knowledge is a thing of this kind. For with respect to those who do not, and those who do possess scientific knowledge; the former fancy that they in this manner possess science, but the scientific possess it in reality. Hence it is impossible that a thing of which there is simply science should subsist otherwise. Whether, therefore, there is another mode of knowing scientifically, we shall afterwards show; but we also say that scientific knowledge is a knowledge obtained through demonstration. But I call demonstration a scientific syllogism. And I call it scientific, according to which, from possessing

it, we know scientifically. If, therefore, to know scientifically is such a thing as we have asserted it to be, it is also necessary that demonstrative science should be from things true, first, immediate, more known than, prior to, and the causes of the conclusion. For thus they will also be the proper principles of that which is demonstrated. For syllogism, indeed, will also be without these; but demonstration will not be without them; since it will not produce science. It is necessary, therefore, that the things from which demonstrative science consists should be true, because it is not possible for that which is not to be known scientifically; as, that the diameter of a square is commensurable with its side. But demonstrative science must be from things first and indemonstrable; for otherwise, the demonstration of them not being possessed, they will not be scientifically known. For to have a scientific knowledge of those things of which there is demonstration, and this, not from accident, is to have demonstration. But it is necessary that they should becauses, should be more known, and prior. They must be causes, indeed, because we then know scientifically when we know the cause; and prior, because they are causes. They must also be previously known, not only according, to the other mode, by which we understand what they signify, but also because it is known that they are

true. But they are prior and more known in a twofold respect. For that which is prior to nature is not the same as that which is prior to us; nor is that which is more known to nature the same as that which is more known to us. But I call things which are prior and more known to us, things more proximate to sense; and I denominate things simply prior and more known, such as are more remote from sense. But things most remote from sense, are such as are especially universal; and such as are most near to sense are particulars. And these are opposed to each other. But that is from things first, which is from appropriate principles. For I call that which is first, and the principle the same thing. But an immediate proposition is the principle of demonstration. And that is an immediate  proposition, to which there is not any other pnor. But a proposition is one part of enunciation, one of one; dialectic, indeed, which similarly assumes either part of contradiction; but demonstrative, which definitely assumes that one part is true. Enunciation is either part of contradiction: and contradiction is an opposition, which has no medium essentially. But of the parts of contradiction, that which signifies something of something, is affirmation; and that which signifies something from something,

is negation. Of an immediate syllogistic principle, however, I call that position, which it is not possible to demonstrate, and which it is not necessary he should possess, who intends to learn any thing. But I call that an axiom, which he who intends to learn any thing must necessarily possess. For there are certain things of this kind; and especially in denominating these, we are accustomed to use this name. But of position, that which receives either of the parts of contradiction as, for instance, that a certain thing is, or that a certain thing is not, is hypothesis; but that which is without this, is definition. For definition is, indeed, position; since unity is posited by the arithmetician to be that which is indivisible according to quantity; but it is not hypothesis. For what unity is, and that unity is, are not the same thing.  Since, however, it is necessary to believe in, and know a thing, in  consequence of possessing such a syllogism as we call demonstration, and this is because these are the things from which syllogism consists, this being the case, it is necessary not only to have a  previous knowledge of all, or some things, but also that they should be more known. For always that on account of which any thing exists, exists itself in a greater degree. Thus, that on account of which we love, is itself more beloved. Hence, if we know and believe on account of such things as are first, we also know and believe those first things in a greater degree, because through those we know and believe such as are posterior. It is not possible, however, for any one to believe more than the things

which he knows, those things which he neither knows, nor with respect to which he is disposed in a better manner, than if he knew them. This, however, will happen, unless believing through demonstration he has a previous knowledge; for it is more necessary to believe either in all, or in certain principles, than in the conclusion. But it is not only necessary, that he who is to possess science through demonstration, should know in a greater degree principles, and believe in them in a

greater degree, than in the thing demonstrated; but also that nothing else should be more credible, or more known to him, than the opposites to the principles from which the syllogism of contrary deception will consist; since it is necessary that he who simply possesses scientific knowledge, should be free from a lapse into error.

Aristotle, Posterior Analytics. Book I, Chapter 3

To some, therefore, because it is necessary that first things should be known, science does not appear to exist; but to others, it appears, to exist indeed, but they are of opinion, that there are demonstrations of all things; neither of which opinions is true or necessary. For those who suppose, in short, that it is not possible to know scientifically, these think that there is a procession to infinity, things posterior not being known throngh such as are prior, of which there are no things that are first. And, in this, they speak rightly; for it is impossible that infinites should be passed through. They add, that if we stop in our progression, and there are principles, these are unknown, since there is not a demonstration of them, which alone they say, is to know scientifically. But if it is not possible to know first things, neither can the things which are from these be known, either simply, or properly, but from hypothesis, if those first things exist. Others, however, assent, indeed, with respect to the attainment of scientific knowledge; for they assert, that it is only to be attained through demonstration; but that nothing prevents there being a demonstration of all things; for demonstration may be effected in a circle, and all things may be proved from each other. But we say, that neither is all science demonstrative, but that the science of things immediate is indemonstrable. And it is evident that this is necessary. For if it is necessary that things prior should be known, and those things from which demonstration consists, and the procession stops at length at things immediate, it is necessary that these should be indemonstrable. This, therefore, is what we assert, and we say that there is not only science, but also a certain principle of science, by which we obtain a knowledge

of terms. But that it is simply impossible to demonstrate in a circle, is evident, since it is necessary that demonstration should consist from things prior, and more known. For it is impossible, that the same things should at one and the same time be prior and posterior to the same, unless after a different manner; as, for instance, some things with reference to us, but others simply, in the way in which they are made known by induction. If this, however, be the case, simply to know will not be well defined, but it is twofold; or the one demonstration is not simply so, viz. the demonstration which is produced from things more known to us. But it happens to tlrose, who say that there is demonstration in a circle, that not only what has now been asserted takes place, but that they say nothing else, than that this thing is if this thing is. In this manner, however, it is easy to demonstrate all things. But it is evident that this happens three terms being posited. For it makes no difference whether any one says that demonstration is reflected through many, or through few terms; nor  whether through few, or through two terms. For when A existing, B necessarily exists, and B existing, C necessarily exists; A existing, C will exist. If, therefore, when A is, it is necessary that B should exist; but when B is, A exists; (for this it is to demonstrate in a circle) let A be posited where C was. To say, therefore, that B existing, A is, is the same thing as to say that C exists. And this is the same thing as to say that A existing C is. But C is the same as A. Hence it happens that those

who assert there is demonstration in a circle, say nothing else than that A existing, A is. But after this manner it is easy to demonstrate all things. Neither, however is this possible except in those things which are consequent to each other, as peculiarities. One thing, therefore, being posited, it has been demonstrated, that there will never necessarily be something else. By one thing, I mean neither one term, nor one thesis being posited. But it is possible that there may be necessarily something else collected from two first and least theses, since it will also be possible to syllogize. If, therefore, A is consequent to B and to C, and these are consequent to each other, and to A; thus, indeed, all postulates may be demonstrated from each other, in the first figure, as is shown in the books On Syllogisms. It is also there demonstrated that in other figures either a syllogism, is not produced, or that it is not concerning the things assumed. But it is not by any means possible to demonstrate in a circle, things which do not reciprocate. Hence since there are but few things of this kind in  demonstrations, it is evident that it is vain and impossible to say that there is a demonstration of things from each other, and on this account that there may be a demonstration of all things.

Aristotle, Posterior Analytics. Book I, Chapter 4

Since, however, it is impossible that a thing of which there is simple science should have a various subsistence, it will be also necessary that the object of science should pertain to demonstrative  science: and demonstrative science is that which we possess, because we possess demonstration. Hence demonstration is a syllogism from necessary propositions. It must be assumed, therefore, from what, and what kind of propositions demonstrations consist. But in the first place let us define what we mean by the terms of every, per se, and universal.  I call, therefore, that thing of every, which is not in a certain thing, and in a certain is not, nor which sometimes is, and sometimes not. As, if animal is predicated of every man; if it is truly said that this is a man, it is also truly said that he is an animal. And if now the one is true, the other also is true. In a similar manner likewise, if a point is in every line. Of this the following is an indication; for when we are interrogated as it were of every, we thus obje ct, either if a thing is not present with a certain individual, or if sometimes it is not present.  But I call those things per se, which are inherent in the predication declaring what a thing is; as, line is inherent in triangle, and point in line. For the essence of them is from these, and these are in the definition. explaining what a thing is. I likewise thus denominate those things which are inherent in their attributes, in the definition declaring what a thing is; as the straight and the curved are inherent in a line, the odd and the even in number, the first and the composite, the equilateral, and the oblong. And they are inherent in all these, in the definition declaring what a thing is, there indeed line, but here number. In a similar manner also, in other things, I say that things of this kind are per se, or  essentially inherent. But such things as are in neither way inherent, I call accidents; as, the being musical, or whiteness, is inherent in an animal. Farther still, I denominate per se, that which is not predicated of any other subject; as, for instance, that which walks, being something else, is that which walks, and is white.  But essence, and such things as signify this particular thing, not being any thing else, are that which they are.  Things, therefore, which are not predicated of a subject, I call per se; but those which are predicated of a subject, I call accidents. Again, after another manner, that which on account of itself is present with each thing, is per se; but that which is present, not on  account of itself, is an accident. Thus it is an accident, if any one walking it should lighten; for it did not lighten on account of walking, but we say that this happened. But if a thing is present on account of itself, it is present per se. Thus if any one having his throat cut should die, and through the wound, he will die in consequeuence of his throat being cut, but it will not happen that he whose throat was cut died. Things, therefore, which are predicated per se in things which are simply objects of science, so as to be inherent in the things predicated, or which are themselves inherent in subjects, are on account of themselves, and from necessity. For it does not happen not to be inherent, either simply, or opposites, as the straight and the inflected in a line, and the even or the odd in number. For a contrary is either privation, or contradiction in the same genus; as that is even which is not odd, in numbers, so far as it follows. Hence if it is necessary to affirm or deny, it is also necessary that those things which are per se should be inherent. Let, therefore the expressions of every, and per se, be  defined after this manner. But I call universal that which is present with every individual of a certain multitude, and per se, and so far as that thing is. It is evident, therefore, that such things as are universal are necessarily present with or inherent in things. But the expressions per se, and so far as it is, are the same. Thus a point and rectitude are per se inherent in a line; and two right angles in a triangle, so far as it is a triangle. For a triangle is per se, or essentially equal to two right angles. But universal is then inherent, when it is demonstrated of any casual thing, and primarily. Thus, for instance, to possess two right angles, is not universally inherent in figure; though it is possible to demonstrate of a figure that it has two right angles, yet this cannot be demonstrated of any casual

figure; nor does he who demonstrates this, use any casual figures. For a square is, indeed, a figure, yet it has not angles equal to two right angles. But any isosceles triangle has angles equal to two right, yet not primarily; for triangle possesses this property prior to the isosceles. In any thing,  therefore, which is first demonstrated to possess two right angles, or any thing else, in this primarily the thing possessed is universally inherent; and the demonstration per se of this is universal: but of other things, after a certain manner, and not per se. Neither is this property universally inherent in an isosceles triangle, but is more widely extended than the isosceles.

Aristotle, Posterior Analytics. Book I, Chapter 5

It is necessary, however, not to be ignorant, that error frequently happens, and that which is  demonstrated is not primarily universal, so far as that which is primarily universal appears to be demonstrated. But we are deceived according to this deception, when either nothing superior can be assumed except that which is particular, or particulars; or when something else can be assumed indeed, but that is anonymous in things differing in species; or when it is as a whole in a part, in  which it is demonstrated. For the demonstration will be present with things partial, and will be of every individual, yet it will not be the demonstration of this first universal. But I say the  demonstration of this first, so far as it is this, when it is of this first universal. If, therefore, any one should show that right lines will not meet, the demonstration of this may seem to be properly made, because this property is in all right lines.  This, however, is not the case, since this does not arise from the lines being thus equal, but so far as they are in some way or other equal. And if the triangle should be no other than isosceles, so far as isosceles it may seem to be inherent. Alternate proportion also may seem to be inherent, so far as they are numbers, so far as they are lines, so far as they are solids, and so far as they are times, as was once shown to be the case separately, when by one

demonstration this might be demonstrated of all of them. Because, however, all these, viz. numbers, lengths, times, and solids, are not one denominated thing, and differ from each other in species, they were assumed separately. But now the demonstration is universal. For this property is not inherent, so far as they are lines, or so far as they are numbers, but so far as they are this thing which they suppose to be universal. On this account; neither if any one should demonstrate one by one of every triangle, by one or another demonstration, viz. of the equilateral, the scalene, and the isosceles separately, that each has angles equal to two right; he will not yet know that triangle itself has angles equal to two right, unless in a sophistic manner; nor universally triangle, though there should be no other triangle besides these. For he will not know so far as it is triangle; nor will he know every triangle, except according to number; but according to form he will not know every triangle, though there is no one which he does not know. When, therefore, does he not know universally, and when does he know simply? It is evident that if there is the same essence of a triangle, and of an equilateral triangle, either of each, or of all, he knows universally. But if they are not the same, but different, and that property is inherent in triangle so far as triangle, he does not know whether, however, is it inherent so far as it is a triangle, or so far as it is an isosceles triangle? And when according to this, is it primarily inherent? And universally of what is the demonstration? It is evident, that it then is, when other things being take away, the property demonstrated will be primarily inherent in this thing of which it is demonstrated. Thus two right angles are inherent in a brazen isosceles triangle; but the being brazen, and the being isosceles being taken away, the same property will be inherent. It will not, however, be inherent, if figure or boundary is taken away. But it is not taken away from these being first taken away. From what, therefore, being first taken away is this property destroyed? If triangle is taken away. For according to this, it is also inherent in other things, and universally the demonstration is of this.

Aristotle, Posterior Analytics. Book I, Chapter 6

If, therefore, demonstrative science is from necessary principles; (for that which is scientifically known cannot subsist otherwise than it does) but properties essentially inherent in things are necessary; (for some are inherent in the predication what a thing is, but others are those, in the very nature of which the subjects are inherent, of which they are so predicated, that one of opposites, is necessarily inherent) – if this be the case, it is evident, that the demonstrative syllogism will

consist of certain things of this kind. For every thing is either thus inherent, or according to accident; but accidents are not necessary. Either, therefore, this must be said, or we must assert that this principle being admitted, demonstration is a necessary thing, and that if demonstration is given of a thing, that thing cannot subsist otherwise than it does. It is requisite, therefore, that the demonstrative syllogism should be from things that are necessary. For it is possible to syllogize from things that are true without demonstrating; but no one can syllogize from things necessary, except him who  demonstrates. For this is now the peculiarity of demonstration. This also is an indication that demonstration is from things necessary, that we object to those who fancy they demonstrate, that the conclusion is not necessary; whether we think it possible that the thing may be otherwise, or whether

we thus object for the sake of disputation. From hence too, the folly of those is apparent, who fancy that they rightly assume principles, if the proposition is probable and true; as the sophists assume when they say that to know is to possess science. For that is not the principle which is probable, or not probable, but that which is the first of the genus about which the demonstration is made; nor is everything which is true appropriate, But that it is necessary the demonstrative syllogism should consist of things that are necessary is also evident from what follows. For if he who cannot assign the reason why a thing is, when there is a demonstration of it, does not possess scientific knowledge; let A be necessarily predicated of C; but let B be the medium through which the demonstration was made, but not from necessity; in this case he will not know why the thing is. For this is not on account of the medium; for it may happen that the medium may not be; but the conclusion is  necessary. Farther still, if some one does not know, though he possesses reason and is safe, the thing being preserved, and he has not forgotten; neither did he before know it. But the medium may perish if it is not necessary. Hence he will possess reason, and will be safe, the thing being preserved, amd yet, will not know it. Neither, therefore, did he before know it. But if the medium is not destroyed, and it is possible that it may perish, that which happens will be possible and contingent. It is, however, impossible that he who, is thus affected should know. Then, therefore, the conclusion is from necessity, nothing hinders but that the medium through which it was demonstrated may not be necessary; for it is possible syllogistically to collect the necessary from things which are not necessary, just as the true may be collected from things which are not true, But when the medium is from necessity, the conclusion also is frorn necessity; just as from true things the true is always  collected. For let A be predicated of B from necessity, and this of C; it is necessary, therefore, that A should be present with C. But when the conclusion is not necessary, neither is it possible that the medium should be necessary. For let A be present with C not from necessity, but let it be present with B, and this with C from necessity. A, therefore, is present with C from necessity; but it was not supposed to be so. Since, therefore, that which any one knows demonstratively must be inherent from necessity, it is also evident that demonstration must be obtained through a necessary medium; for otherwise, be will neither know why that exists, nor that it is necessary for it to exist; but he will either fancy that he knows when he does not know, if he assumes that which is not necessary, as

if it were necessary, or he will not fancy that he knows, whether he knows that it is through media, or why it is, through things immediate. But of accidents which are not per se, in the manner in which things per se are defined, there is not demonstrative science; for it is not possible to demonstrate the conclusion of them from necessity; because accident may not be inherent. For I speak about an accident of this kind. Perhaps, however, some one may doubt why it is necessary to ask these things about these things, unless it is necessary that the conclusion should be? For it makes no difference if some one asking any thing casually, should afterwards give the conclusion. But it is necessary to interrogate, not as if this which is concluded were necessary on account of the things interrogated, but because it is necessary that he who asserts those things should also assert this, and that he should speak truly, if those things are true. Since, however, such things as are inherent per se, are inherent from necessity about each genus, and so far as each is; it is evident that scientific demonstrations are

about things essentially inherent, and consist from things of this kind. For accidents are not  necessary. Hence it is not necessary to know why the conclusion is, not even if those things should always exist, but not per se; such, for instance, as syllogisms formed from signs.  For that which is per se will not be known per se, nor why it is. But to know why a thing is, is to know through cause. It is necessary, therefore, that the middle should be inherent in the third, and the first in the middle.

Aristotle, Posterior Analytics. Book I, Chapter 7

It is not possible, therefore, to demonstrate, passing from one genus to another; as, for instance, it is not possible to demonstrate a geometrical problem by arithmetic. For there are three things in demonstrations. One of these is the demonstrated conclusion; but this is that which is essentially inherent in a certain genus. Another is axioms. But axioms are those things from which demonstration is produced. The third, is the subject genus, the properties of which and essential accidents, demonstration renders manifest. It is possible, therefore, that the things from which demonstration consists may be the same. But in those sciences in which the genus is different, as

in arithmetic and geometry, in these it is not possible to adapt an arithmetical demonstration to the accidents of magnitudes; unless magnitudes are numbers. How this is possible, however, in certain things, will be hereafter shown. But an arithmetical demonstration always has the genus about which demonstration is conversant; and in a similar manner other demonstrations. Hence either it is simply

necessary that there should be the same genus, or it is necessary in a certain respect, if demonstration is to be transferred; but that it is otherwise impossible is evident. For it is necessary that the extremes

and middles should be from the same genus; since unless they are per se, they will be accidents. On this account, it is not possible by geometry to demonstrate that there is one science of contraries; nor to make two cubes equal to one cube. Nor is it possible for any other science to demonstrate a  problem belonging to another science; except such as are so related to each other, as that the one is under the other; such, for instance, as is the relation of optical problems to geometry, and harmonical problems to arithmetic. Nor if any thing is inherent in lines, not so far as they are lines, nor so far as they are from proper principles, does that pertain to geometry; as, if a right line is the most beautiful of lines, or if it is contrary to a circumference. For these things are inherent in lines, not by reason of their proper genus, but so far as they have something common.

Aristotle, Posterior Analytics. Book I, Chapter 8

It is also evident, that if the propositions from which the demonstrative syllogism consists are universal, it is necessary that the conclusion of such a demonstration, and, in short, of the demonstration of itself should be perpetual. There is not, therefore, either demonstration, or, in short, science of corruptible natures, except as from accident; because universal does not belong to them, but an existence sometimes, and after a certain manner. This being the case, it is necessary that one proposition should not be universal, and that it should be corruptible. It is corruptible, indeed,  because the conclusion also will be corruptible, if each proposition is corruptible. And it is not universal, because one of those things of which it is predicated will be, and another will not be. Hence it will not be possible to conclude universally, but that now the thing thus subsists. The like will also take place in definitions; since definition is either the principle of demonstration, or demonstration differing in the position of the terms, or a certain conclusion of demonstration. But the demonstrations and sciences of things which are frequently produced, as of the eclipses of the moon, evidently always exist, so far as they are such; but so far as they are not always, they are according to a part. But as in an eclipse the like also may be said in other things.

Aristotle, Posterior Analytics. Book I, Chapter 9

Since, however, it is evident that a thing cannot be demonstrated except from its own principles, if the thing which is demonstrated is inherent in a subject, so far as the subject is that which it is; to have a scientific knowledge of that thing is not this, if it should be demonstrated from true, indemonstrable, and immediate propositions. For it is possible to demonstrate in such a manner as Bryso demonstrated the quadrature of the circle. For reasonings of this kind show through something  common, that which is inherent in another thing. Hence these arguments are adapted to other things which are not of a kindred nature. That thing, therefore, is not scientifically known, but from accident; for otherwise the demonstration would not also be adapted to another genus. But we scientifically know any thing, not from accident, when we know it according to that according to which it is inherent from principles which are the principles of that thing, so far as it is that thing. Thus, for instance, we scientifically know that a thing has angles equal to two right, when we know that in which the thing spoken of is essentially inherent, from the principles of this thing.  Hence, if that is essentially inherent in the thing in which it is inherent, it is necessary that the middle should be in the same affinity. But if not, yet it will be as when harmonic problems are proved through an arithmetical principle. Things of this kind, however, are demonstrated, indeed, after a similar manner, but they differ. For that they are, it belongs to another science to show; because the subject genus is different. But why they are it is the province of a superior science to show, of which science they are the essential properties. Hence from these things also it is evident, that it is not possible to demonstrate every thing simply, but from its proper principles. And the principles of these, have something common. But if this is evident, it is also evident, that it is not possible to demonstrate the proper principles of everything; for these will be the principles of all things, and the science of them will be the mistress of all sciences. For he has a more scientific knowledge, who knows from superior causes; since he knows from things prior, when he knows not from effects, but from causes. Hence, if he more knows, he especially knows; and if that is science, it is more and especially science. Demonstration, however, is not adapted to another genus, except, as we have said, geometrical to optical or mechanical, and arithmetical to harmonical demonstrations. But it is difficult to know whether a man possesses knowledge or not. For it is difficult to know whether our

knowledge is from the principles of a thing or not; for this it is to know.  We think, however, that we possess scientific knowledge, if we have a syllogism from such things as are true and primary. But it is not so; for it necessary that they should be of a kindred nature with things that are first.

Aristotle, Posterior Analytics. Book I, Chapter 10

I call, however, principles in each genus those things which are indemonstrable. What, therefore, first things signify, and the things concluded from these, is assumed. But with respect to principles,

indeed, it is necessary to assume that they are; and with respect to other things, to demonstrate that they are; as, for instance, what unity is, or what the straight, and a triangle are. It is necessary, however, to assume that unity and magnitude exist, but to demonstrate other things. With respect, however, to those things which are employed in demonstrative sciences, some are peculiar to each science, but others are common. And they are common according to analogy; since each is useful, so far as it is in the genus under sciences. The peculiar, indeed, are such as, that a line is a thing of this kind, and that the straight is a thing of this kind. But the common are such as, that if equal are taken away from equal things, the remainders are equal. Each of these, however, is sufficient, so far as it is  in the genus under science. For the geometrician will effect the same thing though he should make an assumption of all things, but in magnitudes alone. And it will be sufficient to the arithmetician, if the assumption is made in numbers alone. But proper principles are those things which are assumed to be, and about which science considers whatever is inherent per se. Thus, for instance, arithmetic assumes unities, but geometry points and lines. For they assume that these are, and that hey are this particular thing. But with respect to the essential properties of these, what each of them signifies they assume. ‘I’hus, arithmetic assumes what the odd is, or the even, or what a square is, or a cube; but geometry assumes what the irrational is, or what it is to be inflected, or to incline. That they are, however, they demonstrate through common principles and from those things which have been

demonstrated. Astrology (i.e. astronomy) also acts in a similar manner. For all demonstrative science is employed about three things. Of these, two are those things which are posited to be; and these are

the genus, the essential properties of which the science contemplates; and those common things which we call axioms, from which they first demonstrate. The third thing is the properties, the signification of each of which the demonstrator assumes. Nothing, however, hinders but that certain sciences may overlook some of these. Thus a certain science may not make the genus the subject of hypothesis, if it is manifest that it exists; (for it is not similarly manifest that number is, and that the hot and the cold exist) and may not assume what the properties signify, if they are manifest; as neither does it assume what common things signify, as what it signifies to take away equal from equal things, because it is known. Nevertheless, these things are naturally three, viz. that about which demonstration is employed, the things demonstrated, and the principles from which they are demonstrated. But neither hypothesis nor postulate is that which necessarily exists per se, and which is necessarily seen. For demonstration does not pertain to external speech, but to that which is in the souls; since neither does syllogism pertain to the former, but to the latter. For it is always possible to object to external discourse, but to internal discourse it is not always possible. Such things, therefore, as being demonstrable, the demonstrator assumes without demonstration; these, if he assumes things which appear probable to the learner, he supposes; and this is not simply an hypothesis, but with reference to the learner alone. But if when either there is no inherent opinion, or when contrary opinions are inherent, the demonstrator assumes, he requires the same thing to be granted to him. And in this, hypothesis and postulate differ from each other. For postulate is that which is sub-contrary to the opinion of the learner; which though demonstrable some one assumes, and uses without demonstrating it. Definitions, therefore, are not hypotheses; for they do not assert that a thing is, or is not. But in propositions hypotheses are contained. It is only necessary, however, that definitions should be understood. But this is not the case with hypothesis; unless some one should say that the verb to hear is an hypothesis. Those, however, are hypotheses, from the existence of which (or the existence of which being admitted) the conclusion is produced. Nor does the geometrician suppose falsities, as some assert, who say that it is not proper to use a false principle, but that the geometrician speaks falsely, when he says that a line is pedal which is not pedal, or that the line which he describes is a right line, though it is not a right line. The geometrician, however, concludes nothing from the existence of this particular line, which he announces, but concludes that those things have an existence which are manifested through these marks or symbols. Farther still, postulate and every hypothesis, are either as a whole, or as in a part; but definitions are neither of these.

Aristotle, Posterior Analytics. Book I, Chapter 11

That there should be forms, therefore, or one certain thing besides the many, is not necessary to the existence of demonstration.  It is necessary, however, that it should be truly said, there is one thing of

the many; for there will not be universal, unless this is true. But if there is not universal, there will not be a medium; so that neither will there be demonstration. It is necessary, therefore, that there should be a certain one and the same thing not homonymous in many things. No demonstration, however, assumes that it is not possible the same thing should be at one and the same time affirmed and denied, unless it should be also necessary thus to demonstrate the conclusion. But it is demonstrated by first assuming of the medium that it is truly affirmed, and that it is not truly denied. It makes, however, no difference to assume that the middle is, and that it is not: and in a similar

manner also with respect to the third. For if that should be granted of which man is truly predicated, though some one should think that man is not man the conclusion will be truly collected; if only it is  truly said that man is an animal, and not that he is not an animal. For it will be true to say that Callias, though he should not be Callias, yet at the same time is an animal, but not that which is not an animal. The cause, however, of this is, that the first is not only predicated of the middle, but also of another in consequence of existing in the many. Hence if the medium or middle is that thing itself, and is not that thing itself, it makes no difference with respect to the conclusion. But that of every thing affirmation or negation is true, that demonstration assumes which leads to the impossible. A nd these axioms are not always assumed universally, but so far as is sufficient.  But that is sufficient which is assumed in the subject genus. I say in the subject genus, as, for instance, in the genus about which it introduces demonstrations, as we have also before observed. All sciences too communicate with each other according to such things as are common. But I calI common things those which they use as demontrating from these; but not those things about which they demonstrate, nor that which they demonstrate. And dialectic (is common to all sciences. If also there is any science which universally endeavours to prove common principles such as, that of every thing affirmation or negation is true, or that equal things remain from the ablation of such as are equal, or other things of this kind; this also is common to all sciences. Dialectic, however, does not thus pertain to certain definite things, nor is of one certain genus. Nor otherwise it would not interrogate; since he who demonstrates does not interrogate; because the same thing is not proved from opposites as was shown in the treatise On Syllogism.

Aristotle, Posterior Analytics. Book I, Chapter 12

But if syllogistic interrogation, and a proposition which is one part of contradiction are the same; and there are propositions in each science from which the syllogism pertaining to each science consists; if this be the case, there will be a certain scientific interrogation, from which an appropriate syllogism is produced in each science. It is evident, therefore, that not every interrogation is geometrical or medical. And the like also takes place in other arts and sciences. But those are geometrical interrogations, from which any thing is demonstrated about which geometry is conversant, or which are demonstrated from the same principles with geometry, such as are optical interrogations; and in a similar manner in other sciences.  These also must be discussed from geometrical principles and conclusions. Principles, however, are not to be discussed by a  geometrician, so far as he is a geometrician. The like also takes place in other sciences. Neither,

therefore, is every one who possesses science to be interrogated with every interrogation; nor is an answer to be given to every interrogation about anything, but to those things which are contained within the boundaries of the science possessed by him who is interrogated. But it is evident that he who thus disputes with a geometrician, so far as he is a geometrician, disputes in a becoming  manner, if he demonstrates any thing from these principles; and that if he does not thus dispute, he does not dispute properly. It is also manifest, that neither does he confute the geometrician except from accident. Hence there cannot be any geometrical discussions among those who are unskilled in geometry; for it will not be apparent when he who discusses speaks unappropriately. And the like will also take place in other sciences. Since, however, there are geometrical interrogations, are there also such as are ungeometrical? And in each science are such ignorant interrogations as are of a certain quality, geometrical, or ungeometrical? Whether also is a syllogism produced from ignorance, composed from opposites, or a paralogism, but which is according to geometry? Or from another art, as a musical interrogation is ungeometrical about geometry; but to fancy that parallel lines will meet, is in a certain respect geometrical, and after another manner ungeometrical ? For

this is twofold, in the same manner as that which is without rhythm.  And the one is ungeometrical, because it possesses nothing geometrical, as that which is without rhythm, but the other because it possesses the geometrical unappropriately. And this ignorance, which is from principles of this kind, is contrary to science. But in the mathematical disciplines there is not a paralogism similarly as there is in disputations, because the middle is always twofold. For one thing is predicated of every individual of this, and this again is predicated of another every; but that which is predicated is not called every. These things, however, may as it were be seen by intelligence. But in disputations it is latent whether every circle is a figure; though if it should be described, this wou1d be manifest.  But what? Are verses a circle? It is evident that they are not. It is not proper, however, to object against it, if it is an inductive proposition.  For as neither is that a proposition which is not in many things;  because it will not be in all, but that syllogism consists from universal propositions, so neither as is evident, is that an objection; for propositions and objections are the same. For the objection which is adduced, may become either a demonstrative, or a dialectic proposition. But it happens that some speak unsyllogistically, in consequence of assuming things consequent to both extremes; as Caeneus did, who concluded that fire is generated in a multiple proportion, because fire, as he says, and this proportion are rapidly generated. Thus, however, there is not a syllogism; but there will be, if the multiple is consequent to the most rapid proportion, and the most rapid proportion to fire in motion. Sometimes, therefore, it does not happen that a conclusion is made from the things assumed; and sometimes it happens, but is not apparent. If, however, it were impossible to demonstrate what is true from things which are false, analysis would be easy; for they would be converted from necessity. For let A exist; but this existing, these things also exist which I know to be in existence, as, for instance, B. From these, therefore, I demonstrate the existence of that. But those things which pertain to the mathematical disciplines are more converted, because they admit of nothing accidental, (for in this they differ from things which are the subjects of discussion) but definitions. They are increased, however, not through media, but because other things are assumed, as A of B, this of C, again, this of D, and so on to infinity. And also transversely; as, for instance, A, both of C, and of E. As, there is a number so great, or infinite, this is A; an odd number so great, B; and an odd number, C. A, therefore, is of C, and the even is a number so great, D; and F also is an even number. Hence A is of E.

Every odd number (B) is finite or infinite (A):

Every ternary (C) is an odd number (B): Therefore,

Every ternary (C) is finite or infinite (A).

Every even number (D) is finite or infinite (A):

Every binary (E) is an even number (D): Therefore,

Every binary (E) is finite or infinite (A).

Aristotle, Posterior Analytics. Book I, Chapter 13

There is a difference, however, between knowing that a thing is, and why it is, in the first place,  indeed, in the same science, and in this, in a twofold respect. In one way, if the syllogism is not formed through things immediate; for the first cause is not assumed; but the science of the why is obtained through the first cause. But in another way, if the syllogism is through things immediate, indeed, yet not through cause, but because among things which reciprocate it is more known. For nothing hinders that which is not a cause, from being sometimes more known, among things which are mutually predicated; so that demonstration will be through this. Thus, it may be demonstrated that the planets are near, because they do not twinkle. For let C be the planets; B, not to twinkle; A, to be near. B, therefore, is truly predicated of C; for the planets do not twinkle. A also is truly predicated of B; for that which does not twinkle is near. But this may be assumed through induction, or through sense. It is necessary, therefore, that A should be present with C. Hence it is demonstrated

that the planets are near.

That which does not twinkle (B) is near (A):

The planets (C) do not twinkle(B): Therefore,

The planets (C) are near (A).

This syllogism, therefore, is not of the why, but of the that a thing is. For the planets are not near because they do not twinkle; but because they are near, they do not twinkle. For it happens that the one may be proved through the other, and the demonstration will be of the why.  Thus, for instance, let C be the planets; B, to be near ; and A, not to twinkle. B, therefore, is present with C, and A , i.e. not to twinkle, is present with B ; so that A also is present with C.

That which is near (B) does not twinkle (A):

The planets (C) are near (B): Therefore,

The planets (C) do not twinkle (A).

And it is a syllogism of the why; for the first cause was assumed.  Again, that they may show that the moon is spherical, through the increments of light. For if that which is thus increased is spherical, but the moon (i.e. the light of the moon) is thus increased; it is evident that the moon is spherical. Thus, therefore, a syllogism of that is produced. But if the middle is posited contrarily, there will be a syllogism of the why. For the moon is not spherical on account of the increments of light; but in  consequence of being spherical, she receives increments of this kind. Let the moon be C; the spherical, B; and increase, A.

That which is spherical (B) is thus increased (A):

The moon (C) is spherical (B): Therefore,

The moon (C) is thus increased (A).

But in those things in which the media do not reciprocate, and that which is not the cause is more known; the that is, indeed, demonstrated, but not the why. Farther still, this is also the case in those

things in which the middle is externally posited; for in these, the demonstration is of the that, and not of the why; since the cause is not assigned. Thus, for instance, why does not a wall respire? Because

it is not an animal. For if this were the cause of not respiring, it would be requisite that animal should be the cause of respiring; as, if negation is the cause of not being inherent, affirmation is the cause of

the being inherent. Thus, if the incommensuration of things hot and cold, is the cause of not being well, the commensuration of these, is the cause of being well. In like manner also, if affirmation is the cause of the being inherent, negation is the cause of the not being inherent. In things, however, which are thus explained, that which has been mentioned does not happen; for every animal does not respire. But the syllogism of a cause of this kind is produced in the middle figure. For instance, let A be animal; B, to respire; C, a wall. A, therefore, is present with every B; for every thing which respires is an animal; but with no C. Hence neither is B present with any C. A wall, therefore,

does not respire.

Whatever respires (B) is an animal (A):

No wall (C) is an animal (A): Therefore,

No wall (C) respires (B).

Causes, however, of this kind resemble those things which are spoken of according to hyperbole. And this is, by leaving the proximate cause to speak of that middle, which is more widely extended than cause. Such, for instance, is that saying of Anacharsis, that among the Scythians there are no pipers, for neither are there any vines there. According to the same science, therefore, and according to the position of the media, these are the differences between a syllogism of that a thing is, and a syllogism of the why. After another manner also, the why differs from the that, because each is beheld in a different science. But of this kind, are such things as so subsist with reference to each other, that the one is under the other; and such is the subsistence of optics with reference to geometry, mechanics to stereometry, music to arithmetic, and the phaenomena to astrology. Nearly,

however, some of these sciences are synonymous; as, for instance, the mathematical and the nautical  (astronomy) are called astrology, and mathematical harmony, and that which pertains to the ear, are called music. For here to know that a thing is, is the province of those who energize according to sense; but to know why it is, is the province of mathematicians. For these possess the demonstrations of causes, and often do not know that a thing is. Thus, those who contemplate universals are frequently ignorant, from not animadverting, of certain particulars. But these are such as being essentially something else, use forms. For the mathematical disciplines are conversant with forms;

since they are not in a certain subject. For though geometrical forms are in a certain subject, yet they are not in a subject, so far as they are geometrical. But as optics is to geometry, so is some other science to optics; as, for instance, the science pertaining to the rainbow. For to know that it is, is the province of the natural philosopher; but to know why it is, of the optician, either simply, or according to the mathematical science. Many of those sciences also which are not arranged under each other, thus subsist; as, for instance, medicine with reference to geometry. For to know that circular wounds are healed more slowly, is the province of the physician; but why they are more slowly healed, of the geometrician.

Aristotle, Posterior Analytics. Book I, Chapter 14

Of figures, however, the first is especially scientific. For the mathematical sciences through this frame their demonstrations; as, for instance, arithmetic, geometry, optics, and nearly, as I may say, such sciences as direct their attention to the why. For either entirely, or for the most part, and in most sciences, the syllogism of the why is produced through this figure. Hence, on this account also, this figure will be especially scientific. For it is in the most eminent degree the province of knowledge, to contemplate the why. In the next place, it is alone possible through this figure to investigate the science of what a thing is.  For in the middle figure a categoric syllogism is not produced; but the science of what a thing is pertains to affirmation. And in the last figure, a categoric syllogism is, indeed, produced, but not one that is universal. But the what a thing is, is among the number of universals. For man is not a biped animal in a certain respect. Farther still, this figure is not indigent of those; but those are condensed and increased through this, till we arrive at things immediate. It is evident, therefore, that the first figure is in the highest degree adapted to scientific knowledge.

Aristotle, Posterior Analytics. Book I, Chapter 15

As, however, it happened that A was present with B individually, thus also it may happen that it is  not present with B. But I say to be present, or not to be present with individually, because there is not between them any medium. For thus there will not be to be present, or not to be present with according to something else. When, therefore, either A or B is in a certain whole, or when this is also the case with both, it is not possible that A should not be primarily present with B. For let A be in the whole of C. If, therefore, B is not in the whole of C; (for it is possible that A may be in a certain whole, but that B may not be in this whole) there will be a syllogism, in which it will be concluded that A is not present with B. For if C is present with every A, but with no B; A will be present with no B. The like will also take place if B is in a certain whole, as, for instance, in D. For D is present with every B, but with no A. Hence A will be present with no B, as will be syllogistically concluded. After the same manner it will be demonstrated, if both are in a certain whole. But that it is possible that B may not be in the whole in which A is; and again, that A may not be in the whole in which B is, is evident from those co-arrangements which are not mingled with each other. For if no one of those things which are in the class A C D, is predicated of no one of those which are in the class B E F; but A is in the whole of H with which it is co-arranged, it is evident that B will not be in H; for otherwise the co-arrangements would be mingled with each other.

Essence                        H

Body                            A         B          Quality

Animated                     C          E          Colour

Rational animal            D         F          Whiteness.

The like will also take place if B is in a certain whole. But if neither is in any whole, and A is not present with B; it is necessary that it should not be present individually. For if there will be a certain

middle, it is necessary that one of them should be in a certain whole; since there will be a syllogism, either in the first figure, or in the middle figure. If, therefore, in the first figure, B will be in a certain

whole; for it is necessary that the proposition should be affirmative in which it is contained. But if the syllogism is in the middle figure either of them may be in the whole; for the privative being joined to both, a syllogism will be produced. But both the propositions being negative, there will not be a syllogism. It is evident, therefore, that it is possible one thing may not be individually present with another: and when, and how this is possible, we have shown.

Aristotle, Posterior Analytics. Book I, Chapter 16

The ignorance, however, which is denominated not according to negation, but according to disposition, is deception produced through reasoning. But this in those things which are primarily present, or not present, happens in a twofold respect. For it happens either when any one simply apprehends the being present, or not being present, or when he obtains this opinion through syllogism. Of simple opinion, therefore, the deception is simple, but of that which is through syllogism, the deceptions are numerous. For let A not be present with B individually. If, therefore, it is concluded that A is present with B, assuming the middle C, he who thus concludes will be deceived through syllogism. Hence it is possible that both propositions may be false; but it is also possible that one only may be false. For if neither A is present with any C, nor C with any B, but each proposition is contrarily assumed; both will be false. But it is possible that C may so subsist with reference to A and B, that it may neither be under A, nor universally attributed to B.  For it is impossible that B should be in a certain whole; since it was said that A is primarily not present with it. But it is not necessary that A should be universally attributed to all beings. Hence both  propositions will be false.  It is also possible that one proposition may be assumed as true, yet not

either of them casually, but the proposition A C. For the proposition C B will be always false, because B is in no whole. But it is possible that the proposition A C may be true; as, for instance, if A is present individually both with C and B. For when the same thing is primarily predicated of many things, neither will be predicated of neither. It makes, however, no difference if A is not individually present with C. The deception, therefore, of being present, is produced through these things, and after this manner only; for a syllogism of being present was not in another figure. But the deception of not being present with, is in the first and middle figure. Let us, therefore, in the first place show, in how many ways it is produced in the first figure, and how the propositions subsist when it is produced. It may be produced, therefore, when both the propositions are false; as, for instance, if A is present individually with C and B. For if it should be assumed that A is present with no C, but that C is present with every B, the propositions will be false. Deception also may be produced when one of the propositions is false, and through either of them as it may happen. For it is possible that the proposition A C may be true, but the proposition B C false. It is possible that A C may be true; because A is not present with all beings. And it is possible that B C may be false; because it is impossible that C should be present with B, with nothing of Which A is present; for otherwise the proposition A C will be no longer true. At the same time, if both the propositions are true, the conclusion also will be true. It is likewise possible that the proposition B C may be true, when the other proposition is false; as if B is in C, and in A. For it is necessary that one of them should be under the other. Hence, if it should be assumed that A is present with no C, the proposition will be false.  It is evident, therefore, that when one proposition is false, and when both are false, the syllogism will be false. But in the middle figure, it is not possible that both the propositions should be wholly false. For when A is present with every B, it will not be possible to assume any thing which is present with every individual of the one, but with no individual of the other. But it is necessary so to assume the propositions, that the middle term be present with one extreme, but may not be present with the other, in order that there may be a syllogism. If, therefore, when thus assumed they are false; it is evident, that when assumed contrarily, they will subsist vice versa. This, however, is impossible. But nothing hinders that each may be partly false; as, for instance, if C is present with A, and with a certain B. For if it should be assumed that it is present with every A, but with no B, both the propositions, indeed, will be false, yet not wholly so, but in part. The like will also take place, if the privative proposition is posited vice versa.  But it is possible that one proposition, and this either of them, may be false. For that which is present with every A will also be present with B. If, therefore, it should be assumed that C is present with the whole of A, but is not present with the whole of B; the proposition C A will be true, but the proposition C B false. Again, that which is present with no B, will not be present with every A. For if with A it would also be present with B. But it was not present. If, therefore, it should be assumed that it is present with the whole of A, but with no B; the proposition C B will be true; but the other proposition will be false. The like will also take place if the privative proposition is transposed. For that which is present with no A, will not be present with any B. If, therefore, it should be assumed that C is not present with the whole of A, but is present, with the whole of B; the proposition A C will be true; but the other  proposition will be false. And again, it is false to assume that what is present with every B, is present with no A. For it is necessary that if it is present with every B, it should also be present with a certain A. If, therefore, it should be assumed, that C is present with every B, but with no A, the proposition C B will indeed be true, but the proposition C A false. Hence it is evident that when both the propositions are false, and when one only is false, there will be a syllogism deceptive in individuals.

Aristotle, Posterior Analytics. Book I, Chapter 17

In those things, however, which are not individually present, or which are not present when the syllogism of the false is produced through an appropriate medium, both the propositions cannot be false, but that only in which the greater extreme is contained. But I call that an appropriate medium through which a syllogism of contradiction is produced. For let A be present with B, through the medium C. Since, therefore, it is necessary that the proposition C B should be assumed affirmative, if a syllogism is to be produced; it is evident that this proposition will always be true; for it is not converted. But the proposition A C will be false; for this being converted, a contrary syllogism will be produced. The like will also take place if the medium should be assumed from another co-arrangement; as for instance D, if it is in the whole of A, and is predicated of every B. For it is necessary that the proposition B D should remain, but that the other proposition should be converted.  Hence, the one will always be true, but the other will always be false. And nearly deception of this kind is the same as that which is produced, through an appropriate medium. If, however, the syllogism should not be produced through an appropriate medium; when indeed tbe medium is under

A, but is present with no B, it is necessary that both the propositions should be false. For the propositions must be assumed in a way contrary to that in which they subsist, if a syllogism is to be formed. But when they are thus assumed, both will become false; as, if A is present with the whole of D, but D is present with no B. For these being converted, there will be a syllogism, and both the propositions will be false. But when the medium is not under A, as for instance D; the proposition A D, will indeed be true; but the proposition D B will be false. For A D will be true, because D was not in A; but D B will be false, because if it were true, the conclusion also would be true; but it was  false. When, however, deception is produced through the middle figure, it is not possible that both fhe propositions can be wholly false. For when B is under A, there is nothing which can be present with every individual of the one, but with no individual of the other, as was also before observed.  One proposition, however, may be false, and this either, as it may happen. For if C is present with A and with B; if it should be assumed that it is present with A, but is not present with B; the  proposition A C will indeed be true, but the other proposition will be false. Again, if it should be assumed that C is present with B, but with no A; the proposition C B indeed will be true; but the other proposition will be false. If, therefore, the syllogism of deception should be privative, it has

been shown when the deception will be, and through what things it will be produced. But if it should be affirmative, when it is through an appropriate medium, it is impossible that both the propositions should be false. For it is necessary that the proposition C B should remain, if there is to be a  syllogism, as was before observed. Hence the proposition C A will be always false; for it is this  which is converted. The like will also take place, if the medium is assumed, from another co-arrangement, as was also observed in privative deception. For it is necessary that the proposition D B should remain, but that A D should be converted. A nd the deception is the same with the former. But if the syllogism is constructed not through an appropriate medium, if indeed D should be under A, this will be true, but the other will be false. For it is possible that A may be present with many things which are not under each other. If, however, D should not be under A, it is evident indeed that this is always false; for it is assumed affirmative. But D B may be as well true as false. For nothing hinders but that A may be present with no D, and that D may be present with every B. Thus animal is present with no science, but science is present with all music. Again, nothing hinders but that A

may be present with no D, and D with no B. It is evident, therefore, that when tbe medium is not under A, both the propositions may be false, and either of them, as it may happen. Hence too it is evident in how many ways, and through what things syllogistic deceptions may be produced, both in things immediate, and in those which are proved through demonstration.

Aristotle, Posterior Analytics. Book I, Chapter 18

It is also evident, if any sense should be wanting, that a certain science also must necessarily be wanting, which in this case it is impossible to possess; since we learn either by induction, or by demonstration. But demonstration is from universals, and induction from particulars. It is impossible, however, to contemplate universals except through induction; (since things which are said to subsist from abstraction, will he known through induction, if any one wishes to render it apparent that certain things are present with each genus, though they are not separable so far as each is this particular thing,) and it is impossible for those to make an induction who are deprived of sense. For sense is conversant with particulars; since the science of them cannot be received. For neither can science be received from universals without induction, nor through induction without sense.

Aristotle, Posterior Analytics. Book I, Chapter 19

But every syllogism is composed through three terms. And one indeed the affirmative is able to demonstrate that A is present with C, because it is present with B, and B with C. But another is privative, having one proposition, that a certain other thing is present with something else; but the other proposition, that it is not present. It is evident, therefore, that these are principles, and what are called hypotheses. For these being thus assumed, it is necessary to demonstrate; for instance, that A is present with C, through B; and again, that A is present with B, through another medium; and in a similar manner that B is present with C. lt is evident, therefore, that this alone is to be considered by those who syllogize only according to opinion, and dialectically, viz. whether the syllogism is produced from propositions as much as possible probable. Hence, though there is in reality a medium between A and B, but it does not appear that there is; he who syllogizes through this, will syllogise dialectically. But in syllogising with a view to truth, it is necessary to speculate from things inherent. Some things, however thus subsist, because in each genus, there is that which is predicated of something else, not according to accident. But I say according to accident; as, we sometimes say that a white thing is a man, not similarly saying that a man is a white thing. For man not being any thing else is white; but that which is white, is said to be a man, because it happens to a man to be white. There are some things, therefore, of such a kind, as that they are predicated per se. Let, therefore, C be a thing of such a nature, that it is not itself present with any thing else, but let B be primarily present with this, without any thing else between. And again, let E be present with F, in a similar manner, and this with B. Is it, therefore, necessary that this should stop, or is it possible to proceed to infinity? And again, if nothing is predicated per se of A, but is primarily present with H, nothing prior intervening, and H with G, and this with B; is it also necessary that this should stop, or can this likewise proceed to infinity? This inquiry however, thus much differs from the former, that the one is, whether is possible by beginning from a thing of that kind, which is present with nothing else, but something else is present with it, to proceed to infinity upward; but the other is, whether beginning

from that which is itself predicated of another, but of which nothing is predicated, it may be possible to proceed to infinity downward. Farther still, it may be enquired: whether the extremes being finite, it is possible that the media may be infinite? I say, for instance, if A is present with C, but the medium of them is B, and of B and A, there are other media, and of these again others, whether it is possible for these also to proceed to infinity, or whether it is impossible? To consider this, however, is the same thing as to consider whether demonstrations proceed to infinity, and whether there is a demonstration for everything, or the extremes are terminated with reference to each other. In a similar manner also, I say it must be enquired in privative syllogisms and propositions: as, for instance, whether A is primarily present with no B, or there will be a certain medium with which it was not before present. Thus it must be enquired whether there is a medium G which is present with every B; and again, whether A, is not present with something else prior to this, as, whether the medium is H, which is present with every G. For in these also, either those things are infinite with which first they are not present, or the progression stops. But the like does not take place in things which reciprocate. For in those things which are mutually predicated of each other, there is nothing of which, first or last, a thing is predicated. For so far as pertains to this, all things subsist similarly with reference to all, whether those things are infinite, which are predicated of the same, or whether both which are the subject of doubt are infinite; except that the reciprocation cannot be similarly made; but the one is as accident, and the other as predication.

Aristotle, Posterior Analytics. Book I, Chapter 20

That the media, therefore, cannot be infinite, if the predications as well downward as upward stop, is evident. But I call the predication upward or in an ascending series which proceeds to the more universal; and I call that downward or in a descending series, which proceeds to that which is particular, or partial. For if when A predicated of F, the media are infinite, i.e. B; it is evident, it. may

be possible, that from A in a descending series, one thing may be predicated of another to infinity; (for before we can arrive at F, there are infinite media) and from F in an ascending series, there are infinite attributes before we can arrive at A. Hence, if these things are impossible, it is also impossible that there can be infinite media, between A and F. For it is of no consequence, if any one should say, that some things of A B so adhere to each other, that there is nothing intermediate; but that others cannot be assumed. For whatever I may assume of B, the media with reference to A, or with reference to F, will either be infinite, or not. But it is of no consequence from what they first begin to be infinite, whether immediately or not immediately. For the things posterior to these are infinite.

Aristotle, Posterior Analytics. Book I, Chapter 21

It is also evident in privative demonstration that the progression must stop, since in categoric demonstration it is stopped in both series. For let it not be possible, to proceed to infinity, neither upward from the last, (but I call the last that which is not indeed present with anything else, but something else, as, for instance, F is present with it) nor from the first to the last: (I call, however, the first, that which is, indeed, itself predicated of something else, but nothing else is predicated of it). If, therefore, this is not possible, it is evident that in negation the progression must stop. For the not being present with is triply demonstrated.  For either B is present with every individual with which C is present; but A is present with no individual with which B is present. In the proposition B C, therefore, and always in the proof of another interval, it is necessary to proceed to immediate principles.  For this interval is categoric. But with respect to the others, it is evident, that if it is not present with something else prior, as, for instance, D, it will he requisite that this D should be present with every B. And if again, it is not present with something else prior to D, it will be requisite that that should be present with every D. Hence, since the progression downward stops, the progression upward will also stop, and there will be something first with which it is not present.  Again, if B is present with every A, but with no C, A will be present with no C. Again, if it is necessary to demonstrate this, it is evident that it will be demonstrated, either through the superior mode, or  through this, or through the third mode. Of the first mode, therefore, we have already spoken. But the second  will be demonstrated. Thus, however, it will show, as, for instance, that D is present indeed with every B, but with no C, if it is necessary that any thing should be present with B.  And again, if this is not present with C, something else is present with D, which is not present with C. Hence, since the perpetually being present with that which is superior stops, the not being present will also stop. But the third mode was, if A, indeed, is present with every B, but C is not present with every B, C will not be present with every A. Again, this will be demonstrated, either through the above-mentioned modes, or in a similar manner. In those modes, therefore, the progression stops. But if it will be thus demonstrated, again it should be assumed that B is present with E, with every individual of which C is not present. And this again, will be similarly demonstrated. Since, however, it is  supposed that the progression downward stops, it is evident that C also, which is not present with, will stop. But it is also manifest, that if it should not be demonstrated in one way, but in all ways, at one time, indeed, from the first figure, but at another time, from the second or the third, thus likewise the progression will stop. For the ways are finite; but with respect to finite things, when they are finitely assumed, it is necessary that all of them should be finite. That in negation, therefore, the progression stops, if it stops in affirmation, is evident.

Aristotle, Posterior Analytics. Book I, Chapter 22

That the progression, however, must stop in them, will be evident as follows, to those who speculate the affair logically. In things predicated, therefore, in answer to the question what a thing is, this is

evident. For if there is such a thing as definition, or if it may be known what the very nature of a thing is, and if infinites cannot be passed through, it is necessary that those things should be finite which are predicated in answer to the question what a thing is. But we must speak universally as follows: It may be truly said that a thing which is white walks, and that that great thing is wood; and again, that the wood is great, and that the man walks. There is a difference, however, between speaking in this way and in that. For when I say that a thing which is white is wood, then I say that the thing which happens to be white is wood; but that which is white is not as a subject to the wood. For neither being white, nor that which is a certain white thing, was it made wood; so that it is not wood except from accident. But when I say that the wood is white, I do not say that something else is

white and that it happens to it that it is white; (as when l say that what is musical is white, for then I say that the man is white, to whom it happens to be a musician) but I say that the wood is the subject

which was made white, not being any thing else than that which is wood, or a certain piece of wood. If, however, it be requisite to assign names, let to speak in this way be to predicate, but in that way, be either by no means to predicate, or to predicate indeed, yet not simply, but from accident. But let that which is predicated be as white; but that of which it is predicated, as wood. Let it be supposed, therefore, that what is predicated is always predicated of that of which it is predicated, simply, but not according to accident; for thus demonstrations demonstrate. It will, therefore, be predicated,

either in answer to the question what a thing is, or because it is a quality, or a quantity, or a relative, or acts, or suffers, or is somewhere, or when, viz. when one thing is predicated of one. Farther still, those thigs which signify essence, signify that the thing of which  they are predicated is nothing else than that very thing which is predicated, or something belonging to it. But such things as do not signify essence, but are predicated of another subject, which is neither the thing itself that is predicated, nor something belonging to it, are accidents. Thus the white is predicated of man. For man is neither that which is white, nor that which is something belonging to white; but is perhaps

an animal. For man is that which is a certain animal. It is necessary, however, that such things as do not signify essence, should be predicated of a certain subject, and not be something white, which is white, not being any thing else.  For farewell to ideas; since they are but warbling trifles. And if they exist, they do not pertain to the present discussion; for demonstrations are not concerning things of this kind.  Again, if this is not a quality of this thing; and that of this, nor a quality of quality, it is impossible that they should be thus mutually predicated of each other; but it may, indeed, be truly said, but they cannot be mutually predicated. For will they be predicated as essence? As if being the genus, or difference of that which is predicated. It has been demonstrated, however, that these will not be infinite, neither in a descending, nor in an ascending progression. As, for instance, man is

a biped; this is an animal; but this is something else. Nor can animal be predicated of man, this of Callias, and this of something else in an infinite progression in answer to the question what a thing is.  For every thing of this kind may be defined to be essence; but infinites cannot be passed through by intellection. Hence, neither are there infinites in an ascending, nor in a descending progression; for that essence cannot be defined of which infinites are predicated. Indeed, they will not be mutually predicated of each other as genera; for in this case, genus would be a part itself. Nor will quality, nor any other of the categories be mutually predicated, except from accident. For all these are accidents,  and are predicated of essences. Neither will there be infinites in an ascending series. For of each thing that is predicated which signifies either a certain quality, or a certain quantity, or something of things of this kind, or those things which are in the essence of a thing. These things, however are finite, and the genera of the categories are finite; for a category is either quality, or quantity, or relation, or action, or passion, or where, or when. But it is supposed that one thing is predicated of one. Those things, however, which do not signify what a thing is, are not mutually predicated of each other. For all these are accidents; but some are predicated per se, and others after another manner. But we say that all these are predicated of a certain subject; and that accident is not a certain subject.  For we do not admit that any thing among things of this kind is, which not being any thing else is said to be that which it is said to be; but we say that it is predicated of something else, and certain other things, of another thing. Neither, therefore, in an ascending nor in a descending series can one thing be predicated of another infinitely. For the things of which accidents arc predicated, are those

which are contained in the essence of each thing; and these are not infinite. But these and accidents are in an ascending series, and both are not infinite. It is necessary, therefore, that there should be

a certain thing, of which primarily something is predicated, and of this something else. It is also necessary that this progression should stop, and that there should be something, which is neither predicated of another prior thing, nor of which another prior thing is predicated. And thus we have explained this which is one mode of demonstration. There is also another mode, if there is a demonstration of those things of which certain things are previously predicated. But with respect

to those things of which there is demonstration, it is not possible to be better affected toward them, than to know them, nor is it possible to know them without demonstration. But if this thing becomes known through these things, but these things are unknown by us, neither shall be better affected towards them, than if we knew them, nor shall we have a scientific knowledge of that which through these becomes known. If, therefore, it is possible to know any thing simply through demonstration,

and not from certain things, nor from hypothesis, it is necessary that the intermediate predications should stop. For if they do not stop, but there is always something above that which was assumed,

there will be a demonstration of all things. Hence, if infinites cannot be passed through; we shall not know those things of which there is demonstration through demonstration. If, therefore, we are not better affected towards them than if we knew them, it will not be possible to know any thing through demonstration simply, but from hypothesis. Logically, therefore, credibility may from these things be derived concerning what has been said. But it will be more concisely proved analytically as follows, that there cannot be infinite attributes either in an ascending or a descending series in demonstrative sciences, the subject of the present treatise. For demonstration is of such things as are essentially present with things. But they are essentially present in a twofold respect; for such things  are essentially present, as are inherent in their subject in the predication declaring what a thing is; and in which the subjects are inherent in the same predication. Thus the odd is attributed to number, which, indeed, is inherent in number, but number itself is inherent in the definition of the odd. And again, multitude or the divisible is inherent in the definition of number. Neither, however, of these can be infinite; nor as the odd is attributed to number. For again, there would be something else in the odd, in which being inherent in the odd, the odd would be inherent. And if there is, number will be first inherent in those things which are inherent in it. If, therefore, infinites of this kind cannot be inherent in one thing, neither will there be infinites in an ascending series. It is necessary, however,

that all things should be inherent in that which is first, as, for instance, in number, and number in them. Hence they will reciprocate, but will not be more widely extended. Moreover, neither are

those things infinite which are inherent in the predication declaring what a thing is; for if they were, it would not be possible to define. Hence if all attributes are predicated per se; but these are not infinite; things in an ascending progression will stop; and, therefore, this also will be the case with those in a descending progression. But if this be true, those things also which are between the two terms will be finite. And if this is the case, it is now evidently necessary that there should be principles of demonstrations, and that there is not a demonstration of all things, which, as we observed in the beginning, is asserted by some. For if there are principles, neither are all things demonstrable, nor can there be a progression to infinity. For that either of these should be true, is nothing else than that there is no interval immediate and indivisible, but that all things are divisible; since that which is demonstrated, is demonstrated in consequence of the term being inwardly and not outwardly assumed. Hence if it is possible for this to proceed to infinity, it is also possible that there may be infinite media between two terms. This, however, is impossible, if predications stop in an ascending and descending series. But that they do stop, was before shown logically, but now  analytically.

Aristotle, Posterior Analytics. Book I, Chapter 23

These things being demonstrated, it is evident that if one and the same thing is inherent in two things, as, for instance, A with C and with D, when one is not predicated of the other, either in no respect, or not of every individual of it; then it is not always inherent according to something common. Thus the possession of angles equal to two right, is inherent in the isosceles and scalene triangle according to something common. For it is inherent, so far as each of these is a certain figure, and not so far as each is something else. This, however, is not always the case. For let B be that according; to which A is inherent in C D. It is evident, therefore, that B also is inherent in C and in D, according to something else common, and that also according to something else; so that between two terms, infinite terms may be inserted. But this is impossible. It is not, therefore, necessary that the same thing should always be inherent in many things according to something common, since there will be immediate intervals. Moreover, it is necessary that the terms should be in the same genus, and from the same sections, since that which is common will be among the number of things which are essentially inherent. For it is not possible to transfer things, which are demonstrated, from one genus to another genus. It is also evident that when A is present with B, if there is a certain middle, it may be demonstrated that B is present with A. And the elements of this are these things, and whatever are media. For immediate propositions are elements, either all of them, or those which are universal. But if there is not any medium, there is no longer demonstration, but this is the way to principles. In a similar manner also, if A is not present with B, if there is something which is either a middle, or  prior to which A is not present with B, there is demonstration; but if not, there is no  demonstration. Principles and elements, however, are as many as terms. For the propositions consisting of these are the principles of demonstration. And as there are certain indemonstrable principles, by which it is affirmed that this thing is that thing, and that this thing is present with that thing; thus also there are certain indemonstrable principles by which it is affirmed that this thing is not that thing, and that this thing is not present with that thing. Hence some principles will signify that a certain thing is, but others, that a certain thing is not. But when it is requisite to demonstrate

any thing, that must be assumed which is first predicated of B. And let this be C. Let A also, in a similar manner, be predicated of this. And by always proceeding after this manner, a proposition

is never assumed externally, nor is that which is present with A assumed in the demonstration; but the middle is always condensed, till they become indivisibles, and one. They are one, however,

when the immediate is produced, and one proposition simply, viz. an immediate proposition. And as in other things thus also in demonstrations, the principle is simple. But this is not every where

the same; for in weight it is a mina; in melody diesis; and something else in another thing. Thus, in syllogism, that one thing is an immediate proposition; but in demonstration and science it is intellect. In syllogisms, therefore, by which the being inherent is indicated, no medium falls externally. But in privative syllogisms, here, indeed, nothing falls external to that which ought not to be inherent. As if

A is not present with B through C. For if C is present with every B, but A is present with no C; again, if it should be requisite to prove that A is present with no C, the medium of A and C must be assumed. And in this manner we must always proceed. But if it should be requisite to show that D is not present with E, because C is present with every D, but with no, or not with every E, the medium will never fall external to E. And this is that with which it is not necessary to be present. But in the third mode the middle term will never proceed external to that from which, nor which, it is necessary to deny.

Aristotle, Posterior Analytics. Book I, Chapter 24

Since, however, one demonstration is universal, but another partial, and one is categoric, but another privative; it may be doubted which of them is the better. ln a similar manner, it may be doubted about that which is called direct demonstration, and that demonstration which leads to the impossible, which is the better of the two. In the first place, therefore, let us consider about universal and partial demonstration; and this being explained, let us also speak about the demonstration

which is called direct, and that which leads to the impossible. For perhaps it may appear to some thus considering the affair, that partial demonstration is the better of the two. For if that demonstration is better, according to which we obtain greater knowledge; (for this is the virtue of demonstration) but we obtain a greater knowledge of any thing, when we know it per se, than when we know it through something else; (as, we more know that Coriscus is a musician, when we know that Coriscus, than when we know that a man is a musician, and in a similar manner in other things) and if universal demonstration demonstrates because a thing is something else, and not because it is that thing which it is; (as, that an isosceles triangle has angles equal to two right, not because it is isosceles, but because it is a triangle) but partial demonstration demonstrates because a thing is that which it is; if, therefore, the demonstration which is per se is the better, and partial rather than universal demonstration is such, partial will also be better than universal demonstration. Farther still, if universal is not any thing besides particulars, but demonstration produces an opinion, that this thing is something according to which it demonstrates, and that a certain nature of this kind exists in things; (as of triangle besides particular triangles, of figure, besides particular figures, and of number besides particular numbers) but the demontration which is about being is better than that which is about non-being, and that through which we are not deceived, than that through which we are deceived; but universal demonstration is a thing. of this kind; (for proceeding they demonstrate as about the analogous, as that a thing which is of such a kind that it is neither line, nor number, nor solid, nor superficies, but something besides these, is the analogous) if, therefore, this is more universal, but universal demonstration is less conversant with being, than partial demonstration, and produces false opinion; universal will be subordinate to partial demonstration.  May we not, however, say in the first place, that one of these arguments does not more apply to universal than to partial demonstration? For if the possession of angles equal to two right is inherent not so far

as isosceles, but so far as triangle, he who knows that an isosceles triangle possesses this property has a less essential knowledge than he who knows that triangle has this property. In short, if this property is inherent, not so far as a thing is triangle, and this is shown to be the case, it will not be a demonstration. But if it is inherent so far as a thing is a triangle, he who knows a thing so far as it is that which it is, has a greater knowledge of that thing. If, therefore, triangle is more widely extended than isosceles, and there is the same definition, and triangle is not according to the homonymous, and the possession of angles equal to two right is inherent in every triangle; if this be the case, triangle will not have such like angles, so far as it is isosceles, but isosceles will have them so far as it is triangle. Hence he who knows universal, has a greater knowledge so far as pertains to the being inherent, than he who, knows according to a part. Hence too, universal is better than partial demonstration. Again, if there is one certain definition, and it is not an equivocation, universal will not have a less, but a greater subsistence than certain particulars; so far as universals are

incorruptible, but particulars are more corruptible. Again, there is no necessity that we should apprehended this to be something besides particulars, because it signifies one thing, no more than in other things, which do not signify essence, but quality, or relation, or action. But if any one should think that universal is something besides particulars not demonstration but the hearer is the cause of this error. Farther still, if demonstration, indeed, is a syllogism of the cause and of the why; but universal is more causal; for that with which any thing is essentially present, is itself a cause to itself. But universal is the first; universal, therefore, is a cause.  Hence demonstration is better; for it pertains to cause and the why, in a great degree. Again, as far as to this we investigate the why, and we then think that we know when this thing is becoming to be, or is, not because something else is

becoming to be, or is. For thus there is now the end, and the last boundary. For instance, on what account did he come? That he might receive a sum of money. But this, that he might return what he owed. And this, that he might not act unjustly. Thus proceeding, when it can no longer be said that he came on account of something else, nor for the sake of another thing, then we say that he came, that the thing is, and is becoming to be, on account of this as the end, and then we especially know why he came. If, therefore, the like takes place in all causes and enquiries into the why, but in things which are in such a manner causes as that for the sake of which, we thus especially know, in other things also we shall then most eminently know, when this thing no longer exists because another thing exists. When, therefore, we know that the external angles are equal to four right angles, because it is an isosceles triangle; it yet remains to enquire why because isosceles; because it is a triangle; and this because it is a right-lined figure. But if it is this no longer on account of something

else, then we know in the most eminent degree; and then we know universally. Universal, therefore, is better than partial demonstration. Again, by how much the more things subsist according to a

part by so much the more do they fall into infinites; but so far as they are universal they tend to the simple, and to bound. So far, however, as they are infinite, they are not objects of scientific knowledge; but they are objects of this knowledge so far as they are finite. So far, therefore, as they are universal, they are more objects of scientific knowledge, than so far as they subsist according to a part. Hence universals are more demonstrable. But of things which are more demonstrable, the demonstration is more eminent. For relatives are at one and the same time more. The demonstration, therefore, which is more universal is the better demonstration, since it is also demonstration in a

more eminent degree. Farther still, that demonstration is the more eligible, according to which this, and something else are known, than that according to which this thing alone is known. But he who possesses universal, knows also that which is according to a part. He, however, who knows according to a part, does not know universal. Hence, thus also universal demonstration will be more eligible. Again, this may be also shown as follows: It is possible to have a greater knowledge

of universal, because it is demonstrated through a medium which is nearer to the principle. But that which is immediate is most near; and this is the principle. If, therefore, the demonstration which is

from the principle is more accurate than that which is not from the principle; that demonstration which is in a greater degree from the principle is more accurate than that which is in a less degree from the principle. But the demonstration which is more universal is a thing of this kind. Universal demonstration, therefore, is better than that which subsists according to a part. Thus, if it were requisite to demonstrate A of B, but the media should be B C; B will be in the superior place; and,

therefore, the demonstration which is effected through this, is more universal. Some, however, of the above-mentioned arguments are logical. But it is especially evident that universal demonstration is the more principal; because when of two propositions, we have that which is the prior, we also in a certain respect know that which is the posterior, and we possess it in capacity. Thus, if any one knows that every triangle has angles equal to two right, he also knows in a certain respect that an isosceles triangle has angles equal to two right; viz. he knows this in capacity, though he may not know that it is a triangle. But he who possesses this proposition, by no means knows universal, neither in capacity, nor in energy. And the universal proposition, indeed, is intelligible; but that  which is according to a part, ends in sense. And thus much we have said to show that universal is better than partial demonstration.

Aristotle, Posterior Analytics. Book I, Chapter 25

That ostensive  (i.e. affirmative), however, is better than privative (i.e. negative) demonstration, will be evident as follows: Let that demonstration be the better (other things existing the same) which consists of fewer postulates, or hypotheses, or propositions. For if the propositions are similarly known, knowledge will be more swiftly obtained through these. And this is more eligible. But the reason of this proposition, that the demonstration which consists of fewer things is the better, and the universal reason of it, is this. For if the media are similarly known; but things prior are more known, let the demonstration that A is present with E, be through the media B C D; but through the media F G that A is present with E. These, however, will subsist similarly, viz. that A is present with D, and that A is present with E. But that A is present with D, is prior and more known than that A is present with E; for that is demonstrated through this.  And that is more credible through which a thing is demonstrated than that which is demonstrated. The demonstration, therefore, which is effected through fewer things, is better, other things remaining the same. Both, therefore, demonstrate through three terms and two propositions; but the one assumes that something is and the other that  something is, and is not. Hence it is effected through a great number of things; and, therefore, is worse. Again, since it has been demonstrated that it is impossible when both the propositions are privative, a syllogism should be produced; but it is necessary that the one should be of this kind, and that the other should be inherent; in addition to this, it is necessary to assume this; for it is necessary  that categoric propositions, the demonstration being increased, should become many; but it is  impossible that the privative should be more than one in every syllogism. For let A be present with no one of those things with which B is present; but let B be present with every C. If, however, again, it should be necessary to increase the propositions, a middle or medium must be inserted.  Of A B, therefore, let the middle be D; but of B C, let the middle be E. Hence it is evident that E is categoric. But D is categoric, indeed, of B, but is posited as privative with reference to A. For it is necessary that D should be present with every B, but A with no D. One privative proposition, therefore, is  roduced, viz. A D. There is also the same mode in other syllogisms. For the middle of categoric terms, is always attributive from each part. But of a privative interval it is necessary that the middle should be privative from one part. Hence this becomes one proposition of this kind; but the others are categoric. If, therefore, that through which a thing is demonstrated is more known and credible; but privative  demonstration is demonstrated through categoric demonstration, and the latter is not demonstrated through the former, this, since it is prior, more known, and more credible, will be better. Again, since the principle of syllogism is a universal immediate proposition; but a universal proposition in an ostensive demonstration is affirmative, but in a privative is negative; and since an

affirmative proposition is prior to and more known than a negative, for negation is known through affirmation, and affirmation is prior, just as being is prior to non-being; since this is the case, the principle of an ostensive, is better than the principle of a privative demonstration. But the demonstration which uses better principles is better. Farther still, it also partakes in a greater degree of the nature of principle; for the privative is not without the ostensive demonstration.

Aristotle, Posterior Analytics. Book I, Chapter 26

But since categoric is better than privative demonstration, it is evident that it is also better than the  demonstration which leads to the impossible. It is necessary, however, to know what the difference of them is. Let A therefore be present with no B, but let B be present with every C. Hence it is necessary that A should be present with no C.  The terms, therefore, being thus assumed, the privative proposition proving that A is not present with C, will be ostensive. But the demonstration leading to the impossible will subsist as follows: If it should be necessary to demonstrate that A is not present with B, it must be assumed that it is present, and also that B is present with C. Hence it will happen that A is present with C. But let it be known and acknowledged that this is impossible. Hence it is not possible that A should be present with B. If, therefore, it should be acknowledged that B is present with C, it is impossible that A should be present with B. The terms, therefore, are similarly arranged. It makes a difference, however, whether the privative proposition is more known, viz., whether A is not present with B, or A is not present with C.  When, therefore, it is more known that the conclusion is not, a demonstration leading to the impossible is produced. But when the negation which is in the syllogism is more known a demonstrative proof is produced. The negation, however, that A is not present with B, is prior by nature to the negation that A is not present with C.  For those things from which the conclusion is collected, are prior to the conclusion. And this negation that A is not present with C, is the conclusion; but the negation that A is not present with B,  is that from which the conclusion is collected. For if it happens that a certain thing is subverted, it does not follow that this is the conclusion; but those things through which it is subverted are the things from which the conclusion is formed. That, however, from which the conclusion is collected is a syllogism, which so subsists, that one proposition with reference to the other is, either as a whole to a part, or as a part to a whole. But the propositions A C and A B, do not thus subsist with  reference to each other. If, therefore, the demonstration which is from things more known and prior, is more excellent; but both produce credibility, from a certain thing not existing, and the one from that which is prior, but the other from that which is posterior; privative demonstration will be, in short, better than the demonstration which leads to the impossible. Hence, if categoric demonstration is better than this, it is evident that it is also better than the demonstration which leads to the impossible.

Aristotle, Posterior Analytics. Book I, Chapter 27

One science, however, is more accurate than, and is prior to another science; for the science through which a knowledge is obtained that a thing is, and at the same time why it is, and not separately that it is, is more accurate than the science by which it is only known why it is. The science also which is not of a subject, is more accurate than and prior to that which is of a subject; as, for instance,  arithmetic than the harmonic science. And the science which consists of fewer things, than that which is from addition; as, arithmetic than geometry. But I say from addition; as, for instance, the monad is an essence without position; but a point is an essence with position. This I denominate

from addition.

Aristotle, Posterior Analytics. Book I, Chapter 28

But there is one science (i.e. which is of one genus) of those things which are composed from first principles, which principles are the parts or properties of these per se. And there are different  sciences of those things, of which the principles are neither from the same things, nor the one from the other. But of this it is a token, when any one arrives at things indemonstrable; for it is necessary  that they should be in the same genus with the demonstrated conclusions. Of this it is likewise a token, when the things which are demonstrated through them are in the same genus, and are of a kindred nature.

Aristotle, Posterior Analytics. Book I, Chapter 29

It is possible, however, that there may be many demonstrations of the same thing, and this not only when an uncontinued medium is assumed from the same co-ordination; as if of the terms A B, C, D,

and F should be assumed. But this may also be possible from a different co-ordination, Thus, for instance, let A be to be changed; D, to be moved; and B, to be delighted: and again, let G be to be tranquilized. D, therefore, is truly predicated of B, and A of D. For he who is delighted is moved, and that which is moved is changed. Again, A is truly predicated of G, and G of B. For every one who is delighted is tranquillized, and he who is tranquillized is changed. Hence a syllogism is formed through different media, and not from the same coordination; yet not so that neither medium is  predicated of the other; for it is necessary that both should be present with something which is the same. It is requisite also to consider how often a syllogism of the same thing may be produced  through other figures.

Aristotle, Posterior Analytics. Book I, Chapter 30

But there is no science through demonstration of that which is fortuitous. For that which is fortuitous is neither as necessary, nor is that which is for the most part, but as that which is produced besides these; and demonstration is of one of these. For every syllogism is either through necessary propositions, or through those which are for the most part true. And if the propositions indeed are necessary, the conclusion also is necessary; but if they are for the most part true, the conclusion also is a thing of this kind. Hence, if the fortuitous is neither that which exists for the most part, nor which is necessary, there will not be demonstration of it.

Aristotle, Posterior Analytics. Book I, Chapter 31

Neither is it possible that we can possess scientific knowledge through sense. For though sense is of a thing of this kind, and not of something belonging to this, yet it is necessary to have a sensible perception of this particular thing, and somewhere, and now. But it cannot perceive that which is universal, and in all things; for universal is not this particular thing, nor does it exist now; otherwise it would not be universal. For we call that universal which is always, and everywhere. Since,  therefore, demonstrations are universal, but universals cannot be perceived by sense; it is evident that it is not possible to possess scientic knowledge through sense. Indeed it is evident that though it were possible to perceive by sense, that a triangle has angles equal to two right, we should require demonstration, and we should not (as some say) know this property of a triangle scientifically. For it is necessary to have a sensible perception of that which is particular; but science is obtained by knowing universal. Hence, if we were above the moon, and should see that the earth is opposite, we

should not know the cause of the eclipse of the moon. For we should perceive that the moon is now eclipsed, but we should not in short perceive why it is eclipsed; for sense is not a perception of universal. Nevertheless, from perceiving that this frequently happens by investigating universal, we shall possess demonstration. For from many particulars universal becomes manifest. But universal is honourable because it manifests cause. Hence the universal knowledge about things of this kind, of which there is another canse, is more honourable than the senses, and intelligence.  There is another reason, however, about first principles. It is evident, therefore, that it is impossible by sensible perception to have a scientific knowledge of anything demonstrable, unless some one should say, that sensible perception is this, to possess science through demonstration. There are, however, some

things which are referred in problems to a defect of sense. For some things, if we should see them, we should not investigate, not as knowing in consequence of seeing, but as possessing universal from perceiving. Thus if we should see a piece of glass perforated, and the light passing through it, it would also be manifest why it illuminates in consequence of our seeing separately in each piece of glass, but at the same time understanding that the like takes place in all pieces of glass.

Aristotle, Posterior Analytics. Book I, Chapter 32

It is impossible, however, that there should be the same principles of all syllogisms. And in the first place, this will appear to be true to those who logically consider the affair. For of syllogisms some are true, but others false. For though it may be possible to conclude what is true from things that are false, yet this is but rarely effected. Thus, if A is truly predicated of C, but the middle B is false, neither A will be present with B, nor B with C.

Every stone (B) is an animal (A):

Every man (C) is a stone (B): Therefore,

Every man (C) is an animal (A).

But if the media of these propositions are assumed, the proposition of the prosyllogisms will be false, because every false conclusion is produced from false principles; but true conclusions are deduced from true principles. And false and true conclusions are different from each other. In the next place, neither are false conclusions collected from the same principles with themselves; for they are false and contrary to each other, and cannot be simultaneous. Thus it is impossible that justice should be injustice, or timidity; that man should be a horse or an ox; and that the equal should be greater or less. From the things, however, which are posited, it may thus be proved. For neither are there the same principles of all true conclusions; since the principles of many are different in genus, and cannot be adapted. Thus monads cannot be adapted to points; for the former are without, but the latter with position. But it is necessary to adapt terms either to media; or above; or beneath; or some terms within, but others without the extremes. Neither is it possible that there can be certain common principles, from which all things can be demonstrated. (But I call common principles such as this, Everything may be affirrned or denied.) For the genera of beings are different; and some are present  with quantities, but others with qualities alone, with which demonstration is framed through common principles. Again, principles are not much fewer than conclusions. For propositions are principles;  and propositions subsist, a term being either assumed or inserted. Farther, still, conclusions are infinite; but terms are finite. Again, of principles, some are from necessity; but others are contingent. Thus, therefore, to those who consider the affair, it will appear to be impossible that there should be the same finite principles, when the conclusions are infinite. But if it should be said that there are

the same principles in some other way; as for instance, that these are the principles of geometry;  those, of numbers; and those, of medicine; what else is this than to say, that there are principles of the sciencess? But it is ridiculous to say that there are the same principles, because they are the same with themselves; for thus all things will become the same. Moreover, neither is to demonstrate any thing from all things, to investigate whether there are the same principles of all things. For this is very stupid. For neither is this effected in manifest disciplines, nor is it possible in analysis; since immediate propositions are principles; and another conclusion is produced, an immediate proposition being assumed.  But if some one should say that first immediate propositions are the same principles; there is one in each genus. If, however, it is neither possible that any thing can be demonstrated as it ought to be from all principles, nor that principles should be so different, as that of each science there are different principles; it remains, that the principles of all sciences are of a kindred nature, but that different sciences are demonstrated from different principles. It is evident, however, that this is not possible; for it has been shown that the principles are different in genus, of those things which are generically different. For principles are twofold, i.e. from which, and about which. The principles, therefore, from which are common; but those about which are peculiar, as, for instance, number, and magnitude.

Aristotle, Posterior Analytics. Book I, Chapter 33

The object, however, of scientific knowledge and science differ from the object of opinion and  opinion; because science is universal, and through things which have a necessary subsistence; and the necessary cannot subsist otherwise than it does. But some things are true and have an existence, and yet it is possible that they may subsist otherwise than they do. It is evident, therefore, that science is not conversant with these things; (for if it were, it would be impossible for things to subsist otherwise, which are capable of subsisting otherwise) nor is intellect conversant with these; (for I call intellect the principle of science) nor indemonstrable science; (and this is the apprehension of

an immediate proposition) but intellect, science, and opinion, and that which is asserted through these are true. Hence it remains that opinion is conversant with that which is true or false, but which may have a various subsistence; and, this is the apprehension of an immediate, and not necessary proposition. This too accords with the phaenomena; for opinion is unstable, and its nature is of this kind. Besides, no one thinks that he opines, but that he possesses scientific knowledge, when he thinks it is impossible for a thing to subsist otherwise than it does. But when he thinks that a thing does, indeed, thus subsist, and yet that it may subsist otherwise, then nothing hinders but that he may

opine; as if opinion were conversant with a thing of this kind, but science with that which is necessary. How does it happen, therefore, that it is not possible to form an opinion of, and know scientifically the same thing? And why is not opinion science, if any one admits that whatever he knows, he may opine? For both he who knows, and he who opines, follow through media, till they arrive at things immediate. Hence, if the former knows, he also who opines knows. For as it is possible to opine that a thing is, so likewise why it is, and this is the medium. Shall we say, that if he so apprehends things which cannot subsist otherwise, as if he had the definitions through which demonstrations are framed, he will not opine, but know scientifically? But if he should apprehend that they are true, indeed, and yet that these things are not present with them essentially, and according to form, shall we say, that he opines, and that he does not truly know scientifically that  they are, and why they are, even if he should opine through things immediate? But if not through things immediate, that he alone opines that they are? Opinion, however, and science, are not entirely conversant with the same thing; but as both a false and a true opinion, are after a certain manner conversant with the same thing, thus also science and opinion are conversant with the same thing. For by admitting, as some say, that true and false opinion are entirely conversant with the same thing, absurd consequences will ensue, and among others this, that he who opines falsely does not opine. Since, however, the same thing is multifariously predicated, in one way there may be a true and false opinion of th same thing, and in another way there cannot be.  For to suppose that any one can  opine truly that the diameter of a square is commensurable with its side is absurd.  But because the diameter about which opinions subsist, is one and the same thing, thus also opinions are conversant with the same thing. The essence, however, of each according to definition is not the same.  In a similar manner also, science and opinion are conversant with the same thing. For the former is so conversant with animal, as that it is not possible animal should not exist; but the latter is so conversant with it, as that it is possible it may not exist. Just as if the one should be conversant with that which is man essentially, but the other, with man indeed, yet not with that which is man essentially.  For the same thing, i.e. man, is assumed after a different manner. From these things, therefore, it is evident, that it is not possible to opine, and know scientifically the same thing. For otherwise a man might apprehend that the same thing may subsist otherwise than it does, and yet may not subsist otherwise; which is impossible. In different men, however, each of these may be possible about the same thing, as we have before observed; but in the same man it is not possible. For if it were it might be possible to form an opinion at one and the same time that man is an animal essentially (for this it is to be impossible not to be an animal) and is not essentially an animal; for this it is, to be possible not to be an animal.  With respect to what remains, however, in what manner it is necessary to distinguish the dianoetic power, intellect, science, art, prudence, and wisdom, partly pertains to the physical, and partly to the ethical theory.

Aristotle, Posterior Analytics. Book I, Chapter 34

But sagacity is a certain right conjecture of the medium in the shortest time. As, if some one  perceiving that the moon is always splendid in that part which is turned towards the sun should rapidly understand why this takes place, viz. that it is because it is illuminated by the sun; or seeing a person speaking to a rich man should know that his conference is in order to borrow money of him;  or should immediately know why two persons are friends, viz. because they are enemies of the same person. For he who sees the extremes knows all the middle causes. Let then, to be splendid in the part towards the sun be A; to be illuminated by the sun, B; and let the moon be C. Hence B, i.e., to be illuminated by the sun, is present with the moon C; but A, i.e. to be splendid in the part which is turned towards that by which it is illuminated, is present with B. Hence A also is present with C through B.

Whatever is illuminated by the sun (B), shines in that part which is towards the sun (A):

The moon (C) is illuminated by the sun (B): Therefore,

The moon (C) shines in that part which is towards the sun (A).

 

Aristotle, Posterior Analytics. Book II

Aristotle, Posterior Analytics. Book II, Chapter 1

Subjects of investigation are as many in number, as are the things which we scientifically know. But we investigate four things: that a thing is, why it is, if it is, and what it is.  For when we enquire whether it is this thing, or that, directing our attention to many things (as whether the sun is eclipsed or not) we investigate the that. An indication of which is this; that finding it is eclipsed, we cease to investigate; and if from the beginning we knew that it is eclipsed, we should not enquire whether it is eclipsed. But when we knew that it is, then we investigate why it is. Thus, for instance, knowing that the sun is eclipsed, and the earth is shaken, we enquire why the sun is eclipsed, or why the earth is shaken. These things, indeed, we thus investigate.  Some things, however, we investigate after another manner, as if a centaur or God is, or not. But I say, if it is or not simply; and not if it is white or not. When we know, however, that a thing is, we enquire what it is; as, for instance, what God is, or what man is. Hence the things which we investigate, and which when discovered we know,

are these, and are so many.

Aristotle, Posterior Analytics. Book II, Chapter 2

When, however, we enquire of a thing the that, or if it is simply, then we enquire whether there is a medium of it, or not. But when knowing either that it is, or if it is, either in part or simply, we again

enquire why it is, or what it is, then we enquire what the middle is. But I mean by an enquiry into the that, and in a part, such as the question, is the moon eclipsed? Or is it increased?  For in things of

this kind we enquire if a thing is or is not. And by an enquiry into the that simply, I mean, if the moon, or night is, or not. In all enquiries, therefore, it happens that we investigate either if there is a middle, or what the middle is. For the cause is the middle; and this is investigated in all things.  As, is there an eclipse? Is there a certain cause or not? After this, when we know that there is a certain cause, we enquire what the cause is.  For the cause why a thing is not this or that, but is simply essence, or not simply, but some one of the these things which subsist per se, or from accident, is the middle.  When, however, I say a thing is simply essence, I mean the subject, as the moon, or the earth, or the sun, or a triangle; but by a certain thing, I mean, an eclipse, equality, inequality, if it is in the middle, or not. For in all these it is evident, that what a thing is, and why it is, are the same. What is an eclipse? A privation of the light which proceeds from the moon, through the opposition of the earth. Why is there an eclipse? Or why is the moon eclipsed? Because the light of it fails, through the opposition of the earth. What is symphony? A ratio of numbers in the sharp or the flat. Why does the sharp accord with the flat? Because the sharp and the flat have the ratio of numbers. Do the sharp

and the flat, therefore, accord? Is there a ratio then of them in numbers? But when we assume that there is, we then enquire what the ratio of them is. That the enquiry, however, is of the middle, is evinced by those things of which the middle is sensible. For we enquire, not having a sensible perception, for instance, of an eclipse, whether it is, or not. But if we were above the moon, we should not enquire neither if, nor why there is an eclipse; but it would be immediately evident; because from sensible perception we should obtain a knowledge of the universal. For sense would perceive that the earth is now opposed, for it would be evident that the moon is now eclipsed.  But from this the universal would be produced. As we have said, therefore, to know what at a thing is, is the same as to know why it is. But this is either simply, and not some one of the things which are inherent, or, it is some one of the things inherent; such, for instance, as, that it has two right angles, or that it is greater or less. That all enquiries, therefore, are an investigation of the middle, is evident.

Aristotle, Posterior Analytics. Book II, Chapter 3

Let us, however, show how it may be demonstrated what a thing is, what the mode of reduction is, and what definition is, and what are the subjects of it, in the first place, doubting concerning these. But let the beginning of the future doubts be that which is most appropriate to the following discussion. For some one may doubt whether it is possible to know the same thing, and according to the same, by definition and demonstration. Or is this impossible? For definition seems to pertain to what a thing is; but every thing which signifies what a thing is, is universal and categoric. But of syllogisms, some are privative, and others are not universal. Thus, for instance, all the syllogisms in the second figure, are privative; but those in the third figure, are not universal. In the next place, neither is there a definition of all the affirmations in the first figure; as of this, that every triangle

has angles equal to two right. But the reason of this is; because to know scientifically a thing which is demonstrable, is to possess demonstration. Hence, if there is a demonstration of things of this kind, it is evident that there will not also be a definition of them; for otherwise scientific knowledge might also be possessed from definition, without demonstration; since nothing in this case will hinder the possession of it at one and the same time with definition. A sufficient belief of this is also produced from induction; for by defining we never know anything, of those things which are inherent per se, or which are accidents. Farther still, if definition is a certain indication of essence; and it is evident that things of this kind are not essemces; it is manifest that there is not a definition of every thing, of which there is demonstration. But what, is there demonstration then of everything of which there is

definition? Or not? There is one reason, indeed, pertaining to this enquiry; for of one thing, so far as it is one, there is one science. Hence, if to know scientifically that which is demonstrable, is to possess science, a certain impossibility will happen. For he who possesses definition, will know scientifically without demonstration. Again, the principles of demonstrations are definitions; of which principies, it has been before shown that there will not be demonstrations.  For either

principles will be demonstrable and the principles of principles, and this will proceed to infinity; or first principles will be indemonstrable definitions. If, however, there are not definition and demonstration of everything, may there not be of a certain thing? Or is this also impossible? For there is not demonstration of that thing of which there is definition; since definition pertains to what a thing is, and to essence; but all demonstrations appear to suppose and assume what a thing is; as,

mathematical demonstrations, what the monad, and what an odd number are; and in a similar manner other demonstrations. Farther still, every demonstration shows something of something, as, that it is, or that it is not; but in definition one thing is not predicated of another. Thus, for instance, neither animal is predicated of biped, nor this of animal; nor is figure predicated of superficies; for superficies is not figure, nor figure superficies. Again, it is one thing to show what a thing is, and another to show that it is. Definition, therefore, manifests what a thing is; but demonstration shows that either this thing is of this, or is not of it: But of a different thing there is a different demonstration, unless it should be as a certain part of the whole. I say this, however, because it has been shown that the isosceles triangle will have its three angles equal to two right, if it be shown that every triangle has this property. For that is a part; but this is a whole. These, however, viz. that a thing is, and what it is, do not thus subsist with reference to each other; for the one is not a part of the other. It is evident, therefore, that neither is there entirely demonstration of that of which there is definition; nor entirely definition of that of which there is demonstration; and, in short, that it is impossible to possess both of the same thing. Hence also it is manifest, that neither will definition and demonstration be the same, nor will the one be contained in the other; for otherwise, their subjects would subsist similarly. Thus far therefore, let these things be the subject of doubt.

Aristotle, Posterior Analytics. Book II, Chapter 4

With respect, however, to the enquiry what a thing is, whether is there a syllogism and demonstration of it, as the present discussion supposed, or is there not? For a syllogism shows something of  something through a medium; but the what is peculiar, and is predicated in answer to the question what a thing is. It is necessary, however, that these should reciprocate. For if A is the peculiarity of C, it is evident that it is also the peculiarity of B, and B of C; so that all of them reciprocate with each other. But if A is present with every B in the question what a thing is, and universally B is predicated of every C in the same question; it is also necessary that A should be predicated of C in the question what a thing is. If, however, someone without thus doubting should assume principles, it will not be necessary that A should be predicated of C, in the question what a thing is though A should be predicated of B in the same question, but B should not be predicated of those things of which it is predicated, in this question. Hence both these will signify what a thing is. B, therefore, will also

signify what C is. Hence if both signify what a thing is, and what the very nature of it is; in the middle term prior to the conclusion there will be the very nature of a thing. In short, if it is possible to show what man is, let C be man, but A what he is, whether he be a biped animal, or any thing else. If, therefore, a syllogistical conclusion should be formed, it is necessary that A should be predicated of every B; but of this there will be another definition. Hence this also will signify what man is. Hence, that is assumed which ought to be demonstrated; for B signifies what man is.  It is, necessary, however, to consider this in two propositions, and in first and immediate principles; for what is asserted will thus especially become apparent. Those, therefore, who on account of reciprocation, show what the soul is, or what man is, or any thing else, beg the question.  Thus, if any one should think fit to assume that the soul is that which is the cause to itself of life; and that this is number moving itself; it is necessary that he should so assume as a postulate, that the soul is number moving itself, as that these two are the same. For if A is consequent to B, and this to C, it does not on that account follow that A will be the very nature of C, (but it will only be possible to say that it is true); nor if A should be so predicated of every B, that B should be that very thing which A is. For the very nature of animal is predicated of the very nature of man; since it is true that whatever exists as man, exists as animal (just as every man is an animal) yet not in such a manner as that both are one thing. He, therefore, who does not thus assume the propositions will not conclude that A is the very nature of C. But if he thus assumes them, he will assume prior to the conclusion that B is the very nature of C. Hence there will be no demonstration, because he assumes that which was investigated in the beginning.

Aristotle, Posterior Analytics. Book II, Chapter 5

Moreover, neither does the way through divisions conclude, as was observed, in the ainalysis about figures. For it is never necessary for that thing to exist, when these exist; as neither does he who forms an induction demonstrate. For the conclusion ought not to interrogate, nor to exist because it is granted; but it necessarily is when they exist, though it should not be acknowledged by him who  answers. Is man, therefore, an animal, or inanimate? Afterwards he assumes that man is an animal, but does not syllogistically conclude that he is. Again, every animal is either pedestrious or aquatic.  He assumes that man is pedestrious; and that man is that whole, animal pedestrious, is not necessary from what was said, but this also he assumes. It is however of no consequence whether this is done in many, or in few thingss; for it is the same thing. The use of division, therefore, becomes unsyllogistic to those who thus proceed, and unfit for the purpose of concluding what might  otherwise be syllogistically concluded. For what hinders but that the whole of this may be tru1y asserted of man, and yet may not manifest what a thing is, and the very nature of a thing? Again what should hinder the adding, or taking away, or passing beyond something pertaining to essence? These faults, therefore, are committed, indeed, but may be avoided, by assuming all attributes in answer to the question what a thing is, and the first being made a postulate the order of those things which ought to be placed successively in definition shou1d be constituted, and nothing should be omitted . But this is necessary, if every thing falls into the division, and nothing is wanting . For now it is necessary that there should be an individual. At the same time, however, there is not a syllogism; but if it indicates, it indicates after another manner. And this is not at all absurd. For neither perhaps does he who makes an induction demonstrate, yet at the same time, he renders something manifest. But he who selects definition from division, does not collect through syllogism. For as in the   conclusions which are without media if any one says that these things being admitted, it is, necessary that this particular thing should be, it may he asked why; thus also in divisive definitions. What is man? A mortal animal, having feet, a biped, without wings. Why? According to each addition. For he will say, and show by division, as he thinks, that every animal is either mortal, or immortal. But the whole of this sentence is not a definition. Hence though it should be demonstrated by division, yet the definition is not produced by syllogism.

Aristotle, Posterior Analytics. Book II, Chapter 6

May it, however, be demonstrated from hypothesis what a thing is according to essence, assuming that the very nature of a thing is nothing else than that which consists from attributes in the question what a thing is, and is the peculiarity of a thing; but that these things are alone predicated in the question what a thing is, and that the whole is the peculiarity of a thing? For this is the essence of it. Or again, in this proof also, is the very nature of a thing assumed? For it is necessary to demonstrate through a medium. Farther still, as in a syllogism, what it is to syllogize, is not assumed; for the proposition from which the syllogism consists is always a whole, or a part; thus, neither ought what the very nature of a thing is, to be in a syllogism, but this should be separate frorn the things which are posited. And in answer to him who doubts whether this is concluded or not, it must be said, that it is; for this was a syllogism. And in answer to him who says that the very nature of the thing was not concluded, it must be asserted that it was; for what the very nature of the thing is was posited by us. Hence it is necessary that something should be syllogistically collected without the definition of syllogism, or the very nature of a thing.  This will also be the case if any one should exhibit from hypothesis. Thus, if to be divisible is the essence of evil; but of a contrary the essence is contrary, I mean in those things to which something is contrary; and good is contrary to evil, and the indivisible to the divisible; the essence of good is to be indivisible. For here also he proves, assuming the very nature of a thing; but he assumes it in order to demonstrate the very nature of a thing. Let, however, these be different. For in demonstrations it is assumed that this thing is predicated of that; yet not that very thing which ought to be demonstrated, nor that of which there is the same reason, and which reciprocates. Against both, however, i.e. against him who proves from division, and against the

syllogism thus constructed, there is the same doubt, why man will be a biped pedetrious animal, but not an animal and pedestrious. For from the things which were assumed there is no necessity that what is predicated should become one thing; but it will be just as the same man is both a musician and a grammarian.

Aristotle, Posterior Analytics. Book II, Chapter 7

How, therefore, will he who defines show the essence of a thing, or what it is? For he will not render it manifest as demonstrating from things which are granted; because it is necessary when they exist,

that there should be something else. For demonstration is this. Nor will he render it manifest, as by an induction through particulars, that every thing thus subsists because no individual subsists otherwise. For induction does not show what a thing is, but that it is, or is not. What other mode, therefore, remains? For he will not indicate by sense, or by the finger. Farther still, how will he show what man is? For it is necessary that he who knows what man is or any thing else, should also know that he is. For with respect to non-being, no one knows that it is, but what the assertion about it signifies, or the name, as when I say tragelaphos (i.e. an animal composed of a goat and a stag).

But what tragelaphos is, it is impossible to know. Moreover, if he should show what a thing is, and that it is, how will he show this in the same sentence? For definition and also demonstration manifest one certain thing. But what man is is one thing, and the essence of man is another. ln the next place, we say it is necessary to show through demonstration with respect to every thing, that it is, unless it should be essence. But to be is not the essence of anything; for being is not a genus. There will be a demonstration, therefore, that it is; which also the sciences now effect. For what a triangle signifies, the geometrician assumes; but that it is he demonstrates. What, therefore, will he who defines what it is prove? Shall we say a triangle ? Someone, therefore knowing by definition what it is, will not know if it is. This, however, is impossible. But it is also evident, according to the modes of  definitions now observed, that those who define, do not show that a thing is. For though there is an equality of the lines drawn from the middle, yet why is it the thing defined? And why is this a circle? For it might also be said that there is the same definition of orichalcum; since neither do definitions manifest that it is possible for that to be which is asserted; nor that that thing exists of which they say there is a definition. But it is a;ways possible to say why? If, therefore, he who defines shows either what a thing is, or what a name signifies, definition will be a sentence signifying the same thing as a name. This, however, is absurd. For in the first place, there will be a definition of non-essences, and of non-beings; since non-beings also may signify something. Again, all sentences will be definitions. For it will be possible to give a name to any sentence. Hence all discussions would be definitions, and the Iliad would be a definition. Again, no science demonstrates that this name signifies this

thing; neither, therefore, do definitions manifest this. Hence neither do definition and syllogism appear to be the same thing; nor are syllogism and definition of the same thing. To this it may also be added, that definition neither demonstrates, nor shows any thing; and that what a thing is can neither be known by definition, nor by demonstration.

Aristotle, Posterior Analytics. Book II, Chapter 8

Again, it must be considered which of these things is well, and which is not well asserted. Also, what definition is; and whether there is in a certain respect, or by no means, a demonstration and definition

of what a thing is. But since it is the same thing (as we have already said) to know what a thing is; and to know the cause of the what it is; but the reason of this is, that there is a certain cause, and this is either the same, or another, and if it is another, it is either demonstrable, or indemonstrable; this  being the case, if the cause is another, and can be demonstrated, it is necessary that that cause should be a medium, and should be demonstrated in the first figure. For that which is demonstrated is universal and categoric. One mode therefore, will be that which is now investigated, viz. to demonstrate what a thing is through something else. For in order to demonstrate what a thing is, it is necessary that the medium should be what a thing is, and in order to demonstrate peculiarities, that peculiarity should be the medium. Hence of two essential natures of the same thing it will demonstrate the one, but will not demonstrate the other. That this mode, therefore, will not be demonstration, we have before shown; but it is a logical syllogism of the what a thing is. Let us show, however, after what manner this may be effected, again discussing the affair from the beginning. For as we investigate why a thing is, when we know that it is, but sometimes both these become at one and the same time manifest, but it is not possible prior to knowing that it is, to know

why it is; it is evident, that in like manner, the very nature of a thing, or what it is, cannot be known without knowing that it is. For it is impossible to know what a thing is, when ignorant if it is. Sometimes, however, we know if it is, from accident, knowing sometimes something pertaining to the thing. Thus we know it is thunder, because it is a certain sound of the clouds; we know it is an  eclipse, because it is a privation of light; we know it is a man, because it is a certain animal; and we know it is soul, because it moves itself.  With respect, therefore, to such things of which we know that they are from accident, it is by no means necessary that we should be prepared to know

what they are; for neither do we really know that they are. But to enquire what a thing is, not knowing that it is, is to enquire about nothing. With respect to those things, however, of which we know something, it is easy to enquire what they are. Hence as we are disposed to know that a thing is, thus also we are disposed to know what it is. Of those things, therefore, of which we know something pertaining to their very nature, let this be first an example; an eclipse, A; the moon, C; the opposition of the earth, B.

That to which the earth is opposed (B) is eclipsed (A):

The earth is opposed (B) to the moon (C): Therefore,

The moon (C) is eclipsed (A).

To enquire, therefore, whether the moon is eclipsed or not, is to enquire whether B is or not. And this in no respect differs from enquiring if there is a reason of it. And if this is, we also say that that is. Or, in the second place, for instance, we enquire, of which contradiction there is a reason, whether of possessing, or of not possessing two right angles. But when we have found the object of our enquiry we at the same time know that it is, and why it is, if it is demonstrated through media. But if it is not so demonstrated, we know that it is, but not why it is. Let the moon be C; an eclipse, A; not to be able to produce a shadow the moon being full, when nothing is seen interposed between us, B. If, therefore, B is present with C, i.e. not be able to produce a shadow, when nothing is interposed between us is present with the moon, and A, i.e. to be eclipsed is present with this; that the moon, indeed, is eclipsed is evident; but why it is eclipsed is not yet manifest. And that there is an eclipse, indeed, we know; but what it is, we do not know.

That which does not produce a shadow when nothing intervenes (B), is eclipsed (A):

The moon (C) does not produce a shadow when nothing intervenes (B): Therefore,

The moon (C) is eclipsed (A).

Since, however, it is manifest that A is present with C, to enquire why it is present, is to enquire what B is, whether it is the opposition of the earth, or the revolution of the moon, or the extinction of light. But this is the definition of the other extreme, as in these examples it is the definition of A; for an eclipse is the opposition of the earth. What is thunder? The extinction of fire in a cloud. Why does it thunder? Because fire is extinguished in a cloud. Let a cloud be C; thunder, A; and the extinction of fire, B. Hence B is present with C, i.e. with a cloud; for fire is extinguished in it. But A, i.e. sound, is present with B. And B is the definition of A, the first extreme.

Where there is an extinction of fire (B) there is thunder (A):

In a cloud (C) there is an extinction of fire (B): Therefore,

In a cloud (C) there is thunder (A).

If again, there is another medium of this, it will be from the remaining definitions. And thus we have shown how what a thing is, is assumed and becomes known. Hence of what a thing is, there will neither be a syllogism, nor demonstration; nevertheless, it will become manifest through syllogism, and through demonstration. Hence too, it is not possible without demonstration to know what a thing is, of which there is another cause; nor is there a demonstration of it, as we have already observed in the doubts.

Aristotle, Posterior Analytics. Book II, Chapter 9

Of some of the very natures of things, however, there is a certain other cause; but of others there is not. Hence it is evident that some of them are immediate and principles; of which the existence, and

what, they are, it is necessary to suppose, or after another manner render manifest. And this the arithmetician does; for he supposes what unity is, and that it is. But with respect to those very natures of things which have a medium, and of the essence of which there is a certain other cause, it is possible, as we have said, to render these manifest through demonstration, but not demonstrating what they are.

Aristotle, Posterior Analytics. Book II, Chapter 10

But since definition is said to be a sentence explaining what a thing is, it is evident that one  definition will be a certain sentence explaining what a name signifies, or another nominal sentence; as what is the signification of or what is a thing, so far as it is a triangle; which when we know ihat it is, we investigate why it is. But it is difficult thus to assume things of the existence of which we are ignorant. And the cause of this difficulty has been before explained; because neither do we know whether it is or not, except from accident. One sentence, however, is twofold; one by conjunction, as the Iliad; but the other, in consequence of signifying one thing of one thing, not from accident. That which we have mentioned, therefore, is one definition of a definition. But another definition is a sentence, manifesting why a thing is. Hence the former signifies, indeed, but does not demonstrate; and with respect to the latter, it is evident that it will be as it were a demonstration of what a thing is, differing from demonstration in the position of the terms.  For there is a difference between saying why does it thunder? and, What is thunder? For the answer to the former question is, Because fire is extinguished in the clouds. But what is thunder? The sound of fire extinguished in the clouds. Hence after another manner, there is the same sentence. And in that way, indeed, there is a continued demonstration; but in this way, there is a definition. Again, the definition of thunder is, a sound in the clouds. But this is the conclusion of the demonstration of what thunder is. The definition, however, of things immediate, is an indemonstrable thesis of what a thing is. Of definitions, therefore, one is an indemonstrable sentence explaining what a thing is; but another is a syllogism proving what a thing is, differing in case from demonstration; and a third is the conclusion of the demonstration of what a thing is. From what has been said, therefore, it is evident in what manner there is, and in what manner there is not a demonstration of what a thing is; and of what things there is, and of what there is not. It is likewise evident in how many ways definition subsists; how it demonstrates the what, and how it does not; and of what things there is, and of what there is not a definition. Again, how it subsists with respect to demonstration; and in what manner there may, and in what manner there may not be, a demonstration of the same thing.

Aristotle, Posterior Analytics. Book II, Chapter 11

Since, however, we then think that we know scientifically, when we have a knowledge of cause; but causes are four; one, indeed, being that which pertains to the very nature of a thing; another, that which, certain things existing, must necessarily exist; a third, that which first moves; and a fourth, that for the sake of which something else exists. All these are demonstrated through a medium. For one proposition being assumed, the reasoning that when that thing is, it is necessary this should be, is no demonstration, but there must be two propositions at least; viz. when those two propositions have one medium. This one, therefore, being assumed, it is necessary there should be a conclusion. This, however, will be evident as follows; Why is the angle right which is in a semicircle? Or, from what being posited, will it be right? Let a right angle, therefore, be A; the half of two right angles, B; and the angle in a semicircle, C. Hence B is the cause why A, i.e. a right angle, is inherent in C, i.e. in the angle which is in a semicircle. For this angle is equal to A; but the angle C is equal to B; for it is the half of two right angles. B, therefore, being the half of two right angles, A is inherent in C. But this was for the angle in a semicircle to be a right angle.

Every angle which is the half of two right angles (B), is a right angle (A):

Every angle described in a semicircle (C), is the half of two right angles (B): Therefore,

Every angle described in a semicircle (C), is a right angle (A).

This, however, is the same with the very nature, of a thing, because definition signifies this. But it has been shown that the very nature of a thing is a middle cause. Why was there a Median war with the Athenians? What was the cause of waging war with the Athenians? Because the Athenians together with the Eretrians attacked Sardis. For this first excited the war with the Athenians. Let war then be A; first made the attack, B; and the Athenians, C. B, therefore, is present with C; i.e; to have first made the attack belongs to the Athenians. But A also is present with B; for they waged war with those who were the aggressors. A therefore is present with B, i.e. to wage war is present with the aggressors. But this B is present with C, or the Athenians; for they were the aggressors. Hence the cause, or that which first moves, is here also the medium. Among those things, however, of which the cause is for the sake of something or final; as, why does he walk? That he may be well. Why is a house built? That furniture may be preserved.  Among these, the former is for the sake of health; but the latter, for the sake of preservation. There is no difference, however, in asking why is it necessary to walk after supper? And, for the sake of what is it necessary? But let walking after supper be C; the food not to float in the stomach B; and to be well A. Let, therefore, walking after supper be the cause that the food does not float to the mouth of the stomach; and let this be salubrious. For B i.e. for the food not to float, appears to be present with walking, or C; and with this, A, or the salubrious is present. What, therefore, is the cause that A, which is that for the sake of which, or the final cause, is present with C? B is the cause, i.e. the food not floating. But this, is as it were, the definition of it; for A will be thus explained;

For the food not to float in the stomach (B) is salubrious (A):

Walking after supper (C) does not suffer the food to float in the stomach (B): Therefore,

Walking after supper (C) is salubrious (A).

But why is B present with C? Because to be thus affected is to be well. lt is necessary, however, to commute the sentences; and thus the several particulars will be more apparent.

That which is salubrious (A) causes the food not to float (B):

Walking after supper (C) is salubrious (A): Therefore,

Walking after supper (C) causes the food not to float.

But the generations here, and in causes which energize through motion subsist vice versa. For there it is necessary that the middle should be first generated; but here C, which is the last, is first generated; and that for the sake of which, is generated the last. It is possible, however, that the same thing may be for the sake of something, and from necessity; as for in stance, why does light pervade through a lantern? For from necessity that which consists of smaller parts pervades through larger pores, if light is generated by pervading. It also pervades through a lantern for the sake of something, viz. that we may not fall. If, therefore, it is possible it may be, it is also possible that it may be generated; as, if it thunders, fire being extinguished, it is necessary that a crashing noise should be produced, and as the Pythagoreans say for the sake of threatening, that those who are in Tartarus may be terrified. But there are many things of this kind, and especially in things which are produced by, and consist from nature. For natute produces one thing for the sake of something, and another from necessity. But necessity is twofold; for one is according to nature, and impulse; but another is violent and contrary to impulse.  Thus a stone is moved from necessity both upward and downward, but not from the same necessity. In those things, however, which are the productions of reason, some, never subsist from chance, as a house, or a statue, nor from necessity, but for the sake of something; but others are also from fortune, as health and safety. But a subsistence for the sake of something, especially takes placein those things which are capable of a various subsistence, whcn the generation of them is not from fortune, but the end of which is good; and which are produced either by nature, or art. From fortune, however, nothing is produced for the sake of something.

CHAPTERS 12-19 Coming Soon….

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