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Aristotle, Prior Analytics, Book II

© William C. Michael, 2022.

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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

We have now, therefore, explained, in how many figures, through what kind, and what number of propositions, and when and how a syllogism is produced. We have likewise shown to what kind of things he should direct his attention, who subverts or constructs a syllogism, and in what manner it is necessary to investigate about a proposed subject, according to every method; and farther still, in what way we should assume the principles of every question. But since of syllogisms some are universal, and others partial; all the universal, indeed, always conclude a greater number of things. And of those that are partial, the categoric conclude manythings, but the negative collect one conclusion only. For other propositions are converted; but a partial privative proposition is not converted. But the conclusion is a sentence signifying something of something. Hence other syllogisms conclude a greater number of things. Thus, if it is shown that A is present with every, or with a certain B it is also necessary that B should be present with a certain A. And if it is shown that A is present with no B, B also will be present with no A. But this conclusion is different from the former.  If, however, A is not present with a certain B, it is not necessary that B also should not be present with a certain A; for it may be present with every A. This, therefore, is the common cause of all syllogisms, as well universal as partial. It is possible, however, to speak otherwise of universals. For of all those things which are under the middle, or under the conclusion, there will be the same syllogism, if some are posited in the middle, but others in the conclusion. Thus if A B is a conclusion through C, it is necessary that A should be predicated of all those things, which are under B, or under C. For if D is in the whole of B, but B is in the whole of A, D also will be in the whole of A. Again, if E is in the whole of C, and C is in A; E also will be in the whole of A. The like also will take place if the syllogism is privative. But in the second figure, it will be only possible to form a syllogism of that which is under the conclusion. As if A is present with no B, but is present with every C, the conclusion will be that B is present with no C. If, therefore, D is under C, it is evident that B is not present with it. But that it is not present with those things which are under A, is not evident through syllogism; though it will not be present with E, if it is under A. That B, however, is present with no C, was demonstrated through syllogism; but that it is not present with A, was assumed without demonstration. Hence, it will not happen through syllogism, that B is not present with E. In partial syllogisms, however, of those things which are under the conclusion there will not be any necessity; for a syllogism is not produced, when this proposition is assumed in part; but there will be of all those which are under the middle, yet not through that syllogism: as, for instance, if A is present sent with every B, but B is present with a certain C. For there will not be a syllogism of that which is posited under C; but there will be of that which is under B; yet not through the antecedent syllogism. The like also takes place in other figures; for there will not be a conclusion of that which is under the conclusion; but there will be of the other, yet not through that syllogism; as well as in universal syllogisms from an undemonstrated proposition, those things which are under the middle are demonstrated. Hence, either there will not be a conclusion there, or there will also be a conclusion in these.

Chapter 2

It is therefore possible that the propositions may be true, through which a syllogism is produced; it is also possible that they may be false; and it is possible that the one may be true, but the other false.  The conclusion, however, is necessarily true or false. From true propositions, therefore, the false cannot be concluded; but from false propositions that which is true may be inferred, except that not why, but merely that a thing is true may be collected. For there is not a syllogism of the why from false propositions; the cause of which will be unfolded in what follows. In the first place, therefore, that it is not possible the false can be collected from true propositions, is from hence manifest. For if when A is, it is necessary that B should exist; when B is not, it is necessary that A should not exist. Hence, if A is true, it is also necessary that B should be true; or it would happen that the same thing, at the same time is, and is not; which is impossible. Nor must it be conceived that because one term A is posited, it will happen that one certain thing existing, something will happen from necessity; since this is not possible. For that which happens from necessity is the conclusion; but the fewest things through which this is produced, are three terms, but two intervals and propositions. If, therefore, it is true that with whatever B is present, A also is present; and that with whatever C is present, B also is present; it is necessary that with whatever C is present, A also is present; nor can this be false. For at the same time the same thing would exist and not exist. A, therefore, is posited as one thing; two propositions being co-assumed. The like also takes place in privative propositions; for it is not possible from such as are true to show the false. But from false propositions that which is true may be collected, when both the propositions are false, and when one only is false; and this not when either indifferently, but when the second is false, if we assume the whole to be false. If, however, not the whole is assumed to be false, that which is true may be collected, which ever proposition is assumed to be false. For let A be present with the whole of C, but with no B, nor let B be present with C. For this may happen to be the case. Thus, animal is present with no stone, neither is a stone present with any man.  If, therefore, it is assumed that A is present with every B, and B with every C; A will be present with every C. Hence, from both the propositions being false, the conclusion will be true; for every man is an animal.

Every stone is an animal:

Every man is a stone: Therefore,

Every man is an animal.

In a similar manner also a privative conclusion may be formed. For let neither A nor B be present with any C, but let A be present with every B; as for instance, if the same terms being assumed, man should be posited as the middle term. For neither animal nor man is present with any stone, but animal is present with every man. Hence, if with that with which every is present, we assume that none is present; but assume that a thing is present with every individual of that with which it is not present; from both the propositions which are false the conclusion will be true.

No man is an animal:

Every stone is a man: Therefore,

No stone is an animal.

The like may also be shewn, if each proposition is assumed false in part. But if one proposition only is posited false; if the first indeed is wholly false, as A B, the conclusion will not be true. But if the proposition B C is wholly false, the conclusion will be true. I call, however, the proposition wholly false which is contrary to the true; as, if a thing should be assumed to be present with every individual, which is present with none, or if that which is present, with, every individual should be assumed to be present with none. For let A be present with no B, and B be present, with every C. If, therefore, we assume that the proposition B C is true, but that the whole of the proposition A B is false, and that A is present with every B; it is impossible that the conclusion should be true; for it was present with no C; since with no individual of that with which B is present, A was present; but B was present with every C.

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

Every man (C) is an animal (B): Therefore,

Every man (C) is a stone (A).

In like manner, also, the conclusion will not be true if A is present with every B, and B with every C; and the proposition B C is assumed to be true; but the proposition A B wholly false, and that A is present with no individual with which B is present. For A was present with every C; since with whatever B was present, A also was present, but B was present with every C. It is evident, therefore, that when the first proposition is assumed wholly false, whether it be affirmative or privative, but the other proposition is true, a true conclusion will not be produced. If, however, the whole is not assumed to be false, there will be a true conclusion.  For if A is present with every C, but with, a certain B, and B is present with every C; as for instance, animal with every swan, but with, a certain whiteness, and whiteness with every swan; if it is assumed that A is present with every B, and B with every C, A also will truly be present with every C; for every swan is an animal.

Everything white (B) is an animal (A):

Every swan (C) is white (B): Therefore,

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

In a similar manner also, the conclusion will be true if the proposition A B is privative. For A may be present with a certain B, but with no C, and B may be present with every C. Thus, animal may be present with something white, but with no snow; and whiteness may be present with all snow. If, therefore, it were assumed that A is present with no B, but that B is present with every C; A will be present with no C.

Nothing white (B) is an animal (A):

All snow (C) is white (B): Therefore

No snow (C) is an animal (A).

But if the proposition A B were assumed wholly true; but the proposition B C wholly false; there will be a true syllogism. For nothing hinders A from being present with every B and every C, and yet B may be present with no C; as is the case with species of the same genus, but which are not subaltern. For animal is present both with horse and man; but horse is present with no man. If, therefore, it is assumed that A is present with every B, and B with every C, the conclusion will be true, though the whole proposition B C is false.

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

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

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

The like will also take place, if the proposition A B is privative. For it will happen that A will be present neither with any B, nor with any C, and that B will be present with no C; as for instance, another genus with species which are from another genus. For animal is neither present with music, nor with medicine, nor is music present with medicine. If, therefore, it should be assumed that A is present with no B, but that B is present with every C, the conclusion will be true.

No music (B) is an animal (A):

All medicine (C) is music (B): Therefore,

No medicine (C) is an animal (A).

And if the proposition B C is not wholly but partially false, thus also the conclusion will be true. For nothing hinders A from being present with the whole of B and the whole of C, and B may be present with a certain C; as for instance, genus, with species and difference. For animal is present with every man, and with everything pedestrious; but man is present with something, and not with everything, pedestrious. If, therefore, A were assumed to be present with every B, and B with every C; A also will be present with every C ; which is true.

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

Everything pedestrious (C) is a man (B): Therefore,

Everything pedestrious (C) is an animal (A).

The like will also take place if the proposition A B is privative. For it may happen that A is neither present with any B, nor with any C,  and yet B may be present with a certain C; as genus with the species and difference which are from another genus. For animal is neither present with any prudence, nor with anything contemplative; but prudence is present with something contemplative. If, therefore, it were assumed that A is present with no B, and that B is present with every C; A will be present with no C. But this is true.

No prudence (B) is an animal (A):

All contemplative knowledge (C) is prudence (B): Therefore,

No contemplative knowledge (C) is an animal (A).

In partial syllogisms, however, when the whole of the first proposition is false, but the other is true, the conclusion may be true; likewise, when the proposition A B is partly false, but the proposition B C is wholly true; and when the proposition A B is true, but the partial proposition is false; and when both are false. For nothing hinders but that A may be present with no B, but may be present with a certain C, and also that B may be present with a certain C. Thus animal is present with no snow, but is present with something white, and snow also is present with something white. If, therefore, snow is posited as the middle term, and animal as the first term; and if A is assumed to be present with the whole of B, and B with a certain C; the proposition A B will be wholly false; but the proposition B C will be true; and the conclusion will be true.

All snow (B) is an animal (A):

Something white (C) is snow (B): Therefore,

Something white (C) is an animal (A).

The like will also take place, if the proposition A. B is privative.  For A may be present with the whole of B, and not be present with a certain C; but B may be present with a certain C. Thus, animal is present with every man, but is not consequent to something white; but man is present with something white. Hence, if man is posited as the middle term, and A is assumed to be present with no B, but B is assumed to be present with a certain C, the conclusion will be true, though the whole proposition A B is false.

No man (B) is an animal (A):

Something white (C) is a man (B): Therefore,

Something white (C) is not an animal (A).

And if the proposition A B is partly false, when the proposition B C is true, the conclusion will be true. For nothing hinders but that A may be present with B, and with a certain C, and that B also may be present with a certain C. Thus, animal may be present with something beautiful, and with something great, and beauty also may be present with something great. If, therefore, it is assumed that A is present with every B, and B with a certain C; the proposition A B indeed, will be partly false; but the proposition B C will be true; and the conclusion will be true.

Everything beautiful (B) is an animal (A).

Something great (C) is beautiful (B): Therefore,

Something great (C) is an animal (A):

The like will also take place if the proposition A B is privative. For there will be the same terms, and they will be posited after the same manner, in order to the demonstration.

Nothing beautiful (B) is an animal (A):

Something great (C) is beautiful (B): Therefore,

Something great (C) is not an animal (A).

Again, if the proposition A B, indeed, is true, but the proposition B C false; the conclusion will be true. For nothing hinders but that A may be present with the whole of B, and with a certain C, and that B may be present with no C. Thus, animal is present with every swan, and with something black, but a swan is present with nothing black. Hence, if it is assumed that A is present with every B, and B with a certain C; the conclusion will be true, though the proposition B C is false.

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

Something black (C) is a swan (B): Therefore,

Something black (C) is an animal (A).

The like will also take place, if the proposition A B is assumed to be privative. For A may be present with no B, and may not be present with a certain C, but B may be present with no C. Thus genus may be present with species which is from another genus, and with that which is an accident to its own species. For animal, indeed, is present with no number, and is present with something white, but number is present with nothing white. If, therefore, number is posited as the middle term and it is assumed that A is present with no B, but that B is present with a certain C; A will not be present with a certain C, which is true: and the proposition A B is true, but the proposition B C false.

No number (B) is an animal (A):

Something white (C) is number (B): Therefore,

Something white (C) is not an animal (A).

And if the proposition A B is partly false, and if the proposition B C is also false; the conclusion will be true. For nothing hinders but that A may be present with a certain B, and also with a certain C, but B with no C; as, if B should be contrary to C, but both should happen to the same genus. For animal is present with a certain something white, and with a certain something black, but white is present with nothing black. If, therefore, it is assumed that A is present with every B, and B with a certain C, the conclusion will be true.

Everything white (B) is an animal (A):

Something black (C) is white (B): Therefore,

Something black (C) is an animal (A).

In a similar manner also, if the proposition A B is assumed to be privative. For the same terms may be assumed, and they may be posited in the same way, in order to the demonstration.

Nothing white (B) is an animal (A):

Something black (C) is white (B): Therefore,

Something black (C) is not an animal (A).

If also both the propositions are false in the whole, the conclusion will be true. For A may be present with no B, but may be present with a certain C, and B may be present with no C. Thus genus may be present with the species which is from another genus, and with that which happens to its own species. For animal is present with no number, but is present with something white, and number is present with nothing white. If, therefore, it is assumed that A is present with every B, and that B is present with a certain C; the conclusion, indeed, will be true, but both the propositions will be false.

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

Something white (C) is number (B): Therefore,

Something white (C) is an animal (A).

The like also will take place if the proposition A B is privative. For nothing hinders but that A may be present with the whole of B, but may not be present with a certain C, and that B may be present with no C. Thus animal is present with every swan, but is not present with something which is black; and swan is present with nothing black.  Hence, if it is assumed that A is present with no B, but that B is present with a certain C; A will not be present with a certain C. The conclusion, therefore, will be true, but the propositions false.

No swan (B) is an animal (A):

Something black (C) is a swan (B): Therefore,

Something black (C) is not an animal (A).

Chapter 3

In the middle figure also, it is perfectly possible to deduce a true conclusion from false propositions; whether both the propositions are assumed wholly false; or one of them partly false; or one is true, but the other wholly false, whichever of them may be posited false; or whether both are partly false; or one is simply true, but the other partly false; or one is wholly false, but the other partly true, and that as well in universal as in partial syllogisms. For if A is present with no B, but with every C; as, animal is present with no stone, and is present with every horse; if the propositions are posited in a contrary way, and it is assumed that A is present with every B, but with no C; from propositions which are wholly false, the conclusion will be true.

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

No horse (C) is an animal (B): Therefore,

No horse (C) is a stone (A).

The like will also take place, if A is present, indeed, with every B, but with no C; for there will be the same syllogism.

No horse (B) is an animal (A):

Every stone (C) is an animal (A): Therefore,

No stone (C) is a horse (B).

Again, if the one is wholly false, but the other wholly true. For nothing hinders but that A may be present with every B and with every C, and that B may be present with no C; as genus with species which are not subaltern. For animal is present with every horse and every man; and no man is a horse. If, therefore, it is assumed, that animal is present with every individual of the one, but with no individual of the other; the one proposition, indeed, will be wholly false, but the other wholly true; and the conclusion will be true, to whichever proposition negation is added.

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

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

            No man (C) is a horse (B).

No horse (B) is an animal (A):

Every man (C) is an animal (A): Therefore,

No man (C) is a horse (B).

Likewise, if the one is partly false; but the other wholly true. For if is possible that A may be present with a certain B, and with every C, and that B may be present with no C. Thus animal is present with something white, but with every crow, and whiteness is present with no crow. If, therefore, it is assumed that A is present with no B, but is present with the whole of C; the proposition A B, indeed, will be partly false; but the proposition A C will be wholly true: and the conclusion will be true.

Nothing white (B) is an animal (A):

Every crow (C) is an animal (A): Therefore,

No crow (C) is white (B).

And also when the privative is transposed; for the demonstration will be through the same terms.

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

Nothing white (C) is an animal (A): Therefore,

Nothing white (C) is a crow (B).

Likewise, if the affirmative proposition is partly false, but the privative wholly true. For nothing hinders but that A may be present with a certain B, but may not be present with the whole of C, and that B may present with no C. Thus animal is present with something white, but with no pitch, and whiteness is present with no pitch. Hence, if it is assumed that A is present with the whole of B, but with no C; the proposition A B will be partly false; but the proposition A C will be wholly true ; and the conclusion will be true.

Everything white (B) is an animal (A):

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

No pitch (C) is white (B).

And if both the propositions arc partly false, the conclusion will be true. For A may be present with a certain B, and also with a certain C, but B may be present with no C. Thus animal may be present with something white, and with something black; but whiteness is present with nothing black. If, therefore, it is assumed that A is present with every B, but with no C, both the propositions will be partly false, but the conclusion will be true.

Everything white (B) is an animal (A):

Nothing black (C) is an animal (A): Therefore,

Nothing black (C) is white (B).

In like manner there will be a demonstration through the same terms, if the privative proposition is transposed.

Nothing white (B) is an animal (A):

Everything black (C) is an animal (A): Therefore,

Nothing black (C) is white (B).

It is also evident, that this may take place in partial syllogisms. For nothing hinders but that A may be present with every B, and with a certain C, and that B may not be present with a certain C. Thus animal is present, indeed, with every man, and with something white, but man may not be present with something white. If, therefore, it is posited that A is present, indeed, with no B, but is present with a certain C; the universal proposition will be wholly false; but the partial proposition will be true; and the conclusion will be true.

No man (B) is an animal (A):

Something white (C) is an animal (A): Therefore,

Something white (C) is not a man (B).

The like will also take place if the proposition A B is assumed affirmative. For A may be present with no B, and may not be present with a certain C. Thus animal is present with nothing inanimate, and is not present with something white; and the inanimate also is not present with something white. If, therefore, it is posited that A is present with every B, and is not present with a certain C; the universal proposition A B will be wholly false; but the proposition A C will be true; and the conclusion will be true.

Everything inanimate (B) is an animal (A).

Something white (C) is not an animal (A): Therefore,

Something white (C) is not inanimate (B).

Likewise, if the universal proposition, is posited true, and the partial, proposition false. For nothing hinders but that A may neither be consequent to any B, nor to any C, and that B may not be present with a certain C. Thus animal is consequent to no number, and to nothing inanimate, and number is not consequent to a certain thing which is inanimate. If, therefore, it is posited that A is present with no B, and with a certain C; the conclusion will, indeed, be true; and the universal proposition will be true; but the partial proposition will be false.

No number (B) is an animal (A):

Something inanimate (C) is an animal (A): Therefore,

Something inanimate (C) is not number (B).

And in a similar manner, if the universal proposition is posited affirmative. For A may be present with the whole of B, and with the whole of C, and yet B may not be consequent to a certain C; as genus is present with the whole of species and difference. For animal is consequent to every man, and to the whole of that which is pedestrious; but man is not consequent to everything pedestrious. Hence, if it is assumed that A is present with the whole of B, and is not present with a certain C; the universal proposition, indeed, will be true, but the partial proposition will be false; and the conclusion will be true.

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

Something pedestrious (C) is not an animal (A): Therefore,

Something pedestrious (C) is not a man (B).

It is also evident, that from both propositions when false, the conclusion will be true; if it happens that A is present with the whole of B, and the whole C, but B is not consequent to a certain C. For if it is assumed that A is present with no B, but is present with a certain C; both the propositions, indeed, will be false; but the conclusion will be true. In a similar manner also, if the universal proposition is categoric, but the partial proposition privative. For A may be consequent to no B, and to every C, and B may not be present with a certain C. Thus animal is consequent to no science, but is consequent to every man; and science is not consequent to every man. If, therefore, it is assumed that A is present with the whole of B, and is not consequent to a certain C; the propositions will be false; but the conclusion will be true.

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

A certain man (C) is not an animal (A): Therefore,

            A certain man (C) is not science (B).

Chapter 4

In the last figure also a true conclusion may be deduced from false propositions, when both the propositions are wholly false; or when each is partly false; or when the one is wholly true, but the other false; or when the one is partly false, but the other wholly true; or the contrary; and in as many other ways as it is possible to change the propositions.  For nothing hinders but that neither A nor B may be present with any C, and yet B may be present with a certain C. Thus, neither man nor pedestrious is consequent to anything inanimate, and yet man is present with, something pedestrious. If, therefore, it is assumed that A and B are present with every C, the propositions, indeed, will be wholly false, but the conclusion will be true.

Everything inanimate (C) is a man (A):

Everything inanimate (C) is pedestrious (B): Therefore,

Something pedestrious (B) is a man (A).

In like manner also, if the one proposition is privative, but the other affirmative. For B may be present with no C, but A may be present with every C, and A may not be present with a certain B. Thus blackness is present with no swan, but animal is present with every swan, and animal is not present with everything black. Hence, if it is assumed that B is present with every C, but that A is present with no C, A will not be present with a certain B; and the conclusions will be true, but the propositions false.

No swan (C) is an animal (A):

Every swan (C) is black (B): Therefore,

Something black (B) is not an animal (A).

And if each proposition is partly false, the conclusion will be true. For nothing hinders but that A and B may be present with a certain C, and that A may be present with a certain B. Thus whiteness and beauty may be present with a certain animal, and whiteness may be present with something beautiful. If, therefore, it is posited that A and B, are present with every C; the propositions, indeed, will be partly false, but the conclusion will he true.

Every animal (C) is white (A):

Every animal (C) is beautiful (B): Therefore,

Something beautiful (B) is white (A).

And in a similar manner, if the proposition A C is posited privative. For nothing hinders but that A may not be present with a certain C, that B may be present with a certain C, and that A may not be present with every B. Thus whiteness is not present with a certain animal, but beauty is present with a certain animal, and whiteness is not present with everything beautiful. Hence, if it is assumed that A is present with no C, but that B is present with every C; both the propositions will be partly false, but the conclusion will be true.

No animal (C) is white (A):

No animal (C) is beautiful (B): Therefore,

Something beautiful (B) is not white (A).

The like will also take place, if the one proposition is assumed to be wholly false, but the other wholly true. For both A and B may be consequent to every C, but A may not be present with a certain C. Thus animal and whiteness are consequent to every swan, but animal is not present with everything white. These terms, therefore, being posited, if it is assumed that B is present with the whole of C, but that A is not present with the whole of C; the proposition B C will be wholly true; but the proposition A C will be wholly false; and the conclusion will he true.

No swan (C) is an animal (A):

Every swan (C) is white (B): Therefore,

Something white (B) is not an animal (A).

In a similar manner also, if B C is false, but A C true; for these terms, black, swan, inanimate, may be assumed in order to the demonstration.

No swan is black:

Every swan is inanimate: Therefore,

Something inanimate is not black.

This will likewise be the case if both the propositions are assumed affirmative. For nothing hinders but that B may be consequent to every C, but A may not be present with the whole of C, and A may be present with a certain B. Thus animal is present with every swan, but blackness is present with no swan, and blackness is present with a certain animal. Hence, if it is assumed that A and B are present with every C; the proposition B C will be wholly true, but the proposition A C will be wholly false; and the conclusion will be true.

Every swan (C) is black (A):

Every swan (C) is an animal (B): Therefore,

Some animal (B) is black (A).

The like will also take place, if the proposition A C is assumed; for the demonstration will be through the same terms.

Every swan (C) is an animal (A):

Every swan (C) is black (B): Therefore,

Something black (B) is an animal (A).

Again, this will be the case, if the one proposition is wholly true, but the other partly false. For B may be present with every C, but A may be present with a certain C, and A may also be present with a certain B. Thus biped is present with every man, but beauty is not present with every man, and beauty is present with a certain biped. If, therefore, it is assumed that A and B are present with the whole of C, the proposition B C will be wholly true; but the proposition A C will be partly false; and the conclusion will be true.

Every man (C) is beautiful (A):

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

Some biped (B) is beautiful (A).

In a similar manner also, if the proposition A C is true, and the proposition B C, is assumed partly false. For the same terms being transposed, there will be a demonstration.

Every man (C) is a biped (A):

Every man (C) is beautiful (B): Therefore,

Something beautiful (B) is a biped (A).

And if the one proposition is privative, but the other affirmative. For since it is possible that B may be present with the whole of C, but A with a certain C only, when the terms thus subsist, A will not be present with every B. If, therefore, it is assumed that B is present with the whole of C, but A with no C, the privative proposition will be partly false, but the other will be wholly true; and the conclusion will be true. Again, since it has been shown, that A being present with no C, but B being present with a certain C, it is possible that A may not be present with a certain B; it is evident, that when the proposition A C is wholly true, and the proposition B C is partly false, it is possible that the conclusion may be true. For if it is assumed that A is present with no C, but that B is present with every C; the proposition A C will be wholly true; but the proposition B C partly false. But it is evident that in partial syllogisms also, there will entirely be a true conclusion through false propositions. For the same terms are to be assumed, which were assumed when the propositions were universal; viz. in categorical propositions categorical terms, but in privative propositions privative terms. For it is of no consequence, whether when a thing is present with no individual, it is assumed to be present with every individual; or whether, when it is present with a certain individual, it is universally assumed to be present with, or not present with, so far as pertains to the exposition of the terms. The like also takes place in privative propositions. It appears, therefore, that when the conclusion is false, it is necessary that those things from which the reasoning consists, should either all, or some of them be false. But where the conclusion is true, it is not necessary either that a certain thing, or all things should be true; but it is possible, that when nothing is true in a syllogism, the conclusion may be similarly true, and yet not from necessity. The cause, however, of this is, that when two things so subsist with reference to each other, that when the one is, the other also necessarily is; if this is not, neither will the other be; but if it exists it is not necessary that the other should exist. But the same thing existing, and not existing, it is impossible that the same thing should be from necessity; as if A is white, that B is necessarily great; and if A is not white, that B is necessarily great. For when, this thing being white, as A, it is necessary that this thing should be great, as B; but B being great, it is necessary that C should not be white; it is necessary if A is white, that C should not be white. And when two things being proposed, if the one is, it is necessary that the other should be; this not existing, it is necessary that the first should not exist. Hence B, not being great, it is not possible that A can be white. But if when A is not white, it is necessary that B should be great; it will necessarily happen, that if B is not great, B itself is great. This, however, is impossible. For if B is not great, A will not be white from necessity. If, therefore, A not being white, B will be great, it will happen, as through three terms, that if B is not great, it is great.

If A is not white, B is great:

If B is not great, A is not white: Therefore,

If B is not great, it is great – which is impossible.

Chapter 5

To demonstrate, however, things in a circle, and from each other, is nothing else than through the conclusion, and receiving one proposition inverse in predication, to conclude the other proposition, which was assumed in the other syllogism. As if it were requisite to demonstrate that A is present with every C; but it is proved through B: again, if it should demonstrate that A is present with B, assuming that A is present with C, that C is present with B, and A with B. But first, on the contrary, it is assumed that B is present with C. Or if it were requisite to demonstrate that B is present with C, and it should be assumed that A is present with C, which was the conclusion; and that B is present with A. But it was first assumed, on the contrary, that A is present with B. It is not, however, otherwise possible to form a demonstration of them from each other. For whether another middle is assumed, there will not be a demonstration in a circle; for nothing of the same will be assumed; or whether something of these is assumed, it is necessary that one of them alone should be assumed. For if both, there will be the same conclusion, though it is necessary that there should be a different conclusion. In those terms, therefore, which are not converted from one undemonstrated proposition, a syllogism is produced. For it is not possible to demonstrate through these terms, that the third is present with the middle, or the middle with the first. But in those which reciprocate, it is possible to demonstrate all of them through each other; as if A, and B, and C, are converted into each other. For A C will be demonstrated through the middle B; and again, A B through the conclusion, and the proposition B C converted. In like manners also, BC is demonstrated through the conclusion, and the proposition A B inverse. But it is necessary to demonstrate the proposition C B, and the proposition B A; for we alone use these undemonstrated. If, therefore, it were assumed that B is present with every C, and C with every A, there will be a syllogism of B with respect to A. Again, if it were assumed that C is present with every A, and A with every B, it is necessary that C should be present with every B. In both these syllogisms, therefore, the proposition A C is assumed undemonstrated; for the others were demonstrated. Hence, if we should demonstrate this, all of them will be demonstrated through each other. If, therefore, it should be assumed, that C is present with every B, and B with every A, both propositions will be assumed demonstrated, and it is necessary that C should be present with A. Hence it is evident, that in those propositions alone which are converted, demonstrations can be formed in a circle, and through each other; but in others, in the manner which we have before shown. But it also happens in these, that we use what has been demonstrated, in order to frame a demonstration. For C is demonstrated of B, and B of A, assuming that C is predicated of A; but C is demonstrated of A through these propositions. Hence we use the conclusion, in order to frame the demonstration. But in privative syllogisms, a demonstration through each other is effected as follows: Let B be present with every C, but let A be present with no B: the conclusion is, that A is present with no C. If, therefore, it is again necessary to conclude, that A is present with no B, which was assumed before; A, indeed, will be present with no C, but C will be present with every B. For thus the proposition becomes inverse. But if it is necessary to conclude that B is present with C, the proposition A B is no longer to be similarly converted. For it is the same proposition that B is present with no A, and that A is present with no B. It must be assumed, however, that B is present with every individual of that, with no individual of which A is present. Let A be present with no C, which was the conclusion. It is necessary, therefore, that B should be present with every C. Hence, since there are three assertions each becomes a conclusion. And to demonstrate in a circle is this, assuming the conclusion, and one proposition inverse, syllogistically to collect the other. But in partial syllogisms, it is not possible to demonstrate the universal proposition through others, but it is possible thus to demonstrate the partial proposition. That it is not possible, therefore, to demonstrate the universal proposition is evident. For the universal is demonstrated through universal; but the conclusion is not universal; and it is necessary to demonstrate from the conclusion, and from the other proposition. Farther still, neither, in short, is a syllogism produced, when the proposition is converted; for both the propositions are effected in part. But it is possible to demonstrate a partial proposition. For let A be demonstrated of a certain C through B, If, therefore, it should be assumed that B is present with every A, and the conclusion should remain, B will be present with a certain C. For the first figure will be produced, and A will be the middle.

Every B is A:

Some C is B: Therefore,

Some C is A.

If, however, the syllogism is privative, it is not possible to demonstrate the universal proposition, for the reason which was before adduced. But a partial proposition cannot be demonstrated, if A B is similarly converted, as in universal propositions. It is possible, however, to demonstrate it through assumption; as, for instance, that A is not present with a certain thing, and that B is. But if the terms subsist otherwise, a syllogism will not be produced, because the partial proposition is negative.

Chapter 6

In the second figure, however, the affirmative proposition cannot be demonstrated after this manner, but the privative may. The affirmative, therefore, is not demonstrated, because not both the propositions are affirmative. For the conclusion is privative, but the affirmative is demonstrated from both the propositions being affirmative. But the privative proposition is thus demonstrated. Let A be present with every B, and, with no C. The conclusion is, that B is present with no C. If, therefore, it is assumed that B is present with every A, but with no C, it is necessary that A should be present with no C. For the second figure will be produced. The middle is B. But if the proposition A B were assumed privative, but the other proposition categoric; there will be the first figure. For C is present with every A, but B with no C. Hence neither is B present with any A. Neither, therefore, is A present with any B. The middle is C. Through the conclusion, therefore, and one proposition, a syllogism is not produced; but when the other proposition is assumed there will be a syllogism. If, therefore, the syllogism is not universal, the proposition which is in the whole, is not demonstrated, through that cause which we have mentioned before. But the partial proposition is demonstrated, when the universal is categoric. For let A be present with every B, but not with every C; the conclusion is, that B is not present with a certain C. If, therefore, it were assumed that B is present with every A, but not with every C; A will not be present with a certain C. The middle is B. But if the universal proposition is privative, the proposition A C will not be demonstrated, the proposition A C being converted. For it will happen that either both propositions, or that one proposition will be negative. Hence there will not be a syllogism. In a similar manner also, there will be a demonstration, if it is assumed that with that with which B is partly not present, A is partly present.

Chapter 7

In the third figure, however, when both the propositions are assumed universally, a mutual and reciprocal demonstration cannot take place. For the universal is demonstrated through universals; but the conclusion in this figure, is always partial. Hence it is evident, that, in short, a universal proposition cannot be demonstrated through this figure. But if the one proposition is universal, and the other partial, a reciprocal demonstration will at one time be possible, and at another not. When, therefore, both the propositions arc assumed categoric, and universal is joined to the less extreme, it will be possible; but when to the other extreme it will not be possible. For let A be present with every C, but let B be present with a certain C; the conclusion will be A B. If, therefore, it should be assumed that C is present with every A, the universal proposition being converted; and that A is present with a certain B, which was the conclusion; C, indeed, is demonstrated to be present with a certain B; but B is not demonstrated to be present with a certain C. It is necessary, however, if C is present with a certain B, that B also should be present with a certain C. But it is not the same thing, for this thing to be present with that, and that with this; but it must be assumed that if this is partly present with that, that also is partly present with this. But this being assumed, a syllogism will no longer be produced from the conclusion, and the other proposition. If, however, B is present, indeed, with every C, but A with a certain C, it will be possible to demonstrate the proposition A C, when it is assumed that C is present with every B, but A with a certain B. For if C is present with every B, but A with a certain B, it is necessary that A should be present with a certain C. The middle is B. And when the one proposition is categoric, but the other privative, and the categoric is universal, the others may be demonstrated. For let B be present with every C, but let A not be present with a certain C; the conclusion is, that A is not present with a certain B. If, therefore, it should be assumed that C is present with every B, but A was not present with every B, it is necessary that A should not be present with a certain C. The middle is B. But when the privative proposition is universal, the other proposition will not be demonstrated, unless as it was assumed in the former syllogisms, if it should be assumed, that the other is present with some individual of that, with every individual of which this is not present. As, if A, indeed, is present with no C, but B is present with a certain C, the conclusion is, that A is not present with a certain B. If, therefore, it should be assumed that C is present with some individual of that, with every individual of which A is not present, it is necessary that C should be present with a certain B. It is not, however, possible in any other way, when the universal proposition is converted, to demonstrate the other proposition; for there will by no means be a syllogism. It is evident, therefore, that in the first figure, a reciprocal demonstration is effected, through the first, and through the third figure. For when the conclusion is categoric, the reciprocal demonstration is through the first figure; but when it is privative, through the last figure. For let it be assumed that the other (i.e. the subject) is present with every individual of that with no individual of which this (i.e. the predicate) is present. But in the middle figure when the syllogism is universal, the demonstration is through it and through the first figure: and when it is partial, it is through it, and through the last figure. In the third figure, however, all the demonstrations are through the third figure. It is also evident, that in the middle and third figures, the syllogisms which are not produced through them, either are not according to a circular demonstration, or are imperfect.

Chapter 8

To convert, however, is, the conclusion being transposed, to produce a syllogism, either that the greater extreme is not present with the middle, or that this middle is not present with the last. For it is necessary, the conclusion being converted, and one proposition remaining, that the other proposition should be subverted; since if that proposition will be, the conclusion also will be. But it makes a difference whether the conclusion is converted oppositely, or contrarily. For the same syllogism is not produced, when the conclusion is converted either way. This, however, will be evident from what follows. But I say to be opposed, to every individual, and not to every individual, and to some individual, and not to some individual. And I call the being contrarily opposed, the being present with every individual, and with no individual, and the being present with a certain individual, and not with a certain individual. For let A be demonstrated of C, through the medium B. If, therefore, it were assumed that A is present with no C, but is present with every B, B will be present with no C. And if it were assumed that A is present with no C, but that B is present with every C, A will not be present with every B; but it cannot be concluded that it is, in short, present with no B; for universal is not demonstrated through the third figure. In short, it is not possible to subvert universally through conversion, the proposition which is joined to the greater extreme; for it is always subverted through the third figure. For it is necessary to assume both the propositions to the last extreme. And in a similar manner if the syllogism is privative. For let it be demonstrated through B, that A is present with no C. If, therefore, it were assumed that A is present with every C, but is present with no B; B will be present with no C. And if A and B are present with every C, A will be present with a certain B. But it was present with no B. If, however, the conclusion should be converted oppositely, other syllogisms also will be opposite, and not universal. For one proposition will be partial; so that the conclusion also will be partial. For let the syllogism be categoric, and thus be converted. Hence, if A is not present with every C, but is present with every B; B will not be present with every C. And if A is not present with every C, but B is present with every C; A will not be present with every B. The like will also take place if the syllogism is privative. For if A is present with a certain C, but with no B; B will not be present with a certain C, and will not simply be present with no C. And if A is present with a certain C, but B is present with every C, as it was assumed in the beginning; A will be present with a certain B. But in partial syllogisms, when the conclusion is oppositely converted, both the propositions arc subverted; but when it is converted contrarily, neither of them is subverted. For it no longer happens as in universals, that a subversion is effected, the conclusion failing according to conversion; but neither, in short, can a subversion be effected. For let A be demonstrated of a certain C. If, therefore, it should be assumed that A is present with no C, but that B is present with a certain C, A will not be present with a certain B. And if A is present with no C, but is present with every B; B will be present with no C. Hence both the propositions are subverted. If, however, the conclusion is contrarily converted, neither proposition is subverted. For if A is not present with a certain C, but is present with every B; B will not be present with a certain C. That, however, which was proposed from the first, is not yet subverted; for it may be present with a certain individual, and with a certain individual not be present. But of the universal proposition A B, there will not, in short, be a syllogism. For if A is not present with a certain C, but is present with a certain B, neither of the propositions is universal. The like will also take place if the syllogism is privative. For if it should be assumed that A is present with every C, both the propositions would be subverted ; but if it should be assumed that A is present with a certain, neither of them would be subverted. The demonstration, however, is the same.

Chapter 9

But in the second figure, it is not possible to subvert contrarily the proposition which is joined to the greater extreme, in whatever way the conversion may be effected. For the conclusion will always be in the third figure; but there was not in this figure a universal syllogism. And we subvert the other proposition in a manner similar to that in which the conversion was made. But I say similarly, if, indeed, the conversion is made contrarily, it will be subverted contrarily; but if oppositely, in an opposite manner. For let A be present with every B, but with no C; the conclusion is B C. If, therefore, it should be assumed, that B is present with every C, and the proposition A B should remain; A will be present with every C. For the first figure will be produced. But if B is present with every C, and A with no C: A will not be present with every B. The figure is the last. If, however, the conclusion B C should be oppositely converted; the proposition A B may be similarly demonstrated; but the proposition A C oppositely. For if B is present with a certain C, but A with no C; A will not be present with a certain B. Again, if B is present with a certain C, but A with every B; A will be present with a certain C. Hence the syllogism will be produced in an opposite way. There will also be a demonstration in a similar manner, if the propositions should subsist vice versa. But if the syllogism is partial, the conclusion being converted contrarily, neither of the propositions is subverted, as neither was there a subversion of either in the first figure. If, however, the conclusion is oppositely converted both are subverted. For let it be posited that A is present with no B, but is present with a certain C; the conclusion is B C. If, therefore, it were posited that B is present with a certain C; and the proposition A B should remain; the conclusion will be, that A is not present with a certain C. That, however, which was proposed from the first will not be subverted; for it may be present, and not be present with a certain individual. Again, if B is present with a certain C, and A is present with a certain C, there will not be a syllogism; for neither of the assumed propositions is universal. Hence, neither is the proposition A B subverted. But if it should be oppositely converted, both the propositions are subverted. For if B is present with every C, but A is present with no B; A will be present with no C. It was, however, present with a certain C. Again, if B is present with every C, but A is present with a certain C; A will be present with a certain B.  There will also be the same demonstration, if the universal proposition should be categoric.

Chapter 10

But in the third figure, when the conclusion is converted contrarily neither of the propositions is subverted, according to no one of the syllogisms. When, however, the conclusion is converted oppositely, both are subverted, and in all syllogisms. For let it be shown that A is present with a certain B, and let C be assumed as the middle. Let also the propositions be universal. If, therefore, it should be assumed that A is not present with a certain B, but that B is present with every C, a syllogism will not be produced of A and C. Neither if A, indeed, is not present with a certain B, but is present with every C, will there be a syllogism of B and of C. There will also be a similar demonstration, if the propositions are not universal. For either it is necessary that both should be partial, through conversion, or that universal should be joined to the less extreme: but thus there was not a syllogism, neither in the first, nor in the middle figure. But if the propositions are oppositely converted, both will be subverted. For if A is present with no B, but B is present with every C; A will be present with no C. Again, if A is present with no B, but is present with every C; B will be present with no C. The like will also take place if one of the propositions is not universal. 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. But if A is present with no B, but is present with every C; B will be present with no C. In a similar manner also if the syllogism is privative. For let it be demonstrated that A is not present with a certain B; and let the categoric proposition be B C, but the negative AC; for thus a syllogism was produced. When, therefore, the proposition is assumed contrary to the conclusion there will not be a syllogism. For if A was present with a certain B, but B was present with every C, there was not a syllogism of A and of C. Nor if A was present with a certain B, but with no C, was there a syllogism of B and of C. Hence the propositions are not subverted. When, however, the opposite is assumed, the propositions are subverted. For if A is present with every B, and B is present with every C; A will be present with every C. But it was present with no C. Again, if A is present with every B, but is present with no C; B will be present with no C. But it was pre sent with every C. There will also be a similar demonstration if the propositions are not universal. For A C becomes universal and privative; but the other proposition is partial and categoric. If, therefore, A is present with every B, but B is present with a certain C; A will happen to a certain C. But it was present with no C. Again, if A is present with every B, but with no C; B will be present with no C. It was posited, however, to be present with a certain C. But if A is present with a certain B, and B with a certain C, there will not be a syllogism. Nor if A is present with a certain B, but with no C; neither thus will there be a syllogism. Hence in that way, indeed, but not in this, the propositions are subverted. From what has been said, therefore, it is evident, how the conclusion being converted, a syllogism will be produced in each figure; and when contrarily, and when oppositely to the proposition. It is also evident, that in the first figure syllogisms are produced through the middle and the last; and that the proposition, indeed, which is joined to the less extreme, is always subverted through the middle figure; but that the proposition which is joined to the greater extreme, is subverted through the last figure. But in the second figure, through the first, and the last. And the proposition, indeed, which is joined to the less extreme, is always subverted through the first figure; but that which is joined to the greater extreme, is always subverted through the last figure. But in the third figure, through the first, and the middle. And the proposition, indeed, which is joined to the greater extreme, is always subverted through the first, but that which is joined to the less extreme, through the middle figure. What, therefore, it is to convert, and how this is effected in each figure, and what syllogism is produced, is evident.

Chapter 11

A syllogism, however, through the impossible is exhibited, when the contradiction of the conclusion is posited, and another proposition is assumed. But it is produced in all the figures; for it is similar to conversion. Except that it thus much differs, that it is converted indeed, a syllogism being made, and both the propositions being assumed; but it is deduced to the impossible, when the opposite is not previously acknowledged, but is manifestly true. But the terms subsist similarly in both, and the assumption of both is the same. Thus, for instance, if A is present with every B, but the middle is C, if it should be supposed that A, either is not present with every, or is present with no B, but is present with every C, which was true, it is necessary that C should be present with no B, or not with every B. But this is impossible. Hence that which was supposed is false. The opposite, therefore, is true. The like will also take place in other figures; for such things as receive conversion, receive also a syllogism which is constructed through the impossible. All other problems, therefore, are demonstrated through the impossible in all the figures; but the categoric universal, is demonstrated, indeed, in the middle, and in the third figure, but is not demonstrated in the first figure. For let it be supposed that A is not present with every B, or is present with no B, and let the other proposition be assumed from either part, whether that C is present with every A, or B with every D; for thus there will be the first figure. If, therefore, it is supposed that A is not present with every B, a syllogism will not be produced, the proposition being assumed from either part. But if it is supposed that A is present with no B; when the proposition B D is assumed, there will be a syllogism, indeed of the false, yet the thing proposed will not be demonstrated. For if A is present with no B, but B is present with every D, A will be present with no D. But let this be impossible. It is false, therefore, that A is present with no B. If, however, it is false, that it is present with no B, it does not follow that it is true, that it is present with every B. But if the proposition C A is assumed, a syllogism is not produced. Neither is a syllogism produced, when it is supposed that A is not present with every B. Hence it is evident, that the being present with every individual, is not demonstrated in the first figure through the impossible. But to be present with a certain individual, and with no individual, and not with every individual, is demonstrated. For let it be supposed that A is present with no B; but let B be assumed to be present with every, or with a certain C. It is necessary, therefore, that A should not be present with every or should be present with no C. But this is impossible. For let this be true and manifest, that A is present with every C. Hence if this is false, it is necessary that A should be present with a certain B. But if one of the propositions should be assumed toward A, there will not be a syllogism. Nor will there be when it is supposed contrary to the conclusion, as, for instance, not to be present with a certain individual. It is evident, therefore, that the opposite must be made the hypothesis. Again, let it be supposed that A is present with a certain B, and let it be assumed that C is present with every A. It is necessary, therefore, that C should be present with a certain B. But let this be impossible. Hence, that which was supposed is false. But if this be the case, it is true that A is present with no B. The like will also take place if the proposition C A were assumed privative. But if the proposition were assumed toward B, there will not be a syllogism. If, however, the contrary were supposed, there will, indeed, be a syllogism, and the impossible will be demonstrated; but that which was proposed will not be proved. For let it be supposed that A is present with every B; and let it be assumed that C is present with every A. It is necessary, therefore, that C should be present with every B. But this is impossible. Hence it is false that A is present with every B; but it is not yet necessary, that if it is not present with every, it is present with no B. The like will also take place if to B the other proposition is assumed; for there will be a syllogism, and the impossible will be proved. The hypothesis, however, is not subverted; so that the opposite must be supposed. But in order to prove that A is not present with every B, it must be supposed that it is present with every B. For if A is present with every B, and C is present with every A; C will be present with every B. Hence if this is impossible, that which was supposed is false. The like will also take place if the other proposition is assumed to B. And in a similar manner, if the proposition C A is privative; for thus also a syllogism is produced. But if the privative proposition is joined to B, nothing is demonstrated. If, however, it should not be supposed to be present with every, but with a certain individual, it will not be demonstrated, that it is not present with every individual, but that it is present with no individual. For if A is present with a certain B, but C is present with every A; C will be present with a certain B. If, therefore, this is impossible, it is false that A is present with a certain B. Hence it is true that it is present with no B. But this being demonstrated, that which is true is al the same time subverted. For A was present with a certain B, and with a certain B was not present. Farther still, the hypothesis does not happen on account of the hypothesis; for it will be false; since it is not possible to conclude the false from the true. Now, however, it is true; for A is present with a certain B. Hence it must not be supposed that A is present with a certain, but with every B. The like will also take place if we should demonstrate that A is not present with a certain B. For if it is the same thing not to be present with a certain individual, and not to be present with every individual, there is the same demonstration of both. It is evident, therefore, that not the contrary, but the opposite must be supposed in all syllogisms; for thus there will be a necessity of concluding, and the probable axiom. For if affirmation or negation is true of everything; when it is shown that negation is not true, it is necessary that affirmation should be true. Again, unless it is admitted that affirmation is true, it must be admitted that negation is probable. But the contrary must be considered as in neither way adapted. For neither if the being present with no individual is false, is it necessary that the being present with every individual is true, nor is it probable, that if the one is false, the others is true. It is evident, therefore, that in the first figure, all other problems are demonstrated, through the impossible, but that the universal affirmative is not demonstrated.

Chapter 12

In the middle, however, and last figure, this also is demonstrated. For let it be supposed that A is not present with every B; and let it be assumed that A is present with every C. Hence if A is not present with every B, but is present with every C; C is not present with every B. This, however, is impossible. For let it be manifest that C is present with every B. Hence that which was supposed is false. The being present with every individual, therefore, is true. But if the contrary should be supposed, there will be a syllogism, indeed, and the impossible will be proved; yet the thing proposed will not be demonstrated. For if A is present with no B, but is present with every C; C will be present with no B. But this is impossible. Hence it is false that A is present with no B. It does not, however, follow that if this is false, it is true that it is present with every B. But when A is present with a certain B, let it be supposed that A is present with no B, and that it is present with every C. It is necessary, therefore, that C should be present with no B. Hence, if this is impossible, it is necessary that A should be present with a certain B. But if it should be supposed that A is not present with a certain B, there will be the same things as in the first figure. Again, let it be supposed that A is present with a certain B; but let it be present with no C. It is necessary, therefore, that C should not be present with a certain B. But it was present with every C. Hence that which was supposed is false. A, therefore, will be present with no B. But when A is not present with every B; let it be supposed to be present with every B, but with no C. It is necessary, therefore, that C should be present with no B. But this is impossible. Hence it is true, that A is not present with every B. It is evident, therefore, that all the syllogisms are produced through the middle figure.

Chapter 13

In a similar manner also it may be concluded through the last figure. For let it be posited that A is not present with a certain B, but that C is present with every B. A, therefore, will not be present with a certain C. If, therefore, this is impossible, it is false that A is not present with a certain B; so that it is true that it is present with every B. But if it should be supposed that it is present with no B; there will, indeed, be a syllogism, and the impossible will be proved, but the thing proposed will not be demonstrated. For if the contrary should be supposed, there will be the same things as in the former syllogisms. But for the purpose of concluding that A is present with a certain B, this hypothesis is to be assumed. For if A is present with no B, but C is present with a certain B, A will not be present with every C. If, therefore, this is false, it is true that A is present with a certain B. But when A is present with no B, let it be supposed to be present with a certain B. And let it be assumed that C is present with every A. It is necessary, therefore, that A should be present with a certain C. But it was present with no C. Hence it is false that A is present with a certain B. But if it should be supposed that A is present with every B, the thing proposed will not be demonstrated. In order, however, to conclude that a thing is not present with every individual, this hypothesis is to be assumed. For if A is present with every B, and C is present with a certain B; A is present with a certain C. But this was not true. Hence it is false that A is present with every B. And if this be the case, it is true that it is not present with every B. But if it should be supposed that it is present with a certain B; there will be the same things as in the before-mentioned syllogisms. It is evident, therefore, that in all syllogisms which are constructed through the impossible, that which is opposite must be supposed. But it is evident, that in the middle figure also, the affirmative may in a certain respect be demonstrated, and in the last figure, the universal.

Chapter 14

But a demonstration leading to the impossible differs from an ostensive demonstration because it admits that which it wishes to subvert, leading to an acknowledged falsehood ; but an ostensive demonstration begins from acknowledged positions. Both demonstrations, therefore, assume two acknowledged propositions; but the one assumes those from which a syllogism is produced; and the other one of these, and the contradiction of the conclusion. In the one also it is not necessary that the conclusion should be known, nor previously to assume that it is, or that it is not; but in the other it is necessary, previously to assume that it is not. It is, however, of no consequence, whether the conclusion is affirmation, or negation; but the like will take place about both. But everything which is concluded ostensively, may also be demonstrated through the impossible; and that which is concluded through the impossible, may also be demonstrated ostensively; and through the same terms, but not in the same figures. For when the syllogism is produced in the first figure, the truths will be either in the middle, or in the last figure; the privative, indeed, in the middle, but the categoric in the last figure. But when the syllogism is in the middle figure, the truth will be in the first figure, in all the problems. But when the syllogism is in the last figure, the truth will be in the first, and in the middle figure; things affirmative in the first, but things privative in the middle figure. For let it be demonstrated through the first figure, that A is present with no, or not with every B. The hypothesis, therefore, was, that A is present with a certain B; but C was assumed to be present, indeed, with every A, but with no B. For thus a syllogism, and the impossible were produced. But this is the middle figure, if C is present with every A, but with no B. And it is evident from these things, that A is present with no B. The like will also take place if the not being present with every individual is demonstrated. For the hypothesis is, to be present with every individual; but C was assumed to be present with every A, but not with every B. In a similar manner also, if the proposition C A should be assumed to be privative for thus also the middle figure will be produced. Again, let it be shown that A is present with a certain B. The hypothesis, therefore, is, that A is present with no B. But B was assumed to be present with every C; and A to be present with every, or a certain C. For thus the conclusion will be impossible. But this is the last figure, if A and B are present with every C. And from these things it is evident, that it is necessary A should be present with a certain B. The like will also take place if it should be assumed that B or A is present with a certain C. Again, in the middle figure also, let it be shown, that A is present with every B. The hypothesis, therefore, was, that A is not present with every B. But it was assumed, that A is present with every C, and that C is present with every B; for thus there will be the impossible. And this is the first figure if A is present with every C, and C is present with every B. The like will also take place if the being present with a certain individual is demonstrated. For the hypothesis was, that A is present with no B. But it was assumed that A is present with every C, and that C is present with a certain B. If, however, the syllogism should be privative, the hypothesis was, that A is present with a certain B. But it was also assumed that A is present with no C, and that C is present with every B. Hence the first figure is produced. In like manner also, if the syllogism s should not be universal, but A is demonstrated not to be present with a certain B. For the hypothesis was, that A is present with every B; but it was assumed, that A is present with no C, and that C is present with a certain B. For thus the first figure is produced. Again, in the third figure, let it be shown, that A is present with every B. The hypothesis, therefore, was, that A is not present with every B; but it was assumed, that C is present with every B, and that A is present with every C. For thus there will be the impossible. But this is the first figure.  In a similar manner also, if the demonstration is in a certain thing. For the hypothesis will be, that A is present with no B; but it is assumed, that C is present with a certain B, and that A is present with every C. But if the syllogism is privative, the hypothesis is, that A is present with a certain B; but it is assumed that C is present with no A, and that it is present with every B. But this is the middle figure. The like will also take place if the demonstration is not universal. For the hypothesis will be, that A is present with every B; and it is assumed, that C is present with no A, and is present with a certain B. But this is the middle figure. It is evident, therefore, that each of the problems may be demonstrated through the same terms, both ostensively, and through the impossible. In like manner also, it will be possible, when the syllogisms are ostensive, to form a deduction to the impossible, in those terms which are assumed, when the proposition is assumed opposite to the conclusion. For the same syllogisms will be formed, as those which are produced through conversion; so that we shall also immediately have figures, through which each problem will conclude. It is evident, therefore, that every problem is demonstrated according to both modes, i.e. through the impossible, and ostensively; and that it is not possible for the one mode to be separated from the other.

Chapter 15

In what figure, however, it is possible, and in what it is not possible to syllogize from opposite propositions, will he manifest as follows: But I say that opposite propositions are according to diction four; as, for instance, to be present with every individual, to be present with no individual; to be present with every individual, to be present not with every individual; to be present with a certain individual, to be present with no individual; and to be present with a certain individual, and to be present not with a certain individual. In reality, however, the opposite propositions arc three; for to be present with a certain individual, is opposed to the being present not with a certain individual, according to diction only. But of these I call those which are universal, contraries, i.e. to be present with every individual, and to be present with no individual; as, for instance, that every science is worthy, and that no science is worthy: but I call the others opposites. In the first figure, therefore, there is not a syllogism from opposite propositions, neither affirmative, nor negative. Not from affirmative propositions, indeed, because it is necessary that both the propositions should be affirmative; but affirmation and negation are opposites. Nor can there be a syllogism from privative propositions; because opposites affirm and deny the same thing of the same; but the middle in the first figure is not predicated of both the extremes, but one thing is denied of it, and it is predicated of another. These propositions, however, are not opposed. But in the middle figure a syllogism may be produced from opposites and from contraries. For let good be A; but science B and C. If, therefore, it should be assumed that every science is worthy, and also that no science is worthy; A will be present with every B, and with no C; so that B will be present with no C. No science, therefore, is science.

Every science is worthy:

No science is worthy: Therefore,

No science is science.

The like will also take place, if when it is assumed that every science, is worthy, it should afterwards be assumed that medicine is not worthy. For A is present with every B, but with no C. Hence a certain science will not be science.

Every science is worthy:

No medicine (which is a certain science) is worthy: Therefore,

No medicine (which is a certain science) is science.

Likewise, if A is present with every C, but with no B. But B is science; C, medicine; A, opinion. For assuming that no science is opinion, it will be assumed that a certain science is opinion.

No science is opinion:

All medicine (which is a certain science) is opinion: Therefore,

No medicine (which is a certain science) is science.

This mode, however, differs from the former, on account of the conversion made in the terms; for before, affirmation was joined to B, but now it is joined to C. In a similar manner also, if one of the propositions is not universal. For it is always the middle, which is predicated negatively of the one, and affirmatively of the other.  Hence it happens that opposites are concluded; yet not always, nor entirely; but when those things which are under the middle so subsist, as that they are either the same, or are related as a whole to a part. In any other way this is impossible; for the propositions will by no means be either contrary or opposite. But in the third figure, an affirmative syllogism will never be from opposite propositions, for the reason before-mentioned in the first figure. There will, however, be a negative syllogism, whether the terms are universally, or not universally assumed. For let science be B and C; and medicine A. If, therefore, it should be assumed that all medicine is science, and that no medicine is science, B will be assumed to be present with every A, and C with no A. Hence a certain science will not be science.

No medicine is science:

All medicine is science: Therefore,

A certain science is not science.

The like will also take place, if the proposition A B were not assumed universal. For if a certain medicine is science, and again, no medicine is science; it will happen that a certain science is not science.

A certain medicine (A) is not science (B).

All medicine (A) is science (C): Therefore,

A certain science (C) is not science (B).

But the propositions are contrary, the terms being universally assumed; though if one of them is partial they arc opposite. It is necessary, however, to understand, that opposites may be assumed in the manner we have mentioned, as that every science is worthy, and again, that no science is worthy, or that a certain science is not worthy, which is not wont to be latent. It is also possible through other interrogations, that the other part of contradiction maybe concluded; or as we have observed in the Topics, may be assumed. But since the oppositions of affirmations are three, it happens that opposites are assumed in six ways, either in every and no individual, or in every and not in every individual, or in a certain, and in no individual: and this may be converted in the terms. Thus A may be present with every B, but with no C; or may be present with every C and with no B; or with the whole of the one, and not with the whole of the other. And this again may be converted according to the terms. The like will also take place in the third figure. Hence it is evident in how many ways, and in what figures it happens that a syllogism is produced through opposite propositions. But it is also evident, that the truth may be syllogistically concluded from false propositions, as has been before observed. From opposites, however, it cannot be concluded; for a syllogism will always be produced contrary to the thing. Thus, if a thing is good it will be concluded that it is not good; or if it is an animal, that it is not an animal; because the syllogism is from contradiction; and the subject terms are either the same, or the one is a whole, but the other a part. It is also manifest, that in paralogisms, nothing hinders but that there may be a contradiction of the hypothesis; as, if a thing is an odd number, it is not an odd number. For the syllogism from opposite propositions was contrary. If, therefore, such are assumed, there will be a contradiction of the hypothesis. But it is necessary to understand, that contraries cannot be so concluded from one syllogism, as that the conclusion may be, that which is not good is good, or anything else of this kind, unless such a proposition is immediately assumed; as, for instance, that every animal is white and not white, and that man is an animal. For it is necessary either previously to assume contradiction; as that all science is opinion, and is not opinion, and afterwards to assume from it that medicine is a science, indeed, but is no opinion; just as elenchi are produced, or to conclude from two syllogisms. It is not, however, possible that the things assumed should in reality be contrary in any other way than this, as has been before observed.

Chapter 16

To beg, however, and assume the question in the beginning consists, that I may take genus of it, in not demonstrating the thing proposed.  But this happens in many ways; whether, in short, there is not a conclusion, or whether the conclusion is through things more unknown, or similarly unknown, or whether that which is prior is through things posterior.  For demonstration is from things more credible and prior.  Of these modes, therefore, there is begging the question proposed from the beginning.  Since, however, somethings are naturally adapted to be known through themselves, but others through other things; (for principles are known through themselves, but the things contained under the principles, are known through other things) when any one endeavors to demonstrate through itself, that which cannot be known through itself, then he begs that which was proposed from the beginning,  This, however, may take place in such a manner, as that the thing proposed may be immediately postulated.  It also happens, that passing to certain other things, which are naturally adapted to be demonstrated through that thing, that which was investigated from the beginning is through these demonstrated.  As if A should be demonstrated through B, and B through C; but C is naturally adapted to be demonstrated through A. For it happens that A will be demonstrated through itself, by those who thus syllogize; which is effected, indeed, by those, who fancy that they describe parallel lines.  For they deceive themselves, assuming such things as cannot be demonstrated, unless they are parallel.  Hence it happens to those who thus syllogize, that they say, each thing is, if each thing is.  But thus everything will be known through itself, which is impossible.  If, therefore, some one, when it is immanifest that A is present with C, and in a similar manner that A is present with B, begs it may be granted him that A is present with B; it is not yet evident whether he begs the question proposed from the beginning; but it is evident that he does not demonstrate; for that which is similarly immanifest, is not the principle of demonstration. But if B so subsists with reference to C, as that they are the same, or it is evident that these are converted, or that the one is present with the other, then the thing investigated in the beginning is made the object of petition. For that A is present with B may be demonstrated through them, if they are converted. Now, however, this prevents but not the mode. But if it should do this, it will effect what has been mentioned, and a conversion will be made as through three terms. In like manner, if any one should assume that B is present with C, since it is similarly immanifest, as if he should assume that A is present with C; he does not yet beg the question from the beginning, but he does not demonstrate. If, how ever, A and B should be the same, or should be converted, or A should be consequent to B, he will beg the question from the beginning, through the same cause. For what begging the question from the beginning is capable of effecting, we have before shown, viz. that it is to demonstrate a thing through itself, which is not through itself manifest. If, therefore, to beg the question in the beginning, is nothing else than to demonstrate of a thing through itself, that which is not through itself manifest; but this is not to demonstrate, since the thing demonstrated, and that through which it is demonstrated, are similarly immanifest, either because the same things are assumed to be present with the same thing, or the same thing with the same things; if this be the case, in the middle figure, and also in the third, the thing investigated from the beginning, may in each way be similarly the subject of petition. But in a categoric syllogism, the question is the subject of petition in the third and first figure only; and negatively, when the same things are absent from the same thing, and both the propositions do not subsist similarly (the like also takes place in the middle figure) because the terms are not converted in negative syllogisms. To beg the question, however, in the beginning, takes place in demonstrations, when things which thus subsist in reality, are the subjects of petition; but in dialectic syllogisms when those things are requested to be granted, which appear thus to subsist according to opinion.

Chapter 17

But that the false does not happen on account of this, (which in discussions we are frequently accustomed to say) is first found to be the case in syllogisms leading to the impossible, when any one contradicts that which another demonstrates by a deduction to the impossible. For neither will he who does not contradict, assert that, not on this account, but he will contend that it is something false, from those things which were before posited; nor in an ostensive proof; for he does not adduce contradiction. Farther still, when anything is ostensively subverted through ABC, it cannot be said that a syllogism is produced on account of that which is posited. For we then say that is not produced on account of this, when this being subverted, the syllogism is nevertheless completed; which is not the case in ostensive syllogisms. For the position being subverted, the syllogism will no longer subsist which pertains to it. It is evident, therefore, that in syllogisms leading to the impossible, that is asserted not on account of this; and when the hypothesis from the beginning so subsists with reference to the impossible, that both when it is, and when it is not, the impossible will nevertheless happen. Hence the most apparent mode of the false not subsisting on account of the hypothesis, is, when the syllogism produced from media leading to the impossible, is unconjoined with the hypothesis, as we have also observed in the Topics. For this it is, to assume that which is not a cause, as a cause; just as if any one wishing to show that the diameter of a square is incommensurable with its side, should endeavor to demonstrate the argument of Zeno, that motion has no existence, and to this should deduce the impossible. For the false is by no means whatever in continuity, with that which was asserted from the beginning. But there is another mode, if the impossible should be in continuity with the hypothesis, yet it does not happen on account of that. For this may take place, whether the continuity is assumed upward or downward; as if A should be posited to be present with B; B with C; and C with D; but this should be false, that B is present with D. For if A being subverted, B is nevertheless present with C, and C with D, there will not be the false from the hypothesis assumed from the beginning. Or again, if some one should assume the continuity in an upward direction; as if A should be present with B, E with A, and F with E; but it should be false that F is present with A. For thus there will no less be the impossible, the hypothesis being subverted assumed from the beginning. It is necessary, however, to conjoin the impossible with the terms assumed from the beginning; for thus it will be on account of the hypothesis. Thus when the continuity is assumed in a downward direction, it ought to be conjoined with the categoric term. For if it is impossible that A should be present with D; A being taken away, there will no longer be the false. But the continuity being assumed in an upward direction, it ought to be conjoined with the subject term. For if F cannot be present with B; B being subverted, there will no longer be the impossible. The like also takes place when the syllogisms are privative. It is evident, therefore, that unless the impossible is conjoined with the terms assumed from the beginning, the false will not happen on account of the position. Or shall we say that neither thus will there be the false on account of the hypothesis? For if A is posited to be present not with B, but with K, and K with C, and this with D; thus also the impossible will remain. The like will also take place, when the terms are assumed in an upward direction. Since, therefore, the impossible will happen, whether this is, or is not; it will not be on account of the position. Or if this is not, the false nevertheless is produced; it ought not to be so assumed as if something else being posited the impossible will happen; but when this being subverted, the same impossible is concluded, through the remaining propositions. For perhaps there is no absurdity, that the false should be inferred through many hypotheses; as that parallel lines will meet, whether the internal angle is greater than the external, or whether a triangle has more than two right angles.

Chapter 18

False reasoning, however, is produced, on account of that which is primarily false. For every syllogism consists either from two, or from more than two propositions. If, therefore, it consists from two propositions, it is necessary that one, or both of these should be false; for there will not be a false syllogism from true propositions. But if it consists of more than two propositions, as if C should be demonstrated through A B, but these through D E F G; in this case, some one of the above is false; and on this account the reasoning is false. For A and B are concluded through them. Hence through some one of them, the conclusion and the false happen to take place.

Chapter 19

In order, however, to prevent a syllogistical conclusion being adduced against us, we must observe when our opponent interrogates the argument without conclusions, lest the same thing should be twice conceded in the propositions; since we know that a syllogism is not produced without a middle, and a middle is that of which we have frequently spoken. But in what manner it is necessary to observe the middle with respect to every conclusion, is evident from knowing what kind of thing is demonstrated in each figure. And of this we shall not be ignorant, in consequence of knowing how we sustain the disputation. It is, however, requisite when we argue, that we should endeavor to conceal that which we have ordered the respondent to guard against. But this will be effected in the first place, indeed, if the conclusions are not pre-syllogized, but are immanifest, when the necessary propositions are assumed. Again, this will also be effected if things proximate are not made the subjects of interrogation, but such as are especially media. For instance, let it be requisite to conclude A of F; and let the media be B C D E. It is necessary, therefore, to interrogate, whether A is present with B, and again, not whether B is present with C, but whether D is present with E; and afterwards whether B is present with C; and so of the rest. If also the syllogism should be produced through one middle, it is necessary to begin from the middle; for thus especially the respondent may be deceived.

Chapter 20

But since we have when, and in what manner the terms subsisting, a syllogism is produced, it is also evident when, and when there will not be an elenchus. For all things being conceded, or the answers being posited alternately (as, for instance, the one being affirmative, and the other negative) an elenchus may be produced. For there was a syllogism, the terms subsisting, as well in this, as in that way. Hence, if that which is posited, should be contrary to the conclusion, it is necessary that an elenchus should be produced; for an elenchus is a syllogism of contradiction. But if nothing should be granted, it is impossible that an elenchus should be produced; for there was not a syllogism when all the terms are privative; so that neither will there be any elenchus. For if there is an elenchus, it is necessary there should be a syllogism; but if there is a syllogism, it is not necessary there should be an elenchus. The like will also take place, if nothing according to the interrogation should be posited in the whole; for there will be the same determination of the elenchus and the syllogism.

Chapter 21

It sometimes happens, however, that as we are deceived in the position of the terms, thus also deception is produced according to opinion; as if it should happen that the same thing, is primarily present with manythings, and some one should be ignorant of one of these, and should fancy that it is present with no individual, but should know the other. For let A be essentially present with B and with C, and let these be present with every D. If, therefore, some one should fancy that A is present with every B, and this with every D; but A with no C, and this with every D; he will have both science and ignorance of the same thing according to the same. Again, if any should be deceived about those things which are from the same co-ordination; as if A is present with B, but this with C, and C with D; but he should apprehend that A is present with every B, and again, with no C; he will at the same time know and not think that it is present. Will he, therefore, from these things think nothing else, than that he does not form an opinion of that which he knows? For he in a certain respect knows that A is present with C, through B, just as the partial is known in the universal.  Hence, that which he in a certain respect knows, he entirely thinks he does not know, which is impossible. But in that which was before-mentioned, if the middle is not from the same coordination it will not happen that any one can form an opinion of both the propositions according to each of the media; as if A should be present with every B, but with no C, and both these should be present with every D. For it will happen that the first proposition will assume a contrary, either simply, or partially. For if he thinks that A is present with everything with which B is present, but he knows that B is present with D; he will also know that A is present with D.  Hence, if again he thinks that A is present with nothing with which C is present; he will not think that A is present with anything with which B is present. But that he who thinks that it is present with everything with which B is present, should again think that it is not present with something with which B is present, is either, simply, or partially contrary. It is not possible, therefore, thus to think. Nothing, however, hinders, the assuming one proposition according to each middle, or both according to one; as that A is present with every B, and B with D; and again, that A is present with no C. For a deception of this kind is similar to that by which we are deceived about particulars; as if A is present with every B, but B with every C, A will be present with every C. If, therefore, any one knows that A is present with, everything with which B is present, he will also know that it is present with C. Nothing, however, hinders, but that he may be ignorant of the existence of C; as if A is two right angles; B, a triangle; and C, a sensible triangle.

Every triangle (B) has angles equal to two right (A): (Known)

This (C) is a triangle (B): (Unknown) Therefore,

This has angles equal to two right. (Known by universal/Unknown by proper knowledge.)

For some one may think that C docs not exist, knowing that every triangle has angles equal to two right. Hence he will at the same time know, and be ignorant of the same thing. For to know that every triangle has angles equal to two right, is not anything simple, but partly arises from the possession of universal science, and partly from the possession of partial science. Thus, therefore, by universal science he knows that C has angles equal to two right; but he does not know it by partial science. He will not, therefore, possess contraries. The like also takes place with respect to the reasoning in the Meno of Plato, that discipline is reminiscence. For it never happens that there is a pre-existent knowledge of particulars, but together with induction we receive, as it were recognizing, the science of particulars. For somethings we immediately know; as, for instance, the possession of angles equal to two right, if we know that what we see is a triangle. The like also takes place in other things. By universal knowledge, therefore, we survey particulars, but we do not know them through universals with appropriate knowledge. Hence it happens that about these we are deceived, yet not contrarily; but because we have a universal knowledge, and are deceived according to particular knowledge. The like, therefore, takes place in the things of which we have before spoken. For the deception which is according to the middle is not contrary to the science according to syllogism; nor the opinion according to each of the middles. Nothing, however, hinders but that he who knows that A is present with the whole of B, and again, that this is present with C, may think that A is not present with C. Thus, he who knows that every mule is barren, and that this animal is a mule, may fancy that this animal is parturient. For he does not know that A is present with C, unless he at the same time surveys each proposition. Hence it is evident, that if he knows one of the propositions, but does not know the other, he will be deceived, with respect to the manner in which universal subsist with reference to particular sciences. For we know nothing of sensibles which exists external to sense, not even if we have perceived it before, unless so far as we possess universal and proper science, and not because we energize according to that science. For the possession of scientific knowledge is predicated in a threefold respect; either as arising from the possession of universal knowledge, or as from proper knowledge, or as from energizing, so that to be deceived is likewise predicated in as many ways. Nothing, therefore, hinders, but that a man may have a knowledge of and be deceived about the same thing, except not in a contrary manner; which also happens to him who knows according to each proposition, and has not previously considered. For thinking that a mule is parturient, he has not science in energy. Nor again, on account of opinion, has he deception contrary to science; for the deception contrary to universal science is a syllogism. But he who thinks that the very being of good, is the very being of evil, apprehends that the essence of good is the same as the essence of evil. For let the essence of good be A; but the essence of evil, B; and again, let the essence of good be C. Since, therefore, he thinks that B and C are the same, he will also think that C is B; and again, he will in a similar manner think that B is A; so that he will also be of opinion that C is A.

He thinks that the essence of evil (B) is the essence of good (A):

He thinks that the essence of good (C) is the essence of evil (B): Therefore,

He thinks that the essence of good (C) is the essence of good (A).

For just as if it were true, that of which C is predicated, B is predicated; and that of which B is predicated, A is predicated; this being the case, it was also true that A is predicated of C. The like will also take place in the verb to opine; and in the verb to be. For if C and B are the same, and again, B and A; C also is the same as A. Hence the like will also take place in the verb to opine. Is, therefore, this indeed, necessary, if any one should concede the first? But perhaps that is false, that any one will opine that the essence of good is the essence of evil, unless from accident. For it is possible to opine this in many ways. This, however, must be more accurately considered.

Chapter 22

When, however, the extremes are converted, it is also necessary that the middle should be converted with both extremes. For if A is present with C through B; if the conclusion is converted, and C is present with whatever A is present, B also is converted with A; and with whatever A is present, B also is present through the middle C. C likewise is converted with B through the middle A. The like will also take place in the not being present with. As if B is present with C, but A is not present with B; neither will A be present with C. If, therefore, B is converted with A, C also will be converted with A. For let B not be present with A; neither, therefore, will C be present with A; for B was present with every C. And if C is converted with B, A also will be converted with B. For of whatever B is predicated, C also is predicated. And if C is converted with A, B also will be converted with A. For that with which B is present, C also is present; but C is not present with that with which A is present. And this alone begins from the conclusion (but the others not similarly) as is also the case in a categoric syllogism. Again, if A and B are converted, and in a similar manner C and D, but it is necessary that A or C should be present with every individual, B also and D will so subsist, that one of them will be present with every individual. For since B is present with that with which A is present, and D with that with which C is present, but both are not at the same time present with everything with which A or C is present; it is evident that B or D also is present with every individual, and not both of them at one and the same time. For two syllogisms are composed. Again, if A or B is present with every individual, and C or D, but they are not present at one and the same time; if A and C are converted, B also and D are converted. For if B is not present with a certain thing, with which D is present, it is evident that A is present with it. But if A is present, C also will be present; for they are converted; so that C and D will be present at one and the same time; but this is impossible. Thus, if that which is unbegotten is incorruptible, and that which is incorruptible is unbegotten; it is necessary that what is generated should be corruptible, and what is corruptible, generated. But when A is present with the whole of B, and with the whole of C, and is predicated of nothing else, and B also is present with every C; it is necessary that A and B should be converted. For since A is predicated of B C alone, but B also is predicated itself of itself, and of C; it is evident that of those things of which A is predicated, of all those B also will be predicated, except of A. Again, when A and B are present with the whole of C, but C is converted with B, it is necessary that A should be present with every B. For since A is present with every C, but C is present with every B, in consequence of reciprocation, A also will be present with every B. But when of two things which are opposites, as, for instance, A and B, A is more eligible than B, and in a similar manner D is more eligible than C, if A C are more eligible than B D, A is more eligible than D. For in a similar manner A is to be pursued, and B to be avoided; since they are opposites. C also is to be similarly avoided, and D to be pursued; for these likewise are opposed. If, therefore, A is similarly eligible with D, B also is to be similarly avoided with C. For each is similarly opposed to each, that which is to be avoided, to that which is to be pursued. Hence both are to be similarly avoided, or pursued, viz. A C, similarly with B D. But because those are more eligible than these, they cannot be similarly eligible; for if they could, B D would be similarly eligible with A C. But if D is more eligible than A, B also will be less avoidable than C; for the less is opposed to the less. But the greater good and the less evil are more eligible than the less good and the greater evil. The whole, therefore, of B D, is more eligible than A C. Now, however, this is not the case. Hence A is more eligible than D; and consequently C is less avoidable than B. If, therefore, every lover according to love chooses A, viz. to be in such a condition that he may be gratified, and yet not be gratified, which is C, rather than be gratified which is D, and yet not be in a condition to be gratified which is B; it is evident that A, viz. to be in a condition adapted to be gratified, is more eligible than to be gratified. To be beloved, therefore, is more eligible according to love than coition. Hence love is rather the cause of dilection than of coition. But if it is especially the cause of this, this also is the end of it. Hence coition either, in short, is not, or it is for the sake of dilection. For other desires also and arts, are thus produced. It is evident, therefore, how terms subsist according to conversions, and the being more eligible, or more avoidable.

Chapter 23

Now, however, it must be shown, that not only dialectic and demonstrative syllogisms are produced through the before-mentioned figures, but that rhetorical syllogisms also are thus produced, and, in short, every kind of credibility, and according to every method. For we believe all things either through syllogism, or from induction. Induction, therefore, and the syllogism from induction are, when one extreme is concluded through the other of the middle. As if of A C the middle is B, and it should be shown through C, that A is present with B. For thus we make inductions. Thus, let A be long-lived; B, void of bile; C, everything long-lived, as man, horse, and mule. A, therefore, is present with the whole of C; for every C is long-lived. But B also, or that which is void of bile, is present with every C. If, therefore, C is converted with B, and is not extended above the middle, it is necessary that A should be present with B. For it has been before shown, that when any two things are present with the same thing, and the extreme is converted with one of them, the other of the things predicated will also be present with that which is converted. But it is necessary to conceive of C. as if it were composed from all particulars; for induction is produced through all particulars.

Every man, horse, mule (C), is long-lived (A):

Whatever is void of bile (B) is man, horse, mule (C): Therefore,

Whatever is void of bile (B) is long-lived (A).

A syllogism, however, of this kind is of the first proposition, and without a middle. For of those propositions of which there is a middle, the syllogism is produced through the middle; but of those, of which there is not a middle, the syllogism is produced through induction. And after a certain manner induction is opposed to syllogism; for the latter shows the extreme of the third through the middle; but the former shows the extreme of the middle through the third. To nature, therefore, the syllogism which is produced through the middle is prior and more known; but to us the syllogism which is produced through induction is more evident.  

Chapter 24

But example is when the extreme is shown to be present with the middle, through the similar to the third. It is necessary, however, that it should be known that the middle is present with the third, and the first with the similar. Thus, for instance, let A be bad; B, to engage in war against neighbors; C, the Athenians against the Thebans; D the Thebans against the Phocenses. If, therefore, we wish to show that to war against the Thebans is bad, it must be assumed that it is bad to war against neighbors. But the credibility of this is from similars, as that to the Thebans, the war against the Phocenses was pernicious. Since, therefore, war against neighbors is bad; but the war against the Thebans is against neighbors; it is evident that it is bad to war against the Thebans. Hence it is evident that B is present with C, and with D; for both are to engage in war against neighbors. And also that A is present with D; for the war against the Phocenses was not advantageous to the Thebans. But that A is present with B will be shown through D. This will also be effected after the same manner, if belief that the middle is in the extreme is produced through many similars. It is evident, therefore, that example is neither as whole to part, nor as part to whole, but as part to part, when both are under the same things but the one is more known than the other.  It also differs from induction; because the latter shows from all individuals that the extreme is present with the middle and does not conjoin the syllogism with the extreme; but the former conjoins, and does not demonstrate from all individuals.

Chapter 25

Abduction, however, is, when it is evident that the first is present with the middle; but it is immanifest that the middle is present with the lasts though it is similarly credible, or more credible than the conclusion. Farther still, if the media of the last and middle are few; for it entirely happens that we shall be nearer to science. Thus, for instance, let A be that which may be taught; B, science: and C, justice. That science, therefore, may be taught is evident; but whether justice is science is immanifest. Hence if B C is similarly, or more credible than A C, it is abduction; for we are nearer to scientific knowledge in consequence of adding the proposition B C to the conclusion A C, not possessing science before. 

Every science (B) may be taught (A): (Known)

All justice (C) is science (B): (Similarly or more credible than the conclusion)

Therefore,

All justice (C) may be taught (A). (Unknown.)

Again, abduction is, if the media of the terms B C should be few; for thus we shall be nearer to knowledge. As if D should be to be squared; E, a rectilinear figure; and F, a circle. Then if of the proposition E F, there is only one middle, for a circle to become equal to a rectilinear figure through lunulas, will be a thing near to knowledge.

Every rectilinear figure (E) may be squared (D): (Known)

Every circle (F) may become a rectilinear figure (E): (Proved through one middle.)

Therefore,

Every circle (F) may be squared (D). (This is proved through many media.)

But when neither the proposition B C is more credible than the conclusion AC, nor the media are fewer; I do not call this abduction. Nor when the proposition BC is without a middle; for a thing of this kind is science.

Chapter 26

But objection is a proposition contrary to a proposition. It differs, however, from a proposition, because objection may be in part, but a proposition either altogether cannot be in part, or not in universal syllogisms. Objection, however, is urged in a twofold respect, and through two figures. In a twofold respect, indeed, because every objection is either universal or partial. But through two figures; because objections are urged opposite to the propositions, and opposites are only concluded in the first and third figure. For when any one thinks fit to assert that a thing is present with every individual, we object, either that it is present with no individual, or that it is not present with a certain individual. But of these, that a thing is present with no individual is collected from the first figure; and that it is not present with a certain individual is collected from the last figure. Thus, for instance, let A be there is one science; and B, be contraries. When any one, therefore, asserts that there is one science of contraries, it is objected, either that there is not entirely the same science of opposites, but contraries are opposites; so that the first figure is produced.

Proposition.                                                     

There is one science (A) of contraries (B):                    

Objection

There is not one science (A) of opposites (C):

Contraries (B) are opposites  (C): Therefore,                

There is not one science (A) of contraries (B).

Or it is objected that there is not one science of the known and the unknown. And this is the third figure. For of C, i.e. of the known and the unknown, it is true that they are contraries; but it is false that there is one science of them.

Proposition

There is one science (A) of contraries (B):                    

Objection

There is not one science (A) of the known/unknown (C):

The known/unknown (C) are contraries (B): Therefore,

There is not one science (A) of all contraries (B).

The like will also take place in a privative proposition. For if any one thinks fit to assert that there is not one science of contraries; we say either that there is the same science of opposites, or that there is the same science of certain contraries, as of the salubrious and the morbid. That there is one science, therefore, of all things, is objected to from the first figure; but that there is one science of certain things, is objected to from the third figure.

Proposition

There is not one science (A) of contraries (B):             

Objection

There is one science (A) of opposites (C):

Contraries (B) are opposites (C): Therefore,

There is one science (A) of contraries (B).

Proposition

There is not one science (A) of contraries (B):      

Objection

There is one science (A) of the salubrious and morbid (C):

The salubrious and morbid (C) are contraries (B): Therefore,

There is one science (A) of certain contraries (B).

For, in short, in all disputations, it is necessary that he who universally objects, should join the contradiction of the things proposed to that which is universal; as, if some one should think fit to assert that there is not the same science of all contraries, he who objects should say that there is one science of opposites. For thus it is necessary that there should be the first figure; since the middle becomes that which is universal to that which was proposed from the beginning. But it is necessary that he who objects in part, should join contradiction to that to which the subject of the proposition is universal; as, that of the known and the unknown there is not the same science. For contraries are universal with reference to these; and the third figure is produced. For that which is assumed in part is the middle, as, for instance, the known and the unknown; since from those things from which the contrary may be syllogistically collected, we endeavor to urge objections. Hence from these figures alone we adduce objections; for in these alone opposite syllogisms are constructed; since through the second figure it is not possible to conclude affirmatively. Besides, though it  should be possible, yet the objection adduced in the middle figure would require a more extended discussion; as if any one should not grant that A is present with B, because C is not consequent to it. For this is manifest through other propositions. The objection, however, ought not to be converted to other things, but should immediately have the other proposition apparent. Hence there is not a sign from this figure alone. Other objections also are to be considered; such as those which are assumed from the contrary, from the similar, and from that which is according to opinion. It must also be considered whether a partial objection can be assumed from the first figure, or a privative objection from the middle figure.

Chapter 27

The consentaneous, however, and a sign, are not the same. But the consentaneous, indeed, is a probable proposition. For that which is known to be for the most part thus generated, or not generated, or to be, or not to be; this is consentaneous; as, for instance, that the envious hate, or that love is love. But a sign seems to be nothing else than a demonstrative proposition, either necessary, or probable. For that which when it exists, a thing is, or which when it is generated, a thing is first or last generated; this is a sign, that a thing is generated, or is. But an enthymeme is a syllogism from things consentaneous, or from signs. A sign, however, is triply assumed, in as many ways as the middle in the figures of syllogisms. For it is assumed either as in the first figure, or as in the middle, or as in the third. Thus to show that a woman is pregnant, because she has milk in her breasts is from the first figure; for the middle is, to have milk. Let A be to be pregnant; B, to have milk; C, a woman.

Whatever woman has milk (B) is pregnant (A):

This woman (C) has milk (B): Therefore,

This woman (C) is pregnant (A).

But that wise are worthy men; for Pittacus is a worthy man, is concluded through the last figure. Let A be worthy; B, wise men; C, Pittacus. It is true, therefore, that A and B are predicated of C; except that they do not assert the one, because they know it; but they assume the other.

A Paralogism

Pittacus (C) is a worthy man (A):

Pittacus (C) is a wise man (B): Therefore,

Wise (B) are worthy men (A).

But that a woman is pregnant because she is pale, is to be concluded through the middle figure. For since paleness is a consequence of pregnancy, and it is also an attendant on this woman, they fancy that this woman is pregnant. Let paleness be A; to be pregnant B; a woman C.

Whatever woman is pregnant (B) is pale (A):

This woman (C) is pale (A): Therefore,

This woman (C) is pregnant (B).

If, therefore, one proposition should be enunciated, a sign only will be produced; but if the other proposition is also assumed, a syllogism will be produced; as, for instance, that Pittacus is liberal; for the ambitious are liberal; and Pittacus is ambitions. Or again, that wise are good men; for Pittacus is a good man, and also a wise man. Thus, therefore, syllogisms are produced. Except, indeed, that the syllogism which is constructed in the first figure is insoluble, if it is true; for it is universal. But the syllogism which is constructed through the last figure may be solved, though the conclusion should be true; because the syllogism is not universal, nor is the thing proposed concluded. For it is not necessary if Pittacus is a worthy man, that on this account other wise men also should be worthy. But the syllogism which is constructed through the middle figure may always and entirely be solved. For a syllogism will never be produced when the terms thus subsist. For it is not necessary, if the woman who is pregnant is pale, and this woman is pale, that this woman is pregnant. That which is true, therefore, will be inherent in all the figures; but they will have the before-mentioned differences. Either, therefore, a sign must be thus divided; but from these the argument ought to be assumed, which is the middle. For the argument they say is that which produces knowledge; but the middle is especially a thing of this kind. Or those things which are assumed from the extremes, are to be called signs; but that which is from the middle is to be called an argument. For that is most probable and especially true which proves through the first figure. But it is possible to form a judgment of the natural disposition of any one by his bodily frame if it is granted that such passions as are natural change at one and the same time the body and the soul. For some one perhaps learning music suffers some change in his soul; but this passion is not among the number of those which are natural to us; angers and desires which pertain to natural motions rather belonging to this class. If, therefore, this should be granted, and that one thing is the sign of one passion, and we are able to assume the proper passion and sign of each genus; we may be able to form a judgment of the natural disposition by the bodily frame. For if a proper passion is inherent in a certain individual genus, as, for instance, fortitude in lions, it is also necessary that there should be a certain sign; (for it is supposed that the body and soul sympathize with each other) and let this be the possession of great extremities; which also happens to be present with other not whole genera. For the sign is thus proper (or peculiar) because the passion is the peculiarity of the whole genus, and is not the peculiarity of it alone, as we are accustomed to say. The same sign, therefore, will also be inherent in another genus, and man will be brave, and some other animal. It will, therefore, possess that sign; for there was one sign of one passion. If therefore, these things are true, and we are able to collect such signs, in these animals, which have one peculiar passion alone; (but each passion has its own sign, since it is necessary that it should have one sign) we may be able to form a judgment of the natural disposition by the bodily frame. But if the whole genus has two peculiarities; as a lion has fortitude and liberality, how shall we know which of those signs that are properly consequent is the sign of either passion? Shall we say that we may know this, if both are inherent in something else, but not wholly, and that in those things in which each is not inherent wholly, when one is possessed, the other is not? For if an animal is brave, indeed, but not liberal, but it has this from two signs; it is evident that in a lion also, this is the sign of fortitude. But to form a judgment of the natural disposition by the bodily frame, is in the first figure, because the middle reciprocates with the first extreme, but surpasses the third, and does not reciprocate with it. Thus, for instance, let fortitude be A; great extremities, B; and a lion, C. Hence B is present with every individual of that with which C is present, and it is also present with other things. But A is present with every individual of that with which it is present, and not with more individuals, but is converted. For if it were not, there would not be one sign of one passion.

Whatever has great extremities is brave:                       

Every lion has great extremities: Therefore,                

Every lion is brave.                                                            

Whatever has great extremities is brave:

Some man has great extremities: Therefore,

Some man is brave.

THE END


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