Aristotle, Prior Analytics, Book I

© William C. Michael, 2022.

We are happy to host the only online edition of Thomas Taylor’s translation of Aristotle’s Prior Analytics. The text below is an adaptation of Thomas Taylor’s translation of Aristotle’s Prior 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.

Chapter 1

In the first place it is requisite to say what the subject is of the present treatise, and for the sake of what it is undertaken; viz. that it is concerning demonstration, and for the sake of demonstrative science. Afterwards, it is requisite to define what a proposition is, what a term, and what a syllogism; and also what kind of a syllogism is perfect, and what kind is imperfect. In the next place it must be shown, what it is for a thing to be or not to be in a certain whole, and what we say it is to be predicated of every thing or of nothing, of a certain multitude.

A proposition, therefore, is a sentence affirming or denying something of something. And this is universal, in a part, or indefinite. But I denominate universal the being present with every thing or with nothing; in a part, the being present with something, or not with something, or not with every thing; and the indefinite, the being present, or not being present without the universal or particular; such, for instance, as that there is the same science of contraries, or that pleasure is not good.

But a demonstrative differs from a dialectic proposition in this; that the demonstrative proposition is an assumption of one part of contradiction; (for he who demonstrates does not interrogate, but assumes) but the dialectic is an interrogation of contradiction. So far, however, as pertains to the framing a syllogism from either proposition, the one in no respect differs from the other. For he who demonstrates, and he who interrogates syllogize, assuming that something is present with, or is not present with something. Hence, a syllogistic proposition, indeed, will be simply an affirmation or negation of something concerning something, after the manner above-mentioned. But a proposition is demonstrative, if it is true, and is assumed through hypotheses from the beginning. And a dialectic proposition, with respect to him who enquires, is an interrogation of contradiction; but with respect to him who syllogizes, is an assumption of that which is seen and probA Ble, as we have observed in the Topics. What, therefore, a proposition is, and in what the syllogistic, demonstrative, and dialectic proposition differ from each other, will be accurately shown in the following treatises; but for the present purpose, what has been now determined by us may suffice.

But I call that a term into which a proposition is dissolved; as, for instance, that which is predicated, and that of which it is predicated, whether to be or not to be is added or separated.

And a syllogism is a discourse, in which certain things being admitted, something else different from the things admitted necessarily happens, in consequence of the existence of these admitted propositions.  I say, that in consequence of these admitted propositions, something else happens. And when I say that something else happens through these, I mean that there is no need of any external term, in order to the existence of the necessary consequence. Hence I call that a perfect syllogism, which requires nothing else besides the things assumed in order that the necessary consequence may be apparent. But I denominate that an imperfect syllogism, which requires one or more things, which through the supposed terms are necessary, and yet are not assumed through propositions. And it is the same thing, for one thing to be in the whole of another, and for one thing to be predicated of the whole of another, when nothing can be assumed of the subject, of which the other may not be asserted: and to be predicated of nothing is assumed after a similar manner.

Chapter 2

Since, however, every proposition is either of that which is simply present, or of that which is present from necessity, or of that which may happen to be present; and of these, some are affirmative but others negative, according to each appellation, and again, since of affirmative and negative propositions, some are universal, others partial, and others indefinite; this being the case, it is necessary that the universal privative proposition of that which is present should be converted in its terms. Thus, for instance, if no pleasure is good, neither will any good be pleasure. But it is necessary that a categoric proposition should be converted indeed, yet not universally, but in a part.  For instance, if all pleasure is good, it is also necessary that a certain good should be pleasure. And of particular propositions it is necessary that the affirmative should be converted in apart; for if a certain pleasure is good, a certain good will also be pleasure. But it is not necessary that a privative proposition should be converted. For it does not follow that if man is not present with a certain animal, that animal also is not present with a certain man. Let the proposition A B, therefore, be the first privative universal. Hence, if A is present with no B, neither will B be present with any A. For if it should be present with some A, as, for instance, with C, it will not be true that A is present with no B; since C is something of B.  But,if A is present with every B, B will be present with some A. For if with no A, neither will A be present with any B; but it was supposed to be present with every B.  Conversion also is in a similar manner produced, if the proposition is according to a part. For if A is present with some B, it is also necessary that B should be present with some A. For if it is present with no A, neither will A be present with any B. But if A is not present with some B, it is not necessary that B also should not be present with A. For instance, if B is animal, but A man; man, indeed, is not present with every animal, (i.e. is not participated by every animal), but animal is present with every man.

Chapter 3

The like also will take place in necessary propositions; for a universal privative is universally converted. But each of affirmative propositions is converted according to a part.  For if it is necessary that A should be present with no B, it is also necessary that B should be present with no A; for if it should happen to be present with some A, it would also happen that A would be present with some B. But if A is necessarily present with every, or with some B, B also will necessarily be present with some A; for if it is not necessarily present, neither will A be necessarily present with some B. That, however, which is privative in a part, is not converted, for the reason which has been before assigned.

But with respect to contingent propositions (since that which is contingent is multifariously predicated; for we say that the necessary, the not necessary, and the possible may happen) in all those that are affirmative, there will be a similar mode of conversion. For if A may happen to every, or to some B, B also may happen to some A; for if to no A, neither will A happen to any B. For this has been already demonstrated.  In negative propositions, however, the like does not take place; but such things as are said to be contingent, either because they are necessarily not present, or because they are not necessarily present, are converted similarly with the former. For instance, if some one should say it may happen that a man may not be a horse, or that whiteness may be present with no garment. For of these assertions, the one is necessarily not present, and the other is not necessarily present. And the proposition is similarly converted. For if it happens to no man to be a horse, it also happens to no horse to be a man; and if whiteness happens to no garment, a garment also will not happen to any whiteness. For if a garment, necessarily happens to a certain whiteness, whiteness also will necessarily happen to a certain garment; since this was demonstrated before. The like also will take place in a particular negative proposition. But such things as are said to be contingent, because they happen for the most part, and because they are naturally so adapted (after the manner according to which we define the contingent) will not subsist similarly in privative conversions; for a universal privative proposition is not converted, but that which is particular is converted. This, however, will be evident, when we speak of the contingent. But now let thus much be manifest in addition to what has been said, that to happen not to be present with anything, or with something, has an affirmative figure. For “it may happen”, is similarly arranged with “it is”; but “it is” always and entirely produces affirmation in those things to which it is attributed. For instance, “it is” not good, or “it is” not white, or, in short, “it is” not this thing. This, however, will be shown in what follows. But with respect to conversions these will subsist similarly with others.

Chapter 4

These things being determined, let us now show through what things, when, and how every syllogism is produced; and afterwards let us speak concerning demonstration. For it is requisite to speak of syllogism prior to demonstration, because syllogism is more universal. For demonstration, indeed, is a certain syllogism, but not every syllogism is demonstration. When, therefore, three terms so subsist with reference to each other, as that the last is in the whole of the middle, and the middle cither is or is not in the whole of the first; then it is necessary that there should be a perfect syllogism of the extremes. But I call the middle that which is itself in another, another also being in it; and which likewise becomes the middle in position. And I call the extremes that which is itself in another, and that in which another also is. For if A is predicated of every B, and B of every C, it is necessary that A should be predicated of every C, for it has been before shown how we predicate of every individual of a given multitude. In like manner also, if A is predicated of no B, but B is predicated of every C, neither will A be predicated of any C. But if the first follows every middle, and the middle is present with no extreme, there will not be a syllogism of the extremes; for nothing necessary will happen in consequence of the existence of these; since it will happen that the first will be present with every and with no extreme. Hence, neither a particular, nor a universal conclusion will be necessarily produced. But nothing necessary being collected, there will not through these be a syllogism. Let, however, the terms of being present with every individual of a certain multitude be animal, man, horse; and let the terms of being present with no one be animal, man, stone.

1. Every man is an animal:
2. No horse is a man:       
3. Every horse is an animal.

1. Every man is an animal:
2. No stone is a man:
3. No stone is an animal.

Neither then will there be a syllogism, since neither is the first term present with any middle, nor the middle with any extreme. Let the terms of being present be science, line, physician; but let the terms of not being present be science, line, unity.

1. No line is science:
2. No medicine is a line:
3. Every medicine is science.

1. No line is science:
2. No unity is a line:
3. No unity is science

The terms, therefore, being universal it is manifest in this figure, when there will, and when there will not be a syllogism; and also that when there is a syllogism, it is necessary that the terms should subsist as we have said. For it is evident, that if they thus subsist there will be a syllogism. But if one of the terms is universal, and the other particular with reference to the other, when the universal is joined to the greater extreme, whether categoric or privative, but the particular term is categoric with respect to the less extreme, it is necessary that the syllogism should be perfect. But when the universal term is joined to the less extreme, or the terms subsist in some other way, it is impossible there should be a syllogism. I call, however, the greater extreme, that is which the middle is; and the less extreme, that which is under the middle. For let A be present with every B, but B with some C, If, therefore, to be predicated of every individual of a multitude is that which we asserted it to be from the first, A is necessarily present with some C. And if A is present with no B, but B is present with some C, it is necessary that A should not be present with some C. For the manner in which we speak of being predicated of no one of a multitude has been defined by us. Hence there will be a perfect syllogism. A similar conclusion also must be adopted, if the proposition B C is indefinite, being categoric; for there will be the same syllogism of the indefinite, and of that which is assumed in a part.

But if to the less extreme, universal either categoric or privative, is added, there will not be a syllogism; whether an indefinite or a particular proposition affirms or denies. For instance, if A is present, or is not present, with some B; but B is present with some C.  Let then the terms of being present be, good, habit, prudence; and let the terms of not being present be, good, habit, ignorance.

1. Some habit is/is not good:
2. All prudence is a habit:
3. All prudence is good.   

1. Some habit is/is not good:
2. All ignorance is a habit:
3. No ignorance is good.

Again, if B is present with no C, but A is present with some B, or is not present, or is not present with every B; neither thus will there be a syllogism. Let the terms of being present with every individual be white, horse, swan; but the terms of being present with no one be white, horse, crow.

1. Some horse is/is not white:
2. No swan is a horse:
3. Every swan is white.

1. Some horse is/is not white:
2. No crow is a horse:
3. No crow is white.

The same terms also may be assumed if A B should be indefinite. Neither then will there be a syllogism, when universal either categoric or privative is added to the greater extreme; but to the less extreme a privative according to a part of the indefinite, and in a part is assumed; for instance, if A is present with every B, but B is not present with some, or not with every C. For that with which the middle is not present, to this, to every, and to none, the first will be consequent. Thus, let the terms animal, man, white, be supposed; and afterwards, from among those white things of which man is not predicated, let swan and snow be assumed. Hence animal will be predicated of every individual of the one; but of no individual of the other; so that there will not be a syllogism.

1. Every man is an animal:
2. Something white (a swan) is not a man:
3. Every swan is an animal.

1. Every man is an animal:
2. Something white (snow) is not a man:
3. No snow is an animal.

Again, let A be present with no B, but let B not be present with some C; and let the terms be, inanimate, man, white. Afterwards, let white things be assumed, viz. swan and snow, of which man is not predicated. For inanimate is predicated of every individual of the one, but of no individual of the other.

1. No man is inanimate:
2. Something white (snow) is not a man:
3. All snow is inanimate. 

1. No man is inanimate:
2. Something white (a swan) is not a man:
3. No swan is inanimate.

Farther still, this is indefinite, namely, that B is not present with some C; (for it is truly asserted that it is not present with some C, whether it is present with none, or whether it is not present with every C) but terms of this kind being assumed, so as to be present with none, a syllogism will not be produced; for this has been asserted before. It is evident, therefore, that when the terms thus subsist, there will not be a syllogism; since if there could, there would also be a syllogism in these terms. The like also may be demonstrated, if universal privative is posited. Neither will there by any means be a syllogism, if both intervals according to apart are predicated either categorically or privatively; or the one categorically, but the other privatively; or if the one is indefinite, but the other definite; or both are indefinite. But let the common terms of all be, animal, white, man, animal, white, stone.

Something white is/is not an animal:

Some man is/is not white:

Every man is an animal.

Something while is/is not an animal:

Some stone is/is not white:

No stone is an animal.

From what has been said, therefore, it is evident, that if there is a particular syllogism in this figure, it is necessary that the terms should subsist as we have said; that if the terms thus subsist a syllogism is necessarily produced; but by no means, if they subsist in a different manner. It is also manifest, that all the syllogisms in this figure are perfect; for all are perfected through those things which were assumed from the first. Likewise, that all problems are demonstrated through this figure; for in this a thing is shown to be present with every, with none, with some one, and not with some one. But I call a figure of this kind, the first figure.

Chapter 5

But when the same thing (i.e. the middle term) is partly present with every individual, and partly with none; or is present to every or to none of each extreme; I call a figure of this kind the second figure. And I call the middle term in it, that which is predicated of both extremes. But I denominate the extremes those things of which this middle is predicated, the greater extreme being that which is situated near the middle; but the less extreme being that which is situated farther from the middle. But the middle is posited external to the extremes, and is first in position. By no means, therefore, will there be a perfect syllogism in this figure. But there may be a syllogism both when the terms are universal, and when they are not universal. And if the terms, indeed, are universal, there will be a syllogism when the middle is partly present with every, and partly with none; to whichever extreme the privative is added. But a syllogism will by no means be produced in any other way. For let M be predicated of no N, but of every O. Since, therefore, a privative proposition is converted, N will be present with no M. But M was supposed to be present with every O; so that N will, be present with no O. For this was demonstrated before. Again, if M is present with every N, but with no O, neither will O be present with any N. For if M is present with no O, neither, will O be present with any M. But M was present with every N; and hence O will be present with no N. For again, the first figure is produced. But since a privative proposition is converted, neither will N be present with any O.  Hence there will be the same syllogism. These things also may be demonstrated by a deduction to the impossible. It is evident, therefore, that a syllogism, though not a perfect syllogism, may be produced, when the terms thus subsist; for the necessary not only receives its completion from those things which were assumed from the first, but also from other things. But if M is predicated of every N, and of every O, there will not be a syllogism. Let the terms then of being present with be essence, animal, man; but of not being present with be essence, animal, stone. And let the middle term be essence.

Every animal is an essence:

Every man is an essence:

Every man is an animal.

Every animal is an essence:

Every stone is an essence:

No stone is an animal.

Nor will there then be a syllogism, when M is neither predicated of any N, nor of any O. Let the terms of being present with be line, animal, man; but of not being present with, line, animal, stone.

No animal is a line:

No man is a line:

Every man is an animal.

No animal is a line:

No stone is a line:

No stone is an animal.

It is evident, therefore, that if there is a syllogism when the terms are universally posited, it is necessary that the terms should subsist in that manner which we mentioned in the beginning, for if they subsist in any other way, the necessity of concluding will not be produced. But if the middle is universally affected with respect to either extreme; when universal is added to the greater extreme, either categorically, or privatively; but to the lesser extreme, according to a part, and oppositely to universal; (but I say oppositely, if the universal is privative, but the particular affirmative; and if the universal is categoric, but the particular privative) it is necessary that a syllogism privative according to a part should be produced. For if M is present with no N, but is present with a certain O, it is necessary that N should not be present with a certain O. For since a privative proposition may be converted, N will be present with no M: but M was supposed to be present with a certain O: so that N will not be present with a certain O; for a syllogism is produced in the first figure.

Again, if M is present with every N, but is not present with a certain O, it is necessary that N should not be present with a certain O. For if it is present with every O, but M is predicated of every N, it is also necessary that M should be present with every O. But it was supposed that it is not present with a certain O. And if M is present, indeed, with every N, but not with every O, there will be a syllogism, from which it will follow that N is not present with every O. But the demonstration is the same. If, however, M is predicated of every O, but not of every N, there will not be a syllogism. Let the terms of being present with be animal, essence, crow; but of not being present with, animal, white, crow.

Not every essence is an animal:

Every crow is an animal:

Every crow is an essence.

Not every thing white is an animal:

Every crow is an animal:

No crow is white.

Neither will there be a syllogism, when M is predicated of no O, but of a certain N. Let the terms of being present with be animal, essence, stone; but of not being present with animal, essence, science.

Some essence is an animal:

No stone is an animal:  

Every stone is essence.

Some essence is an animal:

No science is an animal:

No science is essence.

When, therefore, particular is opposed to universal, we have shown when, and when there will not be a syllogism. But when the propositions are similar in figure, for instance, when both are privative, or affirmative, there will by no means be a syllogism. For in the first place, let both be privative, and let universal be added to the greater extreme; as, for instance, let M be present with no N, and let it not be present with a certain O: it may happen, therefore, that N may be present with every and with no O. Let the terms of not being present with any be black, snow, animal.

No snow is black:

Some animal is not black:

No animal is snow.

But the terms of being present with every cannot be assumed, if M is present, indeed, with a certain O, and with a certain O is not present. For if N is present with every O, but M is present with no N, M will be present with no O. But it was supposed to be present with a certain O. The terms, therefore, cannot thus be assumed. It may be demonstrated, however, from the indefinite. For since it was truly asserted that M is not present with a certain O, even if it is present with no O; but when it is present with no O, there was not a syllogism, it is evident that neither will there now be a syllogism. Again, let both the propositions be categorical, and let universal be similarly posited; as, for instance, let M be present with every N, and with a certain O. Hence, it may happen that N may be present with every, and with no O. Let the terms of not being present with any be white, swan, snow.

Every swan is white:

Some stone is white:

No stone is a swan.

But the terms of not being present with every cannot be assumed, for the cause which we have before adduced.

Every swan is white:

Some bird is not white:

Every bird is a swan.

Every swan is white:

Every bird is a swan:

Every bird is white.

It may be demonstrated, however, from the indefinite. But if universal is added to the less extreme, and M is present with no O, and is not pre sent with a certain N, it may happen that N may be present with every and with no O. Let the terms of being present with be white, animal, crow; but of not being present with, white, stone, crow.

Some animal is not white:

No crow is white:

Every crow is an animal.

Some stone is not white:

No crow is white:

No crow is a stone.

But if the propositions are categoric, let the terms of not being present with be white, animal, snow; but of being present with be, white, animal, swan.

Some animal is white:

All snow is white:        

No snow is an animal.  

Some aninial is white:

Every swan is white:

Every swan is an animal.

It is evident, therefore, that when the propositions are similar in figure, and the one is universal, but the other particular, there will by no means be a syllogism. Neither will there be a syllogism, if with some one of each term a thing is present, or is not present; or is partly present with someone, and partly not; or to every one of neither, or indefinitely. Let then the common terms of all be white, animal, man; white, animal, inanimate.

Some animal is/is not white:

Some man is/is not white:           

Every man is an animal.

Some animal is/is not white:

Something inanimate is/is not white:

Nothing inanimate is an animal.

From what has been said, therefore, it is evident, that when the terms subsist with reference to each other, in the manner we have mentioned, a syllogism will necessarily be produced; and if a syllogism is produced, it is necessary that the terms should subsist in this manner. It is likewise evident, that all syllogisms which are in this figure are imperfect; for all of them are produced by certain things being assumed which either are necessarily inherent in the terms, or are admitted as hypotheses, as when we demonstrate through the impossible. It is also manifest, that an affirmative syllogism is not produced in this figure; but all the syllogisms are privative, both those that are universal, and those that arc particular.

Chapter 6

When, however, with the same thing, one thing is present with every individual, but another with none; or both with every, or both with none, I call a figure of this kind the third figure. But I call that the middle in it of which we predicate both; and I denominate extremes the things which are predicated; the greater extreme being that which is more remote from the middle, and the less, that which is nearer to the middle. But the middle is arranged external to the extremes, and is last in position. Neither, therefore, will a perfect syllogism be produced in this figure. But there may be a syllogism, the terms being joined to the middle, as well universally as not universally. The terms, therefore, being universally posited, when P and R are present with every S, there will be a syllogism, in which it will be necessarily inferred that P is necessarily present with a certain R. For since a categoric assertion is converted, S will be present with a certain R. Hence since P is present with every S, but S is present with a certain R, it is necessary that P should be present with a certain R. For a syllogism will be produced in the first figure. It is also possible to make the demonstration through the impossible, and through exposition. For if both are present with every S, if some S is assumed, as, for instance, N, both P and R will be present with this; so that P will be present with a certain R. And if R is present with every S, but P is present with no S, there will be a syllogism, in which it will be necessarily inferred that P is not present with a certain R. For there will be the same mode of demonstration, the proposition R S being converted. This may also be demonstrated through the impossible, as in the former syllogisms. But if R is present with no S, and P is present with every S, there will not be a syllogism. Let the terms of being present with be animal, horse, man; but of not being present with, animal, inanimate, man.

Every man is an animal:

No man is a horse:       

Every horse is an animal.

Every man is an animal:

No man is inanimate:

Nothing inanimate is a horse.

Nor will there then be a syllogism, when both are predicated of no S. Let the terms of being present with be animal, horse, inanimate; but of not being present with be, man, horse, inanimate: the medium is inanimate.

Nothing inanimate is an animal:

Nothing inanimate is a horse:

Every horse is an animal.         

Nothing inanimate is a man:

Nothing inanimate is a horse:

No horse is a man.

It is evident, therefore, in this figure also, when there will be, and when there will not be a syllogism, the terms being universally posited. For when both the terms arc categoric there will be a syllogism, in which it will be inferred that extreme is present with a certain extreme. But when both the terms are privative there will not be a syllogism. When, however, the one is privative, and the other affirmative; if, indeed, the greater term is privative, but the other affirmative, there will be a syllogism in which it will be inferred that extreme is not present with a certain extreme. But if the contrary takes place there will not be a syllogism. If, however, one of the terms is universally, but the other particularly joined to the middle; both of them being categoric, it is necessary that a syllogism should be produced, whichever of the terms is universally assumed. For if R, indeed, is present with every S, but P with a certain S, it is necessary that P should be present with a certain R. For since an affirmative assertion is. converted, S will be present with a certain P. Hence, since R is present with every S, but S is present with a certain P, R also will be present with a certain P, so that P also will be present with a certain R. Again, if R is present with a certain S, but P is present with every S, it is necessary that P should be present with a certain R; for there is the same mode of demonstration. These things also may be demonstrated through the impossible, and through exposition, as in the former syllogisms. But if one of the terms is categoric, and the other privative, and the categoric is assumed universally; when the less term, indeed, is categoric, there will be a syllogism. For if R is present with every S, but P is not present with a certain S, it is necessary that P should not be present with a certain R. For if P is present with every R, and R is present with every S; P also will be present with every S; but it is not present. This also may be shown without a deduction to the impossible, if some S is assumed with which P is not present. But when the greater term is categoric, there will not be a syllogism. For instance, if P is present with every S, but R is not present with a certain S. Let the terms of being present with every be animated, man, animal.

Every animal is animated:

Some animal is not a man:

Every man is animated.

But it is not possible to assume the terms of being present with none, if R is present with a certain S, and with a certain S is not present. For if P is present with every S, and R is present with a certain S, P also will be present with a certain R. But it was supposed to be present with no R. Here, therefore, the same thing must be assumed as in the former syllogisms. For the assertion that something is not present with a certain thing being indefinite, also that which is not present with any individual of a certain multitude, is truly said not to be present with a certain individual of that multitude; but not being present with any individual, there will not be a syllogism. It is evident, therefore, that there will not be a syllogism, when there is an assumption of not being present with some individual of a certain multitude. If, however, the privative term is universal, but the particular terra is categoric; when the greater term, indeed, is privative, but the less categoric, there will be a syllogism. For if P is present with no S, but R is present with a certain S; P will not be present with a certain R. For again, there will be the first figure, the proposition R S being converted. But when the less term is privative, there will not be a syllogism. Let the terms of being present with be animal, man, wild; but of not being present with be, animal, science, wild. The middle of both is wild.

Something wild is an animal:

Nothing wild is a man:  

Every man is an animal.

Something wild is an animal:

Nothing wild is science:

No science is an animal.

Nor will there then be a syllogism, when both terms are privative; and the one is universal, but the other particular. Let the terms of not being present with, when the less term is universally joined to the middle, be animal, science, wild; but of being present with be, animal, man, wild.

Something wild is not an animal:

Nothing wild is science:             

No science is an animal.

Something wild is not an animal:

Nothing wild is a man:

Every man is an animal.

But when the greater term is universal, but the less particular, let the terms of not being present with be crow, snow, white.

Nothing white is a crow:

Not every thing white is snow:

No snow is a crow.

The terms, however, of being present wilh cannot be assumed, if R is present, indeed, with a certain S, and with a certain S is not present. For if P is present with every R, but R is present with a certain S, P also will be present with a certain S. It was supposed, however, not to be present with any S. But it is demonstrated from the indefinite. Neither will there by any means be a syllogism, if each extreme term is present, or is not present with a certain middle; or if one is present, but the other is not present; or the one is present with some individual, but the other not with every indiridual; or indefinitely. But let the common terms of all be animal, man, white animal, inanimate, white.

Something white is/is not an animal:

Something white is/is not a man:          

Every man is an animal.           

Something white is/is not an animal:

Something white is/is not inanimate:

Nothing inanimate is an animal.

It is evident, therefore, in this figure also, when there will be, and when there will not be a syllogism; that when the terms so subsist as has been mentioned, a syllogism is necessarily produced; and that if there is a syllogism, it is necessary the terms should subsist in this manner. It is likewise evident, that all the syllogisms in this figure are imperfect; for all of them are perfected by the assumption of certain things; and also that a universal conclusion, neither privative nor affirmative, will not be collected in this figure.

Chapter 7

It is likewise manifest, that in all the figures, when a syllogism is not produced, both the terms being categoric or privative, and particular, nothing necessary, in short, will be inferred. But if the one is categoric, and the other privative, the privative being universally assumed, a syllogism will always be produced of the less extreme with the greater. For instance, if A is present with every, or with a certain B, but B is present with no C. For the propositions being converted, it is necessary that C should not be present with a certain A. The like also will take place in other figures; for a syllogism will always be produced through conversion. It is likewise manifest, that when an indefinite assertion is assumed for a particular attributive, it will produce the same syllogism in all the figures. It is also evident, that all imperfect syllogisms are perfected through the first figure. For all of them receive their completion either demonstratively, or through the impossible; but in both ways the first figure will be produced. And if, indeed, they receive their completion demonstratively, the first figure will be produced, because thus all of them will be perfected through conversion; and conversion will produce the first figure. But if they are demonstrated through the impossible, still the first figure will be produced, because the false being posited, a syllogism will be formed in the first figure. Thus, for instance, in the last figure, if A and B are present with every C, it may be demonstrated that A is present with some B. For if A is present with no B, but B is present with every C, A will be present with no C: but it was supposed that A is present with every C. The like will also take place in other instances. It is also possible to reduce all syllogisms to universal syllogisms of the first figure. For it is evident, that through these the syllogisms in the second figure are perfected; except that all of them are not similarly perfected: but the universal arc perfected, the privative assertion being converted; and each of those that are particular, through a deduction to the impossible. But particular syllogisms in the first figure, are perfected, indeed, through themselves. They may, however, be demonstrated in the second figure, by a deduction to the impossible. For instance, if A is present with every B, but B is present with a certain C, it may be shown that A will be present with a certain C. For if A is present with no C, but is present with every B: B will be present with no C; for we know this through the second figure. In a similar manner there will be a demonstration in a privative syllogism. For if A is present with no B, but B is present with a certain C; A will not be present with a certain C. For if A is present with every C, and with no B; B will be present with no C: but this was the middle figure. Hence, since all the syllogisms in the middle figure, are reduced to universal syllogisms in the first figure; but particular syllogisms in the first figure, are reduced to syllogisms in the middle figure; it is evident, that particular syllogisms in the first figure are reduced to universal syllogisms in the first figure. But the syllogisms in the third figure, the terms, indeed, being universal, are immediately perfected through those syllogisms. When, however, the terms are assumed in a part, they are perfected through particular syllogisms in the first figure. But these are reduced to those; so that particular syllogisms also in the third figure, are reduced to the same. It is evident, therefore, that all of them may be reduced to the universal syllogisms in the first figure. Hence we have shown how those syllogisms subsist which exhibit the being present with, or not being present with; as well by themselves, those which are from the same figure, as with reference to each other, those which are from different figures.

Chapter 8

Since, however, to exist, to exist from necessity, and to exist contingently, are different; (for manythings exist, indeed, yet not from necessity, but other things neither necessarily exist, nor, in short, exist, yet may happen to exist), it is evident, that there will be a different syllogism of each of these, and from terms not having a similitude of subsistence: but one syllogism will consist of necessary terms; another of such as have an existence; and another of such as are contingent in necessary syllogisms, therefore, the like will nearly take place, as in those which simply exist; for the terms being similarly posited in simply existing, and in existing or not existing from necessity, there will be, and there will not be a syllogism; except that they differ in the existing or not existing from necessity, being added to the terms. For a privative assertion is in a similar manner converted, and we similarly assign to be in the whole of a thing, and to be predicated of every.  In other things, therefore, it is demonstrated after the same manner through conversion, that the conclusion is necessary, just as in existing or being present with a thing. But in the middle figure when the universal proposition is affirmative, and the particular proposition privative; and again in the third figure, when the universal is categoric, but the particular proposition privative, there will not similarly be demonstration; but it is necessary, something being proposed with which one of the extremes is not present, to make a syllogism of this; for of this there will be a necessary conclusion.  If, however, a necessary conclusion is produced of the proposed term, a necessary conclusion of some individual of that term will also be produced; for the thing proposed is a part of it. But each of the syllogisms will be formed in its proper figure.

Chapter 9

It also sometimes happens that one of the propositions being necessary, a necessary syllogism will be produced, yet not of either proposition casually, but of that which contains the greater extreme. For instance, it A is assumed to be present or not present with B from necessity; but B is assumed to be alone present with C; for the propositions being thus assumed, A will be present or will not be present from, necessity with C. For since A is present or is not present with every li from necessity, but C is something belonging to B, it is evident, that C will be from necessity one of these. If, however, the proposition A B is not necessary, but B C is necessary, there will not be a necessary conclusion. For if there will be, it will happen that A is necessarily present with a certain B, as may be demonstrated as well in the first as in the third figure. But this is false; for it may happen that B may be a thing of that kind that A may not be present with anything belonging to it. Farther still, from the terms also it is evident, that there will not be a necessary conclusion; as, for instance, if A is motion, B animal, and C man. For man is necessarily an animal; but neither animal, nor man, is necessarily moved. The like will also take place if A B is privative; for there is the same demonstration. But in particular syllogisms, if the universal assertion, is necessary; the conclusion also will be necessary; but if the particular is necessary; the conclusion will not be necessary; whether the universal proposition is privative, or categoric.  In the first place, therefore, let the universal be necessary, and let A be necessarily present with every B, but let B be only present with a certain C. It is necessary, therefore, that A should be necessarily present with a certain C; for C is under B, and A was present from necessity with every B. The like will also take place, if the syllogism is privative; for there will be the same demonstration. But if the particular is necessary; the conclusion will not be necessary; for nothing A Bsurd will happen, as neither in universal syllogisms. A similar consequence also will be the result in particular privative syllogisms. Let the terms be motion, animal, white.

Every animal is moved:

It is necessary that something white should be an animal:

Therefore, something white is moved.

But not necessarily because it is possible that it might not be moved.        

No animal is moved:

            It is necessary that something white should not be an animal:

            Therefore, something white is not moved.

            But this is not necessary, because it may be moved.

Chapter 10

In the second figure, however, if the privative proposition is necessary, the conclusion also will be necessary; but if the categoric proposition is necessary, the conclusion will not be necessary. For, in the first place, let the privative proposition be necessary, and let it not be possible for A to be present with any B, but let it be present with C alone. Since, therefore, a privative proposition may be converted, neither can B be present with any A. But A is present with every C; so that B cannot be present with any C. For C is under A. In a similar manner also the conclusion will be necessary if negation is added to C. For if A cannot be present with any C, neither can C be present with any A. But A is present with every B; so that neither can C be present with any B. For again, the first figure will be produced. Hence neither can B be present with C; since it is in a similar manner converted. But if the categoric proposition is necessary, the conclusion will not be necessary. For let A be present with every B from necessity, and let it alone not be present with any C. The privative proposition, therefore, being converted, the first figure will be produced. But it was shown in the first figure, that when the major privative proposition is not necessary, neither will the conclusion be necessary. Hence neither in these will the conclusion be necessary. Again, if the conclusion is necessary, it will happen that C is necessarily not present with a certain A. For if B is necessarily present with no C, neither will C be necessarily present with any B. But B is necessarily present with a certain A, if A is present from necessity with every B. Hence it is necessary that G should not be present with a certain A. Nothing, however, hinders an A of that kind from being assumed, which may be present with every C. Farther still, it may also be shown from an exposition of the terms, that the conclusion is not simply necessary, but that it necessarily is, these being posited. For instance, let A be animal, B man, C white, and let the propositions be similarly assumed. For it will happen that animal is present with nothing white. Neither, therefore, will man be present with anything white; yet not from necessity. For it may happen that man may be white, yet not so long as animal is present with nothing white. Hence these things being admitted, the conclusion will be necessary, but will not be simply necessary. The like will also take place in particular syllogisms. For when the privative proposition is universal and necessary, the conclusion also will be necessary. But when the categoric proposition is universal and necessary, but the privative is particular and not necessary; the conclusion will not be necessary. In the first place, therefore, let the privative proposition be universal and necessary, and let it not be possible for A to be present with any B, but let it be present with a certain C. Since, therefore a privative proposition, may be converted, B also cannot be present with any A. But A is present with a certain C. Hence, B is necessarily not present with a certain C. Again, let the categoric proposition be universal and necessary, and let the categorical (i.e. affirmation) be added to B.  If, therefore, A is necessarily present with every B, but is not present with a certain C; it is evident, that B is not present with a certain C; but not from necessity. For there will be the same terms in order to the demonstration as were assumed in universal syllogisms. Neither will the conclusion be necessary, if the privative assertion is necessary when assumed in a part. For the demonstratioa may be made through the same terms.

Chapter 11

But in the last figure, when the terms are universally joined to the middle, and both the propositions are categoric, if either of them is necessary, the conclusion also will be necessary. If, however, one of the propositions is privative, but the other categoric; when the privative is necessary, the conclusion also will be necessary. But when the categoric proposition is necessary, the conclusion will not be necessary. For, in the first place, let both the propositions be necessary, and let A and B be present with every C; and let the proposition AC be necessary. Since, therefore, B is present with every C, C also will be present with a certain B, because a universal is converted into a particular proposition. Hence if A is necessarily present with every C, and Cis present with a certain B, A also is necessarily present with a certain B; for B is under (i.e. is something belonging to) C. The first figure, therefore, will again be produced. In a similar manner it may be demonstrated if the proposition B C is necessary; for C is converted with a certain A. Hence if B is necessarily present with every C, but C is present with a certain A, B also will be necessarily present with a certain A, Again, let the proposition A C be privative, but the proposition B C affirmative; and let the privative proposition be necessary. Since, therefore, an affirmative proposition may be converted, C will be present with a certain B, but A will necessarily be present with no C, and also will necessarily not be present with a certain B; for B is under C. But if the categoric proposition is necessary, the conclusion will not be necessary. For let B G be a categoric and necessary proposition; but let the proposition A C be privative and not necessary. Since, therefore, an affirmative proposition may be converted, C also will necessarily be present with a certain B; so that if A is present with no C, but C is present with a certain B, A also will not be present with a certain B; yet not from necessity. For it was demonstrated in the first figure that a privative proposition not being necessary, neither will the conclusion be necessary.  Farther still, this will also be evident from the terms. For let A be good; B animal; and C horse. It may, therefore, happen that good may be present with no horse; but animal is necessarily present with every horse. It is not, however, necessary that a certain animal should not be good, since it may happen that every auimal is good.

No horse is good:

It is necessary that every horse should be an animal:

Therefore, some animal is not good.

Or, if this is not possible, another term must be posited, as to wake, or to sleep; for every animal is the recipient of these.

No horse wakes:

It is necessary that every horse should be an animal:

Therefore, some animal does not sleep.

No horse sleeps:

            It is necessary that every horse should be an animal:

            Therefore, some animal does not wake.

If, therefore, the terms are universally joined to the middle, it has been shown when the conclusion will be necessary. But if one of the terms is universally predicated of the middle and the other partially, both, indeed, being categoric; when the universal proposition becomes necessary, the conclusion also will be necessary. The demonstration, however, is the same as before; for a partial categoric proposition may also be converted. If, therefore, it is necessary that B should be present with every C, but A is under C, it is necessary that B should be present with a certain A. For this proposition may be converted. The like also will take place, if the proposition AC is necessary and universal; for B is under C. But if the partial proposition is necessary, the conclusion will not be necessary. For let the proposition B C be partial and necessary, and let A be present with every C, yet not from necessity. The proposition, therefore, B C being converted, the first figure will be produced: and the universal proposition is not necessary; but the partial is necessary. When, however, the propositions thus subsist, the conclusion is not necessary. Hence neither in the terms now posited will the conclusion be necessary.

Every C is A:                                                     

It is necessary that some C should be B:              

Therefore, some B is A.                                   

Every C is A:

It is necessary that some B should be C:

Therefore, some B is A.

Farther still, this also is evident from the terms. For let A be wakefulness; B be biped; and C be animal. It is necessary, therefore, that B should be present with a certain C, but A may happen to be present with every C, and A is not necessarily present with B. For it is not necessary that a certain biped should sleep or wake.

Every animal wakes:

            It is necessary that some animal should be biped:

Therefore, some biped wakes.

In a similar manner also, the demonstration may be framed through the same terms, if the proposition A should be partial and necessary.

It is necessary that some animal should be a biped:

Every animal wakes:

Therefore, something that wakes is a biped.      

Every animal wakes:

            It is necessary that some biped should be an animal:

            Therefore, some biped wakes.

But if one of the terms is categoric, and the other privative, when the universal proposition is privative and necessary, the conclusion also will be necessary. For if A is contingent to no C, but B is present with a certain C, it is necessary that A should not be present with a certain B. But when the affirmative proposition is necessary, whether it be universal or partial, or privative partial, the conclusion will not be necessary. For we may say that other things are the same, as we have mentioned before. Let the terms, however, when the universal categoric proposition is necessary, be wakefulness, animal, man; and the middle be man.

Some man does not wake:

It is necessary that every man should be an animal:

Therefore, some animal docs not wake.

But when the partial categoric proposition is necessary, let the terms be wakefulness, animal, white. For it is necessary that animal should be present with something white: but it happens that wakefulness is not present with anything white; and it is not necessary that wakefulness should not be present with a certain animal.

Nothing white wakes:

It is necessary that something white should be an animal:

Therefore, some animal does not wake.

But when the privative partial proposition is necessary; let the terms be biped, motion, animal; and the middle be animal.

It is necessary that some animal should not be a biped:

Every animal is moved:

Therefore, something which is moved is not a biped.

Chapter 12

It is evident, therefore, that there is not a syllogism of the being present with, unless both propositions signify the being present with; but that a necessary conclusion may be collected, though the other proposition alone is necessary. But in both, the syllogisms being either affirmative or privative, it is necessary that one of the propositions should be similar to the conclusion. My meaning is with respect to the similar; that if it is concluded a thing is present with, one of the propositions also signifies the being present with. But if it is concluded that a thing is necessarily present, one of the propositions is also necessary. Hence it is evident, that there will not be a conclusion either necessary, or that a thing is present with, unless one of the propositions is assumed necessary, or signifying the being present with. Concerning the necessary, therefore, how it is produced, and what difference it has with respect to that which is present with, nearly what is sufficient has been said.

Chapter 13

In the next place let us speak A Bout the contingent, when, and how, and through what propositions there will be a syllogism. But I call to be contingent, and the contingent, that which not being necessary, if it is admitted to exist, there will on this account be nothing impossible.  For the necessary is said to be contingent homonymously.  But that this is the contingent is evident from opposite negations and affirmations. For these assertions, it does not happen to exist, it is impossible to exist, and it is necessary not to exist, are either the same, or follow each other. Hence the opposites to these also, it happens to exist, it is not impossible to exist, and it is not necessary not to exist, will either be the same, or will follow each other; for of every thing there is either affirmation or negation. That which is contingent, therefore; will be not necessary; and that which is not necessary will be contingent. It happens, however, that all propositions of the contingent, may be converted into each other. I say may be converted not the affirmative into the negative, but such as have an affirmative figure according to opposition. For instance, this proposition, it happens to exist, may be converted into this it happens not to exist. This proposition also, it happens to every may be converted into this it happens to none, or not to every: and this, it happens to a certain thing, into this, it does not happen to every. After the same manner also conversion is effected in other propositions. For since that which is contingent is not necessary; and that which is not necessary may not exist; it is evident, that if it happens, A is present with B, it may also hap pen that it may not be present: and if it happens to be present with every B, it may also happen not to be present with every B. There is likewise a similar reasoning in partial affirmations; for there is the same demonstration. Such like propositions, however, are categoric, and not privative. For the verb “to be contingent” is arranged similarly to the verb “to be”, as we have before observed.

These things being determined, we again say, that to be contingent is predicated in two ways; one, indeed, as that which takes place for the most part, and falls short of the necessary as, for instance, for a man to become hoary, or to be increased, or waste away, or, in short, that which is naturally adapted to exist; for this has not a continued necessity, because man does not always exist; but man existing, this is either from necessity, or for the most part. But in another way that is contingent which is indefinite, and which can subsist thus, and not thus; such as for an animal to walk, or while it is walking, for an earthquake to take place, or, in short, that which is casually produced. For nothing of this kind is more naturally adapted to subsist in this than in a contrary way. Each, therefore, of things contingent is converted according to opposite propositions; yet not after the same manner. But that which is naturally adapted to subsist, is converted into that which does not exist from necessity; for thus it may happen that a man may, not become hoary. And that which is indefinite, is converted into that which cannot more subsist in this than in that way. Science, however, and demonstrative syllogism, are not of those things which are indefinite, because the middle is inordinate; but they are of those things which are naturally adapted to exist. And arguments and speculations are nearly conversant with things which are thus contingent; but of the indefinite contingent, a syllogism may, indeed, be formed, but it is. not usually investigated. These things, however, will be more fully determined in what follows. Let us now show when, and how, and what will be a syllogism from contingent propositions. But the assertion it happens that this thing is present with thatj may be assumed in a twofold respect. For it either signifies, that with which this thing is, present, or that with which this thing may be present. Thus this assertion, A is contingent to that of which there is B, signifies one of these things, either that of which B is predicated, or that of which it may be predicated. But the assertions that A is contingent to that of which tliere is B, and that A may be present with every B, do not differ from each other. It is evident, therefore, that A may be said to be present with every B in two ways. Hence, in the first place, let us show if B is contingent to that of which there is C, and if A is contingent to that of which there is B, what, and what kind of syllogism there will be; for thus both propositions are assumed according to the contingent. But when A is contingent to that with which B is present,, one proposition is of that which exists, but the other, of that which is contingent. Hence we must begin from similars in figure, as we began elsewhere.

Chapter 14

When, therefore, A is contingent to every B, and B to every C, there will be a perfect syllogism, in which it may be collected that A is contingent to every C. But this is evident from definition; for we thus assume the being contingent to every. In like manner also, if A is contingent to no B, but B is contingent to every C, there will be a syllogism in which it may be collected that A is contingent to no C. For to assert that A is contingent to nothing to which B is contingent, is to leave no one of the contingents which are under B. But when A is contingent to every B, but B is contingent to no C, from the assumed propositions no syllogism will be produced; but the proposition B C being converted, according to the being contingent, the same syllogism will be produced as was produced before. For since it happens that B is present with no C, it may also happen to be present with every C; for this was shown before. Hence, since B may happen to be present with every C, and A with every B, again, the same syllogism will be produced. The like will also take place, if negation together with the being contingent are added to both the propositions. I say, for instance, if A is contingent to no B, and B to no C; for through the assumed propositions, no syllogism will be produced. But the propositions B Chig converted, there will again be the same syllogism, as was formed before. It is evident, therefore, that when negation is added to the less extreme, or to both the propositions, either a syllogism will not be produced, or it will be produced indeed, but will not be a perfect syllogism; for the necessity of consecution is effected from conversion. But if one of the propositions is universal, and the other is assumed in a part; the universal being posited at the greater extreme, there will be a perfect syllogism. For if A is contingent to every B, but B is contingent to a certain C, A also will be contingent to a certain C. This, however, is evident from the definition of being contingent to every individual of a certain multitude. Again, if A is contingent to no B, but B may happen to be present with a certain C, it is necessary that A should happen not to be present with a certain C.  But the demonstration is the same. If, however, the proposition which is in a part is assumed privative, but the proposition which is universal is assumed affirmative, and retains the same position; as, for instance, if A may happen to be present with every B, but B may happen not to be present with a certain C; — if this be the case, from the assumed propositions, indeed, an evident syllogism will not be produced. But the particular proposition being converted, and it being admitted, that B may happen to be present with a certain C, there will be the same conclusion as before, as in the former syllogisms. If, however, the major proposition is assumed as particular, but the minor is universal, whether both are posited affirmative, or privative, or dissimilar in figure; or whether both are indefinite, or particular, there will by no means be a syllogism. For nothing hinders B from being more widely extended than A, and from not being equally predicated. But let that by which B is more widely extended than A, be assumed to be C; for to C it will happen that A is present neither to every, nor to none, nor to a certain one, nor not to a certain one; since contingent propositions may be converted, and B may happen to be present with more things than A. Farther still, this also is evident from the terms; for the propositions thus subsisting, the first will be contingent to the last and to none, and will necessarily be present with every individual. But let the common terms of all be these; of being present with, from necessity, animal, white, man; but of not happening to be present with, animal, white, garment.

It happens that something white is/is not animal:

It happens that every/no/some/not every man is white:

It is necessary that every man should be an animal.

It happens that something white is/is not an animal:

It happens that every/no/some/not every garment is white:

Is necessary that no garment should be an animal.

It is evident, therefore, that when the terms subsist after this manner, no syllogism will be produced. For every syllogism is either of that which exists, or of that which exists from necessity, or of that which is contingent. But that this syllogism is neither of that which exists, nor of that which necessarily exists is evident; for the affirmative conclusion is subverted by the privative, and the privative by the affirmative. It remains, therefore, that it must be of that which is contingent. This, however, is impossible; for it has been shown, that when the terms thus subsist, the first is necessarily inherent in all the last, and will happen to be present with no individual. Hence there will not be a syllogism of the contingent; for that which is necessary is not contingent. It is evident, therefore, that when the terms are universally assumed in contingent propositions, there will always be a syllogism in the first figure, both when they are categoric, and when they are privative; except that when they are categoric, there will be a perfect syllogism; but when they are privative, an imperfect syllogism. It is necessary, however, to assume the contingent, not in necessary propositions, but according to the definition mentioned in the preceding chapter. But sometimes a thing of this kind is latent.

Chapter 15

If, however, one of the propositions is assumed to exist, but the other to be contingent when that which contains the greater extreme, signifies to be contingent, all the syllogisms will be perfect, and will be of the contingent, assumed according to the above-mentioned definition. But when the proposition in which the less extreme is contained, signifies to be contingent, all the syllogisms will be imperfect; and the privative syllogisms will not be of the contingent assumed according to that definition, but of that which is necessarily present with no one, or not with every individual, for if it is necessarily present with no one, or not with every individual, we say that it happens to be present with no one, or not with every individual. For let A be contingent to every B, and let B be supposed to be present with every C. Because, therefore, C is under B, but A is contingent to every B, it is evident that A also is contingent to every C. A perfect syllogism, therefore, will be produced. In like manner also, if the proposition A B is privative, but the proposition B C affirmative, and if the proposition A B is assumed to be contingent, and the proposition B C to be present with; there will be a perfect syllogism, in which it may be collected that it will happen that A is present with no C. It is evident, therefore, that when the being present with is posited to the less extreme, perfect syllogisms will be produced. But that when it subsists in a contrary mode there will also be syllogisms, may be shown by a deduction to the impossible; though at the same time it will be evident that the syllogisms will be imperfect; for the demonstration will not be from the assumed propositions. In the first place, however, it must be shown, that if when A exists, it is necessary B should exist; and that if A is possible, B will necessarily be possible. For things thus subsisting, let A be possible, but B impossible. If, therefore, the possible, when it is possible to be should be produced; the impossible, because it is impossible, will not be produced. But if at the same time A is possible, and B impossible, it will happen that A may be produced without B; and if it is produced, that it exists. For that which is generated, when it is generated, is. It is necessary, however to consider the possible and impossible, not only in that which may be generated, but also in that which may be verified, and exists in energy, and in whatever other ways the possible is said to be possible; for the reasoning is similar in all of them. Besides, when we say A is B, this ought not to be understood, as if A being one certain thing, B will be; for nothing necessarily follows from there being one thing, but from there being two things at least: for instance, when propositions subsist in syllogism, after the manner we have mentioned. For if C is predicated of D, but D of F, C also will necessarily be predicated of F. And if each proposition is possible, the conclusion also will be possible. Just, therefore, as if any one should place A as the propositions, but B the conclusion; it will not only happen that when A is necessary, at the same time also B is necessary; but, likewise, when the former is possible, the latter also will be possible.

But this being demonstrated, it is evident, that when the hypothesis is false and not impossible, that also which happens on account of the hypothesis will be false and not impossible. For instance, if A is false indeed, yet not impossible, but when A is, B is; — in this case, B also will be also indeed, yet not impossible. For since it has been shown that if A is, B also is; when A is possible, B also will be possible. But it was supposed that A is possible; B, therefore, will also be possible.

For if it is impossible, the same thing will be at the same time possible and impossible. These things being determined, let A be present with every B, and let B be contingent to every C. It is necessary, therefore, that A should happen to be present with every C. For let it not happen to be present; and let B be admitted to be present with every C. This is false, indeed, but not impossible. If, therefore, A is not contingent to C, but B is present with every C; A will not be contingent to every B; for a syllogism will be produced in the third figure. But it was supposed that A is present with every B. It is necessary, therefore, that A should be contingent to every C. For that which is false being supposed, and not that which is impossible, that which thence happens is impossible.

Every B is A:                                                   

It happens that every C is B:

Therefore, it happens that every C is A.

It is necessary that some C should not be A:

Every C is B:

Therefore, not every B is A.

A deduction also to the impossible may be made in the first figure, if B is supposed to be present with C, For if B is present with every C, but A is contingent to every B, A also will be contingent to every C.  It was supposed, however, that it could not be present with every C.

Every B is A:                 

It happens that every C is B:

Therefore, it happens that every C is A.

It happens that every B is A:

Every C is B:

            Therefore, it happens that every C is A.

It is necessary, however to assume the being present with every individual, not defined by time, as now, or at this time, but simply; for we also produce syllogisms through propositions of this kind. For when a proposition is assumed according to the now, or the present time, there will not be a syllogism; since perhaps nothing hinders but that man sometime or other may be present with every thing that is moved; viz. if nothing else is moved. But that which is moved may be contingent to every horse; and man is contingent to no horse. Farther still, let the first term be animal; the middle that which is moved; and the last term, man. The propositions, therefore, will subsist similarly; but the conclusion will be necessary, and not contingent. For man is necessarily an animal.

Whatever is moved is a man:                            

It happens that every horse is moved:

It is necessary that no horse should be a man.

Whatever is moved is an animal:

            It happens that every man is moved:

It is necessary that every man should be an animal.

It is evident, therefore, that the universal should be assumed simply, and not defined by time. Again, let the proposition A B be universal privative, and let A be assumed to be present with no B, but let it happen that B is present with every C. These things, therefore, being admitted, it is necessary that A should happen to be present with no C. For let it not so happen; and let B be supposed to be present with C as before. Hence it is necessary that A should be present with some B. For a syllogism will be formed in the third figure. This, however, is impossible. Hence A will be contingent to no C; for the false, and not the impossible being supposed, that which is impossible will happen.

No B is A:                   

It happens that every C is B:     

Therefore, it happens that no C is A.

It is necessary that some C should be A:

            Every C is B:

            Therefore, some B is A.

This syllogism, therefore, is not of that contingent which is according to the definition above given, but of that which is necessarily present with no individual. For this is a contradiction of the given hypothesis; because it was supposed that A is necessarily present with some C. But the syllogism which is through the impossible is of an opposite contradiction. Again, it is also evident from the terms, that the conclusion is not contingent. For let A be a crow; B, that which is intelligent; and C, man. A, therefore, is present with no B; for nothing intelligent is a crow. But B is contingcnt to every C; for it happens to every man to be intelligent. A, however, is necessarily present with no C. The conclusion, therefore is not contingent.

Nothing intelligent is a crow:

It happens that every man is intelligent:

It is necessary that no man should be a crow.

The conclusion, however, is not always necessary. For let A be that which is moved; B be science; and C be man. A, therefore, will be present with no B; but B is contingent to every C; and the conclusion will not be necessary. For it is not necessary that no man should be moved, but it also is not necessary, that a certain man should be moved. It is evident, therefore, that the conclusion is of that which is necessarily present with no individual. Hence the terms must be assumed in a better manner. But if the privative is joined to the less extreme, and signifies to be contingent; from the assumed propositions, indeed, there will be no syllogism; but the contingent proposition being converted there will be a syllogism, as in the former instances. For let A be present with every B, but let B be contingent to no C. The terms, therefore, thus subsisting, nothing necessary will be collected. But if the proposition B C is converted, and B is assumed to be contingent to every C, a syllogism will be produced as before. For the terms will have a similar position. The like will also take place when both the intervals are privative, if the interval A B signifies the not being present with, but B C signifies the being contingent to no individual. For through the assumed propositions nothing necessary will be collected; but the contingent proposition being converted, there will be a syllogism. For let it be assumed that A is present with no B, and let B be contingent to no C. Through these, therefore, nothing necessary will be collected. But if it is assumed that B is contingent to every C, which is true, and the proposition A B subsists similarly; again there will be the same syllogism. If, however, it is assumed that B is not present with C, but not that it happens not to be present with it; there will by no means be a syllogism, neither when the proposition A B is privative, nor when it is affirmative. But let the common terms of being present with from necessity be, white, animal, snow; and of not being contingent, white, animal, pitch,

It happens that every/no animal is white:

No snow is an animal:

It is necessary that all snow should be white.

It happens that every/no animal is white:

            No pitch is an animal;

It is necessary that no pitch should be white.

It is evident, therefore, that when the terms are universal, and one of the propositions is assumed to exist, (i.e. is assumed pure), but the other contingent; when the proposition which contains the less extreme is assumed to be contingent, a syllogism will always be produced; except that it will sometimes be produced from the propositions themselves, and sometimes from the proposition being converted. When, however, each of these takes place, and from what cause we have already shown. But if one of the intervals is assumed to be universal, and the other partial; when, indeed, a universal contingent is joined to the greater extreme, whether it be affirmative or negative; but the partial interval is affirmative and pure, there will be a perfect syllogism, just as when the terms are universal. The demonstration, however, is the same as before. But when the interval in which the greater extreme is contained, is pure and not contingent; but the other is partial and contingent; whether both the propositions are posited affirmative or negative; or whether the one is affirmative, but the other negative, there will entirely be an imperfect syllogism. Some, however, will be confirmed through the impossible; but others, through a conversion of the contingent proposition, as in the former syllogisms. But there will be a syllogism through conversion, and when the universal proposition being joined to the greater extreme signifies the being present with, or the not being present with; but the partial proposition being privative assumes the contingent: as, for instance, if A is present indeed, or is not present with every B, but B happens not to be present with a certain C; for the proposition B C being converted according to the being contingent, a syllogism will be produced. But when the particular proposition assumes the not being present with, there will not be a syllogism. Let the terms of being present with be white, animal, snow; but of not being present with be white, animal, pitch. For the demonstration is to be assumed through the indefinite.

It happens that every/no animal is white:

Some snow is not an animal:

It is necessary thatall snow should be white.

It happens that every/no animal is white:

Some pitch is not an animal:

It is necessary that no pitch should be white.

But if universal is joined to the less extreme, and particular to the greater; whether privative, or affirmative, contingent, or pure, there will by no means be a syllogism. Nor will there then be a syllogism, when the propositions are posited in a part, or indefinite; whether they assume the being contingent, or the being present with, or whether the one is contingent, but the other present with. But the demonstration is the same as in the former syllogisms. Let, however, the common terms of being present with from necessity be animal, white, man; but of not being contingent be animal, white, garment.

            It happens that something/not everything white is an animal:

            Every/No/Some/Not every man is white:

            It is necessary that every man should be an animal.

            It happens that something/not everything white is an animal:

            Every/No/Some/Not every garment is white:

            It is necessary that no garment should be an animal.

            Something/Not everything white is an animal:

            It happens that every/no/some/not every man is white:

            It is necessary that every man should be an animal.

            Something/Not everything white is an animal:

            It happens that every/no/some/not every garment is white:

            It is necessary that no garment should be an animal.

It is evident, therefore, that if the major proposition is posited universal, a syllogism will always be produced: but if the minor, that nothing can ever thence be collected.

Chapter 16

When, however, one proposition signifies the being present with, or not being present with, from necessity, but the other signifies the being contingent, there will be a syllogism, the terms subsisting after the same manner; and it will be perfect, when the necessary is joined to the less extreme. But the conclusion, when the terms are categoric, will be of the contingent, and not of that which exists, whether the terms are universally, or not universally posited. But if one interval is affirmative, and the other privative; when the affirmative, indeed, is necessary, the conclusion will in like manner signify the being contingent, and not the not existing, or being present with. And when the privative is necessary, the conclusion will be of the happening not to be present with, and of the not being present with, whether the terms are universal, or not universal. The being contingent also in the conclusion is to be assumed after the same manner as in the former syllogisms. But there will not be a syllogism, in which the not being present with will be necessarily inferred; for it is one thing to be present with not necessarily, and another not to be present with necessarily. It is evident, therefore, that when the terms are affirmative, a necessary conclusion will not be produced. For let A be necessarily present with every B, but let B be contingent to every C. There will, therefore, be an imperfect syllogism, in which it may be collected that A happens to be present with every C. But that it is imperfect is evident from demonstration; for this may be demonstrated after the same manner as in the former syllogisms. Again, let A be contingent to every B, but let B be necessarily present with every C. There will, therefore, be a syllogism, in which it may be collected that A happens to be present with every C, but not that it is simply present with every C. The syllogism also will be perfect and not imperfect for it will be immediately completed through the propositions assumed from the first. But if the propositions are not similar in figure in the first place, let the privative proposition be necessary, and let A necessarily be contingent to no B, but let B be contingent to every C. It is necessary, therefore, that A should be present with no C. For let it be supposed to be present either with every individual, or with a certain individual but it was supposed to be contingent to no B. Since, therefore, a privative proposition may be converted, neither will B be contingent to any A. But A was posited to be present with every or with some C. Hence, B will happen to be present with no, or not with every C. It was supposed, however, from the first to be present with every C.

It is necessary that no B should be A:

It happens that every C is B:

Therefore, no C is A.

It is necssary that no A should be B:

            Some C is A:

Therefore, it is necessary that some C should not be B.

But it is evident, that there will also be a syllogism of the not happening to be present with, since there is a syllogism of the not being present with. Again, let the affirmative proposition be necessary, and let it happen that A is present with no B, but that B is necessarily present with every C. The syllogism, therefore, will be perfect, yet not of the not being present with, but of the happening not to be present with for the proposition was thus assumed from the greater extreme and there cannot be a deduction to the impossible. For if A is supposed to be present with a certain C, and it is admitted that A happens to be present with no B, nothing impossible will thence happen. But if privation is joined to the less extreme, when it signifies to be contingent, there will be a syllogism through conversion, as in the former syllogisms. When, however, it signifies not to be contingent, there will not be a syllogism. Nor will there be a syllogism when both the intervals are privative, unless the contingent is joined to the less extreme. But let the terms be the same; viz. of being present with, white, animal, snow but of not being present with, white, animal, pitch.

It happens that every/no animal is white:

It is necessary that no snow should be an animal:

It is necessary that all snow should be white.

It happens that every/no animal is white:

It is necessary that no pitch should be an animal:

It is necessary that no pitch should be white.

The like also will take place in partial syllogisms. For when the privative interval is necessary, the conclusion will be of the not being present with. Thus, if A happens to be present with no B, but B happens to be present with a certain C, it is necessary that A should not be present with a certain C. For if it is present with every C, but is contingent to no B, neither will B happen to be present with any A. Hence, if A is present with every C, B will be contingent to no C. But it was supposed to be contingent to a certain C.  But when the partial affirmative in a privative syllogism, as, for instance, B C, is necessary or the universal affirming in a categoric syllogism, as, for instance, A B, there will not be a syllogism of the being present with. But the demonstration is the same as in the former syllogisms. If, however, universal is joined to the less extreme, either affirmative, or privative and contingent; but the partial necessary is joined to the greater extreme, there will not be a syllogism. But let the terms of being present with from necessity be, animal, white, man and not being contingent, animal, white, garment.

It is necessary that something white should be/not be an animal:

It happens that every/no man is white:

It is necessary that every man should be an animal.

It is necessary that something white should be/not be an animal:

It happens that every/no garment is white:

It is necessary that no garment should be an animal.

But when the universal is necessary, and the partial contingent the universal being privative, let the terms of being present with be animal, white, crow but of not being present with, animal, white, pitch.

It happens that something white is/is not an animal:

It is necessary that no crow should be white:

It is necessary that every crow should be an animal.

It happens that something white is/is not an animal:

It is necessary that no pitch should be white:

It is necessary that no pitch should be an animal.

But when the universal affirms, let the terms of being present with be, animal, white, swan but of not being contingent, animal, white, snow.

It happens that something white is/is not an animal:

It is necessary that every swan should be white:

It is necessary that every swan should be an animal.

It happens that something white is/is not an animal:

It is necessary that all snow should be white:

It is neccssary that no snow should be an animal.

Nor will there then be a syllogism, when the propositions are assumed indefinite, or both, according to a part. But let the common terms of being present with be animal, white, man and of not being present with, animal, white, inanimate. For animal is necessarily present with, and docs not happen to be present with, something white, and whiteness also is necessarily present with, and does not happen to be present with, something inanimate. And the like takes place in the contingent. Hence these terms are useful to all the modes.

It happens that something white is/is not an animal:

It is necessary that some man should  be/not be white:

It is necessary that every man should be an animal.

It happens that something white is/is not an animal:

It is necessary that something inanimate should be/not be white:

It is necessary that nothing inanimate should be an animal.

It is necessary that something white should be/not be an animal:

It happens that some man is/is not white:

It is necessary that every man should be an animal,

It is necessary that something white should be/not be an animal:

It happens that every thing inanimate ss white:

It is necessary that nothing inanimate should be an aniinal.

From what has been said, therefore, it is evident, that when the terms subsist similarly in that which is present with, and in necessary propositions, a syllogism will, and will not be formed. There is this exception, however, that if the privative proposition is posited according to existing, or being present with, the syllogism will be of the happening not to be present with. But if the privative proposition is necessary, the syllogism will be of the happening not to be present with and of the not being present with. It ia also evident, that all the syllogisms are imperfect, and that they are perfected through the above-mentioned figures.

Chapter 17

In the second figure, however, when both the propositions are assumed contingent, there will be no syllogism, neither when they are categoric, nor when they are privative, neither when they are universal, nor when they are partial. But when one proposition signifies the being present with, and the other the being contingent if the affirmative signifies the being present with; there will never be a syllogism; but if the privative universal signifies the being present with, there will always be a syllogism. The like will also take place when one of the propopositions is assumed necessary, but the other contingent. It is necessary, however, in these syllogisms so to assume the contingent in the conclusions, as it was assumed in the former syllogisms. In the first place, therefore, it must be shown that a contingent privative is not convertible. Thus, if A is contingent to no B, it is not necessary that B also should be contingent to no A. For let this be posited, and let B happen to be present with no A. Since, therefore, contingent affirmations, as well those that are contrary, as those that are opposite, are converted into negations, but B happens to be present with no A, it is evident, that it may also happen that B may be present with every A. This, however, is false. For it does not follow that if this thing may happen to all of that, it is necessary that that thing should happen to this; so that a contingent privative cannot be converted. Again, nothing hinders, but that A may be contingent to no B, and yet B may not be necessarily present with a certain A. Thus, for instance, whiteness may happen not to be present with every man, because it may also happen to be present. But it is not true to say that man happens to be present with nothing white for he is necessarily not present with manythings that are white. And the necessary is not the contingent. Neither can its convertibility be shown from the impossible as if any one should think, since it is false, that B is contingent to no A, that it is true that it is not contingent to none (for these are affirmation and negation). But if this is true, B is necessarily present with a certain A so that A also is necessarily present with a certain B but this is impossible. For it does not follow that if B is not contingent to no A, it is necessarily present with a certain A. For not to be contingent to no individual is predicated in a twofold respect; in one, indeed, if a thing is necessarily present with something and in another, if it necessarily is not present with something. For that which necessarily is not present with a certain A, cannot be truly said to happen not to be present with every A as neither can that which is necessarily present with a certain thing, be truly said to happen to be present with every thing. If, therefore, any one thinks that because C does not happen to be present with every D, it necessarily is not present with a certain D, he thinks falsely; for it may happen to be present with every D. But because a thing is necessarily present with certain things, on this account we say that it is not contingent to every individual. Hence the being present with a certain thing from necessity, and the not being present with a certaia thing from necessity, are opposed to the happening to be present with every individual. There is also a similar opposition to the being contingent to no individual. It is evident, therefore, that when the contingent, and the not contingent, are assumed in the manner we have defined in the beginning, not only the being present with a certain thing from necessity, but also the not being present with a certain thing from necessity, ought to be assumed. But this being assumed nothing impossible will happen so that a syllogism will not be produced. From what has been said, therefore, it is evident, that a contingent privative cannot be converted.

But this being demonstrated, let it be admitted that A is contingent to no B, but is contingent to every C. There will not, therefore, be a syllogism through conversion for it has been shown that a proposition of this kind is not convertible. Neither will there be a syllogism, through a deduction to the impossible. For B being posited to be contingently present with every C, nothing false will happen for it may happen that A may be present with every, and with no C.

It happens that no B is A:

It happens that every C is A:

Therefore, it happens that no C is B.

It happens that no B is A:

It is necessary that every/some C should be B:

Therefore, it happens that every or some C is not A.

In short, if there is a syllogism, it is evident it will be of that which is contingent (because neither of the propositions is assumed of that which exists, or is present with) and this, either affirmative, or privative. It is not possible, however, in either way. For if it is posited affirmative, it may be shown through the terms, that it will not happen to be present with. But if it is posited negative, it may be sho^vn that the conclusion is not contingent, but necessary. For let A be white B, man and C, horse. A, therefore, that is whiteness, may happen to be pre* sent with every individual’of the one, and with no individual of the other. But it neither happens to B to be present, nor yet not to be present with C. That it does not happen to be present indeed, is evident for no horse is a man. But neither does it happen not to be present for it is necessary that no horse should be a man. But the necessary is not contingent. A syllogism, therefore, will not be produced.

It happens that no man is white:

It happens that every horse is white:

It is necessary that no horse should be a man.

This may also be similarly shown, if the privative should be placed in an inverse order, or if both the propositions are assumed affirmative, or both privative; for there will be a demonstration through the same terms.

It happens that every/no man is white:

It happens that every/no horse is white:

It is necessary that no horse should be a man.

And when one proposition is universal, but the other partial or when both are partial, or indefinite; or in any other way in which it may be possible to change the propositions; for the demonstration will always be through the same terms.

It happens that every/no man is white:

It happens that some horse is/is not white:

It is necessary that no horse should be a man.

It happens that some man is/is not white:

It happens that every/no horse is white:

It is necessary that no horse should be a man.

It happens that some man is/is not white:

It happens that some horse is/is not white:

It is necessary that no horse should be a man.

Chapter 18

But if one proposition signifies the existing or being present with, and the other, the being contingent; when the categoric proposition signifies the being present with, but the privative, the being contingent, there will never be a syllogism, neither when the terms are assumed universally, nor when they are assumed partially. The demonstration, however, is the same, and through the same terms. But when the affirmative signifies the being contingent, but the privative the being present with, there will be a syllogism. For let it be assumed that A is present with no B, but is contingent to every C. The privative interval, therefore, being converted, B will be present with no A. But A was contingent to every C. A syllogism, therefore, will be produced, in the first figure, in which it may be collected that B is contingent to no C. In like manner also, a syllogism will be formed, if the privative is added to C. But if both the propositions are privative and the one signifies the not being present with, but the other the happening not to be present with through the assumed propositions, indeed, nothing necessary will happen. If the contingent proposition, however, is converted, there will be a syllogism, in which it may be collected, that B happens to be present with no C, as in the former syllogisms for again, there will be the first figure. But if both the propositions are posited categoric, there will not be a syllogism. Let the terms of being present with be health, animal, man but of not being present with, health, horse, man.

It happens that every animal is well:

Every man is well:

It is necessary that every man should be an animal.

It happens that every horse is well:

Every man is well:

It is necessary that no man should be a horse.

Every animal is well:

It happens that every man is well:

It is necessary that every man should be an animal.

Every horse is well:

It happens that every man is well:

It is necessary that no man shoulld be a horse.

The like will also take place in partial syllogisms. For when the affirmative proposition is pure, whethcr it be assumed universally, or partially, there will be no syllogism. But this may be demonstrated similarly, and through the same terms as before.

It happens that no animal is well:

Some man is well:

It is necessary that every man shouldl be an animal.

Every animal is well:

It happens that some man is not well:

It is necessary that every man shouldl be an animal.

It happens that no horse is well:

Some man is well:

It is necessary that no man should be a horse.

Every horse is well:

It happens that some man is not well:

It is necessary that no man shouldl be a horse.

But when the privative is pure, there will be a syllogism through conversion, as in the former syllogisms. Again, if both intervals are assumed privative, and that which signifies the not being present with is universal from these propositions, indeed, there will not be the necessary. But when the contingent is converted, as before, there will be a syllogism. If, however, the privative interval is, indeed, pure, but is assumed in part, there will not be a syllogism, whether the other proposition be affirmative or privative. Nor will there then be a syllogism, when both the propositions are assumed indefinite, whether affirming, or denying, or partial. But the demonstration is the same, and through the same terms.

Some animal is/is not well:

It happens that some man is/is not well:

 It is necessary that every man should be an animal.

Some horse is/is not well:

It happens that some man is/is not well:

It is necessary that no man should be a horse.

It happens that some animal is/is not well:

Some man is/is not well:

It is necessary that every man should be an animal.

It happens that some horse is/is not well:

Some man is/is not well:

It is necessary that no man should be a horse.

Chapter 19

If, however, one of the propositions signifies the being present with, or not being present with from necessity, but the other signifies the being contingent; when the privative is necessary, there will be a syllogism, in which not only the happening not to be present with will be collected, but also the not being present. But when the affirmative is necessary, there will not be a syllogism. For let it be posited that A is necessarily present with no B, and that it is contingent to every C.  The privative proposition, therefore, being converted, neither will B be present with any A. But A was contingent to every C. Again, therefore, a syllogism will be produced in the first figure, in which it may be collected that B happens to be present with no C. At the same time also it is evident, that neither is B present with any C. For let it be admitted that it is. If, therefore, A is contingent to no B, but B is present with a certain C, A will not be contingent to a certain C. But it was supposed to be contingent to every C. It will likewise be demonstrated after the same manner, if the privative is joined to C. Again, let the categoric interval be necessary, but the other, privative and contingent and let A be contingent to no B, but necessarily present with every C. The terms, therefore, thus subsisting, there will be no syllogism for it may happen that B is necessarily not present with C. For let A be white, B man, C a swan. Whiteness, therefore, is necessarily present with a swan, but is contingent to no man and man is necessarily present with no swan. That there will not, therefore, be a syllogism of the contingent is evident for that which is from necessity is not contingent.

It happens that no man is white:

It is necessary that every swan should be white:

It is necessary that no swan should be a man.

Neither will there be a syllogism of the necessary. For the necessary is either inferred from both the necessary propositions, or from the privative. Farther still, these things being admitted, it may be possible that B may be present with C. For nothing hinders but that C may be under B and that A may be contingent to every B, and may be necessarily present with C as if C is awake; B animal and A, motion. For motion is necessarily present with every thing that is awake but is contingent to every animal and every thing which is awake is an animal.

It happens that no animal is moved:

It is necessary that every thing awake should be moved:

Every thing awake is an animal.

It is evident, therefore, that neither is the not being present with collected since the terms thus subsisting, the being present with is necessary nor are the opposite affirmations collected. Hence there will be no syllogism. There will also be a similar demonstration if the affirmative proposition is posited vice versa. But if the propositions are similar in figure, being privative indeed, a syllogism will always be formed, when the contingent proposition is converted, as in the former syllogisms. For let it be assumed that A is necessarily not present with B, and that it happens not to be present with G. The propositions, therefore, being converted, B will be present with no A, and A will be present with every C. The first figure, therefore, will be produced. The like will also take place if the privative is joined to C. But if both the propositions are posited categoric there will not be a syllogism. For it is evident, that there will not be a syllogism of the not being present with, or of the not being present with from necessity, because a privative proposition is not assumed, neither in the being present with, nor in the being present with from necessity. But neither will there be a syllogism of the not happening to be present with. For the terms being thus posited from necessity, B will not be present with C as, for instance, if A is posited white; B, a swan and C, man. Neither will there be a syllogism of the opposite affirmations because it has been shown that B is necessarily not present with C. A syllogism, therefore, in short, will not be produced.

It is necessary that every swan should be white:

It happens that every man is white:

It is necessary that no man should be a swan.

The like will also take place in partial syllogisms. For when the privative is universal and necessary, there will always be a syllogism of the contingent, and of the not being present with. But the demonstration will be through conversion. When, however, the affirmative is necessary there will never be a syllogism. But this may be demonstrated in the same manner as in the universal modes, and through the same terms.

It happens that no man is white:

It is necessary that some swan should be white:

It is necessary that no swan should be a man.

It happens that no animal is moved:

It is necessary that something awake should be moved:

It is necessary that every thing awake should be an animal.

It is necessary that every swan should be white:

It happens that some man is not white:

It is necessary that no man should be a swan.

Nor will there then be a syllogism, when both the propositions are assumed affirmative for of this there is the same demonstration as before.

It is necessary that every swan should be white:

It happens that some man is a swan:

It is necessary that no man should be a swan.

It happens that every man is white:

It is necessary that some swan should be white:

It is necessary that no swan should be a man.

It is necessary that some swan should be white:

It happens that every man is white:

            It is necessary that no man should be a swan.

It happens that some man is white:

It is necessary that every swan should be white:

It is necessary that no swan should be a man.

But when both the propositions are assumed privative, and that which signifies the not being present with, is universal and necessary; through the propositions, indeed, there will not be the necessary but the contingent proposition being converted, there will be a syllogism, as before. If, however, both the propositions are posited indefinite, or in a part, there will not be a syllogism. But the demonstration is the same, and through the same terms,

It happens that some animal is/is not white:

It is necessary that some man should not be/not be white:

It is necessary that every man should be an animal.

It happens that some animal is/is not white:

It is necessary that something inanimate should be/not be white:

It is necessary that nothing inanimate should be an animal.

It is necessary that some animal should be/not be white:

It happens that some man is/is not white:

It is necessary that every man should be an animal.

It is necessary that some animal should be/not be white:

It happens that something inanimate is/is not white:

It is necessary that nothing inanimate should be an animal.

It is evident, therefore, from what has been said, that when the privative position is posited universal and necessary, a syllogism will always be produced, not only of the happening not to be present with, but also of the bot being present with.  But there will never be a syllogism when the affirmative is posited necessary.  It is also evident, that when the terms subsist after the same manner, is necessary and pure propositions, there will be, and there will not be, a syllogism.  And it is likewise manifest, that all these syllogisms are imperfect, and that they are perfected through the above-mentioned figures.

Chapter 20

But in the last figure, when both the propositions are contingent, and when one only is contingent, there will be a syllogism. When, therefore, the propositions signify the being contingent, the conclusion also will be contingent and when the one signifies the being contingent, but the other the being present with. But when one of the propositions is posited necessary if, indeed, it is affirmative, there will not be a conclusion, neither necessary nor pure. But if it is privative, there will be a syllogism of the not being present with, as before. In these, however, the contingent must be similarly assumed in the conclusions. In the first place, therefore, let both the propositions be contingent, and let A and B happen to be present with every C. Since then an affirmative proposition may be partially converted, but B is contingent to every C, G also will be contingent to a certain B.  Hence, if A is contingent to every C, but C is contingent to a certain B, it is also necessary that A should be contingent to a certain B. For the first figure will be produced. And if A happens to be present with no C, but B is present with every C, it is also necessary that A should happen not to be present with a certain B for again, there will be the first figure through conversion. But if both the propositions are posited privative from the assumed propositions, indeed, there will not be the necessary (i.e. a necessity of concluding). The propositions, however, being converted, there will be a syllogism, as before. For if A and B . happen not to be present with C, if the happening not to be present with is changed, there will again be the first figure through conversion. But if one of the terms is universal, and the other partial; when the terms subsist in the same manner, as in that which is present with, there will be, and there will not be a syllogism. For let A be contingent to every C, but let B be present with a certain C again, there will be the first figure, the partial proposition being converted. For if A is contingent to every C, and C is contingent to a certain B, A also will be contingent to a certain B. The like will also take place, if the universal is joined to the proposition B C. And this in a similar manner will be effected, if the proposition A C is privative, but B C affirmative for again there will be the first figure through conversion. But if both are posited privative, the one universal, and the other partial through the things assumed, indeed, there will not be a syllogism but there will be when they are converted, as before. When, however, both are assumed indefinite, or partial, there will not be a syllogism. For it is necessary that A should be present with every, and with no B.  Let the terms then of being present with be animal, man, white but of not being present with, horse, man, white; and let the middle be white.

It happens that something white is/is not an animal:

It happens that something white is/is not a man:

It is necessary that every man should be an animal.

It happens that something white is/is not a horse:

It happens that something white is/is not a man:

It is necessary that no man should be a horse.

Chapter 21

If, however, one of the propositions signifies the being present with, but the other the being contingent; the conclusion will be, that a thing is contingent, and not that it is present with. But there will be a syllogism, the terms subsisting in the same manner as before. For in the first place, let them be categoric and let A be present with every C, but let B happen to be present with every C. The proposition, therefore, B C being converted, there will be the first figure; and the conclusion will be, that A happens to be present with a certain B. For when one of the propositions in the first figure signifies the being contingent, the conclusion also is contingent. In a similar manner, if the proposition B C signifies the being present with, but the proposition AC the being contingent and if AC is privative, but B C categoric, and either of them is pure for in both ways the conclusion will be contingent, since again, the first figure will be produced. But it has been shown, that when one of the propositions in that figure, signifies the being contingent, the conclusion also will be contingent. If, however, a contingent privative is joined to the less extreme, or both the intervals are assumed privative through the things posited, indeed, there will not be a syllogism but when they are converted, there will be a syllogism, as before. But if one of the propositions is universal, and the other partial both, indeed, being categoric or the universal being privative, but the partial affirmative there will be the same mode of syllogisms; for all of them will be completed through the first figure. Hence it is evident, that there will be a syllogism in which the contingent, and not the beiug present with, will be collected. But if the affirmative proposition is universal, and the privative partial, the demonstration will be through the impossible. For let B be present with every C, and let A happen not to be present with a certain C. It is necessary, therefore, that A should happen not to be present with a certain B. For if A is necessarily present with every B, but B is posited to be present with every C, A is necessarily present with every C. For this was demonstrated before. But it was supposed that A happens not to be present with a certain C. But when both the propositions are assumed indefinite, or partial, there will not be a syllogism. But the demonstration is the same as that which was in universals, and through the same terms.

Something white is/is not an animal:

It happens that something white is/is not a man:

It is necessary that every man should be an animal.

Something white is/is not a horse:

It happens that something white is/is not a man:

It is necessary that no man should be a horse.

It happens that something white is/is not an animal:

Something white is/is not a man

It is necessary that every man should be an animal.

It happens that some animal is/is nota horse:

Something white is/is not a man:

It is necessary that no man should be a horse.

Chapter 22

But if one of the propositions is necessary, and the other contingent, the terms, indeed, being categoric, there will always be a syllogism of the contingent. When, however, one interval is categoric, but the other privative; if, indeed, the affirmative is necessary, there will be a syllogism of the happening not to be present with. But if the interval is privative, there will be a syllogism of the happening not to be present with, and of the not being present with. There will not, however, be a syllogism of the not being present with from necessity, as neither in the other figures. In the first place, therefore, let the terms be categoric, and let A be present from necessity with every C, but let B happen to be present with every C. Because, therefore, A is necessarily present with every C, but C is contingent to a certain B, A also will be contingent to, and will not be necessarily present with a certain B for such will be the conclusion in the first figure. A similar demonstration will take place, if the proposition B C is posited necessary, and the proposition AC contingent.

It happens that every man is white:

It is necessary that every man should be an animal:

Therefore, it happens that some animal iss white.

It happens that every man is white:

It is necessary that some animal should be a man:

Therefore, it happens that some animal is white.

Again, let the one proposition be categoric, but the other privative and let the categoric be necessary. Let also A happen to be present with no C, but let B necessarily be present with every C. Again, therefore, there will be the first figure and the conclusion will be contingent, but not pure for the privative proposition signifies the being contingent. It is evident, therefore, that the conclusion will be contingent for when the propositions thus subsisted in the first figure, the conclusion was contingent. But if the privative proposition should be necessary, the conclusion will be, that the not being present with a certain thing is contingent, and that it is not present with it. For let it be supposed that A is necessarily not present with C, but is contingent to every B. The affirmative proposition, therefore, B C being converted, there will be the first figure, and the privative proposition will be necessary. But when the propositions thus subsist, it will follow that A happens not to be present with a certain C, and that it is not present with it. Hence it is also necessary that A should not be present with a certain B. When, however, the privative is joined to the less extreme, if that is contingent there will be a syllogism, the proposition being converted, as in the former syllogisms. But if it is necessary, there will not be a syllogism, because it is necessary to be present with, every individual, and to happen to be present with no individual. Let the terms then of being present with every individual be, sleep, a sleeping horse, and man, but of being present with no individual sleep, a waking horse, and man.

It happens that every man sleeps:

It is necessary that no man should be a sleeping horse:

It is necessary that every sleeping horse should sleep.

It happens that every man sleeps:

It is necessary that no man should be a waking horse:

It is necessary that no waking horse should sleep.

The like will also take place, if one of the terms is joined to the middle universally, but the other partially. For both being categoric, there will be a syllogism of the being contingent, and not of the being present with; and also, when the one interval is assumed privative, but the other affimiative and the affirmative is necessary. But when the privative is necessary, the conclusion also will be of the not being present with. For there will be the same mode of demonstration, whether the terms are universal, or not universal since it is necessary that the syllogisms should be completed through the first figure. Hence it is necessary that there should be the same conclusion in these, as in those. But when the privative universally assumed is joined to the less extreme, if, indeed, it is contingent there will be a syllogism through conversion. If, however, it is necessary, there will not be a syllogism. But this may be demonstrated after the same manner as in universals, and through the same terms.

It happens that some man sleeps:

It is necessary that no man should be a sleeping horse:

It is necessary that every sleeping horse should sleep.

It happens that, some man sleeps:

It is necessary that no man should be a waking horse:

It is necessary that no waking horse should be asleep.

In this figure, therefore, it is also evident, when, and how there will be a syllogism; and when there will be a syllogism of the contingent, and wlien of the being present with. It is likewise evident, that allthese syllogisms are imperfect, and that they are perfected through the first figure.

Chapter 23

That the syllogisms, therefore, in these figures, are perfected through the universal syllogisms in the first figure, and are reduced to these, is evident from what has been said. But, in short, that every syllogism thus subsists, will now be evident, when it shall be demonstrated that every syllogism is produced through some one of these figures. It is necessary, therefore, that every demonstration, and every syllogism, should show either that something is present with, or is not present with a certain thing and this, either universally, or partially and farther still, either ostensively, or from hypothesis. But a part of that which is from hypothesis is that which is produced through the impossible. In the first place, therefore, let us speak concerning ostensive syllogisms for these being exhibited, it will also be evident in syllogisms leading to the impossible, and, in short, in syllogisms which are from hypothesis. If, therefore, it were requisite to syllogize A of B, either as present with, or as not present with, it would be necessary to assume something of something. If then A, indeed, were assumed of B, that will be assumed which was proposed from the first to be proved. But if A were assumed of C, but C of nothing, nor anything else of it, nor anything else of A, there will be no syllogism for from the assuming one thing of one, nothing necessary will happen. Another proposition, therefore, must be assumed. If then A is assumed of something else, or something else of A, or something else of C, nothing hinders but there may be a syllogism. It will not, however, pertain to B, from the things which are assumed. Nor will there be a syllogism of A with reference to B, when C is predicated of something else, and that of something else, and this something else of another, if no one of these is conjoined with B. For, in short, we have said, that there will never be a syllogism of one thing of another, unless a certain medium is assumed, which in a certain respect is referred to each extreme by predications. For a syllogism is simply from propositions but the syllogism which pertains to this particular thing, is from propositions pertaining to this thing. And the syllogism of this thing referred to that, is from propositions, in which this is referred to that. But it is impossible to assume a proposition pertaining to B, if nothing is either predicated, or denied of it; or again, to assume a proposition of A pertaining to B, if nothing common is assumed, but certain peculiar things are predicated or denied of each. Hence a certain middle of both is to be assumed, which may conjoin the predications, if there will be a syllogism of this thing with reference to that. If, therefore, it is necessary to assume something which is common to both and this happens in a threefold respect for we either predicate A of C, and C of B, or C of both, or both of C; but these are the before-mentioned figures — if this be the case, it is evident, that every syllogism is necessarily produced through some one of these figures. For there is the same reasoning if A is conjoined with B through many media; since there will be the same figure in many media, as in one medium. That all ostensive syllogisms, therefore, are perfected through the above-mentioned figures is evident. That those also which lead to the impossible are perfected through the same will be manifest through these things. For all those syllogisms which conclude through the impossible, collect the false but they show from hypothesis, that which was proposed from the first, when anything impossible happens, contradiction being admitted such, for instance, as that the diameter of a square is incommensurable with the side, because a common measure being given, the odd would be equal to the even. They syllogistically collect, therefore, that the odd would become equal to the even, but they show from hypothesis, that the diameter is incommensurable, since something false happens to take place, from contradiction. For this it is to syllogize through the impossible, viz. to show something impossible, through the hypothesis admitted from the first. Hence, since by those reasonings which lead to the impossible, the false is proved in an ostensive syllogism; but that which was proposed from the first, is shown from hypothesis and since we have before observed, that ostensive syllogisms are perfected through these figures; — it is evident, that the syllogisms also which are produced through the impossible, will be formed through the same figures. And after the same manner also, all others will be produced which reason from hypothesis for in all of them a syllogism will be formed of that which is assumed; but that which was proposed from the first, is proved through confession, or some other hypothesis. But if this is true, it is necessary that every demonstration, and every syllogism, should be produced through the three before-mentioned figures. And this being demonstrated, it is evident, that every syllogism is perfected through the first figure, and is reduced in this figure to universal syllogisms.

Chapter 24

Farther still, in all syllogisms it is necessary that there should be a certain term which is categoric, and a certain term which is universal for without the universal, either there will not be a syllogism, or it will not pertain to the thing proposed, or that will become the subject of petition, which was investigated from the first. For let it be proposed to be demonstrated that the pleasure arising from harmony is a worthy pleasure. If, therefore, any one should require it to be granted to him that pleasure is worthy, not adding all pleasure, there will not be a syllogism. But if he contends that a certain pleasure is good if, indeed, it is different from that arising from harmony, it will be foreign from the thing proposed and if it is this very pleasure he assumes that which he investigated from the first. This, however, will become more manifest in diagrams. For instance, let it be proposed to demonstrate that the angles at the base of an isosceles triangle are equal. Let the lines A, B, be drawn to the centre of a circle. If, therefore, he assumes that the angle A C is equal to the angle B D, not, in short, requiring it to be granted that the angles of. semicircles are equal, and again assumes that the angle C is equal to the angle D, not assuming that the angle of one section in a circle, is equal to another angle of the same section and if, besides, he assumes, that equal parts being taken away from equal whole angles,the remaining angles E F are equal — he will demand that which was proposed to be investigated from the first, unless he assumes, that if equal things are taken away from equal things, equal things will remain. It is evident, therefore, that in all syllogisms, it is necessary there should be the universal. It is likewise manifest, that the universal is shown from all universal terms but that the partial is shown as well in this, as in that way. Hence, if the conclusion is universal, it is also necessary that the terms should be universal. But if the terms are universal, it may happen that the conclasion is not universal. It is also evident, that in every syllogism, either both propositions, or one proposition, is necessarily similar to the conclusion. But I say similar, not only because it is affirmative or privative but also because it is necessary, or pure, or contingent. It is also necessary to consider other modes of predication. It is likewise simply manifest, when there will be, and when there will not be a syllogism when it is possible, and when perfect; and that when there is a syllogism, it is necessary it should have terms according to some one of the before-mentioned modes.

Chapter 25

It is also manifest, that every demonstration will be through three terms, and not through more than three; unless the same conclusion should be produced through different arguments; as, for instance, E through A B, and D through C; or through A B, A C, and B C. For nothing prevents there being many media of the same conclusions. But these being many there is not one syllogism, but there are many syllogisms. Or again, demonstration is not through three, but through more than three terms, when each of the propositions A, B, is assumed through syllogism; as, for instance, A through D E, and again, B through F G. Or when the one is by induction, but the other by syllogism. But thus also there are many syllogisms for there are many conclusions; as, for instance, A, B and C. And if there are not many syllogisms, but one syllogism, thus, indeed, through many syllogisms, the same conclusion may be produced. In order, however, that C may be proved through A B, it is impossible there should be more than three terms. For let the conclusion be E, which is collected from A B C D. It is necessary, therefore, that some one of these should be assumed with reference to something else as a whole, but another as a part. For this was demonstrated before, that when there is a syllogism, it is necessary that some of the terms should thus subsist. Let A, therefore, thus subsist with reference to B. Hence, from these there is a certain conclusion; which, therefore, is either E, or C, or D, or some other different from these. And if, indeed, E is concluded, the syllogism will be from A B alone. But if C and D so subsist, that the one is as a whole, and the other as a part; something also will bet collected from them; and this will either be E, or A, or B, or something else different from these. And if E is collected, or A, or B, either there will be many syllogisms, or in the manner in which we have said it is possible, it will happen that the same thing will be concluded through many terms. But if anything else different from these is collected, there will be many syllogisms unconnected with each other. If however, C does not so subsist with reference to D, as to produce a syllogism, they will be assumed in vain, unless they were assumed for the sake of induction, or concealment, or something else of this kind.

But if from A B not E but some other conclusion is produced: and from C D, either one of these is collected, or something different from, these, many syllogisms will be produced, yet not syllogisms of the subject, or thing proposed. For it was supposed that the syllogism is of E. If, however, no conclusion is produced from C D, it will happen that they are assumed in vain, and the syllogism will not be of that which was investigated from the first. Hence it is evident, that every demonstration and every simple syllogism, will subsist through three terms alone. But this being apparent, it is also evident that, a syllogism consists of two propositions, and not of more than two. For three terms are two propositions, unless something is assumed, as we observed in the beginning, to the perfection of the syllogism. It is evident, therefore, that in the syllogistic discourse, in which the propositions through which the principal conclusion is produced, are not even (for it is necessary that some of the former conclusions should be propositions) — it is evident in this case that this discourse, either collects nothing, or interrogates more than is necessary to the thesis. The syllogisms, therefore, being assumed according to the principal propositions, every syllogism will consist, indeed, of propositions which are even, but from terms which are odd. For the terms are more than the propositions by one. But the conclusions will be the half part of the propositions. When, however, the conclusion is through pro-syllogisms, or through many continued media (as A B through C, and through D) the multitude of terms, indeed, will, in a similar manner, surpass the propositions by one for the term will be inserted, either externally, or in the middle; but in both ways, it will happen that the intervals are fewer than the terms by one. But the propositions are equal to the intervals. These, however, will not always be even, and those odd; but alternately, when the propositions are even, the terms will be odd; and when the terms are even, the propositions will be odd. For together with the term, one proposition is added, wherever the term is added. Hence, since the propositions were even, but the terms odd, it is necessary there should be a commutation, the same addition being made. The conclusions, however, will no longer have the same order, neither with respect to the terms, nor with respect to the propositions. For one term being added, conclusions are added, less by one than the pre-subsisting terms; because to the last term alone a conclusion is not made, but is made to all the rest. Thus, for instance, if D is added to A B C, two conclusions are immediately added, the one to A, and the other to B. The like also takes place in others. If the term also is inserted in the middle place, there will be the same reasoning; for to one term alone, a syllogism will not be produced. Hence the conclusions will be far more than the terms, and the propositions.

Chapter 26

Since, however, we have the particulars with which syllogisms are conversant, the quality of the problems in each figure, and in how many ways they are demonstrated; it is also evident to us, what kind of problem is difficult, and what kind is easy to be proved. For that which is concluded in many figures, and through many cases is more easy; but that which is concluded in fewer figures, and through fewer cases, is more difficult to be proved. A universal affirmative problem therefore is proved through the first figure alone, and through this in one way only. But a privative problem, is proved through the first, and through the middle figure; and through the first, indeed, in one way only; but through the middle in two ways. A partial affirmative problem, however, is proved through the first, and through the last figure; in one way, indeed, through the first, but in a triple way through the last figure. And a partial privative problem, is proved in all the figures; except that in the first figure, indeed, it is proved in one way; but in the middle in a twofold; and in the last in a threefold way. It is evident, therefore, that it is most difficult to construct a universal categoric problem, but that it may be most easily subverted; and, in short, that universal may be more easily subverted than partial problems; because universal problems are subverted whether a thing is present with nothing, or is not present with a certain thing; of which the one, viz. the not being present with a certain thing is proved in all tlie figures; and the other, viz. the being present with nothing, is proved in two figures. There is the same mode also in privative problems. For whether a thing is present with every, or with a certain individual, that which was proposed from the first is subverted. But in partial problems, the confutation takes place in one way, viz. if a thing is proved to be present with every, or with no individual. Partial problems, however, are more easily constructed; for they are constructed in more figures, and through more modes than universal problems. In short, it is not proper to be ignorant that universal are mutually confuted through partial problems, and these through universal problems. Universal, however, cannot be constructed through partial problems, but the latter may through the former. At the same time also it is evident, that it is easier to subvert than to construct a problem. In what manncr, therefore, every syllogism is produced, and through how may terms and propositions, and how they subsist with reference to each other; farther still, what kind of problem may be proved in each figure, what kind in many, and what kind in fewer modes is manifest from what has been said.

Chapter 27

Let us now show how we may possess an abundance of syllogisms for a proposed question, and through what way we may assume principles about every problem. For perhaps it is not only necessary to survey the generation of syllogisms, but also to possess the power of forming them. Of all beings, therefore, some are of such a kind as not to be in reality universally predicated of anything else; such, for instance, as Cleon, and Callias, that which is particular, and that which is sensible; but other things are predicated of these; for each of these is man and animal. But other beings are, indeed, predicated of other things, yet other things are not previously predicated of these. And other beings, are themselves predicated of other things, and other things are predicated of them; as, for instance, man is predicated of Callias, and animal of man. That some things, therefore, are naturally adapted to be predicated of nothing is evident; for of sensibles, each nearly is a thing of such a kind, as not to be predicated of anything except from accident. For we sometimes say, that that white thing is Socrates, and that he who approaches is Callias. But that in a progression upward, we must sometime or other stop, we shall again show.  At present, however, let this be admitted. Of these things, therefore, it is not possible to demonstrate another predicate, except according to opinion; but these may be predicated of other things.  Nor can particulars be predicated of other things, but others things of these. But it is evident, that those which are intermediate, may in both ways, fall under demonstration; for they may be predicated of other things, and other things of them. And nearly arguments and speculations are conversant with these. But it is necessary thus to assume the propositions pertaining to each thing, in the first place, admitting as an hypothesis that which is the subject of discussion, together with definitions, and such things as are the peculiarities of that thing; and, in the next place, such things as are consequent to the thing, and such as cannot not be present with it. But those things with which the thing cannot be present, are not to be assumed, because a privative assertion may be converted. A division also must be made of things consequent, that we may understand what things belong to the question, what a thing is, what are as peculiarities, and what are predicated as accidents; and of these, what are predicated according to opinion, and what according to truth. For the greater abundance any one possesses of these, the more expeditiously will he obtain the conclusion; and the more true they are, the more will he demonstrate. It is necessary however to select not those things which are consequent to a certain thing, but such as are consequent to a whole thing; for instance, not what is consequent to a certain man, but what is consequent to every man. For a syllogism subsists through universal propositions. A proposition, therefore, being indefinite, it is immanifest whether it is universal; but when it is definite, this is manifest. In a similar manner also, those things are to be selected, to the whole of which a thing is consequent, and this for the before-mentioned cause. The whole consequent, however, must not be assumed to follow. I say, for instance, it must not be assumed, that every animal is consequent to man, or every science to music; but only, that they are simply consequent, just as we also propose. For the other is useless and impossible; as, that every man is every animal: or that justice is every thing good. But to that to which something else is consequent, the mark every must be added.  When the subject, however, is comprehended by a certain thing, to which it is necessary to assume consequents, those, indeed, which follow, or which do not follow the universal, are not to be selected in these; for they were assumed in those.  For such things as are consequent to animal, are also consequent to man: and in a similar manner with respect to such things as are not present with. But the peculiarities about each thing are to be assumed.  For there are certain things peculiar to species, not common to genus; since it is necessary that certain peculiarities should be present with different species. Nor are those things to be selected, as if anteceding the universal, to which the things contained under them are consequent. Thus those things to which man is consequent, ought not to be assumed, as if they were the antecedents of animal. For if animal is consequent to man,, it is likewise consequent to all these. But these more appropriately pertain to the selection of the antecedents of man. Those things also are to be assumed, which are for the most part consequent or antecedent. For of problems which happen for the most part, the syllogism also is from propositions, all, or some of which, are for the most part true.  For the conclusion of every syllogism is similar to its principles.  Farther still, things consequent to all things, are not to be selected; for from them there will not be a syllogism; but through what cause will be manifest from what follows.

Chapter 28

He, therefore, who wishes to confirm anything of a certain whole, should look to the subjects of that which is confirmed, of which that is predicated; but of that which ought to be predicated, he should consider such things as are consequent to this. For if anything of these is the same, it is necessary that the one should be present with the other. But if it is to be proved, that a thing is not present with every, but with a certain individual, those things are to be considered which each follows. For if any one of these is the same, the being present with a certain thing is necessary. But when the being present with nothing is necessary; so far as pertains to that with which it is not necessary to be present, regard must be had to the consequents; but so far as pertains to that which ought not to be present with, regard must be had to those things which cannot be present with it. Or on the contrary, on the part of that with which it is necessary not to be present, regard must be had to those things which cannot be present with it; but on the part of that which ought not to be present with, to the consequents. For whichever of these are the same, it will happen that the one is present with no other; because at one time, a syllogism will be produced in the first figure, and at another, in the middle figure. If, however, the not being present with a certain thing is to be proved, the antecedents of that with which it ought not to be present, and to which it is consequent, are to be regarded; but of that which ought not to be present with, those things are to be regarded which cannot be present with it. For if any thing of these is the same, the not being present with a certain thing is necessary. Perhaps, however, what has been said will be more evident as follows: Let the consequents to A be B but let the things to which it is consequent be C; and let the things which cannot be present with it be D. Again, let the things which are present with E be F; but the things to which it is consequent be G.  And let the things which cannot be present with it, be H. If, therefore, a certain C and a certain F are the same, it is necessary that A should be present with every E, for F is present with every E, and A with every C; so that A is present with every E. But if C and G are the same, it is necessary that A should be present with a certain E; for A is consequent to every C, and every G to E. If, however, F and D are the same, A will be present with no E, and this, from a pro-syllogism. For since a privative assertion may be converted, and F is the same with D, A will be present with no F; but F is present with every E.  Again, if B and H are the same, A will be present with no E. For B is present with every A, but with no E. For B and H are the same, and H is present with no E. But if D and G are the same, A will not be present with a certain E. For A will not be present with G, since it is not present with D.  But G is under E; so that it will not be present with a certain E.  If, however, G and B are the same, the syllogism will be inverse. For G will be present with every A (since B is present with A) and E will be present with B; (for B is the same with G), but it is not necessary that A should be present with every E, but it is necessary that it should be present with a certain E, because a universal predication may be converted into a particular predication. It is evident, therefore, that regard must be had to what has been said, from each part of every problem; for through these all syllogisms are formed. But it is necessary in consequents, and the antecedents of each thing, to look to things first, and which are especially universal. For instance on the part of E, more regard is to be paid to K F, than to F only; but on the part of A, more regard must be paid to K C, than to C only. For if A is present with K C, it is also present with F, and with E. But if it is not consequent to this, yet it may be consequent to F, to which the thing itself is consequent. For if it follows the first things, it also follows those things which are placed under these. But if it does not follow these, nevertheless, it may follow those things which are arranged under these.  It is also evident, that this speculation subsists through three terms, and two propositions; and that through the before-mentioned figures, all syllogisms are constructed. For it is shown that A is present with every E, when of C, and of F, something which is the same is assumed. But this will be the middle; and the extremes are A and E. The first figure, therefore, is produced. But it is shown to be present with a certain thing, when C and G are assumed to be the same. But this is the last figure; for G becomes the middle. And it is proved to be present with no individual, when D and F are the same.  But thus also the first figure, and the middle are produced. The first, indeed, because A is present with no F; (since a privative assertion may be converted), but F is present with every E. And it produces the middle figure, because D is present with no A, but is present with every E. It is also proved, not to be present with a ccrtain individual, when D and G are the same. But this is the last figure. For A will be present with no G, and E will be present with every G. It is evident, therefore, that all syllogisms are produced through the before-mentioned figures. It is likewise manifest, that those things are not to be selected which are consequent to all things, because no syllogism will be produced from these. For, in short, a syllogism cannot be constructed from consequents; but privation cannot be proved through those things which arc consequent to all things. For it is necessary to be present with the one, and not to be present with the other. It is also evident, that other modes of selection are useless to the construction of syllogisms as, for instance, if the consequents to each are the same, or if those things to which A is consequent, and those which cannot be present with E; or again such as cannot be present with either; for a syllogism will not be produced through these. For if the consequents should be the same, as, for instance, B and F, the middle figure will be produced, having both the propositions categoric. But if those things are the same to which A is consequent, and which cannot be present with E, as, for instance, C, and H, the first figure will be produced, having the minor proposition privative. But if those are the same which cannot be present with either, as, for instance, D and G, both propositions will be privative, either in the first, or in the middle figure. Thus, however, there will by no means be a syllogism. It is also evident, that certain things are to be assumed in this speculation which are the same, and not certain things which are different or contrary. In the first place, indeed, because this inspection is for the sake of the middle; but it is necessary to assume the middle not different, but the same. In the next place, in those things in which a syllogism happens to be produced, in consequence of contraries being assumed, or things which cannot be present with the same thing; all are reduced to the before-mentioned modes. Thus, if B and F are contraries, or cannot be present with the same thing; these being assumed, there will be a syllogism, that A is present with no E. This, however, is not effected from these assumptions, but from the before-mentioned mode. For B is present with every A, and with no E. Hence it is necessary that B should be the same with a certain H. Again, if B and G cannot be present with the same thing, it may be concluded that A is not present with a certain E; for thus there will be the middle figure. For B is present, indeed, with every A, and with no G. Hence it is necessary that B should be the same with some H. For the impossibility of B and G being present with the same thing, does not differ from B being the same with a certain H; since in H every thing is assumed, which cannot be present with E. It is evident, therefore, from these very inspections that no syllogism will be produced. But if B and F are contraries, it is necessary that B should be the same with a certain H; and that a syllogism should be produced through these. It happens, however, to those who thus inspect, that they look to a way different from the necessary, because they are sometimes ignorant that B and H are the same.

Chapter 29

Syllogisms also leading to the impossible, will subsist after the same manner as ostensive syllogisms. For these likewise are produced through consequents, and those things which each follows; and there is the same inspection in both. For that which is demonstrated ostensively, may also be syllogistically collected through the impossible, and through the same terms: and that which is demonstrated through the impossible, may also be demonstrated ostensively.  Thus, for instance, it may be demonstrated that A is present with no E.  For let A be supposed to be present with a certain E. Since, therefore, B is present with every A, and A is present with a certain E; B will be present with a certain E. But it was present with no E. Again, it may be demonstrated that A is present with a certain E. For if A is present with no E, but E is present with every H, A will be present with no H, but it was supposed to be present with every H.  The like will also take place in other problems. For always, and in all things, the demonstration through the impossible will be from things consequent, and those things which each follows. And in every problem there is the same consideration, whether any one wishes to syllogize ostensivcely, or to lead to the impossible; for both demonstrations consist from the same terms. Thus, for instance, if it should be demonstrated that A is present with no E, because it happens that B is present with a certain E, which is impossible; if it is assumed that B is present with no E, and is present with every A, it is evident, that A will be present with no E. Again, if it should be concluded ostensively that A is present with no E, to those who suppose that it is present with a certain E, it may be shown through the impossible, that it is present with no E. The like will also take place in others. For in all problems it is necessary to assume a common term, different from the subject terms, to which the syllogism concluding the false will be referred. Hence this proposition being converted, but the other remaining the same, there will be an ostensive syllogism through the same terms. But an ostensive syllogism differs from that which leads to the impossible, because in the ostensive, both propositions are posited according to truth; but in that which leads to the impossible, one is posited falsely. These things, however, will be more evident through what follows, when we shall speak about the impossible. But now let thus much be manifest to us, that those who wish to syllogize ostensively, and those who wish to lead to the impossible, must look to these things.  In other syllogisms, however, which are from hypothesis, such as those which are according to transmutation, or according to quality, the consideration consists in the subject terms; not in those assumed from the first, but in those which are changed. But the mode of inspection is the same. It is also necessary to consider, and unfold by division, in how many modes syllogisms from hypothesis are produced. Thus, therefore, each problem is demonstrated. It is also possible syllogistically to collect some of these after another manner; as, for instance, univeirsals through the inspection of particulars, and this from hypothesis. For if C and H are the same, and if E is assumed to be present with H alone, A will be present with every E. And again, if D and H are the same, and E is predicated of H alone, it may be concluded that A is present with no E. It is evident, therefore, that the inspection must be after this manner. The like must also take place in things necessary and contingent. For there is the same consideration; and the syllogism of the being contingent, and of the being present with, will be through terms disposed in the same order. But in contingents, things which are not present with, but which may be present with are to be assumed; for it has been shown that through these a syllogism of the contingent is produced. There is also a similar reasoning in other predications. It is evident, therefore, from what has been said, that not only all syllogisms may be formed in this way, but that they cannot be formed in any other way. For it has been shown that every syllogism is produced through some one of the before-mentioned figures; but these cannot be constituted through anything else than the consequents and antecedents of a thing. For from these propositions consist, and the middle term is assumed. Hence, through other things a syllogism cannot be produced.

Chapter 30

Of all problems, therefore, there is the same way, as well in philosophy, as in every art and discipline. For it is necessary to collect about each of them, those things which are present with, and the subjects with which they are present, and to have of these a great abundance.  It is also necessary to consider these through three terms, subverting, indeed, in this way, but constructing in that; and according to truth, to reason from those things, which are truly described to be present with; but on account of dialectic syllogisms, to reason from probable propositions. With respect, indeed, to the universal principles of syllogisms, we have shown how they subsist, and in what manner it is necessary to investigate them; that we may not direct our attention to all that has been said, nor to constructing and subverting the same, nor forming a construction of every, or a certain individual and subverting wholly, or partially; but that we may look to things fewer and definite. In particulars, however, it is necessary to make a selection, as of good, or science. But the peculiar principles in every science are many. And hence it is the province of experience to deliver the principles of every thing. I say, for instance, that astrological experience delivers the principles of the astrological science; for the phenomena being sufficiently assumed, astrological demonstrations are thus invented. The like also takes place in every other art and science. Hence, if those things are assumed which exist or are present about each individual, it will now be our province readily to exhibit demonstrations. For if nothing which pertains to history is omitted of what is truly present with things, we shall be furnished with the means about every thing of which there is demonstration, of discovering and demonstrating this; and we shall be able to make that apparent, which is naturally incapable of being demonstrated. Universally, therefore, we have nearly shown how propositions ought to be selected; but we have accurately discussed this affair, in the treatise On Dialectic.

Chapter 31

That the division, however, through genera, is a certain small portion of the above-mentioned method, it is easy to see. For division is as it were an imbecile syllogism; for it begs what ought to be demonstrated, and always syllogistically infers something of things superior. And, in the first place, all those who use it are ignorant of this and endeavour to persuade themselves and others that it is possible there may be demonstration about essence, and the very nature of a thing. Hence, neither do they perceive that those who divide syllogize, nor that it is possible in the way we have mentioned. In demonstrations, therefore, when it is requisite syllogistically to infer that something is present with, it is necessary that the medium through which the syllogism is produced, should always be less than the first extreme, and should not be universally predicated of it. On the contrary, division assumes the universal for the middle term. For let animal be A, mortal, B, immortal, G, and man of whom the definition ought to be assumed D. Division, therefore, assumes that every animal is either mortal or immortal; but this is, that the whole of whatever is A, is either B or C. Again, he who divides, always admits that man is an animal; so that he assumes that A is predicated of D.  The syllogism, therefore, is, that every D is either B or C. Hence it is necessary to assume, that man is either mortal or immortal; for it is necessary that an animal should be either mortal or immortal. It is not, however, necessary that it should be mortal, but this is desired to be granted; though, this is that which ought to be syllogistically inferred.

Every animal is either mortal or immortal:

Every man is an animal: Therefore,

Every man is mortal or immortal.

Again, placing A for mortal animal: B, for pedestrious; C, for without feet; and D, for man, it assumes in a similar manner. For it assumes that A is either in B or in C (for every mortal animal is either pedestrious, or without feet), and it assimies that A is predicated of D; (for it assumes that man is a mortal animal) so that it is necessary that man should be either a pedestrious or biped animal. That he is pedestrious, however, is not necessary, but is assumed. But this is that which again ought to be proved.

Every mortal animal is pedestrious, or without feet:

Evcry man is a mortal animal: Therefore,

Every man is pedestrious, or without feet.

And after this manner, it always happens to those who divide, that they assume a universal medium, and the extremes, viz. that of which it is necessary to exhibit, and the differences. But in the last place, they assert nothing clearly, why it is necessary that this should be a man, or anything else which is the subject of investigation. For they pursue every other way, not apprehending that there are those copious supplies which may be obtained. But it is evident, that by this divisive method, it is not possible to subvert, nor to conclude anything syllogistically of accident or peculiarity, nor of genus, nor of those things of which we are ignorant whether they subsist in this, or in that way; as, whether the diameter of a square is commensurable, or incommensurable with the side. For if it should assume that every length is either commensurable or incommensurable, but the diameter of a square is a length, it will collect that the diameter is either commensurable or incommensurable. But if it should assume that the diameter is incommensurable, it will assume that which ought to be syllogistically collected.. Hence, that cannot be demonstrated which was to be demonstrated. For this is the way; and through this, it cannot be proved. Let, however, the commensurable or incommensurable be A; length, B; and the diameter C.

Every length is or is not commensurable:

Every diameter is a length: Therefore,

Every diameter is or is not commensurable.

It is evident, therefore, that this mode of investigation is neither adapted to every speculation, nor is useful in those things in which it especially appears to be appropriate. Hence, from what demonstration is produced, and how, and what is to be regarded in every problem, is manifest from what has been said.

Chapter 32

 In the next place, we must show, how we may reduce syllogisms to the before-mentioned figures; for this is what still remains of the [proposed] speculation. For if we have surveyed the generation of syllogisms, and possess the power of inventing them, and if besides this we shall have analysed them when formed, into the before-mentioned figures, the design which we proposed from the first, will have received its completion. At the same time also it will happen, that what has been before said, will be confirmed, and it will be more evident, that they thus subsist from what will now be said. For it is necessary that everything which is true should itself accord with itself in every respect. In the first place, therefore, it is necessary to endeavour to select the two propositions of a syllogism; for it is easier to divide into greater than into less parts; and composites are greater than the things from which they are composed. In the next place, it is necessary to consider whether it is in a whole, or in a part. And if both propositions should not be assumed, one of them is to be posited. For those who write or interrogate, sometimes proposing the universal, do not receive the other which is contained in the universal; or they propose theses, indeed, but omit those through which these are concluded; and in vain interrogate other things. It must be considered, therefore, whether anything superfluous is assumed, and whether anything necessary is omitted. And this, indeed, is to be posited, but that to be taken away, until we arrive at two propositions; for without these the sentences which are thus the subject of interrogations cannot be reduced. In some sentences, therefore, it is easy to see what is wanting; but some are latent, and appear to be syllogisms, because something necessarily happens from the things vhich are posited; as, if it should be assumed, that essence not being subverted, essence is not subverted; but those things being subverted from which a thing consists, that also which is composed from these is subverted.  For those things being posited, it is necessary, indeed, that a part of essence should be essence, yet this is not syllogistically concluded through the things assumed, but the propositions are wanting. Again, if man existing, it is necessary there should be animal; and animal existing, that there should be essence; then man existing, it is necessary there should be essence. This, however, is not yet syllogistically collected, for the propositions do not subsist as we have said they should. But we are deceived in these, because something necessary happens from the things posited, and a syllogism also is a thing attended with necessity. The necessary, however, is more extended than syllogism; for every syllogism is necessary; but not every thing necessary is a syllogism. Hence if certain things being posited, anything happens, reduction must not be immediately attempted, but two propositions must first be assumed. Afterwards a division must thus be made into terms. But that term which is said to be in both the propositions, must be posited as the middle term; for it is necessary that the middle should exist in both terms, in all the figures.  If, therefore, the middle predicates and is predicated; or if it, indeed, predicates, but something else is denied of it; there will be the first figure. But if it predicates and is denied by something, there will be the middle figure. And if other things are predicated of it; or one thing is denied, but another is predicated, there will be the last figure. For thus the middle will subsist in each figure. The like will also take place if the propositions should not be universal: for there is the same definition of the middle. It is evident, therefore, that in discourse, when the same thing is not frequently asserted, a syllogism will not be formed; for the middle is not assumed. But since we know what kind of problem is concluded in each figure, and in which figure universal is concluded, and in which particular, it is evident that we must not direct our attention to all the figures, but to that which is adapted to each problem. Such things, however, as are concluded in many figures, we may know the figure of by the position of the middle.

Chapter 33

It frequently, therefore, happens that we are deceived about syllogisms, in consequence of the necessity of concluding as we have before observed. But we are sometimes deceived through the similitude of the position of the terms, of which we ought not to be ignorant. Thus if A is predicated of B, and B of C, it would seem that the terms thus subsisting there will be a syllogism. Neither, however, is anything necessary produced, nor a syllogism. For let A be that which always is; B, Aristomenes as the object of intellection; and C, Aristomenes. It is true, therefore, that A is present with B; for Aristomenes is always the object of intellection. It is also true that B is present with C; for Aristomenes is Aristomenes the object of intellection. But A is not present with C; for Aristomenes is corruptible. For a syllogism will not be formed, when the terms thus subsist; but it is necessary that a universal proposition A B should be assumed. But this is false, viz. to think that every Aristomenes, who is the object of intellection, always exists. Again, let C, be Miccalus; B, Miccalus the musician ;A, to die tomorrow. B, therefore, is truly predicated of C; for Miccalus is Miccalus the musician; and A is truly predicated of B; for the musician Miccalus may die tomorrow; but A is falsely predicated of C. This instance, therefore, does not differ from the former; for it is not universally true that Miccalus the musician will die tomorrow. But this not being assumed, there was not a syllogism. This deception, therefore, is produced in a small difference. For, we make a concession, as if there were no difference between saying that this thing is present with that, and this thing is present with every individual of that.

Chapter 34

It also frequently happens that we are deceived, because the terms which are arranged in the proposition, are not well expounded, as if A should be health; B, disease; and C, man. For it is true to say, that A cannot be present with any B; (for health is present with no disease); and again, it is true that B is present with every C; (for every man is receptive of disease); whence it would seem to happen as a consequence that health can be present with no man. But the cause of this is, that the terms are not rightly expounded according to the diction. For the words significant of habits being transmuted, there will not be a syllogism as if the word well is posited instead of health, and the word ill instead of disease. For it is not true to say, that to be well cannot be present with him who is ill. But this not being assumed, a syllogism will not be produced, unless of that which is contingent; and this is not impossible. For it may happen that health is present with no man. Again, there will in a similar manner be the false, in the middle figure. For health happens to be present with no disease, and may happen to be present with every man; and, therefore, disease will not be present with any man.  But the false happens to take place in the third figure, according to the being contingent. For it may happen that health and disease, science and ignorance, and, in short, contraries, may be present with every individual of the same thing; but it is impossible that they should be present with each other.  This, however, does not accord with what has been before said. For when it happens that many things are present with the same thing, it will also happen that they are present with each other. It is evident, therefore, that in all these, deception is produced from the exposition of the terms. For the words being changed by which the habits are signified, nothing false will be collected. Hence it is manifest, that in such like propositions, that which is according to habit, is always to be assumed, and posited for a term, instead, of habit.

Chapter 35

It is not requisite, however, always to investigate a name for the purpose of expounding terms; for there will frequently be sentences ia which a name is not posited. Hence it is difficult to reduce syllogisms of this kind. But it also sometimes happens that we are deceived through such an investigation as this; as, for instance, because a syllogism is of things immediate. For let A be two right angles; B, a triangle; C, an isosceles triangle. A, therefore, is present with C, through B; but it is present with B no longer through anything else; for a triangle has essentially two right angles. Hence there will not be a middle of the proposition A B which is demonstrable. It is evident, therefore, that the middle is not always to be so assumed, as if it were a particular definite thing, (ως τοδε τι ) but that sometimes a sentence is to be assumed, which happens to be the case in the instance just adduced.

Chapter 36

But for the first to be present with the middle and this with the extreme, ought not to be assumed, as if the first, of the middle, and this, of the extreme, were always similarly predicated of each other. And the like must also be said of the not being present with. In as many ways, however, as to be is predicated, and anything is truly asserted, in so many ways, it is requisite to think, the being present with, and the not being present with are signified; as, for instance, that of contraries there is one science. For let A be, there is one science; and B, things contrary to each other. A, therefore, is present with B, not as if contraries are one science; but because it is true to say of them, that there is one science of them. But it sometimes happens that the first is predicated of the middle, but that the middle is not predicated of the third. For instance, if wisdom is science, but wisdom is of good, the conclusion is, that science is of good. Hence good is not wisdom; but wisdom is science. But sometimes the middle is predicated of the third; and the first is not predicated of the middle. For instance, if there is a science of every quality and of every contrary; but good is contrary to evil and is a quality; the conclusion is that there is a science of good. Neither good, however, nor quality, nor contrary, is science; but good is these.  Sometimes also, neither the first is predicated of the middle, nor this of the third; the first being sometimes, indeed, predicated of the middle, and sometimes not. For instance, of that of which there is science, there is a genus; but there is a science of good; and the conclusion is, that there is a genus of good. But of these no one is predicated of no one. If, however, of that of which there is science, this is genus; but there is a science of good; the conclusion is, that good is a genus. Of the extreme, therefore, the first is predicated, but they are not predicated of each others. An assumption must be made after the same manner in the not being present with. For this thing not being present with this, does not always signify that this thing is not this, but sometimes that this is not of this, or that this is not with this. Thus, for instance, there is not a motion of motion, or a generation of generation; but there is a motion and generation of pleasure; pleasure, therefore, is not generation or motion. Again, of laughter there is a sign; but there is not a sign of a sign; so that laughter is not a sign. The like will also take place in other things, in which the problem is subverted, in consequence of genus being in a certain respect referred to it.  Again, occasion is not opportune time; for with divinity there is occasion, but there is not opportune time, because nothing is useful to divinity. For it is necessary to place as terms, occasion, opportune time, and divinity; but the proposition must be assumed according to the case of the noun. For, in short, we, assert this universally, that terms are always to be posited according to the appellations of nouns; as, for instance, man, or good, or contraries; not of man, or of good, or of contraries. But propositions are to be assumed according to the cases of each word. For they are either to be assumed to this, as the equal; or of this as the double; or this thing, as striking, or seeing; or this one, as man, animal; or if a noun falls in any other way, according to a proposition.

 Chapter 37

For this thing, however, to be present with this, and for this to be truly asserted of this, must be assumed in as many ways, as predications are divided. These also must be assumed, either in a certain respect, or simply; and farther still, either simple, or connected.  The like also must be assumed, in the not being present with. These things, however, must be better considered and defined.

Chapter 38

That, however, which is repeated in propositions, must be joined to the first extreme, and not to the middle term. I say, for instance, if there should be a syllogism, in which it is collected that there is a science of justice, because it is good; the expression, because it is good, or so far as it is good, must be joined to the first extreme. For let A be science, that it is good; B, good; and C, justice. A, therefore, is truly predicated of B; for of good there is science that it is good. B also is truly predicated of C; for justice is that which is good. Thus, therefore, the analysis is produced.

Of good there is science that it is good:

Justice is good: Therefore,

Of justice there is science that it is good.

But if to B there is added, that it is good, it will not be true. For A, indeed, will be truly predicated of B; but that B is predicated of C will not be true. For to predicate of justice good that it is good, is false, and not intelligible. In a similar manner also it may be shown, that the salubrious is an object of science so far as it is good; or that hircocervus, or an animal formed from the union of a goat and a stag, is an object of opinion, so far as it is a non-entity; or that man is corruptible, so far as he is sensible. For in all things which are added to an attribute, repetition must be added to the greater extreme. There is not, however, the same position of the terms, when anything is simply syllogistically collected, or this particular thing, or in a certain respect, or after a certain manner. I say, as, for instance, when good is shown to be an object of science, and when a thing is shown to be an object of science because it is good. But if good is simply shown to be an object of science, being must be constituted as the middle term.

Every being is an object of science:

Good is being: Therefore,

Good is an object of science.

If, however, it should be proved that it may be scientifically known to be good, a certain being, must be assumed for the middle term. For let A be science that it is a certain being; B, a certain being; and C, good. A, therefore, is truly predicated of B; for there is science of a certain being that it is a certain being. But B also is predicated of C because C is a certain being. Hence A will be predicated of C. There will, therefore, be science of good that it is good. For the expression a certain being, is the sign of peculiar or proper essence. But if being is posited as the middle term, and being simply is added to the extreme, and not a certain being, there will not be a syllogism, that there is science of good that it is good, but that it is being. For instance, let A be science that it is being; B, being; and C, good.

Of being there is science that it is being:

Good is being: Therefore,

Of good there is science that it is being.

It is evident, therefore, that in those syllogisms which conclude from a part, the terms must be thus assumed.

Chapter 39

It is also necessary to assume things which are capable of effecting the same thing, viz. nouns for nouns, and sentences for sentences, and always to assume a noun for a sentence; for thus the exposition of the terms will be easier. For instance, if it is of no consequence, whether it is said that which may be apprehended is not the genus of that which may be opined, or that which may be opined, is not anything which may be apprehended; for that which is signified is the same in each; in this case, instead of the before-mentioned sentence, that which may be apprehended, and that which may be opined, must be posited as terms.

Chapter 40

Since, however, it is not the same thing, for pleasure to be good, and for pleasure to be the good; the terms must not be similarly posited. But if, indeed, there is a syllogism that pleasure is the good, the good must be posited as a term; and if that pleasure is good, good must be posited as a term.  The same method must also be adopted in other things.

Chapter 41

It is not, however, the same thing, neither in reality nor in words to assert that with which B is present, with every individual of this A is present; and to say that with every individual of that with which B is present, A also is present.  For nothing hinders but that B may be present with C, yet not with every C.  For instance, let B be something beautiful; and C, something white. If, therefore, something beautiful is present with something white, it is true to say that beauty is present with that which is white, yet not perhaps with every thing white. If, therefore, A is present with B, but not with every thing of which B is predicated; neither if B is present with every C, nor if it is alone present with a certain C, it is not only not necessary that A should be present with every C, but that it should not, indeed, be present with a certain C. But if with that of which B is truly predicated, with every individual of this, A is present, it will happen that A will be predicated of every individual of that, of every individual of which B is predicated.  If, however, A is predicated of that, of every individual of which B is predicated, nothing will hinder B from being present with C, with not every, or with no individual of which A is present. In three terms, therefore, it is evident that the assertion, that of which B is predicated, A also is predicated of every individual of this, signifies that of those things of which B is predicated, of all these, A also is predicated.  And if B is predicated of every individual, A also will thus be predicated. But if it is not predicated of every individual, it is not necessary that A should be predicated of every individual. It is not requisite, however, to think, that a certain absurdity will happen from the exposition of the terms. For we do not in proving employ the assertion that this is a particular definite thing, but we adduce it, just as a geometrician says that this line is a foot in length, is a right line, and is without breadth, though it is not so. The geometrician, however, does not so use these, as if he syllogized from these. For, in short, unless there is that which is as a whole to a part, and something else which is to this, as a part to a whole, he who demonstrates, demonstrates from nothing of this kind; for neither is a syllogism produced from these. But we use exposition, in the same manner as we use sense, when we speak to a learner. For we do not use it, as if it were not possible to demonstrate without these, as we use propositions from which a syllogism is composed.

Chapter 42

Nor ought we to be ignorant that in the same syllogism, not all the conclusions are produced through one figure, but through different figures. It is evident, therefore, that analyzations also should thus be made. Since, however, not every problem is proved in every figure, but certain problems are proved in each; it is evident from the conclusion, in what figure the investigation is to be made.

Chapter 43

With respect, however, to the arguments urged against definitions, by which one certain thing posited in the definition is reprehended, that term must be posited which is reprehended, and not the whole definition; for it will happen that we shall be less disturbed on account of prolixity.  Thus if it is to be shown that water is potable, and humid, potable and water must be posited as terms.

Chapter 44

Farther still, we must not endeavour to reduce syllogisms which are from hypothesis. For they cannot be reduced from the things which are posited; because they do not prove through syllogism, but all of them being assented to demonstrate through compact. Thus, if any one supposing that unless there is one certain power of contraries, neither will there be one science of them, afterwards should dialectically show, that there is not one power of contraries, as, for instance, of the salubrious and the insalubrious; for the salubrious and the insalubrious subsist at one and the same time; in this case it will be demonstrated, that there is not one power of all contraries, but it is not demonstrated that there is not one science of contraries; though it is necessary to acknowledge that there is, yet not from syllogism but from hypothesis. This syllogism, therefore, cannot be reduced. But that syllogism in which it is proved that there is not one power of contraries may be reduced; for this perhaps is a syllogism, but that is hypothesis. The like also takes place in syllogisms which conclude through the impossible; for neither is it possible to analyze these; but a deduction to the impossible may be analyzed, for it is demonstrated by syllogism. But the other cannot be analyzed; for it is concluded from hypothesis. They differ, however, from the before-mentioned syllogisms from hypothesis, because in them, indeed, it is necessary that something should have been previously acknowledged, in order that afterwards there may be a consent; as if it should be shown that if there is one power of contraries, there is also the same science of them; but here what was before not acknowledged, is after the demonstration admitted, because the falsity is evident; as if admitting that the diameter of a square is commensurable with the side, odd things should be equal to such as are even. Many other things also are concluded from hypothesis, which it is necessary to consider and clearly explain. What, therefore, the differences are of these, and in how many ways syllogisms from hypothesis are produced, we shall afterwards show. Let only thus much be now manifest for us, that such like syllogisms cannot be resolved into figures; and from what cause we have shown.

Chapter 45

Such problems, however, as are proved in many figures, if they are proved in one syllogism, may be referred to another. Thus a privative syllogism in the first figure, may be referred to the second figure; and that syllogism which is in the middle may be referred to the first figure.  Not all, however, but some only can be thus analyzed. But this will be evident in what follows. For if A is present with no B, but B is present with every C, A will be present with no C. Thus, therefore, the first figure is produced. But if a privative assertion is converted, there will be the middle figure. For B will be present with no A, and with every C. The like will also take place if the syllogism is not universal but partial. As if A is present with no B, but B is present with a certain C; for the privative proposition being converted, there will be the middle figure. Of the syllogisms, however, which are in the middle figure, the universal, indeed, are referred to the first figure; but of the partial one alone is referred. For let A be present with no B, but with every C. The privative assertion, therefore, being converted, there will be the first figure. For B will be present with no A, but A will be present with every C. But if affirmation is joined to B, and privation to C, C must be posited as the first term. For this is present with no A, and A is present with every B. Hence C will be present with no B. Neither, therefore, will B be present with any C. For a privative assertion may be converted. But if the syllogism is partial, when privation is joined to the greater extreme, the syllogism may be resolved into the first figure; as if A is present with no B, and with a certain C. For the privative assertion being converted, there will be the first figure. For B will be present with no A, and A will be present with a certain C. When, however, affirmation is joined to the greater extreme the syllogism cannot be resolved; as, if A is present with every B, but not with every C. For the proposition A B does not admit conversion; nor when a conversion is made will there be a syllogism.  Again, not all the syllogisms which are in the third, can be resolved into the first figure; but all those which are in the first, may be resolved into the third figure. For let A be present with every B, and B be present with a certain C. Since, therefore, a partial categoric assertion may be converted, C also will be present with a certain B. But A was present with every B; so that the third figure will be produced. The like will also take place if the syllogism is privative; for a categoric proposition may be converted in part. Hence A will be present with no B, but will be present with a certain C. But of the syllogisms which are in the last figure (i.e. the third) one only is not resolved into the first, when the privative assertion is not posited universal; all the rest are resolved. For let A be predicated of every C, and also B. C, therefore, may be converted partially to each extreme. Hence it will be present with a certain B; so that there will be the first figure, if A, indeed, is present with every C, but C is present with a certain B.  And if A is present with every C, but B is present with a certain C, there is the same reasoning; for B is reciprocated with C. But if B is present with every C, and A is present with a certain C, B must be posited as the first term. For B is present with every C, and C is present with a certain A; so that B is present with a certain A. But since that which is in a part may be converted, A also will be present with a certain B. And if the syllogism is privative, when the terms are universal, a similar assumption must be made. For let B be present with every C, but A with no C. Hence C will be present with a certain B. But A is present with no C; so that the middle will be C. The like will also take place if the privative assertion is universal, and the categoric partial. For A is present with no C, but C is present with a certain B. If, however, the privative proposition is assumed in part, there will not be an analysis; as if B is present with every C, but A is not present with a certain C; for the proposition B C being converted, both propositions will be according to a part. But it is evident, that in order for these figures to be analyzed into each other, the proposition which contains the less extreme, must be converted in each figure; for this being transposed, a transition will be effected. Of the syllogisms, however, which are in the middle figure, one is resolved, and another is not resolved into the third figure. For when the universal proposition is privative, an analysis is effected. For if A is present, indeed, with no B, but is present with a certain C, both extremes similarly reciprocate with A. Hence B is present with no A, but C is present with a certain A. The middle, therefore, is A. But when A is present with every B, and is not present with a certain C, an analysis will not be produced. For neither of the propositions from the conversion will be universal. Tlie syllogisms also of the third may be resolved into the middle figure, when the privative assertion is universal. As if A is present with no C, but B is present with some, or with every C; for C will be present with no A, but will be present with a certain B. But if the privative assertion is partial, there will not be an analysis; for a partial negative does not admit of conversion. It is evident, therefore, that the same syllogisms are not analyzed in these figures, which neither are analyzed into the first figure; and that when syllogisms are reduced to the first figure, these alone are confirmed through a deduction to the impossible. In what manner, therefore, it is necessary to reduce syllogisms, and that figures may be resolved into each otlier, is evident from what has been said.

Chapter 46

It makes some dificrcnce, however, in constructing or subverting a problem, to be of opinion that these expressions not to be this particular thing, and to be not this particular thing, signify the same or a different thing; as, for instance, not to be white, and to be not white. For they do not signify the same thing; nor of the expression to be white, is this the negation, to be not white; but, not to be white. But the reason of this is as follows: The expression, he is able to walk, subsists similarly with the expression, he is able not to walk; the expression, it is white, with the expression, it is not white; and he knows good, with the expression, he knows that which is not good. For this expression, he knows good, and the expression, he has a knowledge of good, do not at all differ from each other; nor is there any difference between these expressions, he is able to walk, and he has the power of walking. Hence the opposites also, he is not able to walk, and he has not the power of walking, do not differ from each other. If, therefore, the expression, he has not the power of walking, signfies the same thing as the expression, he has the power of not walking; these will be at one and the same time present with the same thing.  For the same person is able to walk, and not to walk; and has a knowledge of good, and of that which is not good; but affirmation and negation being opposites, are not at one and the same time present with the same thing.  As, therefore, it is not the same thing, not to know good, and to know that which is not good; neither is it the same thing, to be not good, and not to be good.  For of things analogous, if the one is different, the other also is different.  Nor is it the same thing, to be not equal, and not to be equal.  For to the one, i.e., to that which is not equal, something is subjected, viz., the being not equal, and this is the unequal; but to the other, nothing is subjected.  Hence, not every thing is equal or unequal; but every thing is equal, or not equal.  Farther still, this assertion, it is not white wood, and the assertion, not is white wood, do not subsist together, or at one and the same time.  For if it is wood not white, it will be wood; but that which is not white wood, is not necessarily wood.  Hence it is evident, that of the expression, it is good, the negation is not, it is not good.  If, therefore, of every one thing, either affirmation or negation is true; if there is not negation, it is evident, that there will in a certain respect be affirmation. But of every affirmation there is negation; and hence of this affirmation it is not good the negation is, it is not not good. They have this order, however, with respect to each other: Let to be good be A; not to be good, B; to be not good C, under B; not to be not good D, under A. With every individual, therefore, either A or B will be present, and each with nothing which is the same. And with whatever C is present, it is also necessary that B should be present. For if it is true to say that a thing is not white, it is also true to say that not it is white. For it is impossible that at one and the same time a thing should be white and not white; or that it should be wood not white, and be white wood. Hence, unless affirmation is present, negation will be present. But C is not always consequent to B. For that, in short, which is not wood, will not be white wood. On the contrary, therefore, with whatever A is present, D also is present; for either C or D is present. Since, however, it is not possible that to be not white, and to be white, should subsist together at one and the same time, D will be present. For of that which is white, it is true to say, that it is not not white. But A is not predicated of every D; for of that, in short, which is not wood, it is not true to predicate A, viz. to assert that it is white wood. Hence D will be true; and A will not be true, viz. that it is white wood. It is also evident that A is present with nothing which is the same, though B and D may be present with something which is the same. Privations also subsist similarly to this position with respect to attributions. For let equal be A; not equal, B; unequal, C; not unequal, D.  In many things also with some of which the same thing is present, and with others not, the negation may be similarly true, that not all things are white, or that not each thing is white; but that each thing is not white, or that all things are not white, is false. In like manner also, of this affirmation, every animal is white, the negation is not, every  animal is not white; for both are false; but this, not every animal is white. Since, however, it is evident, that the assertions, is not white, and not is white, have different significations, and that the one is affirmation, but the other negation; it is evident, it is manifest that there is not the same mode of demonstrating each. For instance, there is not the same mode of demonstrating the following assertions: Whatever is an animal is not white, or it happens not to be white; and that it is true to say it is not white; for this is to be not white. But of the assertion, it is true to say it is white, or not white, there is the same mode of demonstrating. For both are constructively demonstrated through the first figure since the word true is similarly arranged with the verb is. For of the assertion, it is true to say it is white, the negation is not, it is true to say it is not white, but, it is not true to say it is white. But if it is true to say that whatever is a man is a musician, or is not a musician; it must be assumed that whatever is an animal, is a musician, or is not a musician, and it will be demonstrated.  But that whatever is a man is not a musician, will be demonstrated by refuting, according to the before-mentioned three modes. In short, when A and B so subsist, that they cannot be present at the same time with the same thing, but from necessity one of them is present with every individual; and again, C and D after a similar manner; but A is consequent to C, and does not reciprocate; then also D will be consequent to B, and will not reciprocate. And A, indeed, and D, may be present with the same thing, but B and C cannot. In the first place, therefore, it hence appears that D is consequent to B. For since one of C D is necessarily present with every individual, but with that with which B is present, C cannot be present, because it co-introduces with itself A, but A and B cannot be present with the same thing; it is evident, that D is a consequent. Again, since C does not reciprocate with A, but C or D is present with every individual, it will happen that A and D will be present with the same thing. But B and C cannot be present with the same thing, because A is consequent to C; for something impossible would happen. It is evident, therefore, that neither does B reciprocate with D, because it would happen that A is present together with D.  It sometimes also happens that we are deceived in such an arrangement of the terms as this, because opposites are not rightly assumed, one of which must necessarily be present with every individual. As if A and B should not happen to be present at the same time with the same thing, but it is necessary that with that with which one is not present, the other should be present; and again, C and D subsist similarly; but A is consequent to every C; for it will happen that B is necessarily present with that with which D is present, which is false. For let the negation of A B be assumed, and let it be F, and again, the negation of C D, and let it be H. It is necessary, therefore, that either A or F should be present with every individual; for either affirmation or negation must be present. And again, either C or H must be present; for they are affirmation and negation. And it was supposed that A is present with every thing with which C is present; so that with whatever F is present, H also will be present. Again, because of F B, one is present with every individual, and in a similar manner one of H D, but H is consequent to F, B also will be consequent to D; for this we know. If, therefore, A is consequent to C, B also will be consequent to D. But this is false; for the consecution was vice versa in things which thus subsist. For it is not perhaps necessary that either A or F should be present with every individual; nor either F or B; for F is not the negation of A. For of good, the negation is, not good. These assertions, however, it is not good, and it is neither good, nor evil, are not the same. The like also takes place in C D; for the negations which are assumed are two.