Azione Romana

Analitici primiLibro I

Aristotele (384–322 a.C.) · Analytica priora · Ἀναλυτικὰ πρότερα · Bekker 24a–70b

Libro I, capitolo 1 Of Proposition, Term, Syllogism, and its Elements.24a10–24b30

Inglese

24a10We must first state the subject of our inquiry and the faculty to which it belongs: its subject is demonstration and the faculty that carries it out demonstrative science. 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 24a15one term of all, or none, of another.

24a16A 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 24a20to show whether it is universal or particular, 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 24a25premiss depends on the adversary’s choice between two contradictories. 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 24a35demonstrative, 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, when a man is proceeding by question, 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 The nature then of a premiss and the difference between syllogistic, demonstrative, and dialectical premisses, may be taken as sufficiently 24b15defined by us in relation to our present need, but will be stated accurately in the sequel.2

24b16I 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.

24b19A syllogism is discourse in which, certain things being stated, something other than what is stated follows of 24b20necessity from their being so. 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.

24b23I 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 24b25more propositions, which are indeed the necessary consequences of the terms set down, but have not been expressly stated as premisses.

24b27That 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 24b30of none’ must be understood in the same way.

Note del traduttore
  1. 1 τροῦ 29, 1043 ὃ.
  2. 2 The nature of demonstrative premisses is discussed in the 2051, Axn.; that of dialectical premisses in the Zo/zcs.

Citato nell'enciclopedia: GIUDIZIO · PROPOSIZIONE · SILLOGISMO

Libro I, capitolo 2 On the Conversion of Propositions.25a1–26

Inglese

25a1Every 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, 25a5others 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; 25a10the particular affirmative must convert in part (for if some pleasure is good, 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.

25a14First then take a universal negative with the terms 25a15A and B. 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. But 25a20we 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 25a25and A for man. Not every animal is a man; but every man is an animal.

Libro I, capitolo 3 On the Conversion of Modal Propositions.25a27–25b25

Inglese

25a27The same manner of conversion will hold good also in respect of necessary premisses. The universal negative converts universally; each of the affirmatives converts into 25a30a 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, 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 25a35necessarily. But the particular negative does not convert, for the same reason which we have already stated.1

25a37In 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 25a40statements will all convert in a manner similar to those described.2 For if it is possible that all or some B is A, it 25bwill be possible that some A is B. For if that were not possible, then no B could possibly be A. This has been already proved.3 But in negative statements the case is different. Whatever is said to be possible, either because B necessarily is A,4 or because B is not necessarily A, admits 25b5of conversion like other negative statements, 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 25b10to 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, 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. The particular negative also must be treated like those dealt with above.5 But if anything is said to be possible because 25b15it is the general rule and natural (and it is in this way we define the possible), the negative premisses can no longer be converted like the simple negatives; the universal negative premiss does not convert, and the particular does. This will be plain when we speak about the possible.6 At present we may take this much as clear in addition to what has been 25b20said: 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’, 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 25b25proved in the sequel.7 Ji conversion these premisses will behave like the other affirmative propositions.

Note del traduttore
  1. 1 11... 12, 22-6.
  2. 2 In ll. 7-13.
  3. 3 430-2.
  4. 4 Omit μὴ in l. 4 with A, B, Phil., and Waitz.
  5. 5 214-17,
  6. 6 In ἃ 12, * cc. 13, 17. ὃς͵ 46.
  7. 7 In the Posterior Analytics.

Libro I, capitolo 4 Of Syllogism, and of the first Figure.25b26–26b33

Inglese

25b27After these distinctions we now state by what means, when, and how every syllogism is produced; subsequently we must speak of demonstration. Syllogism should be discussed before demonstration, because syllogism is the 25b30more general: the demonstration is a sort of syllogism, but not every syllogism is a demonstration.

25b32Whenever 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, the extremes must be related by 25b35a 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. If1 A is predicated of all B, and B of all C, A must be predicated of all C: we 25b40have already explained2 what we mean by ‘predicated of 26aall3. Similarly also, if A is predicated of no B, and B of all C, it is necessary that no C will be A.

26a2But4 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 26a5first should belong either to all or to none of the last, 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. Nor5 again can a syllogism be formed when neither the 26a10first term belongs to any of the middle, 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.

26a13If then the terms are universally related, it is clear in this figure when a syllogism will be possible and when not, and 26a15that if a syllogism is possible the terms must be related as described, and if they are so related there will be a syllogism.

26a17But 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 26a20with reference to the minor term affirmatively: but whenever the universality is posited in relation to the minor term, 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. Let6 all B be A and some C be B. Then if ‘predicated of all’ means what was said above,7 it is necessary 26a25that some C is A. And if8 no B is A, but some C is B, it is necessary that some C is not A. (The meaning of ‘predicated of none’ has also been defined.9) So there will be a perfect syllogism. This holds good also if the premiss BC10 should be indefinite, provided that it is affirmative: for we shall have the same syllogism whether the premiss is indefinite or particular.

26a30But if the universality is posited with respect to the minor term either affirmatively or negatively, a syllogism will not be possible, whether the major premiss is: positive or negative, indefinite or particular: e.g.11 if some B is or is not A, and all C is. As an example of a positive relation between 26a35the extremes take the terms good, state, wisdom: of a negative relation, good, state, ignorance. Again‘12 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.

26b1Nor 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.13 if all B is A, and some C is not B, or if not all C is B. For the major term may be predicable both of all and of none of the minor, 26b5to some of which the middle term cannot be attributed. Suppose the terms are animal, 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 bea syllogism. 26b10Again14 let no B be A, but let some C not be B. 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.

26b14Further since it is indefinite to say some C is not B, and 26b15it is true that some C is not B, 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 stated *), it is clear that this arrangement of terms will not afford a syllogism: otherwise one would have been possible with 26b20a universal negative minor premiss. A similar proof may also be given if the universal premiss15 is negative.

26b22Nor can there in any way be a syllogism if both the relations of subject and predicate are particular, cither positively or negatively, or the one negative and the other affirmative,16 or one indefinite and the other definite, or both indefinite. 26b25Terms common to all the above are animal, white, horse: animal, white, stone.

26b26It 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 26b30they are all completed by means of the premisses originally taken) and that all conclusions are proved by this figure, viz. universal and particular, affirmative and negative. Such a figure I call the first.

Note del traduttore
  1. 1 Barbara, major A, minor A.
  2. 2 24° 28,
  3. 3 Celarent, major E, minor A.
  4. 4 Major A, minor E.
  5. 5 Major E, minor E.
  6. 6 Darii.
  7. 7 24) 28.
  8. 8 Ferio.
  9. 9 24b30.
  10. 10 The Aristotelian formula for the proposition, AB, in which δ represents the subject and A the predicate (A belongs to B), has been retained throughout, because in most places this suits the context better than the modern formula in which A represents the subject and B the predicate.
  11. 11 Major 7 or O, minor A.
  12. 12 Major 7 or O, minor E.
  13. 13 Major A, minor O,
  14. 14 Major E, minor O. 2D,’ Major A, minor O. * i.e. the major premiss.
  15. 15 δ Major E, minor ὦ,
  16. 16 TI, OO, IO, OF.

Citato nell'enciclopedia: SILLOGISMO

Libro I, capitolo 5 Of the second Figure.26b34–28a9

Inglese

26b34Whenever the same thing belongs to all of one subject, 26b35and 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. The middle term 27astands 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.

27a3If 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 27a5the negative relation), 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.1 This has already been proved.2 Again if M belongs 27a10to all N, but to no O, then N will belong to no O.3 For if M belongs to no O, O belongs to no M: but M (as was said) belongs to all .V: O then will belong to no .V: 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.

27a15It is possible to prove these results also by reduction ad impossibile. ;

27a16It is clear then that a syllogism is formed when the terms are so related, but not a perfect syllogism: for necessity is not perfectly established merely from the original premisses; others also are needed.

27a18But if M is predicated of every .V and O, there cannot be a syllogism. Terms to illustrate a positive relation between the extremes are substance, animal, man; a negative 27a20relation, substance, animal, number—substance being the middle term.

27a21‘Nor is a syllogism possible when M is predicated neither of any N nor of any O. Terms to illustrate a positive relation are line, animal, man: a negative relation, line, animal, stone.

27a24It is clear then that if a syllogism is formed when the terms are universally related, the terms must be related as we 27a25stated at the outset4 for if they are otherwise related no necessary consequence follows.

27a26If the middle term is related universally to one of the extremes, a particular negative syllogism must result whenever the middle term is related universally to the major whether positively or negatively, and particularly to the minor and in a manner opposite to that of the universal statement: by ‘an opposite manner’ I mean, if the 27a30universal statement is negative, the particular is affirmative: if the universal is affirmative, the particular is negative. For if I belongs to no .V, but to some O, it is necessary that .V does not belong to some O.5 For since the negative statement is convertible, N will belong to no MI: but M was admitted to 27a35belong to some O: therefore .N will not belong to some O: for the result is reached by means of the first figure. Again if M belongs to all N, but not to some O, it is necessary that .V does not belong to some O:6 for if .V belongs to all O, and MI is predicated also of all .V, A must belong 27bto all O: but we assumed that M does not belong to some O. And if M belongs to all .V but not to all O, we shall conclude that N does not belong to all O: the proof is the same as the above. But if M is predicated of all O, but not of all .V, there will be no syllogism. Take the terms 27b5animal, substance, raven; animal, white, raven. Nor will there be a conclusion when M is predicated of no O, but of some .V. Terms to illustrate a positive relation between the extremes are animal, substance, unit: a negative relation, animal, substance, science.

27b9If then the universal statement is opposed to the particular, 27b10we have stated when a syllogism will be possible and when not: but if the premisses are similar in form, I mean both negative or both affirmative, a syllogism will not be possible anyhow. First let them be negative, and let the major premiss be universal, e.g. let M belong to no .V, and not to 27b15some O. It is possible then for .V to belong either to all O or to no O. Terms to illustrate the negative relation are black, snow, animal. But it is not possible to find terms of which the extremes are related positively and universally, if M belongs to some O, and does not belong to some O. For if V belonged to all O, but JI to no .V, then M would belong to no O: but we assumed that it belongs to some O. In this 27b20way then it is not admissible to take terms: our point must be proved from the indefinite nature of the particular statement. For since it is true that M does not belong to some O, even if it belongs to no O, and since if it belongs to no O a syllogism is (as we have seen7) not possible, clearly it will not be possible now either.

27b24Again let the premisses be affirmative, and let the major premiss as before be universal, e.g. let M belong to all V 27b25and to some O. It is possible then for TV to belong to all O or to no O. Terms to illustrate the negative relation are white, swan, stone. But it is not possible to take terms to illustrate the universal affirmative relation, for the reason already stated :? the point must be proved from the indefinite nature of the particular statement. But if the minor premiss 27b30is universal, and I belongs to no O, and not to some N, it is possible for N to belong either to all O or to no O. Terms for the positive relation are white, animal, raven: for the negative relation, white, stone, raven. If the premisses are affirmative, terms for the negative relation are white, animal, snow; for the positive relation, white, animal, swan. Evidently then, whenever the premisses are similar in form, 27b35and one is universal, the other particular, a syllogism cannot be formed anyhow. Nor is one possible if the middle term belongs to some of each of the extremes, or does not belong to some of either, or belongs to some of the one, not to some of the other, or belongs to neither universally,” or is related to them indefinitely. Common terms for all the above are white, animal, man: white, animal, inanimate.

28a1It is clear then from what has been said that if the terms are related to one another in the way stated, a syllogism results of necessity; and if there is a syllogism, the terms must be so related. But it is evident also that all the syllogisms in this figure are imperfect: for all are made 28a5perfect by certain supplementary statements, which either are contained in the terms of necessity or are assumed as hypotheses, i.e. when we prove per impossibile. And it is evident that an affirmative conclusion is not attained by means of this figure, but all are negative, whether universal or particular.

Note del traduttore
  1. 1 Cesare.
  2. 2 25b4o. τς
  3. 3 Camestres. Read οὐδὲ τῷ Ξ τὸ Ν in l. 10 with A,, Waitz, and perhaps Philoponus.
  4. 4 1. 3.
  5. 5 Festino.
  6. 6 Baroco. . 645-24,3 C Bat, 21.18.
  7. 7 3 An alternative and clearer expression for ‘does not belong to some of either’.

Libro I, capitolo 6 Of Syllogisms in the third Figure.28a10–29a18

Inglese

28a10But if one term belongs to all, and another to none, of a third, or if both belong to all, or to none, of it, I call such a figure the third; by middle term in it I mean that of which both the predicates are predicated, by extremes I mean the predicates, by the major extreme that which is further from the middle, by the minor that which is nearer to it. The 28a15middle term stands outside the extremes, and is last in position. A syllogism cannot be perfect in this figure either, but it may be valid whether the terms are related universally or not to the middle term.

28a18If they are universal, whenever both P and R belong to all S, it follows that P will necessarily belong to some R.1 For, since the affirmative statement is convertible, S will 28a20belong to some R: consequently since P belongs to all S, and S to some R, P must belong to some R: for a syllogism in the first figure is produced. It is possible to demonstrate this also per impossibile and by exposition. For if both P and R belong to all S, should one of the Ss, e.g. N, be taken, 28a25both P and R will belong to this, and thus P will belong to some R.

28a27If R belongs to all S, and P to no S, there will be a syllogism to prove that P will necessarily not belong to some R.2 This may be demonstrated in the same way as before by converting the premiss RS.3 It might be 28a30proved also per impossibile, as in the former cases. But if R belongs to no S, P to all .S, there will be no syllogism. Terms for the positive relation are animal, horse, man: for the negative relation animal, inanimate, man.

28a33Nor can there be a syllogism when both terms are asserted of no S. Terms for the positive relation are animal, horse, 28a35inanimate; for the negative relation man, horse, inanimate— inanimate being the middle term.

28a37It is clear then in this figure also when a syllogism will be possible and when not, if the terms are related universally. For whenever both the terms are affirmative, there will be a syllogism to prove that one extreme belongs to some of the other; but when they are negative, no syllogism will 28bbe possible. But when one is negative, the other affirmative, if the major is negative, the minor affirmative, there will be a syllogism to prove that the one extreme does not belong to some of the other: but if the relation is reversed, no syllogism will be possible.

28b5If one term is related universally to the middle, the other in part only, when both are affirmative there must be a syllogism, no matter which of the premisses is universal. For if R belongs to all S, P to some S, P must belong to some R.4 For since the affirmative statement is convertible 28b10S will belong to some P: consequently since R belongs to all S, and S to some P, R must also belong to some P: therefore P must belong to some R.

28b12Again if R belongs to some S, and P to all S, P must belong to some R.5 This may be demonstrated in the same way as the preceding. And it is possible to demonstrate it also per impossibile and by exposition, as in the former 28b15cases. But if one term is affirmative, the other negative, and if the affirmative is universal, a syllogism will be possible whenever the minor term is affirmative. For if R belongs to all S, but P does not belong to some S, it is necessary that P does not belong to some R. For if P belongs to all R, and R belongs to all S,6 then P will belong to all S: 28b20but we assumed that it did not. Proof is possible also without reduction ad impossibile, if one of the ^s be taken to which P does not belong.

28b22But whenever the major is affirmative, no syllogism will be possible, e.g. if P belongs to all S, and R does not belong to some S. Terms for the universal affirmative relation are animate, man, animal. For the universal negative relation 28b25it is not possible to get terms, if A belongs to some S, and does not belong to some S. For if P belongs to all S, and R to some S, then P will belong to some R: but we assumed! that it belongs to no R. We must put the matter as before. Since the expression ‘it does not belong to some’ is indefinite, it may be used truly of that also which 28b30belongs to none. But if R belongs to no S, no syllogism is possible, as has been shown.7 Clearly then no syllogism will be possible here.

28b32But if the negative term is universal, whenever the major is negative and the minor affirmative there will be a syllogism. For if P belongs to no S, and R belongs to some S, P will not belong to some R:+*8 for we shall have the first figure 28b35again, if the premiss RS is converted.

28b36But when the minor is negative, there will be no syllogism. Terms for the positive relation are animal, man, wild: for the negative relation, animal, science, wild—the middle in both being the term wild.

28b39Nor is a syllogism possible when both are stated in the negative, but one is universal, the other particular. When 29athe minor is related universally to the middle, take the terms animal, science, wild; animal, man, wild. When the major is related universally to the middle, take as terms for a negative relation raven, snow, white. For a positive relation terms cannot be found, if R belongs to some .S, and 29a5does not belong to some S. For if P belongs to all R, and R to some S, then P belongs to some S: but we assumed that it belongs to no S. Our point, then, must be proved from the indefinite nature of the particular statement.

29a7Nor is a syllogism possible anyhow, if each of the extremes belongs to some of the middle, or does not belong, or one belongs and the other does not to some of the middle, or one belongs to some of the middle, the other not to all, or if the premisses are indefinite. Common terms for all are 29a10animal, man, white: animal, inanimate, white.

29a11It is clear then in this figure also when a syllogism will be possible, and when not; and that if the terms are as stated, a syllogism results of necessity, and if there is a syllogism, the terms must be so related. It is clear also that all the ‘i.e. in supposing the universal negative relation between the extremes. 29a15syllogisms in this figure are imperfect (for all are made perfect by certain supplementary assumptions), and that it will not be possible to reach a universal conclusion by means of this figure, whether negative or affirmative.

Note del traduttore
  1. 1 Darapti.
  2. 2 Felapton.
  3. 3 See note 268 29.
  4. 4 Disamis.
  5. 5 Datisi. > Bocardo.
  6. 6 Comma after = in l. 19.
  7. 7 27b20,
  8. 8 28 30. 4 Ferison.

Libro I, capitolo 7 Of the three first Figures, and of the Completion of Incomplete Syllogisms.29a19–29b28

Inglese

29a19It is evident also that in all the figures, whenever a proper 29a20syllogism does not result, if both the terms are affirmative or negative nothing necessary follows at all, but if one is affirmative, the other negative, and if the negative is stated universally, a syllogism always results relating the minor? to the major term,1 e. g. if A belongs to all or some B, and B belongs to no C: for if the premisses are converted 29a25it is necessary that C does not belong to some A.2 Similarly also in the other figures: a syllogism always results by means of conversion. It is evident also that the substitution of an indefinite for a particular affirmative will effect the same syllogism in all the figures.

29a30It is clear too that all the imperfect syllogisms are made perfect by means of the first figure. For all are brought to a conclusion either ostensively or per impossibile. In both ways the first figure is formed: if they are made perfect ostensively, because (as we saw) all are brought to a conclusion by means of conversion, and conversion produces the 29a35first figure: if they are proved per impossibile, because on the assumption of the false statement the syllogism comes about by means of the first figure, e.g. in the last figure, if A and B belong to all C, it follows that A belongs to some B: for if A belonged to no B, and B belongs to all C, A would belong to no C: but (as we stated) it belongs to all C. Similarly also with the rest.

29b1It is possible also to reduce all syllogisms to the universal syllogisms in the first figure. Those in the second figure are clearly made perfect by these, though not all in the same way; the universal syllogisms are made perfect by converting 29b5the negative premiss, each of the particular syllogisms by reduction ad impossibile. In the first figure particular syllogisms are indeed made perfect by themselves, but it is possible also to prove them by means of the second figure, reducing them ad impossibile, e.g. if A belongs to all B, and B to some C, it follows that A belongs to some C. For if it belonged to no C, and belongs to all B, then B will 29b10belong to no C: this we know by means of the second figure. Similarly also demonstration will be possible in the case of the negative. For if A belongs to no B, and B belongs to some C, A will not belong to some C: for if it belonged to all C, and belongs to no B, then B will belong to no C: and 29b15this (as we saw) is the middle figure. Consequently, since all syllogisms in the middle figure can be reduced to universal syllogisms in the first figure, and since particular syllogisms in the first figure can be reduced to syllogisms in the middle figure, it is clear that particular syllogisms! can be reduced to universal syllogisms in the first figure. Syllogisms in the 29b20third figure, if the terms are universal, are directly made perfect by means of those syllogisms;3 but, when one of the premisses is particular, by means of the particular syllogisms in the first figure: and these (we have seen) may be reduced to the universal syllogisms in the first figure: consequently also the particular syllogisms in the third figure may be so reduced. It is clear then that all syllogisms may 29b25be reduced to the universal syllogisms in the first figure.

29b26We have stated then how syllogisms which prove that something belongs or does not belong to something else are constituted, both how syllogisms of the same figure are constituted in themselves, and how syllogisms of different figures are related to one another.

Note del traduttore
  1. 1 As predicate.
  2. 2 As subject. 5. Fesapo, Fresison.
  3. 3 se. in the first figure. * viz. by reduction fer zipossibile to Celarent and Barbara.

Libro I, capitolo 8 Of Syllogisms derived from two necessary Propositions.29b29–30a14

Inglese

29b29Since there is a difference according as something belongs, 29b30necessarily belongs, or may belong to something else (for many things belong indeed, but not necessarily, others neither necessarily nor indeed at all, but it is possible for them to belong), it is clear that there will be different syllogisms to prove each of these relations, and syllogisms with differently related terms, one syllogism concluding from what is necessary, another from what is, a third from what 29b35is possible.

29b36There is hardly any difference between syllogisms from necessary premisses and syllogisms from premisses which merely assert. When the terms are put in the same way, then, whether something belongs or necessarily belongs (or does not belong) to something else, a syllogism will or will not result alike in both cases, the only difference being the 30aaddition of the expression ‘necessarily’ to the terms. For the negative statement is convertible alike in both cases, and we should give the same account of the expressions ‘to be contained in something as in a whole’ and ‘to be predicated of all of something’. With the exceptions to be made below, the conclusion will be proved to be necessary 30a5by means of conversion, in the same manner as in the case of simple predication. But in the middle figure when the universal statement is affirmative, and the particular negative, and again in the third figure when the universal is affirmative and the particular negative, the demonstration will not take the same form, but it is necessary by the ‘exposition’ of a part of the subject of the particular negative 30a10proposition, to which the predicate does not belong, to make the syllogism in reference to this: with terms so chosen the conclusion will necessarily follow. But if the relation is necessary in respect of the part taken, it must hold of some of that term in which this part is included: for the part taken is just some of that. And each of the resulting syllogisms is in the appropriate figure.1

Note del traduttore
  1. 1 Baroco. All N is necessarily 277. Some Ο is necessarily not M, .. Some Ὁ is necessarily not A’. Bocardo. Some S is necessarily not ?. All S is necessarily R. οὖν Some R is necessarily not P. When the propositions are assertoric, the conclusions are proved by reduction ad zimposstbile. The contradictory of ‘Some Ὁ is necessarily not WV’ is ‘Every Ὁ is possibly NV’: but if this is combined with ‘All N is necessarily M’, the combination of an apodictic with a problematic premiss does not give an apodictic conclusion. Aristotle therefore falls back on another method of proof. If some O is necessarily not M, take some part of O—viz. Q—all of which is necessarily not M. Then It is necessary that all N be M. It is necessary that no Q be J. .. It is necessary that no Q be V. εἷς It is necessary that some O be not N. Baroco is proved by means of Camestres; similarly Bocardo is proved by means of Felapton—each by a syllogism in the same figure

Libro I, capitolo 9 Of Syllogisms, whereof one Proposition is necessary, and the other pure in the first Figure.30a15–30b6

Inglese

30a15It happens sometimes also that when one premiss is necessary the conclusion is necessary, not however when either premiss is necessary, but only when the major is, e.g. if A is taken as necessarily belonging or not belonging to B, but B is taken as simply belonging to C: for if the 30a20premisses are taken in this way, A will necessarily belong or not belong to C. For since A necessarily belongs, or does not belong, to every B, and since C is one of the Bs, it is clear that for C1 also the positive or the negative relation to A will hold necessarily. But if the major premiss is not necessary, but the minor is necessary, the conclusion 30a25will not be necessary. For if it were, it would result both through the first figure and through the third that A belongs necessarily to some B. But this is false; for B may be such that it is possible that A should belong to none of it. Further, an example also makes it clear that the conclusion 30a30will not be necessary, e.g. if A were movement, B animal, C man: man is an animal necessarily, but an animal does not move necessarily, nor does man. Similarly also if the major premiss is negative; for the proof is the same.

30a34In particular syllogisms, if the universal premiss is necessary, 30a35then the conclusion will be necessary; but if the particular, the conclusion will not be necessary, whether the universal premiss is negative or affirmative. First let the universal be necessary, and let A belong to all B necessarily, but let B simply belong to some C: it is necessary then that 30a40A belongs to some C necessarily: for C falls under B, and 30bA was assumed to belong necessarily to all B. Similarly also if the syllogism should be negative: for the proof will be the same. But if the particular premiss is necessary, the conclusion will not be necessary: for from the denial of such a conclusion nothing impossible results,? just as it does not 30b5in the universal syllogisms. The same is true of negative syllogisms. Try the terms movement, animal, white.

Note del traduttore
  1. 1 Read ro r in l. 22 with A, B, C, Phil., and Waitz. * i.e. from the assumption ‘all Cis possibly not A’. Cf. 36a22-5.

Libro I, capitolo 10 Of the same in the second Figure.30b7–31a17

Inglese

30b6In the second figure, if the negative premiss is necessary, then the conclusion will be necessary, but if the affirmative, as itself (l. 13). Camestres and Felapton can then by conversion be proved by means of Celarent and Ferio (ll. 3–5). not necessary. First let the negative be necessary; let A 30b10be possible of no B, and simply belong to C. Since then the negative statement is convertible, B is possible of no A. But A belongs to all C; consequently B is possible of no C. For C falls under A. The same result would be obtained if the minor premiss were1 negative: for if A is possible of no 30b15C, C is possible of no A: but A belongs to all B, consequently C is possible of none of the Bs: for again we have obtained the first figure. Neither then is B possible of C: for conversion is possible without modifying the relation.

30b19But if the affirmative premiss is necessary, the conclusion 30b20will not be necessary. Let A belong to all B necessarily, but to no C simply. If then the negative premiss is converted; the first figure results. But it has been proved? in the case of the first figure that if the negative major premiss is not necessary the conclusion will not be necessary either. Therefore the same result will obtain here. Further, if the 30b25conclusion is necessary, it follows that C necessarily does not belong to some A. For if B necessarily belongs to no C, C will necessarily belong to no B. But B at any rate must belong to some A, if it is true (as was assumed) that A necessarily belongs to all B. Consequently it is necessary 30b30that C does not belong to some A. But nothing prevents such an A being taken that it is possible for C to belong to all of it. Further one might show by an exposition of terms that the conclusion is not necessary without qualification, though it is a necessary conclusion from the premisses. For example let A be animal, B man, C white, and let the premisses be assumed to correspond to what we had before:2 30b35sit is possible that animal should belong to nothing white. Man then will not belong to anything white, but not necessarily: for it is possible for man to be born white, not however so long as animal belongs to nothing white. Consequently under these conditions the conclusion will be necessary, but it is not necessary without qualification.

31a1Similar results will obtain also in particular syllogisms. For whenever the negative premiss is both universal and necessary, then the conclusion will be necessary: but whenever the affirmative premiss is universal, the negative particular, 31a5the conclusion will not be necessary. First then let the negative premiss be both universal and necessary: let it be possible for no B that A should belong to it, and let A simply belong to some C. Since the negative statement is convertible, it will be possible for no A that B should belong toit: but A belongs to some C; consequently B necessarily 31a10does not belong to some of the Cs. Again let the affirmative premiss be both universal and necessary, and let the major premiss be affirmative. If then A necessarily belongs to all B, but does not belong to some C, it is clear that B will not belong to some C, but not necessarily. For the same terms can be used to demonstrate the point, which were used in 31a15the universal syllogisms. Nor again, if the negative statement is necessary but particular, will the conclusion be necessary. The point can be demonstrated by means of the same terms.

Note del traduttore
  1. 1 Read τεθείη in l. 14 with Al, Phil.!, and Them.
  2. 2 293-33. 1, 20.

Libro I, capitolo 11 Of the same in the third Figure.31a18–32a5

Inglese

31a18In the last1 figure when the terms are related universally to the middle, and both premisses are affirmative, if one of 31a20the two is necessary, then the conclusion will be necessary. But if one is negative, the other affirmative, whenever the negative is necessary the conclusion also will be necessary, but whenever the affirmative is necessary the conclusion will not be necessary. First let both the premisses be affirmative, 31a25and let A and B belong to all C, and let AC be necessary. Since then B belongs to all C, C also will belong to some B, because the universal is convertible into the particular: consequently if A belongs necessarily to all C, and C belongs to some B, it is necessary that A should belong to some B 31a30also. For B is under C. The first figure then is formed. A similar proof will be given also if BC is necessary. For C is convertible with some A: consequently if B belongs necessarily to all C, it will belong necessarily also to some A.

31a34Again let AC be negative, BC affirmative, and let the 31a35negative premiss be necessary. Since then C is convertible with some B, but A necessarily belongs to no C, A will necessarily not belong to some B either: for B is under C. But if the affirmative is necessary, the conclusion will not be necessary. For suppose BC is affirmative and necessary, while AC is negative and not necessary. Since then the 31a40affirmative is convertible, C also will belong to some B necessarily: consequently if A belongs to none of the Cs, 31bwhile C belongs! to some of the Us, A will not belong to some of the Ss—but not of necessity; for it has been proved, in the case of the first figure, that if the negative premiss is not necessary, neither will the conclusion be necessary. Further, the point may be made clear by considering the 31b5terms. Let the term A be ‘good’, let that which B signifies be ‘animal’, let the term C be ‘horse’. It is possible then that the term good should belong to no horse, and it is necessary that the term animal should belong to every horse: but it is not necessary that some animal should not be good, since it is possible for every animal to be good. Or if that is not possible, take as the term ‘awake’ or ‘asleep’: for 31b10every animal can accept these.

31b11If, then, the premisses are universal, we have stated when the conclusion will be necessary. But if one premiss is universal, the other particular, and if both are affirmative, whenever the universal is necessary the conclusion also must 31b15be necessary. The demonstration is the same as before ;2 for the particular affirmative also is convertible. If then it is necessary that B should belong to all C, and A falls under C,’ it is necessary that B should belong to some A. But if B must belong to some A, then A must belong to some B: for conversion is possible. Similarly also if AC should be 31b20necessary and universal: for B falls under C.3 But if the particular premiss is necessary, the conclusion will not be necessary. Let the premiss BC be both particular and necessary, and let A belong to all C, not however necessarily. If the proposition BC is converted the first figure is formed, 31b25and the universal premiss is not necessary, but the particular is necessary. But when the premisses were thus, the conclusion (as we proved4 was not necessary: consequently it is not here either. Further, the point is clear if we look at the terms. Let A be waking, B biped, and C animal. It is necessary that B should belong to some C, but it is possible 31b30for A to belong to C, and that A should belong to B is not necessary. For there is no necessity that some biped should be asleep or awake. Similarly and by means of the same terms proof can be made, should the proposition AC be both particular and necessary.

31b34But if one premiss is affirmative, the other negative, whenever the universal is both negative and necessary the 31b35conclusion also will be necessary. For if it is not possible that A should belong to any C, but B belongs to some C, it is necessary that A should not belong to some B. But whenever the affirmative proposition is necessary, whether universal or particular, or the negative is particular, the conclusion will not be necessary. The proof of this by 31b40reduction will be the same as before;5 but if terms are wanted, when the universal affirmative is necessary, take the terms ‘waking ’—‘animal ’—‘man’, ‘man’ being middle, 32aand when the affirmative is particular and necessary, take the terms ‘waking ’—‘animal ’—‘white’: for it is necessary that animal should belong to some white thing, but it is possible that waking should belong to none, and it is not necessary that waking should not belong to some animal. But when the negative proposition being particular is 32a5necessary, take the terms ‘biped’, ‘moving’, ‘animal’, ‘animal’ being middle.

Note del traduttore
  1. 1 30b33-40.
  2. 2 sc. necessarily.
  3. 3 424-33. 5 i.e. some C is A. * i.e. some C is }.
  4. 4 302 35-7, P1-5.
  5. 5 Cf ἃ 37-» 4, b 20-7.

Libro I, capitolo 12 A comparison of pure with necessary Syllogisms.32a6–16

Inglese

32a7It is clear then that a simple conclusion is not reached unless both premisses are simple assertions, but a necessary conclusion is possible although one only of the premisses is necessary. But in both cases, whether the syllogisms are 32a10affirmative or negative, it is necessary that one premiss should be similar to the conclusion. I mean by ‘similar’, if the conclusion is a simple assertion, the premiss must be simple; if the conclusion is necessary, the premiss must be necessary. Consequently this also is clear, that the conclusion will be neither necessary nor simple unless a necessary or simple premiss is assumed.

Libro I, capitolo 13 Of the Contingent, and its concomitant Propositions.32a16–32b37

Inglese

32a15Perhaps enough has been said about the proof of necessity, how it comes about and how it differs from the proof of a simple statement. We proceed to discuss that which is possible, when and how and by what means it can be proved. I use the terms ‘to be possible’ and ‘the possible’ of that which is not necessary but, being assumed, 32a20results in nothing impossible. We say indeed ambiguously of the necessary that it is possible. But that my definition of the possible is correct is clear from the phrases by which we deny or on the contrary affirm possibility. For the expressions ‘it is not possible to belong’, ‘it is impossible to belong’, and ‘it is necessary not to belong’ are either identical or follow from one another; consequently their opposites 32a25also, ‘it is possible to belong’, ‘it is not impossible to belong’, and ‘it is not necessary not to belong’, will either be identical or follow from one another. For of everything the affirmation or the denial holds good. That which is possible then will be not necessary and that which is not necessary will be possible. It results that all premisses in 32a30the mode of possibility are convertible into one another. I mean not that the affirmative are convertible into the negative, but that those which are affirmative in form admit of conversion by opposition, e.g. ‘it is possible to belong’ may be converted into ‘it is possible not to belong’, and ‘it is possible for A to belong to all B’ into ‘it is possible for A to belong to no B’ or ‘not to all B’, and ‘it is possible 32a35for A to belong to some B into ‘it is possible for A not to belong to some B’. And similarly the other propositions in this mode can be converted. For since that which is possible is not necessary, and that which is not necessary may possibly not belong, it is clear that if it is possible that A should belong to B, it is possible also that it should not belong to B: and if it is possible that it should belong to all, it is also possible that it should not belong to all. The same 32a40holds good in the case of particular affirmations: for the 32bproof is identical. And such premisses are affirmative and not negative; for ‘to be possible’ is in the same rank as ‘to be’, as was said above.1

32b4Having made these distinctions we next point out that 32b5the expression ‘to be possible’ is used in two ways. In one it means to happen generally and fall short of necessity, e.g. man’s turning grey or growing or decaying, or generally what naturally belongs to a thing (for this has not its necessity unbroken, since man’s existence is not continuous for ever, although if a man does exist, it comes about either necessarily or generally). In another sense the expression means the indefinite, which can be both thus and not thus, e.g. an animal’s walking or an earthquake’s taking place while it is walking, or generally what happens by chance: for none of these inclines by nature in the one way more than in the opposite.

32b14That which is possible in each of its two senses is convertible 32b15into its opposite, not however in the same way: but what is natural is convertible because it does not necessarily belong (for in this sense it is possible that a man should not grow grey2 and what is indefinite is convertible because it inclines this way no more than that. Science and demonstrative syllogism are not concerned with things which are indefinite, because the middle term is uncertain; 32b20but they are concerned with things that are natural, and as a rule arguments and inquiries are made about things which are possible in this sense. Syllogisms indeed can be made about the former, but it is unusual at any rate to inquire about them.

32b23These matters will be treated more definitely in the sequel3 our business at present is to state the moods and nature of the syllogism made from possible premisses. The expression 32b25‘it is possible for this to belong to that’ may be understood in two senses: ‘that’ may mean either that to which ‘that’ belongs or that to which it may belong; for the expression ‘A is possible of the subject of B’ means that it is possible cither of that of which B is stated or of that of which B may possibly be stated. It makes no difference whether we say, 32b30A is possible of the subject of B, or all B admits of A. It is clear then that the expression ‘A may possibly belong to all B’ might be used in two senses. First then we must state the nature and characteristics of the syllogism which arises if B is possible of the subject of C, and A is possible of the subject of B. For4 thus both premisses are assumed 32b35in the mode of possibility; but whenever A is possible of that of which B is true, one premiss is a simple assertion, the other a problematic. Consequently we must start from premisses which are similar in form,5 as in the other cases.

Note del traduttore
  1. 1 25b21.
  2. 2 i.e. it is because man does not necessarily grow grey that ‘man may grow grey’ is convertible into ‘man may not grow grey’.
  3. 3 Post. An. i. δ.
  4. 4 Read ὁμοιοσχημόνων in l. 37 with A,, B, C, Al., Phil., and Waitz.
  5. 5 32b25-37,

Libro I, capitolo 14 Of Syllogisms with two contingent Propositions in the first Figure.32b38–33b24

Inglese

32b38Whenever A may possibly belong to all B, and B to all C, there will be a perfect syllogism to prove that A may possibly 32b40belong to all C. This is clear from the definition: 33afor it was in this way that we explained ‘to be possible for one term to belong to all of another’.1 Similarly if it is possible for A to belong to no B, and for B to belong to all C, then it is possible for A to belong to no C. For the statement that it is possible for A not to belong to that of which B may be true means (as we saw) that none of those things which can 33a5possibly fall under the term B is left out of account. But whenever A may belong to all B, and B may belong to no C, then indeed no syllogism results from the premisses assumed, but if the premiss BC is converted after the manner of problematic propositions, the same syllogism results as before.2 For since it is possible that B should 33a10belong to no C, it is possible also that it should belong to all C. This has been stated above.3 Consequently if B is possible for all C, and A is possible for all B, the same syllogism again results. Similarly if in both the premisses the negative is joined with ‘it is possible’: e.g. if A may 33a15belong to none of the Bs, and B to none of the Cs. No syllogism results from the assumed premisses, but if they are converted we shall have the same syllogism as before.” It is clear then that if the minor premiss is negative, or if both premisses are negative, either no syllogism results, or if 33a20one does it is not perfect. For the necessity results from the conversion.

33a22But if one of the premisses is universal, the other particular, when the major premiss is universal there will be a perfect syllogism. For if A is possible for all B, and B for some C, then A is possible for some C. This is clear from the 33a25definition of being possible.’ Again if A may belong to no B, and B may belong to some of the Cs, it is necessary that A may possibly not belong to some of the Cs. The proof is the same as above. But if the particular premiss is negative, and the universal is affirmative, the major still being universal and the minor particular, e.g. A is possible 33a30for all B, B may possibly not belong to some C, then a clear syllogism does not result from the assumed premisses, but if the particular premiss is converted and it is laid down that B possibly may belong to some C, we shall have the same conclusion as before,? as in the cases given at the beginning.4

33a35But if the major premiss is particular, the minor universal, whether both are affirmative, or negative, or different in quality, or if both are indefinite or particular, in no way will a syllogism be possible. For nothing prevents B from reaching beyond A, so that as predicates they cover unequal areas. Let C be that by which B extends beyond A. 33bTo C it is not possible that A should belong—either to all or to none or to some or not to some, since premisses in the mode of possibility are convertible and it is possible for B to belong to more things than A can. Further, this is obvious if we take terms; for if the premisses are as assumed, the 33b5major term is both possible for none of the minor and must belong to all of it. Take as terms common to all the cases under consideration ‘animal ’—‘white ’"—‘man’, where the major belongs necessarily to the minor; ‘animal ’— ‘white ’—‘garment’, where it is not possible that the major should belong to the minor. It is clear then that if the terms are related in this manner, no syllogism results. For 33b10every syllogism proves that something belongs either simply or necessarily or possibly. It is clear that there is no proof of the first or of the second. For the affirmative is destroyed by the negative, and the negative by the affirmative. There remains the proof of possibility. But this is impossible. For it has been proved that if the terms are related in this 33b15manner it is both necessary that the major should belong to all the minor and not possible that it should belong to any. Consequently there cannot be a syllogism to prove the possibility; for the necessary (as we stated) is not possible.’

33b19It is clear that if the terms are universal in possible premisses a syllogism always results in the first figure, 33b20whether they are affirmative or negative, only a perfect syllogism results in the first case, an imperfect in the second. But possibility must be understood according to the definition laid down,? not as covering necessity. This is sometimes forgotten.

Note del traduttore
  1. 1 In 32b38-40,
  2. 2 32a34.
  3. 3 Read ὅσπερ for ws in l. 17 with B,
  4. 4 1 320 25-37, 21.24. 5.1], 5-17. ce Nalh oo eae 3 32918.

Libro I, capitolo 15 Of Syllogisms with one simple and another contingent Proposition in the first Figure.33b25–35b22

Inglese

33b25If one premiss is a simple proposition, the other a problematic, whenever the major premiss indicates possibility all the syllogisms will be perfect and establish possibility in the sense defined ;* but whenever the minor premiss indicates possibility all the syllogisms will be imperfect, and those which are negative will establish not 33b30possibility according to the definition, but that the major does not necessarily belong to any, or to all, of the minor. For if this is so, we say it is possible that it should belong to none or not to all. Let A be possible for all B, and let B belong to all C. Since C falls under B, and A is possible for 33b35all B, clearly it is possible for all C also. So a perfect syllogism results. Likewise if the premiss AB is negative, and the premiss BC is affirmative, the former stating possible, the latter simple attribution, a perfect syllogism 33b40results proving that A possibly belongs to no C.

34a1It is clear that perfect syllogisms result if the minor premiss states simple belonging: but that syllogisms will result if the modality of the premisses is reversed, must be proved per impossibile. At the same time it will be evident that they are imperfect: for the proof proceeds not from 34a5the premisses assumed. First we must state that if B’s being follows necessarily from A’s being, B’s possibility will follow necessarily from A’s possibility. Suppose, the terms being so related,1 that A is possible, and B is impossible. If then that which is possible, when it is possible for it to be, might happen, and if that which is impossible, when it 34a10is impossible, could not happen, and if at the same time A is possible and B impossible, it would be possible for A to happen without B, and if to happen, then to be. For that which has happened, when it has happened, is. But we must take the impossible and the possible not only in the sphere of becoming, but also in the spheres of truth and predicability, and the various other spheres in which we 34a15speak of the possible: for it will be alike in all. Further we must understand the statement that B's being depends on A’s being, not as meaning that if some single thing A is, B will be: for nothing follows of necessity from the being of some one thing, but from two at least, i.e. when the premisses are related in the manner stated to be that of the 34a20syllogism. For if C is predicated of D, and D of F, then C is necessarily predicated of F. And if each is possible, the conclusion also is possible. If then, for example, one should indicate the premisses by A, and the conclusion by B, it would not only result that if A is necessary B is necessary, but also that if A is possible, B is possible.

34a25Since this is proved it is evident that if a false and not impossible assumption is made, the consequence of the assumption will also be false and not impossible: e.g. if A is false, but not impossible, and if B is the consequence of A, B also will be false but not impossible. For since it has been proved that if A’s being is the consequence of A’s 34a30being, then B's possibility will follow from A’s possibility (and A is assumed to be possible), consequently B will be possible: for if it were impossible, the same thing would at the same time be possible and impossible.

34a34Since we have defined these points, let A belong to all B, 34a35and B be possible for all C: it is necessary then that A should be a possible attribute for all C. Suppose that it is not possible, but assume that B belongs to all C: this is false but not impossible. If then A is not possible for C but B belongs to all C, then A is not possible for all B: for 34a40a syllogism is formed in the third figure. But it was assumed that A is a possible attribute for all B. It is necessary then 34bthat A is possible for all C. For though the assumption we made? is false and not impossible, the conclusion is impossible.2 It is possible also in the first figure to bring about the impossibility, by assuming that B belongs to C. For if B belongs to all C, and A is possible for all B, then A 34b5would be possible for all C. But the assumption was made that A is not possible for all C.

34b7We must understand ‘that which belongs to all’ with no limitation in respect of time, e.g. to the present or to a particular period, but simply without qualification. For it is by the help of such premisses that we make syllogisms, 34b10Since if the premiss is understood with reference to the present moment, there cannot be a syllogism. For nothing perhaps prevents ‘man’ belonging at a particular time to everything that is moving, i.e. if nothing else were moving: but ‘moving’ is possible for every horse; yet ‘man’ is possible for no horse. Further let the major term be 34b15‘animal’, the middle ‘moving’, the minor ‘man’. The premisses then will be as before, but the conclusion necessary, not possible. For man is necessarily animal. It is clear then that the universal must be understood simply, without limitation in respect of time. :

34b19Again let the premiss AB be universal and negative, and 34b20assume that A belongs to no B, but B possibly belongs to all C. These propositions being laid down, it is necessary that A possibly belongs to no C. Suppose that it cannot belong, and that B belongs to C, as above.3 It is necessary then that A belongs to some B: for we have a syllogism in 34b25the third figure: but this is impossible. Thus it will be possible for A to belong to no C; for if that is supposed false, the consequence is an impossible one. This syllogism then does not establish that which is possible according to the definition,4 but that which does not necessarily belong to any part of the subject (for this is the contradictory of the assumption which was made: for it was supposed that 34b30A necessarily belongs to some C, but the syllogism per impossibile establishes the contradictory which is opposed to this)5 Further, it is clear also from an example that the conclusion will not establish possibility. Let A be ‘raven’, B 'intelligent', and C ‘man’. A then belongs to no B: for 34b35no intelligent thing is a raven. But B is possible for all C: for every man may possibly be intelligent. But A necessarily belongs to no C: so the conclusion does not establish possibility. But neither is it always necessary. Let A be ‘moving’, B ‘science’, C ‘man’. A then will belong to no B; but B is possible for all C. And the conclusion will not be 34b40necessary. For it is not necessary that no man should 35amove; rather it is not necessary that any man should move. Clearly then the conclusion establishes that one term does not necessarily belong to any instance of another term. But we must take our terms better.

35a4If the minor premiss is negative and indicates possibility, from the actual premisses taken there can be no syllogism, but if the problematic premiss is converted, a syllogism will be possible, as before6 Let A belong to all B, and let B possibly belong to no C. If the terms are arranged thus, nothing necessarily follows: but if the proposition BC is converted and it is assumed that B is possible for all C, 35a10a syllogism results as before:7 for the terms are in the same relative positions.8 Likewise if both the relations are negative, if the major premiss states that A does not belong to B, and the minor premiss indicates that B may possibly belong to no C. Through the premisses actually taken nothing necessary results in any way; but if the problematic 35a15premiss is converted, we shall have a syllogism. Suppose that A belongs to no B, and B may possibly belong to no C. Through these comes nothing necessary. But if B is assumed to be possible for all C (and this is true) and if the premiss AB remains as before, we shall again have the 35a20same syllogism. But if it be assumed that B does not belong to any C, instead of possibly not belonging, there cannot be a syllogism anyhow, whether the premiss AB is negative or affirmative. As common instances of a necessary and positive relation we may take the terms white— animal—snow: of a necessary and negative relation, white— animal—pitch.

35a25Clearly then if the terms are universal, and one of the premisses is assertoric, the other problematic, whenever the minor premiss is problematic a syllogism always results, only sometimes it results from the premisses that are taken, sometimes it requires the conversion of one premiss. We 35a30have stated when each of these happens and the reason why. But if one of the relations is universal, the other particular, then whenever the major premiss is universal and problematic, whether affirmative or negative, and the particular is affirmative and assertoric, there will be a perfect syllogism, just as when the terms are universal. 35a35The demonstration is the same as before. But whenever the major premiss is universal, but assertoric, not problematic, and the minor is particular and problematic, whether both premisses are negative or affirmative, or one is negative, the other affirmative, in all cases there will be an imperfect 35a40syllogism. Only some of them will be proved per impossibile, 35bothers by the conversion of the problematic premiss, as has been shown above.9 And a syllogism will be possible by means of conversion when the major premiss is universal and assertoric, whether positive or negative, and the minor 35b5particular, negative, and problematic, e.g. if A belongs to all B or to no B, and I may possibly not belong to some C. For if the premiss BC is converted in respect of possibility, a syllogism results. But whenever the particular premiss is assertoric and negative, there cannot be a syllogism. As instances of the positive relation we may take the terms 35b10white—animal—snow; of the negative, white—animal— pitch. For the demonstration must be made through the indefinite nature of the particular premiss. But if the minor premiss is universal, and the major particular, whether either premiss is negative or affirmative, problematic or assertoric, nohow is a syllogism possible. Nor is a syllogism 35b15possible when the premisses are particular or indefinite, whether problematic or assertoric, or the one problematic, the other assertoric. The demonstration is the same as above. As instances of the necessary and positive relation we may take the terms animal—white—man; of the necessary and negative relation, animal—white—garment. It is 35b20evident then that if the major premiss is universal, a syllogism always results, but if the minor is universal nothing at all can ever be proved.

Note del traduttore
  1. 1 1 That 4’s being follows necessarily from 4’s being.
  2. 2 That all Cis B.
  3. 3 And therefore the other premiss, that A is not possible for all C, must have been impossible. = αὐ Ὁ.
  4. 4 Cf. 328 18.
  5. 5 Read a comma after ὑπάρχειν l. 30 and remove the bracket to after ἀντιφάσεως 1. 31.
  6. 6 aat 3
  7. 7 . B37. 34 34.
  8. 8 i.e, the major premiss ts pure, the minor problematic,
  9. 9 Cf. 26 14, 2720

Libro I, capitolo 16 Of Syllogisms with one Premise necessary, and the other contingent in the first Figure.35b23–36b25

Inglese

35b23Whenever one premiss is necessary, the other problematic, there will be a syllogism when the terms are related as 35b25before1 anda perfect syllogism when the minor premiss is necessary. If the premisses are affirmative the conclusion will be problematic, not assertoric, whether the premisses are universal or not: but if one is affirmative, the other negative, when the affirmative is necessary the conclusion 35b30will be problematic, not negative assertoric; but when the negative is necessary the conclusion will be problematic negative, and assertoric negative, whether the premisses are universal or not. Possibility in the conclusion must be understood in the same manner as before.2 There cannot be an inference to the necessary negative proposition: for 35b35‘not necessarily to belong’ is different from ‘necessarily not to belong’.

35b37If the premisses are affirmative, clearly the conclusion which follows is not necessary. Suppose A necessarily belongs to all B, and let B be possible for all C. We shall have an imperfect syllogism to prove that A may belong to all C. That 35b40it is imperfect is clear from the proof: for it will be proved 36ain the same manner as above. Again, let A be possible for all L, and let B necessarily belong to all C. We shall then have a syllogism to prove that A may belong to all C, 36a5not that A does belong to all C: and it is perfect, not imperfect: for it is completed directly through the original premisses.

36a7But if the premisses are not similar in quality, suppose first that the negative premiss is necessary, and let A necessarily not be possible for any B, but let B be possible 36a10for all C. It is necessary then that A belongs to no C. For suppose A to belong to all C or to some C. Now we assumed that A is not possible for any B. Since then the negative proposition is convertible, B is not possible for any A. But A is supposed to belong to all C or to some C. Consequently B will not be possible for any C or for all C. 36a15But it was originally laid down that B is possible for all C. And it is clear that the possibility of not belonging can be inferred, since the fact of not belonging is inferred. Again, let the affirmative premiss be necessary, and let A possibly not belong to any B, and let B necessarily belong to all C. 36a20The syllogism will be perfect, but it will establish a problematic negative, not an assertoric negative. For the major premiss was problematic, and further it is not possible to prove the assertoric conclusion per impossibile. For if it were supposed that A belongs to some C, and it is laid down that A possibly does not belong to any B, no impossible relation between B and C follows from these premisses. But if the 36a25;minor premiss is’ negative, when it is problematic a syllogism is possible by conversion, as above; but when it is necessary no syllogism can be formed. Nor again when both premisses are negative, and the minor is necessary. The same terms as before3 serve both for the positive 36a30relation—white—animal—snow, and for the negative relation—white—animal—pitch.

36a32The same relation will obtain in particular syllogisms. Whenever the negative proposition is necessary, the conclusion will be negative assertoric: e.g. if it is not possible 36a35that A should belong to any B, but B may belong to some of the Cs, it is necessary that A should not belong to some of the Cs. For if A belongs to all C, but cannot belong to any B, neither can B belong to any A. So if A belongs to all C, to none of the Cs can B belong. But it was laid down that B may belong to some C. But when the particular 36a40affirmative in the negative syllogism, e.g. BC the minor premiss, or the universal proposition in the affirmative syllogism. 36be.g. AB the major premiss, is necessary, there will not be an assertoric conclusion. The demonstration is the same as before.4 But if the minor premiss is universal, and problematic, whether affirmative or negative, and the major 36b5premiss is particular and necessary, there cannot be a syllogism. Premisses of this kind are possible both where the relation is positive and necessary, e.g. animal—white— man, and where it is necessary and negative, e.g. animal— white—garment. But when the universal is necessary, the particular problematic, if the universal is negative we may take the terms animal—white—raven to illustrate the positive 36b10relation, or animal—white—pitch to illustrate the negative; and if the universal is affirmative we may take the terms animal—white—swan to illustrate the positive relation, and animal —white—snow to illustrate the negative and necessary relation. Nor again is a syllogism possible when the premisses are indefinite, or both particular. Terms applicable in either case to illustrate the positive relation are animal—white—man: to illustrate the negative, animal 36b15—white—inanimate. For the relation of animal to some white, and of white to some inanimate, is both necessary and positive and necessary and negative. Similarly if the relation is problematic: so the terms may be used for all cases.

36b19Clearly then from what has been said a syllogism results 36b20or not from similar relations of the terms whether we are dealing with simple existence or necessity, with this exception, that if the negative premiss is assertoric the conclusion is problematic, but if the negative premiss is necessary the conclusion is both problematic and negative assertoric. [It is clear also that all the syllogisms are imperfect and are 36b25perfected by means of the figures above mentioned.?]

Note del traduttore
  1. 1 33°34-P17,
  2. 2 Cf. *25-b8, ὅ 33P29, 34h27, “343.34-Ὁ6.
  3. 3 35a7. Cf. 3377. 2? 3510,
  4. 4 419-25, > Maier, Sy/ogistik des Aristoteles, ii. I. 176, n. 2, shows that this sentence has been wrongly introduced from 39% I.

Libro I, capitolo 17 Of Syllogisms with two contingent Premises in the second Figure.36b26–37b18

Inglese

36b26In the second figure whenever both premisses are problematic, no syllogism is possible, whether the premisses are affirmative or negative, universal or particular. But when one premiss is assertoric, the other problematic, if the 36b30affirmative is assertoric no syllogism is possible, but if the universal negative is assertoric a conclusion can always be drawn. Similarly when one premiss is necessary, the other problematic. Here also we must understand the term ‘possible’ in the conclusions, in the same sense as before.1

36b35First2 we must point out that the negative problematic proposition is not convertible, e.g. if A may belong to no B, it does not follow that R may belong to no A. For suppose it to follow and assume that B may belong to no A. Since then problematic affirmations are convertible with negations, 36b40whether they are contraries or contradictories, and since B 37amay belong to no A, it is clear that B may belong to all A. But this is false: for if all this can be that, it does not follow that all that can be this: consequently the negative proposition is not convertible. Further, these propositions are not incompatible, ‘.A may belong to no B’, B necessarily 37a5does not belong to some of the As’; e.g. it is possible that no man should be white (for it is also possible that every man should be white), but it is not true to say that it is possible that no white thing should be a man: for many white things are necessarily not men, and the necessary (as we saw *) is other than the possible.

37a9Moreover it is not possible to prove the convertibility of 37a10these propositions by a reduction ad absurdum, i. e. by claiming assent to the following argument: ‘since it is false that B may belong to no A, it is true that it cannot belong to no A, for the one statement is the contradictory of the other. But if this is so, it is true that B necessarily belongs to some of the As: consequently A necessarily belongs to some of the Us, But this is impossible. The argument cannot be admitted, for it does not follow that some A is 37a15necessarily B, if it is not possible that no A should be B. For the latter expression is used in two senses, one if some A is necessarily B, another if some A is necessarily not B. For it is not true to say that that which necessarily does not belong to some of the As may possibly not belong to any A, just as it is not true to say that what necessarily 37a20belongs to some A may possibly belong to all A. If any one then should claim that because it is not possible for C to belong to all D, it necessarily does not belong to some D, he would make a false assumption: for it does belong to all D, but because in some cases it belongs necessarily, therefore we say that it is not possible for it to belong to all. Hence both the propositions ‘A necessarily belongs to 37a25some B’ and ‘A necessarily does not belong to some B’ are opposed to the proposition ‘A may belong to all B’. Similarly also they are opposed to the proposition ‘A may belong to no B’. It is clear then that in relation to what is possible and not possible, in the sense originally defined,3 we must assume, not that A necessarily belongs to some B, but that A necessarily does not belong to some B. But if 37a30this is assumed, no absurdity results: consequently no; syllogism. It is clear from what has been said that the negative proposition is not convertible.4

37a32This being proved, suppose it possible that A may belong to no Band to all C. By means of conversion no syllogism will result: for the major premiss, as has been said, is not 37a35convertible. Nor can a proof be obtained by a reduction ad absurdum: for if it is assumed that B can belong to all C5, no false consequence results: for A may belong both to all C and to no C. In general, if there is a syllogism, it is clear that its conclusion will be problematic because neither of 37a40the premisses is assertoric; and this must be either affirmative or negative. But neither is possible. Suppose the conclusion 37bis affirmative: it will be proved by an example that the predicate cannot belong to the subject. Suppose the conclusion is negative: it will be proved that it is not problematic but necessary. Let A be white, B man, C 37b5horse. It is possible then for A to belong to all of the one and to none of the other. But it is not possible for B to belong nor not to belong to C. That it is not possible for it to belong, is clear. For no horse is a man. Neither is it possible for it not to belong. For6 it is necessary that no horse should be a man, but the necessary we found to be 37b10different from the possible? No syllogism then results. A similar proof can be given if the major premiss is negative, the minor affirmative, or if both are affirmative or negative. The demonstration can be made by means of the same terms. And whenever one premiss is universal, the other particular, or both are particular or indefinite, or 37b15in whatever other way the premisses can be altered, the proof will always proceed through the same terms. Clearly then, if both the premisses are problematic, no syllogism results.

Note del traduttore
  1. 1 3329, 34a27. 7 32°28. ;
  2. 2 Colon after δ, full stop after ἀδύνιιτον in l. 14, with Maier,
  3. 3 32918.
  4. 4 2 The argument put into the mouth of Aristotle’s opponent in 1]. 10-14 is as follows: If A may be true of no B, B may be true of no A. (YX) For if not, B cannot be true of no A. (Y) . .. B must be true of some A. .. A must be true of some L. But this is impossible, since ex hypothes? A may be true of no B. .. & may be true of no A. Aristotle’s criticism in ll. 14-31 is as follows: The step from .¥ to Y is unsound. ‘B must be true of some A’ is not the only alternative to ‘B may be true of no A’. ‘There is also the alternative ‘B must be untrue of some A’. Necessity, not only the necessity that some 7? be A, but equally the necessity that some δ be not A, is incompatible with the foss/dility that no B be A. The proper inference then in place of (Y) is ‘Either B τεσ be true of some A, or B must be untrue of some A’, And from the second alternative no impossible conclusion follows, so that the proof fer iniposstbtle that B may be true of no A fails. Waitz’s reading in 1, 28 οὐ μόνον (cod. 2) τὸ ἐξ ἀνάγκης ... ἀλλὰ καὶ (2C) τὸ ἐξ ἀνάγκης is supported by Philop. and Them. But Al. has the lechio diffictlior without μόνον and καί, and the other is evidently only an attempt to make things easier. Not either alternative, nor both, but the disjunction of the two, is the proper inference from .Y. But in answer to the opponent’s assumption of }” we must make the counter-assumption ‘B must be untrue of some A’,
  5. 5 If Aristotle is to be saved from a fallacious inference we must, with Maier, in ll. 35, 36 insert μή before παντί and before ὑπάρχειν. But in view of the consent of the MSS. and the ancient commentators the mistake seems to go back to Aristotle.
  6. 6 32a28,

Libro I, capitolo 18 Of Syllogisms with one Proposition simple, and the other contingent, in the second Figure.37b19–38a12

Inglese

37b19But if one premiss is assertoric, the other problematic, 37b20If the affirmative is assertoric and the negative problematic no syllogism will be possible, whether the premisses are universal or particular. The proof is the same as above, and by means of the same terms. But when the affirmative premiss is problematic, and the negative assertoric, 37b25we Shall have a syllogism. Suppose A belongs to no B, but can belong to all C. If the negative proposition is converted, B will belong to no A. But A ex hypothesi can belong to all C: so a syllogism is made, proving by means of the first figure that B may belong to no C. Similarly also if the minor premiss is negative. But if both premisses 37b30are negative, one being assertoric, the other problematic, nothing follows necessarily from these premisses as they stand, but if the problematic premiss is converted into its complementary affirmative1 a syllogism is formed to prove that B may belong to no C, as before: for we shall again 37b35have the first figure. But if both premisses are affirmative, no syllogism will be possible. This arrangement of terms is possible both when the relation is positive, e.g. health, animal, man, and when it is negative, e.g. health, horse, man.

37b40The same will hold good if the syllogisms are particular. Whenever the affirmative proposition is assertoric, whether 38auniversal or particular, no syllogism is possible (this is proved similarly and by the same examples as above), but when the negative proposition is assertoric, a conclusion can be drawn by means of conversion, as before. Again if 38a5both the relations are negative, and the assertoric proposition is universal, although no conclusion follows from the actual premisses, a syllogism can be obtained by converting the problematic premiss into its complementary affirmative as before. But if the negative proposition is assertoric, but particular, no syllogism is possible, whether the other premiss 38a10is affirmative or negative. Nor can a conclusion be drawn when both premisses are indefinite, whether affirmative or negative, or particular. The proof is the same and by the same terms.

Note del traduttore
  1. 1 1 Cf. 32a29.

Libro I, capitolo 19 Of Syllogisms with one Premise necessary and the other contingent, in the second Figure.38a13–39a3

Inglese

38a13If one of the premisses is necessary, the other problematic, then if the negative is necessary a syllogistic conclusion can 38a15be drawn, not merely a negative problematic but also a negative assertoric conclusion; but if the affirmative premiss is necessary, no conclusion is possible. Suppose that A necessarily belongs to no B, but may belong to all C. If the negative premiss is converted B will belong to no A: but A ex hypothesis is capable of belonging to all C: so once 38a20more a conclusion is drawn by the first figure that B may belong to no C. But at the same time it is clear that B will not belong to any C. For assume that it does: then if A cannot belong to any B, and B belongs to some of the Cs, A cannot belong to some of the Cs: but ex hypothesis it 38a25may belong to all. A similar proof can be given if the minor premiss is negative. Again let the affirmative proposition be necessary, and the other problematic; i.e. suppose that A may belong to no B, but necessarily belongs to all C. When the terms are arranged in this way, no syllogism is 38a30possible. For1 (I) it sometimes turns out that B necessarily does not belong to C. Let A be white, B man, C swan. White then necessarily belongs to swan, but may belong to no man; and man necessarily belongs to no swan. Clearly then we cannot draw a problematic conclusion; for that 38a35which is necessary is admittedly distinct from that which is possible. (2) Nor again can we draw a necessary conclusion: for that presupposes that both premisses are necessary, or at any rate the negative premiss.2 (3) Further3 it is possible also, when the terms are so arranged, that B should belong to C: for nothing prevents C falling under B, A being possible 38a40for all ,B, and necessarily belonging to C; e.g. if C stands for ‘awake’, B for ‘animal’, A for ‘motion’. For motion 38bnecessarily belongs to what is awake, and is possible for every animal: and everything that is awake is animal. Clearly then the conclusion cannot be the negative assertion, if the relation must be positive when the terms are related as above. Nor can the opposite affirmations4 be established: consequently no syllogism is possible. A similar proof is 38b5possible if the major premiss is affirmative.

38b6But if the premisses are similar in quality, when they are negative a syllogism can always be formed by converting the problematic premiss into its complementary affirmative as before.5 Suppose A necessarily does not belong to B, 38b10and possibly may not belong to C: if the premisses are converted B belongs to no A, and A may possibly belong to all C: thus we have the first figure. Similarly if the minor premiss is negative.6 But if the premisses are affirmative there cannot be a syllogism. Clearly the conclusion 38b15cannot be a negative assertoric or a negative necessary proposition because no negative premiss has been laid down either in the assertoric or in the necessary mode. Nor can the conclusion be a problematic negative proposition. For if the terms are so related, there are cases in which B necessarily 38b20will not belong to C; e.g. suppose that A is white, B swan, C man. Nor can the opposite affirmations7 be established, since we have shown a case in which B necessarily does not belong to C. A syllogism then is not possible at all.

38b24Similar relations will obtain in particular syllogisms. For 38b25whenever the negative proposition is universal and necessary, a syllogism will always be possible to prove both a problematic and a negative assertoric proposition (the proof proceeds by conversion) ; but when the affirmative proposition is universal and necessary, no syllogistic conclusion can be drawn. This can be proved in the same way as for universal propositions, and by the same terms.8 Nor is 38b30a syllogistic conclusion possible when both premisses are affirmative: this also may be proved as above. But when both premisses are negative, and the premiss that definitely disconnects two terms is universal and necessary,9 though nothing follows necessarily from the premisses as they are stated, a conclusion can be drawn as above10 if the problematic 38b35premiss is converted into its complementary affirmative. But if both are indefinite or particular, no syllogism can be formed. The same proof will serve, and the same terms.’

38b38It is clear then from what has been said that if the universal and negative premiss is necessary, a syllogism is 38b40always possible, proving not merely a negative problematic, but also a negative assertoric proposition; but if the affirmative premiss is necessary no conclusion can be drawn. It is clear too that a syllogism is possible or not under the same 39aconditions whether the mode of the premisses is assertoric or necessary. And it is clear that all the syllogisms are imperfect, and are completed by means of the figures mentioned.

Note del traduttore
  1. 1 Cf. 30° 7, 31a21.
  2. 2 Read καταφάσεων in l. 4 with cod. n, Al. [Amm.], and Waitz. The opposite affirmations are
  3. 3 C may be 2B’
  4. 4 C may be 2B’
  5. 5 Cis B’. 5. Cf. 32a29.
  6. 6 sc. and necessary.
  7. 7 Read καταφάσεων in l. 21 with Al. and Waitz.
  8. 8 Cf. *26-) 5, 11, 12-23.
  9. 9 ‘And necessary’ is pointless, as the whole chapter is concerned only with combinations of a necessary with a problematic premiss. Possibly we should read ἡ for καί in l. 32. The reading of Al.’s lemma στερητικαὶ καὶ καθόλου δὲ ἀναγκαία suggests that καί may have originated | by dittography. 5], 25-7.
  10. 10 Cf. 36° 12-18.

Libro I, capitolo 20 Of Syllogisms with both Propositions contingent in the third Figure.39a4–39b6

Inglese

39a4In the last figure a syllogism is possible whether both or 39a5only one of the premisses is problematic. When the premisses are problematic the conclusion will be problematic; and also when one premiss is problematic, the other assertoric. But when the other premiss is necessary, if it is affirmative the conclusion will be neither necessary nor assertoric; but 39a10if it is negative the syllogism will result in a negative assertoric proposition, as above.1 In these also we must understand the expression ‘possible’ in the conclusion in the same way as before.

39a14First let the premisses be problematic and suppose that 39a15both A and B may possibly belong to every C. Since then the affirmative proposition is convertible into a particular, and B may possibly belong to every C, it follows that C may possibly belong to some B. So, if A is possible for every C, and C is possible for some of the Bs, then A is possible for some of the Bs. For we have got the first figure. And if 39a20A may possibly belong to no C, but B may possibly belong to all C, it follows that A may possibly not belong to some B: for we shall have the first figure again by conversion. But if both premisses should be negative no necessary consequence will follow from them as they are stated, but if the 39a25premisses are converted into their corresponding affirmatives there will be a syllogism as before. For if A and B may possibly not belong to C, if ‘may possibly belong’ is substituted we shall again have the first figure by means of conversion, But if one of the premisses is universal, the other particular, a syllogism will be possible, or not, under the 39a30same arrangement of the terms as in the case of assertoric propositions. Suppose that A may possibly belong to all C, and B to some C. We shall have the first figure again if the particular premiss is converted. For if A is possible for all C, and C for some of the ^s, then A is possible for 39a35some of the Bs. Similarly if the proposition BC is universal. Likewise also if the proposition AC is negative, and the proposition BC affirmative: for we shall again have the first figure by conversion. But if both premisses should be negative—the one universal and the other particular—although 39bno syllogistic conclusion will follow from the premisses as they are put, it will follow if they are converted, as above. But when both premisses are indefinite or particular, no syllogism can be formed: for A must belong sometimes to all B and sometimes to no B. To illustrate the affirmative 39b5relation take the terms animal—man—white; to illustrate the negative, take the terms horse—man—white—white being the middle term.

Note del traduttore
  1. 1 387 14,

Libro I, capitolo 21 Of Syllogisms with one Proposition contingent and the other simple in the third Figure.39b7–40a3

Inglese

39b8If one premiss is pure, the other problematic, the conclusion will be problematic, not pure; and a syllogism will 39b10be possible under the same arrangement of the terms as before.1 First let the premisses be affirmative: suppose that A belongs to all C, and B may possibly belong to all C. If the proposition BC is converted, we shall have the first figure, and the conclusion that A may possibly belong to 39b15some of the Bs. For when one of the premisses in the first figure is problematic, the conclusion also (as we saw2) is problematic. Similarly if the proposition BC is pure, AC problematic; or if AC is negative, BC affirmative, no matter which of the two is pure; in both cases the conclusion will 39b20be problematic: for the first figure is obtained once more, and it has been proved that if one premiss is problematic in that figure the conclusion also will be problematic. But if the minor premiss BC is negative,’ or if both premisses are negative, no syllogistic conclusion can be drawn from the premisses as they stand, but if they are converted a 39b25syllogism is obtained as before.

39b26If one of the premisses is universal, the other particular, then when both are affirmative, or when the universal is negative, the particular affirmative, we shall have the same sort of syllogisms: for all are completed by means of the 39b30first figure. So it is clear that we shall have not a pure but a problematic syllogistic conclusion. But if the affirmative premiss is universal, the negative particular, the proof will proceed by a reduction ad impossibile. Suppose that B belongs to all C, and A may possibly not belong to some C: it 39b35follows that A may possibly not belong to some B. For3 if A necessarily belongs to all B, and B (as has been assumed) belongs to all C, A will necessarily belong to all C: for this has been proved before.4 But it was assumed at the outset that A may possibly not belong to some C.

40a1Whenever both premisses are indefinite or particular, no syllogism will be possible. The demonstration is the same as was given in the case of universal premisses,” and proceeds by means of the same terms.

Note del traduttore
  1. 1 i.e. where the premisses were pure, or problematic.
  2. 2 33b25-40. > Omit ἐνδεχόμενον in l. 22 with cod. ἢ, Al., Phil., Them., and Waitz. ἐνδεχόμενον can easily be supplied in thought, since it is obvious that a negative assertorf¢e minor gives no conclusion in the third figure.
  3. 3 308 15-23.
  4. 4 No such demonstration occurs in the discussion of the case of two universal premisses. The reference is a careless one to the discussion of the case of two problematic premisses, 39b2-6.

Libro I, capitolo 22 Of Syllogisms with one Premise necessary, and the other contingent in the third Figure.40a4–40b16

Inglese

40a4If one of the premisses is necessary, the other problematic, 40a5when the premisses are affirmative a problematic affirmative conclusion can always be drawn; when one proposition is affirmative, the other negative, if the affirmative is necessary a problematic negative can be inferred; but if the negative proposition is necessary both a problematic and a pure negative conclusion are possible. But a necessary negative 40a10conclusion will not be possible, any more than in the other figures. Suppose first that the premisses are affirmative, i.e. that A necessarily belongs to all C, and B may possibly belong to all C. Since then A must belong to all C, and C may belong to some B, it follows that A may (not does) 40a15belong to some B: for so it resulted1 in the first figure. A similar proof may be given if the proposition BC is necessary, and AC is problematic. Again suppose one proposition is affirmative, the other negative, the affirmative being necessary: i.e. suppose A may possibly belong to 40a20no C, but B necessarily belongs to all C. We shall have the first figure once more: and—since the negative premiss is problematic—it is clear that the conclusion will be problematic: for when the premisses stand thus in the first figure, the conclusion (as we found2) is problematic. But if the 40a25negative premiss is necessary, the conclusion will be not only that A may possibly not belong to some B but also that it does not belong to some B. For3 suppose that A necessarily does not belong to C, but B may belong to all C. If the affirmative proposition BC is converted, we shall have the first figure, and the negative premiss is necessary. But 40a30when the premisses stood thus, it resulted? that A might possibly not belong to some C, and that it did not belong to some C; consequently here it follows that A does not belong to some B. But when the minor premiss is negative, if it is problematic we shall have a syllogism by altering 40a35the premiss into its complementary affirmative, as before; but if it is necessary no syllogism can be formed. For A sometimes necessarily belongs to all B, and sometimes cannot possibly belong to any B. To illustrate the former take the terms sleep-sleeping horse—man; to illustrate the latter take the terms sleep—waking horse—man.

40a39Similar results will obtain if one of the terms is related 40a40universally to the middle, the other in part. If both premisses 40bare affirmative, the conclusion will be problematic, not pure; and also when one premiss is negative, the other affirmative, the latter being necessary. But when the negative premiss is necessary, the conclusion also will be a pure 40b5negative proposition; for the same kind of proof can be given whether the terms are universal or not. For the syllogisms must be made perfect by means of the first figure, so that a result which follows in the first figure follows also in the third. But when the minor premiss is 40b10negative and universal, if it is problematic a syllogism can be formed by means of conversion; but if it is necessary a syllogism is not possible. ‘The proof will follow the same course as where the premisses are universal; and the same terms may be used.

40b13It is clear then in this figure also when and how a syllogism can be formed, and when the conclusion is problematic, and when it is pure. It is evident also that all syllogisms in 40b15this figure are imperfect, and that they are made perfect by means of the first figure.

Note del traduttore
  1. 1 35a26-8.
  2. 2 36° 17-25.
  3. 3 36a32-9. E 2

Libro I, capitolo 23 It is demonstrated that every Syllogism is completed by the first Figure.40b17–41b5

Inglese

40b17It is clear from what has been said that the syllogisms in these figures are made perfect by means of universal syllogisms in the first figure and are reduced to them. That 40b20every syllogism without qualification can be so treated, will be clear presently, when it has been proved that every syllogism is formed through one or other of these figures.

40b23It is necessary that every demonstration and every syllogism should prove either that something belongs or that it 40b25does not, and this either universally or in part, and further either ostensively or hypothetically. One sort of hypothetical proof is the reduction ad impossibile. Let us speak first of ostensive syllogisms: for after these have been pointed out the truth of our contention will be clear with regard to those which are proved per impossibile, and in general hypothetically. ; 40b30f then one wants to prove syllogistically A of B, either as an attribute of it or as not an attribute of it, one must assert something of something else. If now A should be asserted of B, the proposition originally in question will have been assumed. But if A should be asserted of C, but C should not be asserted of anything, nor anything of it, nor anything else of A, no syllogism will be possible. For 40b35nothing necessarily follows from the assertion of some one thing concerning some other single thing. Thus we must take another premiss as well. If then be asserted of something else, or something else of A, or something different of C, nothing prevents a syllogism being formed, but it will not be in relation to B through the premisses 40b40taken. Nor when C belongs to something else, and that to something else and so on, no connexion however being made 41awith B, will a syllogism be possible concerning A in its relation to B. For in general we stated1 that no syllogism can establish the attribution of one thing to another, unless some middle term is taken, which is somehow related to each by way of predication. For2 the syllogism in general 41a5is made out of premisses, and a syllogism referring to thiss out of premisses with the same reference, and a syllogism relating this to that proceeds through premisses which relate this to that. But it is impossible to take a premiss in reference to B, if we neither affirm nor deny anything of it; or again to take a premiss relating A to B, if we take 41a10nothing common, but affirm or deny peculiar attributes of each. So we must take something midway between the two, which will connect the predications, if we are to have a syllogism relating this to that. If then we must take something common in relation to both, and this is possible 41a15in three ways (either by predicating A of C, and C of B, or C of both, or both of C), and these are the figures of which we have spoken, it is clear that every syllogism must be made in one or other of these figures. The argument is the same if several middle terms should be necessary to establish the relation to B; for the figure will be the same whether there 41a20is one middle term or many.

41a21It is clear then that the ostensive syllogisms are effected by means of the aforesaid figures; these considerations will show that reductiones ad impossibile also are effected in the same way. For all who effect an argument per impossibile infer syllogistically what is false, and prove the original conclusion 41a25hypothetically when something impossible results from the assumption of its contradictory; e.g. that the diagonal of the square is incommensurate with the side, because odd numbers are equal to evens if it is supposed to be commensurate.” One infers syllogistically that odd numbers come out equal to evens, and one proves hypothetically the incommensurability of the diagonal, since 41a30a falsehood results through contradicting this. For this we found to be reasoning per impossibile, viz. proving something impossible by means of an hypothesis conceded at the beginning. Consequently, since the falsehood is established in reductions ad impossibile by an ostensive syllogism, and the original conclusion is proved hypothetically, and we have 41a35already stated that ostensive syllogisms are effected by means of these figures, it is evident that syllogisms per impossibile also will be made through these figures. Likewise all the other hypothetical syllogisms: for in every case the syllogism leads up to the proposition that is substituted 41a40for the original thesis; but the original thesis is reached by means of a concession or some other hypothesis.3 But if 41bthis is true, every demonstration and every syllogism must be formed by means of the three figures mentioned above. But when this has been shown it is clear that every syllogism is perfected by means of the first figure and is reducible to 41b5the universal syllogisms in this figure.

Note del traduttore
  1. 1 Cf. 25 32.
  2. 2 The proof is given in Euclid, /A/ements, Bk. x, App. 27 (ed. Heiberg and Menge). Cf. B. Russell, /ztroduction to Mathematical | Philosophy, p. 67.
  3. 3 Aristotle is thinking of the method of establishing a proposition A is B by inducing the opponent to agree that A is B if XY is Y. All that remains then is to establish syllogistically that .Y is Y. That A is B thus follows from the agreement.

Citato nell'enciclopedia: AD HOMINEM, ARGOMENTO · SILLOGISMO

Libro I, capitolo 24 Of the Quality and Quantity of the Premises in Syllogism.—Of the Conclusion.41b6–35

Inglese

41b6Further in every syllogism one of the premisses must be affirmative, and universality must be present: unless one of the premisses is universal either a syllogism will not be possible, or it will not refer to the subject proposed, or the original position will be begged. Suppose we have to prove 41b10that pleasure in music is good. If one should claim as a premiss that pleasure is good without adding ‘all’, no syllogism will be possible; if one should claim that some pleasure is good, then if it is different from pleasure in music, it is not relevant to the subject proposed; if it is this very pleasure, one is assuming that which was proposed at the outset to be proved. This is more obvious in geometrical proofs, e. g. that the angles at the base of an isosceles 41b15triangle are equal. Suppose the lines A and B have been drawn to the centre. If then one should assume that the angle AC is equal to the angle BD, without claiming generally that angles of semicircles are equal; and again if one should assume that the angle C is equal to the angle D, without the additional assumption that every angle of a segment Is equal to every other angle of the same segment; and further if one should assume that when equal angles are taken from the whole angles, which are themselves equal, 41b20the remainders E and F are equal, he will beg the thing to be proved, unless he also states that when equals are taken from equals the remainders are equal.1

41b22It is clear then that in every syllogism there must be a universal premiss, and that a universal statement is proved only when all the premisses are universal, while a particular statement is proved both from two universal premisses and from one only: consequently if the conclusion 41b25is universal, the premisses also must be universal, but if the

41b26'2 The diagram Aristotle has in mind appears to be the following:

41b26A B

41b27premisses are universal it is possible that the conclusion may not be universal. And it is clear also that in every syllogism either both or one of the premisses must be like the conclusion. I mean not only in being affirmative or negative, but also in 41b30being necessary, pure, or problematic. We must consider also the other forms of predication.

41b32It is clear also when a syllogism in general can be made and when it cannot; and when a valid,3 when a perfect syllogism can be formed; and that if a syllogism is formed the terms must be arranged in one of the ways that have 41b35been mentioned.

Note del traduttore
  1. 1 NE,
  2. 2 σις. Ὁ “-΄ | Here A and B are the equal sides, Φ and F the angles at the base of the isosceles triangle. Cand D are the angles formed by the base | with the circumference. The angles formed by the equal sides with the base are loosely called AC, 2D. That the angles of the semicircle of the segment mean those formed by the diameter and the chord | respectively with the circumference (as supposed by Al., Phil., Pacius, | and Blancanus), not those zz the semicircle and 7z the segment (as supposed by Waitz) seems to be sufficiently indicated by the language of Euclid, iii. 16, 31. Contrast ἡ ἐν ἡμικυκλίῳ, Post. An. 94a28, Jee. 1. but imperfect.
  3. 3 Insert καὶ AT after AB in l. 39 with Ay, C, Al., Phil., and Waitz.

Citato nell'enciclopedia: SILLOGISMO

Libro I, capitolo 25 Every Syllogism consists of only three Terms, and of two Premises.41b36–42b26

Inglese

41b36It is clear too that every demonstration will proceed through three terms and no more, unless the same conclusion is established by different pairs of propositions; e.g. the conclusion E may be established through the propositions A and B, and through the propositions C and D, or through the propositions A and B, or A and C, or B and C.1 For 41b40nothing prevents there being several middles for the same terms. But in that case there is not one but several 42asyllogisms. Or again when each of the propositions A and B is obtained by syllogistic inference, e.g. dA by means of D and E, and again B by means of F and G. Or one may be obtained by syllogistic, the other by inductive inference. But thus also the syllogisms are many; for the conclusions 42a5are many, e.g. A and B and C. But if this can be called one syllogism, not many, the same conclusion may be reached by more than three terms in this way, but it cannot be reached as C is established by means of A and B? Suppose that the proposition E is inferred from the premisses A, B, C, and D. It is necessary then that of these one 42a10should be related to another as whole to part: for it has already been proved that if a syllogism is formed some of its terms must be related in this way.2 Suppose then that A stands in this relation to B. Some conclusion then follows from them. It must cither be E or one or other of Cand PD, or something other than these.

42a15(I) If it is E the syllogism will have A and B for its sole premisses. But if C and D are so related that one is whole, the other part, some conclusion will follow from them also; and it must be either E, or one or other of the propositions A and B, or something other than these. And if it is (i) E, or (ii) A or B, either (i) the syllogisms will be more than one, or (ii) the same thing happens to be inferred by means of several terms only in the sense which we saw to be possible.3 42a20But if (iii) the conclusion is other than E or A or B, the syllogisms will be many, and unconnected with one another. But if C is not so related to D as to make a syllogism, the propositions will have been assumed to no purpose, unless for the sake of induction or of obscuring the argument or something of the sort.

42a24(2) But if from the propositions A and B there follows not 42a25E but some other conclusion, and if from C and D either A or B follows or something else, then there are several syllogisms, and they do not establish the conclusion proposed: for we assumed that the syllogism proved E. And if no conclusion follows from C and D, it turns out that these propositions have been assumed to no purpose, and the syllogism does 42a30not prove the original proposition.

42a31So it is clear that every demonstration and every syllogism will proceed through three terms only.

42a32This being evident, it is clear that a syllogistic conclusion follows from two premisses and not from more than two. For the three terms make two premisses, unless a new premiss is assumed, as was said at the beginning,4 to perfect 42a35the syllogisms. It is clear therefore that in whatever syllogistic argument the premisses through which the main conclusion follows (for some of the preceding conclusions must be premisses) are not even in number, this argument either has not been drawn syllogistically or it has assumed 42a40more than was necessary to establish its thesis.

42b1If then syllogisms are taken with respect to their main premisses, every syllogism will consist of an even number of premisses and an odd number of terms (for the terms exceed the premisses by one), and the conclusions will be half the 42b5number of the premisses. But whenever a conclusion is reached by means of prosyllogisms or by means of several continuous middle terms,5 e.g. the proposition AH by means of the middle terms C and D, the number of the terms will similarly exceed that of the premisses by one (for the extra term must either be added outside or inserted: but in either case it follows that the relations of predication are one fewer 42b10than the terms related), and the premisses will be equal in number to the relations of predication. The premisses however will not always be even, the terms odd; but they will alternate—when the premisses are even, the terms must be odd; when the terms are even, the premisses must be odd: for along with one term one premiss is added, if a term is added from any quarter. Consequently since the premisses 42b15were (as we saw) even, and the terms odd, we must make them alternately even and odd at each addition. But the conclusions will not follow the same arrangement either in respect to the terms or to the premisses. For if one term is added, conclusions will be added less by one than the pre-existing terms: for the conclusion is drawn not in relation 42b20to the single term last added, but in relation to all the rest, e.g. if to ABC the term D is added, two conclusions are thereby added, one in relation to A, the other in relation to B. Similarly with any further additions. And similarly too if the term is inserted in the middle: for in relation to one term only, a syllogism will not be constructed. Consequently 42b25the conclusions will be much more numerous than the terms or the premisses.

Note del traduttore
  1. 1 i.e. by way of a simple syllogism. This is incompatible with there being more than three terms.
  2. 2 4o 30.
  3. 3 1.6.
  4. 4 The reference is to the new premisses produced by conversion, , when a syllogism in the second or third figure is being reduced to one | in the first. Cf. 240 24.
  5. 5 Omit μή in l. 6 with cod. ἢ, Al., Them., and Waitz.

Libro I, capitolo 26 On the comparative Difficulty of certain Problems, and by what Figures they are proved.42b27–43a19

Inglese

42b27Since we understand the subjects with which syllogisms are concerned, what sort of conclusion is established in each figure, and in how many moods this is done, it is evident to us both what sort of problem is difficult and what sort is easy 42b30to prove. For that which is concluded in many figures and through many moods is easier; that which is concluded in few figures and through few moods is more difficult to attempt. The universal affirmative is proved by means of the first figure only and by this in only one mood; the universal negative is proved both through the first figure and through 42b35the second, through the first in one mood, through the second in two. The particular affirmative is proved through the first and through the last figure, in one mood through the first, in three moods through the last. The particular negative is proved in all the figures, but once in the first, in 42b40two moods in the second, in three moods in the third. It is 43aclear then that the universal affirmative is most difficult to establish, most easy to overthrow. In general, universals are easier game for the destroyer than particulars: for whether the predicate belongs to none or not to some, they are destroyed: and the particular negative is proved in all 43a5the figures, the universal negative in two. Similarly with universal negatives: the original statement is destroyed, whether the predicate belongs to all or to some: and this we found possible in two figures. But particular statements can be refuted in one way only—by proving that the predicate belongs either to all or to none. But particular statements are easier to establish: for proof is possible 43a10in more figures and through more moods. And in general we must not forget that it is possible to refute statements by means of one another, I mean, universal statements by means of particular, and particular statements by means of universal: but it is not possible to establish universal statements by means of particular, though it is possible to establish particular statements by means of universal. At the same time it is evident that it is easier to refute 43a15than to establish.

43a16The manner in which every syllogism is produced, the number of the terms and premisses through which it proceeds, the relation of the premisses to one another, the character of the problem proved in each figure, and the number of the figures appropriate to each problem, all these matters are clear from what has been said.

43a20We must now state how we may ourselves always have a

Libro I, capitolo 27 Of the Invention and Construction of Syllogisms.43a20–43b38

Inglese

43a21supply of syllogisms in reference to the problem proposed and by what road we may reach the principles relative to the problem: for perhaps we ought not only to investigate the construction of syllogisms, but also to have the power of making them.

43a25Of all the things which exist some are such that they cannot be predicated of anything else truly and universally, e.g. Cleon and Call i as, i. e. the individual and sensible, but other things may be predicated of them (for each of these is both man and animal); and some things are themselves 43a30predicated of others, but nothing prior is predicated of them; and some are predicated of others, and yet others of them, e.g. man of Call i as and animal of man. It is clear then that some things are naturally not stated of anything: for as a rule each sensible thing is such that it cannot be predicated of anything, save incidentally: for we sometimes say 43a35that that white object is Socrates, or that that which approaches is Call i as. We shall explain in another place1 that there is an upward limit also to the process of predicating: for the present we must assume this. Of these ultimate predicates it is not possible to demonstrate another predicate, save as a matter of opinion, but these may be predicated of other things. Neither can individuals 43a40be predicated of other things, though other things can be predicated of them. Whatever lies between these limits can be spoken of in both ways: they may be stated of others, and others stated of them. And as a rule arguments and inquiries are concerned with these things.

43b1We must select the premisses suitable to each problem in this manner: first we must lay down the subject and the definitions and the properties of the thing; next we must lay down those attributes which follow2 the thing, and again those which the thing follows, and those which cannot 43b5belong to it. But those to which it cannot belong need not be selected, because the negative statement implied above is convertible. Of the attributes which follow we must distinguish those which fall within the definition, those which are predicated as properties, and those which are predicated as accidents, and of the latter those which apparently and those which really belong. The larger the 43b10supply a man has of these, the more quickly will he reach a conclusion; and in proportion as he apprehends those which are truer, the more cogently will he demonstrate. But he must select not those which follow some particular but those which follow the thing as a whole, e. g. not what follows a particular man but what follows every man: for the syllogism proceeds through universal premisses. If the 43b15statement is indefinite, it is uncertain whether the premiss is universal, but if the statement is definite, the matter is clear. Similarly one must select those attributes which the subject follows as wholes, for the reason given. But that which follows one must not suppose to follow as a whole, e.g. that every animal follows man or every science music, but only that it follows, without qualification, as indeed we 43b20state it in a proposition: for the other statement is useless and impossible, e.g. that every man is every animal or justice is all good. But that which something follows receives the mark ‘every’. Whenever the subject, for which we must obtain the attributes that follow, is contained by something else, what follows or does not follow the highest term universally must not be selected in dealing with 43b25the subordinate term (for these attributes have been taken in dealing with the superior term; for what follows animal also follows man, and what does not belong to animal does not belong to man); but we must choose those attributes which are peculiar to each subject. For some things are peculiar to the species as distinct from the genus; for species being distinct there must be attributes peculiar to each. Nor must we take as things which the superior term follows, those things which the inferior term follows, 43b30e. g. take as subjects of the predicate ‘animal’ what are really subjects of the predicate ‘man’. It is necessary indeed, if animal follows man, that it should follow all these also. But these belong more properly to the choice of what concerns man. One must apprehend also normal consequents and normal antecedents; for propositions which obtain normally are established syllogistically from premisses 43b35Which obtain normally, some if not all of them having this character of normality. For the conclusion of each syllogism resembles its principles. We must not however choose attributes which are consequent upon all the terms:3 for no syllogism can be made out of such premisses. The reason why this is so will be clear in the sequel.4

Note del traduttore
  1. 1 Post. An, i. 19-22.
  2. 2 The term ‘follow’ has been used to translate ἔπεσθαι with the implication of logical sequence. Though the usage is hardly idiomatic in regard to terms, one of which is consequent on or implied by the other, it has become current with respect to propositions.
  3. 3 i.e. on the major and minor terms. ‘Two affirmative premisses in the second figure give no conclusion.
  4. 4 44b20,

Libro I, capitolo 28 Special Rules upon the same Subject.43b39–45a22

Inglese

43b39If men wish to establish something about some whole, 43b40they must look to the subjects of that which is being established (the subjects of which it happens to be asserted), and the attributes which follow that of which it is to be predicated. For if any of these subjects is the same as any of these attributes, the attribute originally in question must belong to the subject originally in question.1 But if the purpose is to establish not a universal but a particular proposition, they must look for the terms of which the 44aterms in question are predicable: for if any of these are identical, the attribute in question must belong to some of the subject in question.2 | Whenever the one term has to belong to none of the other, one must look to the consequents of the subject, and to those attributes which cannot possibly be present in the predicate in question:3 or conversely to the attributes which cannot possibly be present in the subject, and to the consequents of the predicate. If any members of these groups are identical, one of the terms in question cannot possibly belong to any of the other. For sometimes a syllogism in the first figure results,”4 sometimes a syllogism in the second. But if the object is to establish a particular negative proposition, we must find antecedents of the subject in question and attributes 44a10which cannot possibly belong to the predicate in question.’ If any members of these two groups are identical, it follows that one of the terms in question does not belong to some of the other. Perhaps each of these statements will become clearer in the following way. Suppose the consequents of A are designated by B, the antecedents of A by C, attributes which cannot possibly belong to A 44a15by D. Suppose again that the attributes of E are designated by F, the antecedents of E by G, and attributes which cannot belong to E by I. If then one of the Cs should be identical with one of the Fs, A must belong to all E: for F belongs to all E, and A5 to all C, consequently A belongs 44a20to all E. If Cand G are identical, A must belong to some of the Es: for A follows C, and E follows all G. If F and D are identical, A will belong to none of the Es by a prosyllogism: for since the negative proposition is convertible, and F is identical with ),D, A will belong to none of the Fs, but F belongs to all E. Again, if Band A are 44a25identical, A will belong to none of the Es: for B will belong to all A, but to no E:6 for it was assumed to be identical with H, and H belonged to none of the Es. If D and G are identical, A will not belong to some of the Es: for it will not belong to G, because it does not belong to D: but 44a30G falls under E: consequently A will not belong to some of the Es. If B is identical with G, there will be a converted syllogism: for E will belong to all A, since B belongs to A and E to B (for B was found to be identical with G): but that A should belong to all E is not necessary, but it must belong to some E because it is possible to convert 44a35the universal statement into a particular.

44a36It is clear then that in every proposition which requires proof we must look to the aforesaid relations of the subject and predicate in question: for all syllogisms proceed through these. But if we are seeking consequents and antecedents we must look for those which are primary and most universal, 44a40e.g. in reference to E we must look to KF rather than to F’ alone, and in reference to. A we must look to A C rather than 44bto Alone.’ For if A belongs to K, it belongs both to F and to E: but if it does not follow K, it may yet follow F. Similarly we must consider the antecedents of A itself: for if a term follows the primary antecedents, it will follow those also which are subordinate, but if it does not follow the 44b5former, it may yet follow the latter.

44b6It is clear too that the inquiry proceeds through the three terms and the two premisses, and that all the syllogisms proceed through the aforesaid figures. For it is proved that A belongs to all E, whenever an identical term is found among the Cs and Fs. This will be the middle term; A and 44b10f will be the extremes. So the first figure is formed. And “A will belong to some ,E, whenever Cand G are apprehended to be the same. This is the last figure: for G becomes the middle term. And A will belong to no E, when D and F are identical. Thus we have both the first figure and the middle figure; the first, because A belongs to no F, since 44b15the negative statement is convertible, and F belongs to all E; the middle figure because D belongs to no A, and to all E. And A will not belong to some E, whenever D and G are identical. This is the last figure: for A will belong to no G, and E will belong to all G. Clearly then 44b20all syllogisms proceed through the aforesaid figures, and we must not select consequents of all the terms,7 because no syllogism is produced from them. For (as we saw)8 it is not possible at all to establish a proposition from consequents, and it is not possible to refute by means of a consequent of both the terns in question: for the middle term must belong to the one, and not belong to the other.

44b25It is clear too that other methods of inquiry by selection of middle terms are useless to produce a syllogism, e.g. if the consequents of the terms in question are identical, or if the antecedents of A are identical with those attributes which cannot possibly belong to E, or if those attributes are identical which cannot belong to either term: for no syllogism is produced by means of these. For if the 44b30consequents are identical, e.g. B and /, we have the middle figure with both premisses affirmative: if the antecedents of A are identical with attributes which cannot belong to E, e.g. C with H, we have the first figure with its minor premiss negative. If attributes which cannot belong 44b35to either term are identical, e.g. C and H, both premisses are negative, either in the first or in the middle figure. But no syllogism is possible in this way.

44b38It is evident too that we must find out which terms in this inquiry are identical, not which are different or contrary, 44b40first because the object of our investigation is the middle term, and the middle term must be not diverse but identical. 45aSecondly, wherever it happens that a syllogism results from taking contraries or terms which cannot belong to the same thing, all arguments can be reduced to the aforesaid moods, e.g. if B and F are contraries or cannot belong to the same 45a5thing. For if these are taken, a syllogism will be formed to prove that A belongs to none of the Es, not however from the premisses taken but in the aforesaid mood. For B will belong to all A and to no E. Consequently B must be identical with one of the Hs. Again, if B and G cannot 45a10belong to the same thing, it follows that A will not belong to some of the Es: for then too we shall have the middle figure: for B will belong to all A and to no G.9 Consequently B must be identical with some of the Hs. For the fact that B and G cannot belong to the same thing differs in no way from the fact that B is identical with 45a15some of the Hs: for that includes everything which cannot belong to E.

45a17It is clear then that from the inquiries taken by themselves no syllogism results; but if B and F are contraries B must be! identical with one of the Hs, and the syllogism 45a20results through these terms. It turns out then that those who inquire in this manner are looking gratuitously for some other way than the necessary way because they have failed to observe the identity of the Bs with the Hs.

Note del traduttore
  1. 1 We thus get a syllogism in Barbara.
  2. 2 Darapti.
  3. 3 Cesare. δ᾽ Camestres,
  4. 4 By converting the major premiss of the Cesare syllogism or the minor premiss of the Camestres syllogism. ὃ Felapton, by conversion.
  5. 5 τῷ A in Bekker, 1. 19, is a misprint for ro A.
  6. 6 Read τῷ δ᾽ for τὸ δ᾽ in l. 26 with Ag, C, and Waitz. ; % Read E in l. 31 with A, B,, C, and treat ro yap... H ll. 32-3 as | parenthetical (Waitz).
  7. 7 Aristotle has in mind the proof in ® 12-19, where All E is F. JP = ©, All Cis A. “. All Lis A. He now points out that it is preferable to take both the antecedents and the consequents of A and of E in their most general form, e.g. to take ΛΖ, a καθόλου which includes L and AC, a καθόλου which includes C. If all A/is A, then all F and.:. all E is A, and by taking account | of A¥ as well as of F we shall have put the proof in a more satisfactory because more universal way. i.e. the consequents of A and E.
  8. 8 97a18-20, 23-8.
  9. 9 And .. not to some E. | * This does not actually follow.

Libro I, capitolo 29 The same Method applied to other than categorical Syllogisms.45a23–46a2

Inglese

45a23Syllogisms which lead to impossible conclusions are similar to ostensive syllogisms; they also are formed by means of 45a25the consequents and antecedents of the terms in question. In both cases the same inquiry is involved. For what is proved ostensively may also be concluded syllogistically per impossibile by means of the same terms; and what is proved per impossibile may also be proved ostensively, e.g. that A belongs to none of the Es. For1 suppose A to belong to some E: then since B belongs to all A and A 45a30to some of the Es, B will belong to some of the Es: but it was assumed that it belongs to none. Again we may prove that A belongs to some E: for if A belonged to none of the Es, and E belongs to all G, A will belong to none of the Gs: but it was assumed to belong to all. Similarly with the other propositions requiring proof. The proof 45a35per impossibile will always and in all cases be from the consequents and antecedents of the terms in question. Whatever the problem the same inquiry is necessary whether one wishes to use an ostensive syllogism or a reduction to impossibility. For both the demonstrations start from the same terms, e. g. suppose it has been proved that A belongs to no E, because it turns out that otherwise 45a40B belongs to some of the Es and this is impossible—if now it is assumed that B belongs to no E and to all A, it is clear 45bthat A will belong to no E. Again if it has been proved by an ostensive syllogism that A belongs to no E, assume that A belongs to some E and it will be proved per impossibile to belong to no E. Similarly with the rest. In all cases it is necessary to find some common term other than 45b5the subjects of inquiry, to which the syllogism establishing the false conclusion may relate, so that if this premiss is converted,2 and the other remains as it is, the syllogism will be ostensive by means of the same terms. For the ostensive syllogism differs from the reduction ad impossibile in this: in the ostensive syllogism both premisses are laid 45b10down in accordance with the truth, in the reduction ad impossibile one of the premisses is assumed falsely.

45b12These points will be made clearer by the sequel,3 when we discuss the reduction to impossibility: at present this much must be clear, that we must look to terms of the kinds mentioned whether we wish to use an ostensive syllogism 45b15or a reduction to impossibility. In the other hypothetical syllogisms, I mean those which proceed by substitution,4 or by positing a certain quality,5 the inquiry will be directed to the terms of the problem to be proved—not the terms of the original problem, but the new terms introduced; and the method of the inquiry will be the same as before. But 45b20we must consider and determine in how many ways hypothetical syllogisms are possible.

45b21Each of the problems then can be proved in the manner described; but it is possible to establish some of them syllogistically in another way, e.g. universal problems by the inquiry which leads up to a particular conclusion, with the addition of an hypothesis.6 For if the Cs and the Gs should be identical, but E should be assumed to belong to 45b25the Gs only, then A would belong to every E: and again if the Ds and the Gs should be identical, but E should be predicated, of the Gs only, it follows that A will belong to none of the Es. Clearly then we must consider the matter in this way also. The method is the same whether the relation is necessary or possible. For the inquiry will be the same, and the syllogism will proceed through terms7 45b30arranged in the same order whether a possible or a pure proposition is proved. We must find in the case of possible relations, as well as terms that belong, terms which can belong though they actually do not: for we have proved that the syllogism which establishes a possible relation 45b35proceeds through these terms as well. Similarly also with the other modes of predication.!

45b37It is clear then from what has been said not only that all syllogisms can be formed in this way, but also that they cannot be formed in any other. For every syllogism has been proved to be formed through one of the aforementioned 45b40figures, and these cannot be composed through other terms than the consequents and antecedents of the terms in question: 46afor from these we obtain the premisses and find the middle term. Consequently a syllogism cannot be formed by means of other terms.

Note del traduttore
  1. 1 Read ἀνάγκη δ᾽ εἰ for ἐὰν δὲ in 1, 18 with Bnu and Waitz.
  2. 2 i.e. if this false conclusion is replaced by its contradictory and | this is treated as a premiss.
  3. 3 ii. 14.
  4. 4 Cf. 41% 309.
  5. 5 Al. and Phil. interpret this as referring to arguments ἀπὸ τοῦ μᾶλλον καὶ ἧττον καὶ ὁμοίου, from the possession of a quality in unequal | or equal degree by two terms, i.e. arguments a for‘ioré and by analogy.
  6. 6 i.e. the assumption that C = G, which in 4419-21 proved that | some E is A, will, if we add the hypothesis that only G is E, prove | that all Ε΄ is A; and the assumption that 7) = G, which in 448 28-30 proved that some E is not A, will, if we suppose that only G 152, | prove that no E is A.
  7. 7 "2 } e.g. propositions asserting non-necessity, impossibility, &c. @ Read éxarepov in l. 5 with A, B, C, Al., and Waitz.

Libro I, capitolo 30 The preceding method of Demonstration applicable to all Problems.46a3–30

Inglese

46a3The method is the same in all cases, in philosophy, in any art or study. We must look for the attributes and the 46a5subjects of both our terms,” and we must supply ourselves with as many of these as possible, and consider them by means of the three terms, refuting statements in one way, confirming them in another, in the pursuit of truth starting from premisses in which the arrangement of the terms is in accordance with truth, while if we look for dialectical syllogisms 46a10we must start from probable premisses. The principles of syllogisms have been stated in general terms, both how they are characterized and how we must hunt for them, so as not to look to everything that is said about the terms of the problem or to the same points whether we are confirming or refuting, or again whether we are confirming 46a15of all or of some, and whether we are refuting of all or some; we must look to fewer points and they must be definite. We have also stated how we must select with reference to everything that is, e.g. about good or knowledge. But in each science the principles which are peculiar1 are the most numerous. Consequently it is the business of experience to give the principles which belong to each subject. I mean for example that astronomical experience 46a20supplies the principles of astronomical science: for once the phenomena were adequately apprehended, the demonstrations of astronomy were discovered. Similarly with any other art or science. Consequently, if the attributes of the thing are apprehended, our business will then be to exhibit readily the demonstrations. For if none of the true 46a25attributes of things had been omitted in the historical survey, we should be able to discover the proof and demonstrate everything which admitted of proof, and to make that clear, whose nature does not admit of proof.

46a28In general then we have explained fairly well how we must select premisses: we have discussed the matter 46a30accurately in the treatise concerning dialectic.2

Note del traduttore
  1. 1 Read "fu in l. 17 with Al. and Waitz.
  2. 2 Topics, especially i. 14.

Citato nell'enciclopedia: INDUZIONE

Libro I, capitolo 31 Upon Division; and its Imperfection as to Demonstration.46a31–46b40

Inglese

46a31It is easy to see that division into classes1 is a small part of the method we have described: for division is, so to speak, a weak syllogism; for what it ought to prove, it begs, and it always establishes something more general than the attribute in question. First, this very point had 46a35escaped all those who used the method of division; and they attempted to persuade men that it was possible to make a demonstration of substance and essence. Consequently they did not understand what it is possible to prove syllogistically by division,? nor did they understand that it was possible to prove syllogistically in the manner we have described.2 In demonstrations, when there is a need to 46a40prove a positive statement, the middle term through which 46bthe syllogism is formed must always be inferior to and not comprehend the first of the extremes. But division has a contrary intention: for it takes the universal as middle. Let animal be the term signified by A, mortal by B, and immortal by C, and let man, whose definition is to be got, 46b5be signified by D. The man who divides assumes that every animal is either mortal or immortal: i.e. whatever is A is all either B or C. Again, always dividing, he lays it down that man is an animal, so he assumes A of D as belonging to it. Now the true conclusion is that every D 46b10is either B or C, consequently man must be either mortal or immortal, but it is not necessary that man should be a mortal animal—this is begged: and this is what ought to have been proved syllogistically. And again, taking A as mortal animal, B as footed, C as footless, and D as man, he assumes in the same way that A inheres either in B or in C (for every mortal animal is either footed or footless), and he assumes A of D (for he assumed man, as we saw, to be a mortal animal) ; consequently it is necessary that man should be either a footed or a footless animal; but it is not necessary that man should be footed: this he assumes: and it is just this again which he ought to have demonstrated. Always dividing 46b20then in this way it turns out that these logicians assume as middle the universal term, and as extremes that which ought to have been the subject of demonstration and the differentiae. In conclusion, they do not make it clear, and show it to be necessary, that this is man or whatever the subject of inquiry may be: for they pursue the other method 46b25altogether, never even suspecting the presence of the rich supply of evidence which might be used. It is clear that it is neither possible to refute a statement by this method of division, nor to draw a conclusion about an accident or property of a thing, nor about its genus, nor in cases in which it is unknown whether it is thus or thus, e. g. whether the diagonal is incommensurate. For if he assumes that 46b30every length is either commensurate or incommensurate, and the diagonal is a length, he has proved that the diagonal is either incommensurate or commensurate. But if he should assume that it is incommensurate, he will have assumed what he ought to have proved. He cannot then prove it: for this is his method, but proof is not possible by this method. Let A stand for ‘incommensurate or commensurate’, B for 46b35‘length’, C for ‘diagonal’. It is clear then that this method of investigation is not suitable for every inquiry, nor is it useful in those cases in which it is thought to be most suitable. ,

46b39From what has been said it is clear from what elements demonstrations are formed and in what manner, and to what points we must look in each problem.

Note del traduttore
  1. 1 Aristotle is thinking of Plato’s establishment of definitions by _ means of division by dichotomy. ὃ Read διαιρουμένους in l. 38 with codd. mn, Al., Phil., Them., and Waitz.
  2. 2 In ce. I-30.

Citato nell'enciclopedia: DIVISIONE · SILLOGISMO

Libro I, capitolo 32 Reduction of Syllogisms to the above Figures.46b40–47b14

Inglese

46b39Our next business is to state how we can reduce syllogisms 47ato the aforementioned figures: for this part of the inquiry still remains. If we should investigate the production of the syllogisms and had the power of discovering them, and further if we could resolve the syllogisms produced into 47a5the aforementioned figures, our original problem would be brought to a conclusion. It will happen at the same time that what has been already said will be confirmed and its truth made clearer by what we are about to say. For everything that is true must in every respect agree with itself.

47a10First then we must attempt to select the two premisses of the syllogism (for it is easier to divide into large parts than into small,1 and the composite parts are larger than the elements out of which they are made); next we must inquire which are universal and which particular, and if both premisses have not been stated, we must ourselves assume the one which is missing. For sometimes men put 47a15forward the universal premiss, but do not posit the premiss which is contained in it, either in writing or in discussion: or men put forward the premisses of the principal syllogism, but omit those through which they are inferred, and invite the concession of others to no purpose.? We must inquire then whether anything unnecessary has been assumed, or anything necessary has been omitted, and we 47a20must posit the one and take away the other, until we have reached the two premisses: for unless we have these, we cannot reduce2 arguments put forward in the way described. In some arguments it is easy to see what is wanting, but some escape us, and appear to be syllogisms, because something necessary results from what has been laid down, e.g. if the assumptions were made that substance is 47a25not annihilated by the annihilation of what is not substance, and that if the elements out of which a thing is made are annihilated, then that which is made out of them is destroyed: these propositions being laid down, it is necessary that any part of substance is substance; this has not however been drawn by syllogism from the propositions assumed, but premisses are wanting. Again if it is necessary that animal should exist, if man does, and that substance should exist, if animal does, it is necessary that substance 47a30should exist if man does: but as yet the conclusion has not been drawn syllogistically: for the premisses are not in the shape we required. We are deceived in such cases because something necessary results from what is assumed, since the syllogism also is necessary. But that which is necessary is wider than the syllogism: for every syllogism is necessary, 47a35but not everything which is necessary is a syllogism. Consequently, though something results when certain propositions are assumed, we must not try to reduce it directly, but must first state the two premisses, then divide them into their terms. We must take that term as middle which is stated in both the premisses: for it is necessary that the 47a40middle should be found in both premisses in all the figures.

47b1If then the middle term is a predicate and a subject of predication, or if it is a predicate, and something else is denied of it, we shall have the first figure: if it both is a predicate and is denied of something, the middle figure: if other things are predicated of it, or one is denied, the other 47b5predicated, the last figure. For it was thus that we found the middle term placed in each figure. It is placed similarly too if the premisses are not universal: for the middle term is determined in the same way. Clearly then, if the same term is not stated more than once in the course of an argument, a syllogism cannot be made: for a middle term has not been taken. Since we know what sort of thesis is 47b10established in each figure, and in which the universal, in what sort the particular is established, clearly we must not look for all the figures, but for that which is appropriate to the thesis in hand. If the thesis is established in more figures than one, we shall recognize the figure by the position of the middle term.

Note del traduttore
  1. 1 i.e, the terms.
  2. 2 Top. viii. I: 3 Read ἀναγαγεῖν in l. 21 with B, Cy, Al., and Waitz.

Libro I, capitolo 33 On Error, arising from the quantity of Propositions.47b15–40

Inglese

47b15Men are frequently deceived about syllogisms because the inference is necessary, as has been said above1 sometimes they are deceived by the similarity in the positing of the terms; and this ought not to escape our notice. E.. if A is stated of B, and B of C: it would seem that a syllogism is possible since the terms stand thus: but nothing 47b20necessary results, nor does a syllogism. Let A represent the term ‘being eternal’, B ‘Aristomenes as an object of thought’, C ‘Aristomenes’. It is true then that A belongs to B. For Aristomenes as an object of thought is eternal. But B also belongs to C: for Aristomenes is Aristomenes 47b25as an object of thought. But A does not belong to C: for Aristomenes is perishable. For no? syllogism was made although the terms stood thus: that required that the premiss AB should be stated universally. But this is false, that every Aristomenes who is an object of thought is eternal, since Aristomenes is perishable. Again let C stand 47b30for ‘Miccalus’, B for ‘musical Miccalus’, A for ‘perishing to-morrow’. It is true to predicate B of C: for Miccalus is musical Miccalus. Also A can be predicated of B: for musical Miccalus might perish to-morrow.2 But to state A of C is false at any rate. This argument then is identical 47b35with the former; for it is not true universally that musical Miccalus perishes to-morrow: but unless this is assumed, no syllogism (as we have shown) is possible.

47b38This deception then arises through ignoring a small distinction. For we accept the conclusion as though it made no difference whether we said ‘This belongs to that’ or ‘This belongs to all of that’.

Note del traduttore
  1. 1 τῶ 41,
  2. 2 Read οὐ γὰρ in l. 26 with A, B, C, and Waitz. | ° i.e. Miccalus might to-morrow cease to be musical.

Libro I, capitolo 34 Error arising from inaccurate exposition of Terms.47b40–48a28

Inglese

48a1Men will frequently fall into fallacies through not setting out the terms of the premiss well, e.g. suppose A to be health, B disease, C man. It is true to say that A cannot belong to any B (for health belongs to no disease) and 48a5again that B belongs to every C (for every man is capable of disease). It would seem to follow that health cannot belong to any man. The reason for this is that the terms are not set out well in the statement, since if the things which are in the conditions are substituted, no syllogism 48a10can be made, e.g. if ‘healthy’ is substituted for ‘health’ and ‘diseased’ for ‘disease’. For it is not true to say that being healthy cannot belong to one who is diseased. But unless this is assumed no conclusion results, save in respect of possibility: but such a conclusion is not impossible: for 48a15sit is possible that health should belong to no man. . Again the fallacy may occur in a similar way in the middle figure: ‘it is not possible that health should belong to any disease, but it is possible that health should belong to every man, consequently it is not possible that disease should belong to any man’. In the third figure the fallacy results in reference to possibility. For health and disease, and 48a20knowledge and ignorance, and in general contraries, may possibly belong to the same thing, but cannot belong to one another. This is not in agreement with what was said before: for we stated1 that when several things could belong to the same thing, they could belong to one another.

48a24It is evident then that in all these cases the fallacy arises 48a25from the setting out of the terms: for if the things that are in the conditions are substituted, no fallacy arises. It is clear then that in such premisses what possesses the condition ought always to be substituted for the condition and taken as the term.

Note del traduttore
  1. 1 39a14-19.

Libro I, capitolo 35 Middle not always to be assumed as a particular definite thing, ὡς τόδε τι.48a29–39

Inglese

48a29We must not always seek to set out the terms in a single 48a30word: for we shall often have complexes of words to which a single name is not given. Hence it is difficult to reduce syllogisms with such terms. Sometimes too fallacies will result from such a search, e.g. the belief that syllogism can establish that which has no mean. Let A stand for two right angles, B for triangle, C for isosceles triangle. A then 48a35belongs to C because of B: but A belongs to B without the mediation of another term: for the triangle in virtue of its own nature contains two right angles, consequently there will be no middle term for the proposition AB, although it is demonstrable. For it is clear that the middle must not always be assumed to be an individual thing, but sometimes a complex of words, as happens in the case mentioned.

Libro I, capitolo 36 On the arrangement of Terms, according to nominal appellation ; and of Propositions according to case.48a40–49a5

Inglese

48a40That the first term belongs to the middle, and the middle to the extreme,1 must not be understood in the sense that they can always be predicated of one another or that the 48bfirst term will be predicated of the middle in the same way as the middle is predicated of the last term. The same holds if the premisses are negative. But we must suppose the verb ‘to belong’ to have as many meanings as the senses in which the verb ‘to be’ is used, and in which the assertion that a thing ‘is’ may be said to be true. Take 48b5for example the statement that there is a single science of contraries. Let A stand for ‘there being a single science’, and B for things which are contrary to one another. Then A belongs to B, not in the sense that contraries are? the fact of there being a single science of them, but in the sense that it is true to say of the contraries that there is a single science of them.

48b10It happens sometimes that the first term is stated of the middle, but the middle is not stated of the third term, e.g. if wisdom is knowledge, and wisdom is of the good, the conclusion is that there is knowledge of the good. The good then is not knowledge, though wisdom is knowledge. 48b15Sometimes the middle term is stated of the third, but the first is not stated of the middle, e.g. if there is a science of everything that has a quality, or is a contrary, and the good both is a contrary and has a quality, the conclusion is that there is a science of the good, but the good is not science, nor is that which has a quality or is a contrary, though the good is both of these. Sometimes 48b20neither the first term is stated of the middle, nor the middle of the third, while the first is sometimes stated of the third, and sometimes not: e.g. if there is a genus of that of which there is a science, and if there is a science of the good, we conclude that there is a genus of the good, But nothing is predicated of anything. And if that 48b25of which there is a science is a genus, and if there is a science of the good, we conclude that the good is a genus. The first term then is predicated of the extreme, but in the premisses one thing is not stated of another.

48b28The same holds good where the relation is negative. For ‘that does not belong to this’ does not always mean 48b30that ‘this is not that’, but sometimes that ‘this is not of that’ or ‘for that’, e.g. ‘there is not a motion of a motion or a becoming of a becoming, but there is a becoming of pleasure: so pleasure is not a becoming.’ Or again it may be said that there is a sign of laughter, but there is not a sign of a sign, consequently laughter is not a sign. This holds in the other cases too, in which the thesis is refuted 48b35because the genus is asserted in a particular way, in relation to the terms of the thesis! Again take the inference ‘opportunity is not the right time: for opportunity belongs to God, but the right time does not, since nothing is useful to God’. We must take as terms opportunity—right time —God: but the premiss must be understood according to the case of the noun. For we state this universally without 48b40qualification, that the terms ought always to be stated in the nominative, e.g. man, good, contraries, not in oblique 49acases, e.g. of man, of good, of contraries, but the premisses ought to be understood with reference to the cases of each term-cither the dative, e.g. ‘equal to this’, or the genitive, e.g. ‘double of this’, or the accusative, e.g. ‘that which strikes or sees this’, or the nominative, e.g. ‘man is an 49a5animal’, or in whatever other way the word falls in the premiss.

Note del traduttore
  1. 1 i.e. the minor. some relation to them such as is indicated by the use of an oblique case. } .e. negative syllogisms in the second figure in which the middle term is not strictly predicated of the extremes but is said to stand in some relation to them such as Is indicated by the use of an oblique case.

Libro I, capitolo 37 Rules of Reference to the forms of Predication.49a6–10

Inglese

49a6The expressions ‘this belongs to that’ and ‘this holds true of that’ must be understood in as many ways as there are different categories, and these categories must be taken either with or without qualification, and further as simple or compound: the same holds good of the corresponding 49a10negative expressions. We must consider these points and define them better.

Libro I, capitolo 38 Of Propositional Iteration and the Addition to a Predicate.49a11–49b2

Inglese

49a11A term which is repeated in the premisses ought to be joined to the first extreme, not to the middle. I mean for example that if a syllogism should be made proving that there is knowledge of justice, that it is good, the expression ‘that it is good’ (or ‘qua good’) should be joined to the 49a15first term. Let A stand for ‘knowledge that it is good’, B for good, C for justice. It is true to predicate A of B. For1 of the good there is knowledge that it is good. Also it is true to predicate B of C. For justice is identical with a good. In this way an analysis of the argument can be made. But if the expression ‘that it is good’ were 49a20added to B, the conclusion will not follow: for A will be true of B, but B will not be true of C. For to predicate of justice the term ‘good that it is good’ is false and not intelligible. Similarly if it should be proved that the healthy is an object of knowledge gad good, or goat-stag an object of knowledge qua not existing,2 or man perishable gud an object of sense: in every case in which an addition 49a25is made to the predicate, the addition must be joined to the extreme.”

49a26The position of the terms is not the same when something is established without qualification and when it is qualified by some attribute or condition, e.g. when the good is proved to be an object of knowledge and when it is proved to be an object of knowledge that it is good.3 If it 49a30has been proved to be an object of knowledge without qualification, we must put as middle term ‘that which is’, but if we add the qualification ‘that it is good’, the middle term must be ‘that which is something’. Let A stand for ‘knowledge that it is something’, B stand for ‘something’, and C stand for ‘good’, It is true to predicate A of B: for ex hypothesi there is a science of that which is something, that it is something. B too is true of C: for that which C 49a35represents is something. Consequently A is true of C: there will then be knowledge of the good, that it is good: for ex hypothesis the term ‘something’ indicates the thing’s special nature. But if ‘being’ were taken as middle and ‘being’ simply were joined to the extreme, not ‘being something’, we should not have had a syllogism proving that there is knowledge of the good, that it is good, but that 49bit is; e.g. let A stand for knowledge that it is, B for being, C for good. Clearly then in syllogisms which are thus limited we must take the terms in the way stated.

Note del traduttore
  1. 1 i.e. in the sense that it can be known not to exist. Omit δοξαστὸν in l. 24 with A, B, C, Al., Phil., and Waitz.
  2. 2 1,6. the major term.
  3. 3 3 Omit τι in l. 29 with Al., Phil., Them., and Waitz.

Libro I, capitolo 39 The Simplification of Terms in the Solution of Syllogism.49b3–9

Inglese

49b3We ought also to exchange terms which have the same value, word for word, and phrase for phrase, and word and 49b5phrase, and always take a word in preference to a phrase: for thus the setting out of the terms will be easier. For example if it makes no difference whether we say that the supposable is not the genus of the opinable or that the opinable is not identical with a particular kind of supposable (for what is meant is the same in both statements), it is better to take as the terms the supposable and the opinable in preference to the phrase suggested.

Libro I, capitolo 40 The definite Article to be added according to the nature of the Conclusion.49b10–13

Inglese

49b10Since the expressions ‘pleasure is good’ and ‘pleasure is the good’ are not identical, we must not set out the terms in the same way; but if the syllogism is to prove that pleasure is the good, the term must be ‘the good’, but if the object is to prove that pleasure is good, the term will be ‘good’. Similarly in all other cases.

Libro I, capitolo 41 On the Distinction of certain forms of Universal Predication.49b14–50a4

Inglese

49b15It is not the same, either in fact or in speech, that A belongs to all of that to which B belongs, and that A belongs to all of that to all of which B belongs: for nothing prevents B from belonging to C, though not to all C: e.g. let B stand for beautiful, and C for white. If beauty belongs to something white, it is true to say that beauty belongs to that which is white; but not perhaps to everything that is 49b20white. If then A belongs to B, but not to everything of which B is predicated, then whether B belongs to all C or merely belongs to C, it is not necessary that A should belong, I do not say to all C, but even to C at all. But if A belongs to everything of which B is truly stated, it will follow that A can be said of all of that of all? of which B is 49b25said. If however A is said of that of all of which B may be said, nothing prevents B belonging to C, and yet A not belonging to all C or to any Cat all. If then we take three terms it is clear that the expression ‘A is said of all of which B is said1 means this, ‘A is said of all the things of which 49b30B is said'. And if B is said of all of a third term, so also is A: but if B is not said of all of the third term, there is no necessity that A should be said of all of it.

49b32We must not suppose that something absurd results through setting out the terms: for we do not use the existence of this particular thing, but imitate the 49b35geometrician who says that ‘this line a foot long’ or ‘this straight line’ or ‘this line without breadth’ exists although it does not, but does not use the diagrams in the sense that he reasons from them. For in general, if two things are not related as whole to part and part to whole, the prover does not prove from them, and so no syllogism is formed. 50aWe (I mean the learner) use the process of setting out terms like perception by sense, not as though it were impossible to demonstrate without these illustrative terms, as it is to demonstrate without the premisses of the syllogism.

Note del traduttore
  1. 1 Omit the comma after λέγηται in l. 26 with Waitz. _ 7 Omit the comma after B in l. 28 with Waitz. The Greek phrase is there ambiguous, and Aristotle’s object is to remove this ambiguity.

Libro I, capitolo 42 That not all Conclusions in the same Syllogism are produced through one Figure.50a5–10

Inglese

50a5We should not forget that in the same syllogism not all conclusions are reached through one figure, but one through one figure, another through another. Clearly then we must analyse arguments in accordance with this. Since not every problem is proved in every figure, but certain problems 50a10in each figure, it is clear from the conclusion in what figure the premisses should be sought.

Libro I, capitolo 43 Of Arguments against Definition, simplified.50a11–15

Inglese

50a11In reference to those arguments aiming at a definition which have been directed to prove some part of the definition, we must take as a term the point to which the argument has been directed, not the whole definition: for so we shall be less likely to be disturbed by the length of the term: e.g. if a man proves that water is a drinkable liquid, we must 50a15take as terms drinkable and water.

Libro I, capitolo 44 Of the Reduction of Hypotheticals and of Syllogisms ad impossibile.50a16–50b4

Inglese

50a16Further we must not try to reduce hypothetical syllogisms; for with the given premisses it is not possible to reduce them. For they have not been proved by syllogism, but assented to by agreement. For instance if a man should suppose 50a20that unless there is one faculty of contraries, there cannot be one science, and should then argue that not every! faculty is of contraries, e.g. of what is healthy and what is sickly: for the same thing will then be at the same time healthy and sickly. He has shown1 that there is not one faculty of all contraries, but he has not proved that there is not 50a25a science. And yet one must agree. But the agreement does not come from a syllogism, but from an hypothesis. This argument cannot be reduced: but the proof that there is not a single faculty can. The latter argument perhaps was a syllogism: but the former was an hypothesis.

50a29The same holds good of arguments which are brought 50a30to a conclusion per impossibile. These cannot be analysed either; but the reduction to what is impossible can be analysed since it is proved by syllogism, though the rest of the argument cannot, because the conclusion is reached from an hypothesis. But these differ from the previous arguments: for in the former a preliminary agreement must be reached if one is to accept the conclusion; e.g. an agreement that if there is proved to be one faculty of contraries, then contraries 50a35fall under the same science; whereas in the latter, even if no preliminary agreement has been made, men still accept the reasoning, because the falsity} is patent, e.g. the falsity of what follows from the assumption that the diagonal is commensurate, viz. that then odd numbers are equal to evens.”2

50a39Many other arguments are brought to a conclusion by the 50a40help of an hypothesis; these we ought to consider and mark out clearly. We shall describe in the sequel3 their differences, 50band the various ways in which hypothetical arguments are formed: but at present this much must be clear, that it is not possible to resolve such arguments into the figures. And we have explained the reason.

Note del traduttore
  1. 1 Read πᾶσα for pia in 1, 21 with B, Al., and Waitz. > Read ἐπιδέδεικται for ἀποδέδεικται in l. 24 with A, B, C, and Waitz.
  2. 2 Cf. 41926,
  3. 3 This promise is not fulfilled in Aristotle’s extant works. |

Libro I, capitolo 45 The Reduction of Syllogisms from one Figure to another.50b5–51b4

Inglese

50b5Whatever problems are proved in more than one figure, it they have been established in one figure by syllogism, can be reduced to another figure, e.g. a negative syllogism in the first figure can be reduced to the second, and a syllogism in the middle figure to the first, not all however but some only. The point will be clear in the sequel. If A belongs 50b10to no B, and B to all C, then A belongs to no C. Thus the first figure; but if the negative statement is converted, we shall have the middle figure. For B belongs to no A, and to all C. Similarly if the syllogism is not universal but particular, e.g. if A belongs to no B, and B to some C. 50b15Convert the negative statement and you will have the middle figure.

50b17The universal syllogisms in the second figure can be reduced to the first, but only one of the two particular syllogisms. Let A belong to no B and to all C. Convert 50b20the negative statement, and you will have the first figure. For B will belong to no A, and A to all C. But if the affirmative statement concerns B, and the negative C, C must be made first term. For C belongs to no A, and A to all B: therefore C belongs to no B. B then belongs to no C: for 50b25the negative statement is convertible.

50b26But if the syllogism is particular, whenever the negative statement concerns the major extreme, reduction to the first figure will be possible, e.g. if A belongs to no B and to some C: convert the negative statement and you will have the first figure. For B will belong to no A, and A to some 50b30C. But when the affirmative statement concerns the major extreme, no resolution will be possible, e.g. if A belongs to all B, but not to all C: for the statement AB does not admit of conversion,1 nor would there be a syllogism if it did.

50b35Again syllogisms in the third figure cannot all be resolved into the first, though all syllogisms in the first figure can be resolved into the third. Let A belong to all B and B to some C. Since the particular affirmative is convertible, C will belong to some B: but A belonged to all B: so that the third figure is formed. Similarly if the syllogism is negative: for the particular affirmative is convertible: therefore 50b40A will belong to no B, and to some C.

51a1Of the syllogisms in the last figure one only cannot be resolved into the first, viz. when the negative statement is not universal: all the rest can be resolved. Let A and B be affirmed of all C: then C can be converted partially with 51a5either A or B: C then belongs to some B. Consequently we shall get the first figure, if A belongs to all C, and C to some of the Bs. If A belongs to all C and B to some C, the argument is the same: for B is convertible in reference to C. But if B belongs to all C and A to some C, the first 51a10term must be B: for B belongs to all C, and C to some A, therefore B belongs to some A. But since the particular statement is convertible, A will belong to some B. If the syllogism is negative, when the terms are universal we must take them in a similar way. Let B belong to all C, and A 51a15to no C: then C will belong to some B, and A to no C; and so C will be middle term. Similarly if the negative statement is universal, the affirmative particular: for A will belong to no C, and C to some of the Bs. But if the negative statement is particular, no resolution will be possible, e. g. if B belongs to all C, and A does not belong 51a20to some C: convert the statement BC and both premisses will be particular.

51a22It is clear that in order to resolve the figures2 into one another the premiss which concerns the minor extreme must be converted in both the figures: for when this premiss is 51a25altered, the transition to the other figure is made.

51a26One of the syllogisms in the middle figure can, the other cannot, be resolved into the third figure. Whenever the universal statement is negative, resolution is possible. For if A belongs to no B and to some C, both B and C alike are convertible in relation to A, so that B belongs to no A, and 51a30C to some A. A therefore is middle term. But when A belongs to all B, and not to some C, resolution will not be possible: for neither of the premisses is universal after conversion.

51a34Syllogisms in the third figure can be resolved into the 51a35middle figure, whenever the negative statement is universal, e.g. if A belongs to no C, and B to some or all C. For C then will belong to no A and to some B. But if the negative statement is particular, no resolution will be possible: for the particular negative does not admit of conversion.

51a40It is clear then that the same syllogisms cannot be resolved in these figures which could not be resolved into the 51bfirst figure, and that when syllogisms are reduced to the first figure these alone are confirmed by reduction to what is impossible. ,

51b3It is clear from what we have said how we ought to reduce syllogisms, and that the figures may be resolved into one another.

Note del traduttore
  1. 1 i.e. simple conversion.
  2. 2 i.e. the first and third figures.

Libro I, capitolo 46 Of the Quality and Signification of the Definite, and Indefinite, and Privative.51b5–52b34

Inglese

51b5In establishing or refuting, it makes some difference whether we suppose the expressions ‘not to be this’ and ‘to be not-this’ are identical or different in meaning, e.g. ‘not to be white’ and ‘to be not-white’. For they do not mean the same thing, nor is ‘to be not-white’ the negation 51b10of ‘to be white’, but ‘not to be white’. The reason for this is as follows. The relation of ‘he can walk’ to ‘he can not-walk’ is similar to the relation of ‘it is white’ to ‘it is not-white’; so is that of ‘he knows what is good’ to ‘he knows what is not-good’. For there is no difference between the expressions ‘he knows what is good’ and ‘he is knowing what 51b15is good’, or ‘he can walk’ and ‘he is able to walk’: therefore there is no difference between their contraries ‘he cannot walk ’—‘he is not able to walk’. If then ‘he is not able to walk’ means the same as ‘he is able not to walk’, capacity to walk and incapacity to walk will belong at the same time to the same person (for the same man can both walk and not-walk, 51b20and is possessed of knowledge of what is good and of what is not-good), but an affirmation and a denial which are opposed to one another do not belong at the same time to the same thing. As then ‘not to know what is good’ is not the same as ‘to know what is not good’, so ‘to be not-good’ is not the same as ‘not to be good’. For when two pairs correspond, if the one pair are different from one another, the 51b25other pair also must be different. Nor is ‘to be not-equal’ the same as ‘not to be equal’: for there is something underlying the one, viz. that which is not-equal, and this is the unequal, but there is nothing underlying. the other. Wherefore not everything is either equal or unequal, but everything is equal or is not equal. Further the expressions ‘it is a not-white log’ and ‘it is not a white log’ do not imply one another’s 51b30truth. For if ‘it is a not-white log’, it must be a log: but that which is not a white log need not be a log at all. Therefore it is clear that ‘it is not-good' is not the denial of ‘it is good’. If then every single statement may truly be said to be either an affirmation or a negation, if it is not a negation clearly it must in a sense be an affirmation. But every affirmation has a corresponding 51b35negation. The negation then of ‘it is not-good’ is ‘it is not not-good’. The relation of these statements to one another is as follows. Let A stand for ‘to be good’, B for ‘not to be good’, let C stand for ‘to be not-good’ and be placed under B,1 and let D stand for ‘not to be not-good’ and be placed under A, Then either A or B will belong to everything, but they will never belong to the same thing; 51b40and either C or D will belong to everything, but they will never belong to the same thing. And B must belong to everything to which C belongs. For if it is true to say 52a‘it is not-white’, it is true also to say ‘it is not white’: for it is impossible that a thing should simultaneously be white and be not-white, or be a not-white log and be a white log; consequently if the affirmation does not belong, the denial must belong. But C does not always belong to B: for what 52a5is not a log at all, cannot be a not-white log either. On the other hand D belongs to everything to which A belongs. For either C or D belongs to everything to which A belongs. But since a thing cannot be simultaneously not-white and white, must belong to everything to which A belongs. For of that which is white it is true to say that it is not not-white. But A is not true of all D. For of that which 52a10is not a log at all it is not true to say A, viz. that it is a white2 log. Consequently D is true, but A is not true, i.e. that it is a white log. It is clear also that A and C cannot together belong to the same thing, and that B and D may possibly belong to the same thing.

52a15Privative terms are similarly related to positive terms in respect of this arrangement. Let A stand for ‘equal’, B for ‘not equal’, C for ‘unequal’, D for ‘not unequal’.

52a18In many things also, to some of which something belongs which does not belong to others, the negation may be true 52a20in a similar way,3 viz. that all are not white or that each is not white, while that each is not-white or all are not-white is false. Similarly also ‘every animal is not-white’ is not the negation of ‘every animal is white’ (for both are false): the proper negation is ‘every animal is not white’. Since it 52a25is clear that ‘it is not-white’ and ‘it is not white’ mean different things, and one is an affirmation, the other a denial, it is evident that the method of proving each cannot be the same, e.g. that whatever is an animal is not white or may not be white, and that it is true to call it not-white; for this means that it is not-white. But we may prove that it is true 52a30to call it white or not-white in the same way—for both are proved constructively by means of the first figure. For the expression ‘it is true’ stands on a similar footing to ‘it is’. For the negation of ‘it is true to call it white’ is not ‘it is true to call it not-white’ but ‘it is not true to call it white’. If then it is to be4 true to say that whatever is a man is 52a35musical or is not-musical, we must assume that whatever is an animal either is musical or is not-musical; and the proof has been made. That whatever is a man is not musical is proved destructively in the three ways mentioned.‘5

52a39In general whenever A and B are such that they cannot 52a40belong at the same time to the same thing, and one of the two necessarily belongs to everything, and again C and D 52bare related in the same way, and A follows C but the relation cannot be reversed, then )D must follow B and the relation cannot be reversed. And A and D may belong to the same thing, but B and C cannot. First it is clear from the 52b5following consideration that D follows B. For since either C or D necessarily belongs to everything; and since C cannot belong to that to which B belongs, because it carries A along with it and A and B cannot belong to the same thing; it is clear that D must follow B. Again since C does not reciprocate with A, but C or D belongs to everything, it is 52b10possible that A and D should belong to the same thing. But B and C cannot belong to the same thing, because A follows C; and so something impossible results. It is clear then that B does not reciprocate with D either, since it is possible that D and A should belong at the same time to the same thing.

52b14It results sometimes even in such an arrangement of terms 52b15that one is deceived through not apprehending the opposites rightly, one of which must belong to everything, e.g. we may reason that ‘if A and B cannot belong at the same time to the same thing, but it is necessary that one of them should belong to whatever the other does not belong to: and again C and D are related in the same way, and A follows everything which C follows: it will result6 that B belongs necessarily to everything to which D belongs’: but this 52b20is false. ‘Assume that F stands for the negation of A and B, and again that H stands for the negation of Cand D. It is necessary then that either A or F should belong to everything: for either the affirmation or the denial must belong. And again either C or I must belong to everything: for they are related as affirmation and denial. And ex hypothesi A belongs to everything to which C belongs. Therefore H 52b25belongs to everything to which F belongs. Again since cither F or L belongs to everything, and similarly either H or D, and since H follows F, B must follow D: for we know this. If then A follows C, B must follow D’. But this is false: for as we proved”7 the sequence is reversed in terms so constituted. The fallacy arises because perhaps it is not 52b30necessary that A or F should belong to everything, or that f’ or B should belong to everything: for F is not the denial of A. For not-good is the negation of good: and not-good is not identical with ‘neither good nor not-good’. Similarly also with Cand D. For two negations have been assumed in respect to one term.8

Note del traduttore
  1. 1 The text implies the following diagram: A (It is good.) B (It is not good.) D) (it is not not-good.) C (It is not-good.) Aristotle points out that A and B are contradictory. Cand P ,, » AandC ,, contrary. Band PY ,, compatible. 7) is inferable from A. B”” 29 C.
  2. 2 Omit οὐ inl. 11 with B, Cy, Al, and Waitz.
  3. 3 Cf. ll. 4,
  4. 4 S Read ἔσται in 1, 34.
  5. 5 Celarent, Cesare, Camestres.
  6. 6 Omit γὰρ in l. 19 with A and B,
  7. 7 From 4 39-> 13.
  8. 8 Jn I. 18, 21.

Latino di Boezio: Boethius, Migne, Patrologia Latina 64 (Paris 1847), coll. 639–712 (Corpus Corporum, University of Zurich). Public domain (1847). Digital text: Corpus Corporum.
Inglese (Oxford, 1928): A. J. Jenkinson, The Works of Aristotle translated into English, ed. W. D. Ross, vol. I (Oxford: Clarendon Press, 1928) (archive.org, University of Toronto scan). Public domain in the United States (published 1928) and in Canada (translator died 1928). Our transcription of the scan.
Inglese (Owen, 1853): Octavius Freire Owen, London: George Bell & Sons, 1889 (Bohn's Classical Library), vol. I, from the plates of the first edition (London: H. G. Bohn, 1853), same pagination (archive.org). Public domain. Our transcription of the scan.

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