If therefore this is the rule with judgements, and if spoken affirmations and denials are judgements expressed in words, it is plain that the universal denial is the contrary of the affirmation about the same subject. [24b] Thus the propositions ‘everything good is good’, ‘every man is good’, have for their contraries the propositions ‘nothing good is good’, ‘no man is good’. The contradictory propositions, (5) on the other hand, are ‘not everything good is good’, ‘not every man is good’.
It is evident, also, that neither true judgements nor true propositions can be contrary the one to the other. For whereas, when two propositions are true, a man may state both at the same time without inconsistency, contrary propositions are those which state contrary conditions, and contrary conditions cannot subsist at one and the same time in the same subject.
* * *
1 Cf. 16a 22–26.
2 Cf. Poet. 1456b 11.
3 Cf. 17b 26–9.
4 Cf. 17b 29–37.
5 Cf. 16a 19, 30.
6 Analytica Priora, 51b 36–52a 17.
7 Cf. 17b 38.
8 Topica, viii. 7.
ANALYTICA PRIORA
Translated by A. J. Jenkinson
CONTENTS
BOOK I
A. Structure of the Syllogism.
1. PRELIMINARY DISCUSSIONS.
CHAPTER
1. Subject and scope of the Analytics. Certain definitions and divisions.
2. Conversion of pure propositions.
3. Conversion of necessary and contingent propositions.
2. EXPOSITION OF THE THREE FIGURES.
4. Pure syllogisms in the first figure.
5. Pure syllogisms in the second figure.
6. Pure syllogisms in the third figure.
7. Common properties of the three figures.
[Chapters 8–12 omitted.]
13. Preliminary discussion of the contingent.
[Chapters 14–22 omitted.]
3. SUPPLEMENTARY DISCUSSIONS.
23. Every syllogism is in one of the three figures, is completed through the first figure, and reducible to a universal mood of the first figure.
24. Quality and quantity of the premisses of the syllogism.
25. Number of the terms, propositions, and conclusions.
26. The kinds of proposition to be established or disproved in each figure.
B. Mode of discovery of arguments.
1. GENERAL.
27. Rules for categorical syllogisms, applicable to all problems.
28. Rules for categorical syllogisms, peculiar to different problems.
29. Rules for reductio ad impossibile, hypothetical syllogisms, and modal syllogisms.
30.
2. PROPER TO THE SEVERAL SCIENCES AND ARTS.
31.
3. DIVISION.
C. Analysis (1) of arguments into figures and moods of syllogism.
[Chapters 32–46 omitted.]
BOOK II
Properties and defects of syllogism; arguments akin to syllogism.
A. PROPERTIES.
[Chapters 1–15 omitted.]
B. DEFECTS.
16. Petitio principii.
17. False Cause.
18. Falsity of conclusion due to falsity in one or more premisses.
19. How to impede opposing arguments and conceal one’s own.
20. When refutation is possible.
21. Error.
C. ARGUMENTS AKIN TO SYLLOGISM.
22. Rules for conversion and for the comparison of desirable and undesirable objects.
23. Induction.
24. Example.
25. Reduction.
26. Objection.
27. Enthymeme.
ANALYTICA PRIORA
(Prior Analytics)
BOOK I
1 We must first state the subject of our inquiry and the faculty to which it belongs: (10) its subject is demonstration and the faculty that carries it out demonstrative science. [24a] We must next define a premiss, a term, and a syllogism, and the nature of a perfect and of an imperfect syllogism; and after that, the inclusion or non-inclusion of one term in another as in a whole, and what we mean by predicating one term of all, or none, of another. (15)
A premiss then is a sentence affirming or denying one thing of another. This is either universal or particular or indefinite. By universal I mean the statement that something belongs to all or none of something else; by particular that it belongs to some or not to some or not to all; by indefinite that it does or does not belong, without any mark to show whether it is universal or particular, (20) e. g. ‘contraries are subjects of the same science’, or ‘pleasure is not good’. The demonstrative premiss differs from the dialectical, because the demonstrative premiss is the assertion of one of two contradictory statements (the demonstrator does not ask for his premiss, but lays it down), whereas the dialectical premiss depends on the adversary’s choice between two contradictories. (25) But this will make no difference to the production of a syllogism in either case; for both the demonstrator and the dialectician argue syllogistically after stating that something does or does not belong to something else. Therefore a syllogistic premiss without qualification will be an affirmation or denial of something concerning something else in the way we have described; it will be demonstrative, if it is true and obtained through the first principles of its science; while a dialectical premiss is the giving of a choice between two contradictories, (30) when a man is proceeding by question, (10) but when he is syllogizing it is the assertion of that which is apparent and generally admitted, as has been said in the Topics.1 [24b] The nature then of a premiss and the difference between syllogistic, demonstrative, and dialectical premisses, may be taken as sufficiently defined by us in relation to our present need, (15) but will be stated accurately in the sequel.2
I call that a term into which the premiss is resolved, i. e. both the predicate and that of which it is predicated, ‘being’ being added and ‘not being’ removed, or vice versa.
A syllogism is discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so. (20) I mean by the last phrase that they produce the consequence, and by this, that no further term is required from without in order to make the consequence necessary.
I call that a perfect syllogism which needs nothing other than what has been stated to make plain what necessarily follows; a syllogism is imperfect, if it needs either one or more propositions, (25) which are indeed the necessary consequences of the terms set down, but have not been expressly stated as premisses.
That one term should be included in another as in a whole is the same as for the other to be predicated of all of the first. And we say that one term is predicated of all of another, whenever no instance of the subject can be found of which the other term cannot be asserted: ‘to be predicated of none’ must be understood in the same way. (30)
2 [25a] Every premiss states that something either is or must be or may be the attribute of something else; of premisses of these three kinds some are affirmative, others negative, in respect of each of the three modes of attribution; again some affirmative and negative premisses are universal, (5) others particular, others indefinite. It is necessary then that in universal attribution the terms of the negative premiss should be convertible, e. g. if no pleasure is good, then no good will be pleasure; the terms of the affirmative must be convertible, not however universally, but in part, e. g. if every pleasure is good, some good must be pleasure; the particular affirmative must convert in part (for if some pleasure is good, (10) then some good will be pleasure); but the particular negative need not convert, for if some animal is not man, it does not follow that some man is not animal.
First then take a universal negative with the terms A and B. (15) If no B is A, neither can any A be B. For if some A (say C) were B, it would not be true that no B is A; for C is a B. But if every B is A, then some A is B. For if no A were B, then no B could be A.
(20) But we assumed that every B is A. Similarly too, if the premiss is particular. For if some B is A, then some of the As must be B. For if none were, then no B would be A. But if some B is not A, there is no necessity that some of the As should not be B; e. g. let B stand for animal and A for man. Not every animal is a man: but every man is an animal. (25)
3 The same manner of conversion will hold good also in respect of necessary premisses. The universal negative converts universally; each of the affirmatives converts into a particular. If it is necessary that no B is A, it is necessary also that no A is B. For if it is possible that some A is B, (30) it would be possible also that some B is A. If all or some B is A of necessity, it is necessary also that some A is B: for if there were no necessity, neither would some of the Bs be A necessarily. But the particular negative does not convert, (35) for the same reason which we have already stated.3
In respect of possible premisses, since possibility is used in several senses (for we say that what is necessary and what is not necessary and what is potential is possible), affirmative statements will all convert in a manner similar to those described.4 For if it is possible that all or some B is A, (40) it will be possible that some A is B. [25b] For if that were not possible, then no B could possibly be A. This has been already proved.5 But in negative statements the case is different. Whatever is said to be possible, either because B necessarily is A, or because B is not necessarily A, admits of conversion like other negative statements, (5) e. g. if one should say, it is possible that man is not horse, or that no garment is white. For in the former case the one term necessarily does not belong to the other; in the latter there is no necessity that it should: and the premiss converts like other negative statements. For if it is possible for no man to be a horse, it is also admissible for no horse to be a man; and if it is admissible for no garment to be white, (10) it is also admissible for nothing white to be a garment. For if any white thing must be a garment, then some garment will necessarily be white. This has been already proved.6 The particular negative also must be treated like those dealt with above.7 But if anything is said to be possible because it is the general rule and natural (and it is in this way we define the possible), (15) the negative premisses can no longer be converted like the simple negative; the universal negative premiss does not convert, and the particular does. This will be plain when we speak about the possible.8 At present we may take this much as clear in addition to what has been said: the statement that it is possible that no B is A or some B is not A is affirmative in form: for the expression ‘is possible’ ranks along with ‘is’, (20) and ‘is’ makes an affirmation always and in every case, whatever the terms to which it is added in predication, e. g. ‘it is not-good’ or ‘it is not-white’ or in a word ‘it is not-this’. But this also will be proved in the sequel.9 (25) In conversion these premisses will behave like the other affirmative propositions.
4 After these distinctions we now state by what means, when, and how every syllogism is produced; subsequently10 we must speak of demonstration. Syllogism should be discussed before demonstration, (30) because syllogism is the more general: the demonstration is a sort of syllogism, but not every syllogism is a demonstration.
Whenever three terms are so related to one another that the last is contained in the middle as in a whole, and the middle is either contained in, or excluded from, the first as in or from a whole, (35) the extremes must be related by a perfect syllogism. I call that term middle which is itself contained in another and contains another in itself: in position also this comes in the middle. By extremes I mean both that term which is itself contained in another and that in which another is contained. If11 A is predicated of all B, and B of all C, (40) A must be predicated of all C: we have already explained12 what we mean by ‘predicated of all’. [26a] Similarly13 also, if A is predicated of no B, and B of all C, it is necessary that no C will be A.
But14 if the first term belongs to all the middle, but the middle to none of the last term, there will be no syllogism in respect of the extremes; for nothing necessary follows from the terms being so related; for it is possible that the first should belong either to all or to none of the last, (5) so that neither a particular nor a universal conclusion is necessary. But if there is no necessary consequence, there cannot be a syllogism by means of these premisses. As an example of a universal affirmative relation between the extremes we may take the terms animal, man, horse; of a universal negative relation, the terms animal, man, stone. Nor15 again can a syllogism be formed when neither the first term belongs to any of the middle, (10) nor the middle to any of the last. As an example of a positive relation between the extremes take the terms science, line, medicine: of a negative relation science, line, unit.
If then the terms are universally related, it is clear in this figure when a syllogism will be possible and when not, and that if a syllogism is possible the terms must be related as described, (15) and if they are so related there will be a syllogism.
But if one term is related universally, the other in part only, to its subject, there must be a perfect syllogism whenever universality is posited with reference to the major term either affirmatively or negatively, and particularity with reference to the minor term affirmatively: but whenever the universality is posited in relation to the minor term, (20) or the terms are related in any other way, a syllogism is impossible. I call that term the major in which the middle is contained and that term the minor which comes under the middle. Let16 all B be A and some C be B. Then if ‘predicated of all’ means what was said above,17 it is necessary that some C is A. And18 if no B is A, (25) but some C is B, it is necessary that some C is not A. (The meaning of ‘predicated of none’ has also been defined.19) So there will be a perfect syllogism. This holds good also if the premiss BC20 should be indefinite, provided that it is affirmative: for we shall have the same syllogism whether the premiss is indefinite or particular.
But if the universality is posited with respect to the minor term either affirmatively or negatively, (30) a syllogism will not be possible, whether the major premiss is positive or negative, indefinite or particular: e. g.21 if some B is or is not A, and all C is B. As an example of a positive relation between the extremes take the terms good, state, (35) wisdom: of a negative relation, good, state, ignorance. Again22 if no C is B, but some B is or is not A, or not every B is A, there cannot be a syllogism. Take the terms white, horse, swan: white, horse, raven. The same terms may be taken also if the premiss BA is indefinite.
Nor when the major premiss is universal, whether affirmative or negative, and the minor premiss is negative and particular, can there be a syllogism, whether the minor premiss be indefinite or particular: e. g.23 if all B is A, and some C is not B, or if not all C is B. [26b] For the major term may be predicable both of all and of none of the minor, to some of which the middle term cannot be attributed. Suppose the terms are animal, (5) man, white: next take some of the white things of which man is not predicated—swan and snow: animal is predicated of all of the one, but of none of the other. Consequently there cannot be a syllogism. Again24 let no B be A, but let some C not be B. (10) Take the terms inanimate, man, white: then take some white things of which man is not predicated—swan and snow: the term inanimate is predicated of all of the one, of none of the other.
Further since it is indefinite to say some C is not B, and it is true that some C is not B, (15) whether no C is B, or not all C is B, and since if terms are assumed such that no C is B, no syllogism follows (this has already been stated25), it is clear that this arrangement of terms26 will not afford a syllogism: otherwise one would have been possible with a universal negative minor premiss. (20) A similar proof may also be given if the universal premiss27 is negative.28
Nor can there in any way be a syllogism if both the relations of subject and predicate are particular, either positively or negatively, or the one negative and the other affirmative,29 or one indefinite and the other definite, or both indefinite. Terms common to all the above
are animal, (25) white, horse: animal, white, stone.
It is clear then from what has been said that if there is a syllogism in this figure with a particular conclusion, the terms must be related as we have stated: if they are related otherwise, no syllogism is possible anyhow. It is evident also that all the syllogisms in this figure are perfect (for they are all completed by means of the premisses originally taken) and that all conclusions are proved by this figure, (30) viz. universal and particular, affirmative and negative. Such a figure I call the first.
5 Whenever the same thing belongs to all of one subject, (35) and to none of another, or to all of each subject or to none of either, I call such a figure the second; by middle term in it I mean that which is predicated of both subjects, by extremes the terms of which this is said, by major extreme that which lies near the middle, by minor that which is further away from the middle. [27a] The middle term stands outside the extremes, and is first in position. A syllogism cannot be perfect anyhow in this figure, but it may be valid whether the terms are related universally or not.
If then the terms are related universally a syllogism will be possible, whenever the middle belongs to all of one subject and to none of another (it does not matter which has the negative relation), (5) but in no other way. Let M be predicated of no N, but of all O. Since, then, the negative relation is convertible, N will belong to no M: but M was assumed to belong to all O: consequently N will belong to no O.30 This has already been proved.31 Again if M belongs to all N, but to no O, then N will belong to no O.32 For if M belongs to no O, (10) O belongs to no M: but M (as was said) belongs to all N: O then will belong to no N: for the first figure has again been formed. But since the negative relation is convertible, N will belong to no O. Thus it will be the same syllogism that proves both conclusions.
The Basic Works of Aristotle (Modern Library Classics) Page 11