Book 1
Chap. 1. Of Proposition, Term, Syllogism, and its Elements.
Chap. 2. On the Conversion of Propositions.
Chap. 3. On the Conversion of Modal Propositions.
Chap. 4. Of Syllogism, and of the first Figure.
Chap. 5. Of the second Figure.
Chap. 6. Of Syllogisms in the third Figure.
Chap. 7. Of the three first Figures, and of the Completion of Incomplete Syllogisms.
Chap. 8. Of Syllogisms derived from two necessary Propositions.
Chap. 9. Of Syllogisms, whereof one Proposition is necessary, and the other pure in the first Figure.
Chap. 10. Of the same in the second Figure.
Chap. 11. Of the same in the third Figure.
Chap. 12. A comparison of pure with necessary Syllogisms.
Chap. 13. Of the Contingent, and its concomitant Propositions.
Chap. 14. Of Syllogisms with two contingent Propositions in the first Figure.
Chap. 15. Of Syllogisms with one simple and another contingent Proposition in the first Figure.
Chap. 16. Of Syllogisms with one Premise necessary, and the other contingent in the first Figure.
Chap. 17. Of Syllogisms with two contingent Premises in the second Figure.
Chap. 18. Of Syllogisms with one Proposition simple, and the other contingent, in the second Figure.
Chap. 19. Of Syllogisms with one Premise necessary and the other contingent, in the second Figure.
Chap. 20. Of Syllogisms with both Propositions contingent in the third Figure.
Chap. 21. Of Syllogisms with one Proposition contingent and the other simple in the third Figure.
Chap. 22. Of Syllogisms with one Premise necessary, and the other contingent in the third Figure.
Chap. 23. It is demonstrated that every Syllogism is completed by the first Figure.
Chap. 24. Of the Quality and Quantity of the Premises in Syllogism.—Of the Conclusion.
Chap. 25. Every Syllogism consists of only three Terms, and of two Premises.
Chap. 26. On the comparative Difficulty of certain Problems, and by what Figures they are proved.
Chap. 27. Of the Invention and Construction of Syllogisms.
Chap. 28. Special Rules upon the same Subject.
Chap. 29. The same Method applied to other than categorical Syllogisms.
Chap. 30. The preceding method of Demonstration applicable to all Problems.
Chap. 31. Upon Division; and its Imperfection as to Demonstration.
Chap. 32. Reduction of Syllogisms to the above Figures.
Chap. 33. On Error, arising from the quantity of Propositions.
Chap. 34. Error arising from inaccurate exposition of Terms.
Chap. 35. Middle not always to be assumed as a particular thing, ὡς τόδε τι.
Chap. 36. On the arrangement of Terms, according to nominal appellation; and of Propositions according to case.
Chap. 37. Rules of Reference to the forms of Predication.
Chap. 38. Of Propositional Iteration and the Addition to a Predicate.
Chap. 39. The Simplification of Terms in the Solution of Syllogism.
Chap. 40. The definite Article to be added according to the nature of the Conclusion.
Chap. 41. On the Distinction of certain forms of Universal Predication.
Chap. 42. That not all Conclusions in the same Syllogism are produced through one Figure.
Chap. 43. Of Arguments against Definition, simplified.
Chap. 44. Of the Reduction of Hypotheticals and of Syllogisms ad impossibile.
Chap. 45. The Reduction of Syllogisms from one Figure to another.
Chap. 46. Of the Quality and Signification of the Definite, and Indefinite, and Privative.
Book 2
Chap. 1. Recapitulation.—Of the Conclusions of certain Syllogisms.
Chap. 2. On a true Conclusion deduced from false Premises in the first Figure.
Chap. 3. The same in the middle Figure.
Chap. 4. Similar Observations upon a true Conclusion from false Premises in the third Figure.
Chap. 5. Of Demonstration in a Circle, in the first Figure.
Chap. 6. Of the same in the second Figure.
Chap. 7. Of the same in the third Figure.
Chap. 8. Of Conversion of Syllogisms in the first Figure.
Chap. 9. Of Conversion of Syllogisms in the second Figure.
Chap. 10. Of the same in the third Figure.
Chap. 11. Of Deduction to the Impossible in the first Figure.
Chap. 12. Of the same in the second Figure.
Chap. 13. Of the same in the third Figure.
Chap. 14. Of the difference between the Ostensive, and the Deduction to the Impossible.
Chap. 15. Of the Method of concluding from Opposites in the several Figures.
Chap. 16. Of the "Petitio Principii," or Begging the Question.
Chap. 17. A Consideration of the Syllogism, in which it is argued, that the false does not happen—"on account of this," παρὰ τοῦτο συμβαίνειν, τὸ ψεῦδος
Chap. 18. Of false Reasoning.
Chap. 19. Of the Prevention of a Catasyllogism.
Chap. 20. Of the Elenchus.
Chap. 21. Of Deception, as to Supposition—κατὰ τὴν ὑπόληψιν
Chap. 22. On the Conversion of the Extremes in the first Figure.
Chap. 23. Of Induction.
Chap. 24. Of Example.
Chap. 25. Of Abduction.
Chap. 26. Of Objection.
Chap. 27. Of Likelihood, Sign, and Enthymeme.
It is first requisite to say what is the subject, concerning which, and why, the present treatise is undertaken, namely, that it is concerning demonstration, and for the sake of demonstrative science; we must afterwards define, what is a proposition, what a term, and what a syllogism, also what kind of syllogism is perfect, and what imperfect; lastly, what it is for a thing to be, or not to be, in a certain whole, and what we say it is to be predicated of every thing, or of nothing (of a class).
A proposition then is a sentence which affirms or denies something of something, and this is universal, or particular, or indefinite; I denominate universal, the being present with all or none; particular, the being present with something, or not with something, or not with every thing; but the indefinite the being present or not being present, without the universal or particular (sign); as for example, that there is the same science of contraries, or that pleasure is not good. But a demonstrative proposition differs from a dialectic in this, that the demonstrative is an assumption of one part of the contradiction, for a demonstrator does not interrogate, but assume, but the dialectic is an interrogation of contradiction. As regards however forming a syllogism from either proposition, there will be no difference between one and the other, since he who demonstrates and he who interrogates syllogize, assuming that something is or is not present with something. Wherefore a syllogistic proposition will be simply an affirmation or negation of something concerning something, after the above-mentioned mode: it is however demonstrative if it be true, and assumed through hypotheses from the beginning, and the dialectic proposition is to him who inquires an interrogation of contradiction, but to him who syllogizes, an assumption of what is seen and probable, as we have shown in the Topics. What therefore a proposition is, and wherein the syllogistic demonstrative and dialectic differ, will be shown accurately in the following treatises, but for our present requirements what has now been determined by us may perhaps suffice. Again, I call that a "term," into which a proposition is resolved, as for instance, the predicate and that of which it is predicated, whether to be or not to be is added or separated. Lastly, a syllogism is a sentence in which certain things being laid down, something else different from the premises necessarily results, in consequence of their existence. I say that, "in consequence of their existence," something results through them, but though something happens through them, there is no need of any external term in order to the existence of the necessary (consequence). Wherefore I call a perfect syllogism that which requires nothing else, beyond (the premises) assumed, for the necessary (consequence) to appear: but an imperfect syllogism, that which requires besides, one or more things, which are necessary, through the supposed terms, but have not been assumed through propositions. But for one thing to be in the whole of another, and for one thing to be predicated of the whole of another, are the same thing, and we say it is predicated of the whole, when nothing can be assumed of the subject, of which the other may not be asserted, and as regards being predicated of nothing, in like manner.
Since every proposition is either of that which is present (simply), or is present necessarily or contingently, and of these some are affirmative, but others negative, according to each appellation; again, since of affirmative and negative propositions some are universal, others particular, and others indefinite, it is necessary that the universal negative proposition of what is present should be converted in its terms; for instance, if "no pleasure is good," "neither will any good be pleasure." But an affirmative proposition we must of necessity convert not universally, but particularly, as if "all pleasure is good," it is also necessary that "a certain good should be pleasure;" but of particular propositions, we must convert the affirmative proposition particularly, since if "a certain pleasure is good," so also "will a certain good be pleasure;" a negative proposition however need not be thus converted, since it does not follow, if "man" is not present with "a certain animal," that animal also is not present with a certain man.
Let then first the proposition A B be an universal negative; if A is present with no B, neither will B be present with any A, for if it should be present with some A, for example with C, it will not be true, that A is present with no B, since C is something of B. If, again, A is present with every B, B will be also present with some A, for if with no A, neither will A be present with any B, but it was supposed to be present with every B. In a similar manner also if the proposition be particular, for if A be present with some B, B must also necessarily be present with some A, for if it were present with none, neither would A be present with any B, but if A is not present with some B, B need not be present with some A, for example, if B is "animal," but A, "man," for man is not present with "every animal," but "animal" is present with "every man."
The same system will hold good in necessary propositions, for an universal negative is universally convertible, but either affirmative proposition particularly; for if it is necessary that A should be present with no B, it is also necessary that B should be present with no A, for if it should happen to be present with any, A also might happen to be present with some B. But if A is of necessity present with every or with some certain B, B is also necessarily present with some certain A; for if it were not necessarily, neither would A of necessity be present with some certain B: a particular negative however is not converted, for the reason we have before assigned.
In contingent propositions, (since contingency is multifariously predicated, for we call the necessary, and the not necessary, and the possible, contingent,) in all affirmatives, conversion will occur in a similar manner, for if A is contingent to every or to some certain B, B may also be contingent to some A; for if it were to none, neither would A be to any B, for this has been shown before. The like however does not occur in negative propositions, but such things as are called contingent either from their being necessarily not present, or from their being not necessarily present, (are converted) similarly (with the former); e. g. if a man should say, that it is contingent, for "a man," not to be "a horse," or for "whiteness" to be present with no "garment." For of these, the one, is necessarily not present, but the other, is not necessarily, present; and the proposition is similarly convertible, for if it be contingent to no "man" to be "a horse," it also concurs with no "horse" to be "a man," and if "whiteness" happens to no "garment," a "garment" also happens to no "whiteness;" for if it did happen to any, "whiteness" will also necessarily happen to "a certain garment," and this has been shown before, and in like manner with respect to the particular negative proposition. But whatever things are called contingent as being for the most part and from their nature, (after which manner we define the contingent,) will not subsist similarly in negative conversions, for an universal negative proposition is not converted, but a particular one is, this however will be evident when we speak of the contingent. At present, in addition to what we have said, let thus much be manifest, that to happen to nothing, or not to be present with any thing, has an affirmative figure, for "it is contingent," is similarly arranged with "it is," and "it is" always and entirely produces affirmation in whatever it is attributed to, e. g. "it is not good," or, "it is not white," or in short, "it is not this thing." This will however be shown in what follows, but as regards conversions, these will coincide with the rest.
These things being determined, let us now describe by what, when, and how, every syllogism is produced, and let us afterwards speak of demonstration, for we must speak of syllogism prior to demonstration, because syllogism is more universal, since, indeed, demonstration is a certain syllogism, but not every syllogism is demonstration.
When, then, three terms so subsist, with reference to each other, as that the last is in the whole of the middle, and the middle either is, or is not, in the whole of the first, then it is necessary that there should be a perfect syllogism of the extremes. But I call that the middle, which is itself in another, whilst another is in it, and which also becomes the middle by position, but the extreme that which is itself in another, and in which another also is. For if A is predicated of every B, and B of every C, A must necessarily be predicated of every C, for it has been before shown, how we predicate "of every;" so also if A is predicated of no B, but B is predicated of every C, A will not be predicated of any C. But if the first is in every middle, but the middle is in no last, there is not a syllogism of the extremes, for nothing necessarily results from the existence of these, since the first happens to be present with every, and with no extreme; so that neither a particular nor universal (conclusion) necessarily results, and nothing necessary resulting, there will not be through these a syllogism. Let the terms of being present universally, be "animal," "man," "horse," and let the terms of being present with no one be "animal," "man," "stone." Since, then, neither the first term is present with the middle, nor the middle with any extreme, there will not thus be a syllogism. Let the terms of being present, be "science," "line," "medicine," but of not being present, "science," "line," "unity;" the terms then being universal, it is manifest in this figure, when there will and when there will not be a syllogism, also that when there is a syllogism, it is necessary that the terms should subsist, as we have said, and that if they do thus subsist there will evidently be a syllogism.
But if one of the terms be universal and the other particular, in relation to the other, when the universal is joined to the major extreme, whether affirmative or negative, but the particular to the minor affirmative, there must necessarily be a perfect syllogism, but when the (universal) is joined to the minor, or the terms are arranged in some other way, a (syllogism) is impossible. I call the major extreme that in which the middle is, and the minor that which is under the middle. For let A be present with every B, but B with some C, if then to be predicated "of every" is what has been asserted from the first, A must necessarily be present with some C, and if A is present with no B, but B with some C, A must necessarily not be present with some C, for what we mean by the being predicated of no one has been defined, so that there will be a perfect syllogism. In like manner, if B, C, being affirmative, be indefinite, for there will be the same syllogism, both of the indefinite, and of that which is assumed as a particular.
If indeed to the minor extreme an universal affirmative or negative be added, there will not be a syllogism, whether the indefinite, or particular, affirms or denies, e. g. if A is or is not present with some B, but B is present to every C; let the terms of affirmation be "good," "habit," "prudence," and those of negation, "good," "habit," "ignorance." Again, if B is present with no C, but A is present or is not present with some B, or not with every B; neither thus will there be a syllogism; let the terms of being present with every (individual) be "white," "horse," "swan;" but those of being present with no one, be "white," "horse," "crow." The same also may be taken if A, B be indefinite. Neither will there be a syllogism, when to the major extreme the universal affirmative or negative is added; but to the minor, a particular negative, whether it be indefinitely or particularly taken, e. g. if A is present with every B; but B is not present with some, or not with every C, for to what the middle is not present, to this, both to every, and to none, the first will be consequent. For let the terms, "animal," "man," "white," be supposed, afterwards from among those white things, of which man is not predicated, let "swan" and "snow" be taken; hence "animal" is predicated of every individual of the one, but of no individual of the other, wherefore there will not be a syllogism. Again, let A be present with no B, but B not be present with some C, let the terms also be "inanimate," "man," "white," then let "swan" and "snow" be taken from those white things, of which man is not predicated, for inanimate is predicated of every individual of the one, but of no individual of the other. Once more, since it is indefinite for B not to be present with some C, (for it is truly asserted, that it is not present with some C, whether it is present with none, or not with every C,) such terms being taken, so as to be present with none, there will be no syllogism (and this has been declared before). Wherefore it is evident, that when the terms are thus, there will not be a syllogism, since if one could be, there could be also one in these, and in like manner it may be shown, if even an universal negative be taken. Nor will there by any means be a syllogism, if both particular intervals be predicated either as affirmative or tive, or the one affirmative and the other negative, or the one indefinite, or the other definite, or both indefinite; but let the common terms of all be "animal," "white," "man," "animal," "white," "stone."
From what has been said, then, it is evident, that if there be a particular syllogism in this figure, the terms must necessarily be as we have said, and that if the terms be thus, there will necessarily be a syllogism, but by no means if they are otherwise. It is also clear, that all the syllogisms in this figure are perfect, for all are perfected through the first assumptions; and that all problems are demonstrated by this figure, for by this, to be present with all, and with none, and with some, and not with some, (are proved,) and such I call the first figure.
When the same (middle term) is present with every individual, (of the one,) but with none, (of the other,) or is present to every or to none of each, a figure of this kind I call the second figure. The middle term also in it, I call that which is predicated of both extremes, and the extremes I denominate those of which this middle is predicated, the greater extreme being that which is placed near the middle, but the less, that which is farther from the middle. Now the middle is placed beyond the extremes, and is first in position; wherefore by no means will there be a perfect syllogism in this figure. There may however be one, both when the terms are, and are not, universal, and if they be universal there will be a syllogism when the middle is present with all and with none, to which ever extreme the negation is added, but by no means in any other way. For let M be predicated of no N, but of every O; since then a negative proposition is convertible, N will be present with no M; but M was supposed to be present with every O, wherefore N will be present with no O, for this has been proved before. Again, if M be present with every N, but with no O, neither will O be present with any N, for if M be present with no O, neither will be O present with any M; but M was present with every N, hence also O will be present with no N; for again the first figure is produced; since however a negative proposition is converted, neither will N be present with any O; hence there will be the same syllogism. We may also demonstrate the same things, by a deduction to the impossible; it is evident therefore, that when the terms are thus, a syllogism, though not a perfect one, is produced, for the necessary is not only perfected from first assumptions, but from other things also. If also M is predicated of every N and of every O, there will not be a syllogism, let the terms of being present be "substance," "animal," "man," and of not being present "substance," "animal," "stone," the middle term "substance." Nor will there then be a syllogism, when M is neither predicated of any N, nor of any O, let the terms of being present be "line," "animal," "man;" but of not being present, "line," "animal," "stone."
Hence it is evident, that if there is a syllogism when the terms are universal, the latter must necessarily be, as we said at the beginning, for if they are otherwise, no necessary (conclusion) follows. But if the middle be universal in respect to either extreme, when universal belongs to the major either affirmatively or negatively, but to the minor particularly, and in a manner opposite to the universal, (I mean by opposition, if the universal be negative, but the particular affirmative, or if the universal is affirmative, but the particular negative,) it is necessary that a particular negative syllogism should result. For if M is present with no N, but with a certain O, N must necessarily not be present with a certain O, for since a negative proposition is convertible, N will be present with no M, but M was by hypothesis present with a certain O, wherefore N will not be present with a certain O, for a syllogism is produced in the first figure.
Again, if M is present with every N, but not with a certain O, N must of necessity not be present with a certain O, for if it is present with every O, and M is predicated of every N, M must necessarily be present with every O, but it was supposed not to be present with a certain O, and if M is present with every N, and not with every O, there will be a syllogism, that N is not present with every O, and the demonstration will be the same. But if M is predicated of every O, but not of every N, there will not be a syllogism; let the terms of presence be "animal," "substance," "crow," and of absence "animal," "white," "crow;" neither will there be a syllogism when M is predicated of no O, but of a certain N, let the terms of presence be "animal," "substance," "stone," but of absence, "animal," "substance," "science."
When therefore universal is opposed to particular, we have declared when there will, and when there will not, be a syllogism; but when the propositions are of the same quality, as both being negative or affirmative, there will not by any means be a syllogism. For first, let them be negative, and let the universal belong to the major extreme, as let M be present with no N, and not be present with a certain O, it may happen therefore that N shall be present with every and with no O; let the terms of universal absence be "black," "snow," "animal;" but we cannot take the terms of universal presence, if M is present with a certain O, and with a certain O not present. For if N is present with every O, but M with no N, M will be present with no O, but by hypothesis, it was present with some O, wherefore it is not possible thus to assume the terms. We may prove it nevertheless from the indefinite,