Aristotle, Prior Analytics, Book II

by William C. Michael

© William C. Michael, 2022. We are happy to host the only online edition of Thomas Taylor’s translation of Aristotle’s Prior Analytics. The text below is an adaptation of Thomas Taylor’s translation of Aristotle’s Prior Analytics (1805) and is intended for use by students of the Classical Liberal Arts Academy. This text may not be copied or used in any way without written permission from Mr. William C. Michael. Table of contentsChapter 1Chapter 2Chapter 3Chapter 4Chapter 5Chapter 6Chapter 7Chapter 8Chapter 9Chapter 10Chapter 11Chapter 12Chapter 13Chapter 14Chapter 15Chapter 16Chapter 17Chapter 18Chapter 19Chapter 20Chapter 21Chapter 22Chapter 23Chapter 24Chapter 25Chapter 26Chapter 27 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 © is an animal (B): Therefore, Every man © 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 © is white (B): Therefore, Every swan © 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 © is white (B): Therefore No snow © 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 © is a horse (B): Therefore, Every man © 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 © is music (B): Therefore, No medicine © 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 © is a man (B): Therefore, Everything pedestrious © 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 © is prudence (B): Therefore, No contemplative knowledge © 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 © is snow (B): Therefore, Something white © 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 © is a man (B): Therefore, Something white © 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 © is beautiful (B): Therefore, Something great © 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 © is beautiful (B): Therefore, Something great © 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 © is a swan (B): Therefore, Something black © 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 © is number (B): Therefore, Something white © 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 © is white (B): Therefore, Something black © 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 © is white (B): Therefore, Something black © 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 © is number (B): Therefore, Something white © 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 © is a swan (B): Therefore, Something black © 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.