Organon (Owen)/Prior Analytics/Book 1

(1853) Translator's annotations not included.

Chap. 1. Of Proposition, Term, Syllogism, and its Elements.

1.1. Purport of this treatise—the attainment of demonstrative science.
1.2. Definition of (πρότασις) proposition. It is either,
1. καθόλου, universal,
2. ἐνμέρει, particular,
3. or ἀδιόριστον, indefinite.
1.3. Difference between the demonstrative (ἀποδεικτικὴ) and the διαλεκτικὴ πρότασις.
1.4. The syllogistic proposition.
1.5. The demonstrative.
1.6. Definition of a term—ὅρος.
1.7. And of a syllogism.
1. The latter either perfect, τέλειος, or,
2. ἀτελης.
1.8. Definition of predication de omni et nullo

Chap. 2. On the Conversion of Propositions.

2.1. Doctrine of conversion, with example of conversion in E, universally.
2.2. A and I to be converted particularly.
2.3. Conversion of O unnecessary.
2.4. Examples.

Chap. 3. On the Conversion of Modal Propositions.

3.1. Rule for modal conversion the same as for pure propositions. Example of the necesary modal.
3.2. Of the contingent, with example.
3.3. Of things called contingent, with the differences in conversion between E and O.

Chap. 4. Of Syllogism, and of the first Figure.

4.1. Syllogism being more universal than demonstration is first discussed—its nature and construction.
4.2. Definition of ὁ μέσος, and of ἄκρα—example of syllogism.
4.3. Definition of τὸ μεῖζον, and τὸ ἔλαττον ἀκρον.
4.4. Syllogistic ratio the same for indefinite as for the particular.
4.5. No syllogism if the minor be universal, but the major particular, or indefinite.
4.6. Nor when the major is A or E, but the minor O.
4.7. Nor when both are particular, etc.
4.8. Σχῆμα πρῶτον. The first figure complete, and comprehends all classes of affirmation and negation.

Chap. 5. Of the second Figure.

5.1. Σχῆμα, B., its denomination, with the position of the terms—no perfect syllogism in this figure—its connexion with both universal and particular quantity.
5.2. From universal affirmatives there is no consequence.
5.3. When the major is A or E, and the minor I or O, the conclusion is O.
5.4. If both premises be of the same quality, no syllogism results.
5.5. No affirmative conclusion in this figure.

Chap. 6. Of Syllogisms in the third Figure.

6.1. Σχῆμα Γ, the third figure, its characteristic—the middle is the subject of both premises—no perfect syllogism in this figure.
6.2. When both premises are affirmative there will be a syllogism, but not when both are negative—the major moreover may be negative, and the minor, affirmative.
6.3. No universal conclusion derived from this figure.

Chap. 7. Of the three first Figures, and of the Completion of Incomplete Syllogisms.

7.1. If one premise be A or I, and the other E, there will be a conclusion in which the minor is predicated of the major.
7.2. All syllogisms may be reduced to universals in the first figure (ἀναγαγεῖν)—the various methods.

Chap. 8. Of Syllogisms derived from two necessary Propositions.

8.1. Variety of syllogisms, viz. those τοῦ ὑπαρχειν—and those τοῦ ἀναγκαῖον εἶναι, and τοῦ ἐνδέχεσθαι. Cf. Whately, b. 2. ch. 4.
8.2. Necessary syllogisms resemble generally those which are absolute.

Chap. 9. Of Syllogisms, whereof one Proposition is necessary, and the other pure in the first Figure.

9.1. Conclusion of a syllogism with one premise nessary often follows the major premise,—example and proof,—universals and particulars.
9.2. Case of I necessary.

Chap. 10. Of the same in the second Figure.

10.1. In the second figure, when a necessary is joined with a pure premise, the conclusion follows the negative necessary premise.—Example and proof.
10.2. If the affirmative be necessary, the conclusion will not be.
10.3. Case the same with particulars.

Chap. 11. Of the same in the third Figure.

11.1. In this figure if either premise be necessary, and both be A, the conclusion will be necessary.
11.2. If one proposition be A or I, when A is necessary the conclusion is not necessary, but not when I is necessary.
11.3. When the affirmative is necessary either A or I, or when O is assumed, there will not be a necessary conclusion.

Chap. 12. A comparison of pure with necessary Syllogisms.

12.1. Distinction between an absolute and necessary conclusion as regards the latter's dependence upon the premises; their connexion also with it.

Chap. 13. Of the Contingent, and its concomitant Propositions.

13.1. Definition of the contingent (τοῦ ὲνδεχομένον) given and confirmed. (Vide Metaph. lib. v. 2,) also Interpret. 13.
13.2. Contingent προτάσεις capable of conversion.
13.3. The contingent predicated in two ways—the one general, the other indefinite—the method of conversion not the same to each.
13.4. The indefinite contingent of less use in syllogism.
13.5. An inquiry into the construction of contingent syllogisms prepared.

Chap. 14. Of Syllogisms with two contingent Propositions in the first Figure.

14.1. With the contingent premises both universal there will be a perfect syllogism.
14.2. When the premises are both negative or the minor negative, there is either no syllogism or an incomplete one—case of the major universal with the minor particular, different.
14.3. Vice versâ
14.4. When the premises are universal, A or E, there is always a syllogism in the first figure—the former (A) complete—the latter (E) incomplete. (Vide last chapter.)

Chap. 15. Of Syllogisms with one simple and another contingent Proposition in the first Figure.

15.1. No syllogism with mixed premises, pure and modal—if the major is contingent the syllogism will be perfect, not otherwise.
1. Case of a perfect syllogism, when the minor is pure.
2. Digression to prove the nature of true consequence in respect of the possible and impossible, and necessary.
3. From a false hypothesis, not impossible, a similar conclusion follows.
4. Universal predication has no reference to time. (Cf. Aldrich and Hill's Logic.)
15.2. E pure. A contingent.
15.3. Minor negative contingent.
15.4. Both premises negative.
15.5. General law of mixed syllogisms; when minor premise is contingent, a syllogism is constructed, either directly or by conversion.
15.6. Of particulars with an universal major.
2. Major A or E pure.
15.7. If the major is particular there will be no syllogism, nor if both premises be particular or indefinite.

Chap. 16. Of Syllogisms with one Premise necessary, and the other contingent in the first Figure.

16.1. The law relative to syllogisms of this character.
16.2. When both premises are A, there will not be a necessary conclusion.
1. Negative necessary.
2. Affirmative necessary.
3. Minor negative contingent.
16.3. Case of particular syllogisms.
16.4. Case of both premises indefinite or particular.
16.5. Conclusion from the above. (Compare c.15.)

Chap. 17. Of Syllogisms with two contingent Premises in the second Figure.

17.1. Rule for contingent syllogisms in this figure.
17.2. Terms of a contingent negative not convertible.
17.3. Contingency predicated negatively in two ways—the character of the consequent opposition.
17.4. From two premises universal (A) or (E) contingent in the 2nd figure, no syllogism is constructed.
17.5. Nor from one univ. and the other par., or both par. or in def.

Chap. 18. Of Syllogisms with one Proposition simple, and the other contingent, in the second Figure.

18.1. Rule for universals in this figure, with one pure premise, and the other contingent.
18.2. Particular syllogisms.

Chap. 19. Of Syllogisms with one Premise necessary and the other contingent, in the second Figure.

19.1. Rule, in these when the negative premise is necessary, a syllogism may be constructed.
1. Case.
2. Case of a necessary affirmative.
3. Case of both negative.
4. Case of both affirmative.
19.2. Particular syllogisms.
19.3. Conclusion. (Cf. cap. 18)

Chap. 20. Of Syllogisms with both Propositions contingent in the third Figure.

20.1. Review—rule for propositions of this class.
1. Both premises contingent.
4. One premise universal and the other particular.
6. Both particular or indefinite.

Chap. 21. Of Syllogisms with one Proposition contingent and the other simple in the third Figure.

21.1. Rule of consequence—a contingent is inferred from one absolute and another contingent premise. (Vide supra.)
1st case, Both affirmative.
2nd, Minor simple affirmative, major contingent and negative.
3rd, From a negative minor or from two negatives, no syllogism results.
4. Cases of particulars.

Chap. 22. Of Syllogisms with one Premise necessary, and the other contingent in the third Figure.

22.1. Rules for universals in the third figure, with one necessary, and the other contingent premise.
1. Each proposition, affirmative.
2. Major negative, minor affirmative.
3. Vice versâ.
4. Case of particulars.

Chap. 23. It is demonstrated that every Syllogism is completed by the first Figure.

23.1. Observations preliminary to proving that every syllogism results from universals of the first figure.
23.2. Syllogism must demonstrate the absolute universally or particularly. Of the ostensive.
23.3. For a simple conclusion we must have two propositions.
23.4. These connected by a middle term; which connexion is threefold. (Vide Aldrich.)
2. Of syllogisms per impossibile there is the same method.
1. What this kind of syllogism is.
3. Also of syllogisms, ἐξ ὑποθέσεως—recapitulation.

Chap. 24. Of the Quality and Quantity of the Premises in Syllogism.—Of the Conclusion.

24.1. One affirmative and one universal term necessary in all syllogisms.
24.2. An universal conclusion follows from universal premises but sometimes only a particular results.
24.3. One premise must resemble the conclusion in character and quality.
24.4. Recapitulation.

Chap. 25. Every Syllogism consists of only three Terms, and of two Premises.

25.1. Demonstration is conveyed by three terms only—proof.
25.2. The same conclusion may arise from many syllogisms.
25.3. These three terms are included in two propositions. Vide Aldrich and Whately.
25.4. Of the number of terms, propositions, and conclusions in composite syllogisms.

Chap. 26. On the comparative Difficulty of certain Problems, and by what Figures they are proved.

26.1. The conclusion by more figures constitutes the relative facility of demonstration. Enumeration of the conclusion in the second figures.
26.2. Universals easier of subversion than particulars.
26.3. Particulars easier of construction.
26.4. Recapitulation.

Chap. 27. Of the Invention and Construction of Syllogisms.

27.1. How to provide syllogisms, from certain principles.
27.2. The several sorts of predicates. Some cannot be truly predicated universally, of other than individuals, etc.
2. How to assume propositions as to these, in order to inference.
1. Distinctions to be drawn.
2. ἰδεα to be assumed. Vide Aldrich and Hill.

Chap. 28. Special Rules upon the same Subject.

28.1. What should be the inspection of terms that an universal or particular affirmative or negative may be demonstrated.
28.2. Every portion of the problem to be examined.
28.3. Speculation consists of three terms and two propositions.
28.4. Other modes than the first useless, as regards selection of the middle.
28.5. We must select in investigation, not that wherein the terms differ, but in which they agree.
28.6. Recapitulation.

Chap. 29. The same Method applied to other than categorical Syllogisms.

29.1. The same method to be observed for selecting a middle term in syllogisms of "the impossible," as in the others.
29.2. Wherein the ostensive and per impossibile syllogisms differ.
29.3. The mode of investigation the same in hypotheticals.
29.4. Conclusion.

Chap. 30. The preceding method of Demonstration applicable to all Problems.

30.1. The method of demonstration laid down previously, is applicable to all objects of philosophical inquiry.
30.2. Experience is to supply the principles of demonstration in every science.
30.3. The end of analytical investigation to elucidate subjects naturally abstruse.

Chap. 31. Upon Division; and its Imperfection as to Demonstration.

31.1. Division, its use and abuse in argument. It is a species of weak syllogism.
31.2. In demonstration of the absolute, the middle must be less, and not universal in respect of the first extreme.
31.3. Division not suitable for refutation, nor for various kinds of question.

Chap. 32. Reduction of Syllogisms to the above Figures.

32.1. Method of reducing every syllogism to one of the three figures to be considered. (Compare ch. 28.)
Rule 1st. Propositions to be investigated as to quantity, &c.
2nd rule. Examine their superfluities and deficiencies as to the proper construction of syllogism.
3rd rule. Consider the reality of inference.
4th rule. Ascertain the figure to which properly the problem belongs, by the middle.

Chap. 33. On Error, arising from the quantity of Propositions.

33.1. Cause of deception about syllogisms—our inattention to the relative quantity of propositions.

Chap. 34. Error arising from inaccurate exposition of Terms.

34.1. Nature of deception shown as arising from terms inaccurately set out.

Chap. 35. Middle not always to be assumed as a particular thing, ὡς τόδε τι.

35.1. One word cannot always be used for some terms, inasmuch as they are sentences.

Chap. 36. On the arrangement of Terms, according to nominal appellation; and of Propositions according to case.

36.1. For the construction of a syllogism, it is not always requisite that one term should be predicated of the other "casu recto." Since either major or minor premise, or both, may have an oblique case.
36.2. Method the same with negatives.
36.3. Method of assuming propositions and terms.

Chap. 37. Rules of Reference to the forms of Predication.

37.1. For true and absolute predication we must accept the several varieties of categorical division.

Chap. 38. Of Propositional Iteration and the Addition to a Predicate.

38.1. Whatever is reiterated must be annexed to the major, not to the middle term.
38.2. The terms not the same as to assumption whether the inference is simple or with a certain qualification.

Chap. 39. The Simplification of Terms in the Solution of Syllogism.

39.1. In syllogistic analysis terminal simplicity and perspicuity to be studied.

Chap. 40. The definite Article to be added according to the nature of the Conclusion.

40.1. Effect of the addition of the article, and rule.

Chap. 41. On the Distinction of certain forms of Universal Predication.

41.1. The expression καθοὑ τὸ Β κατὰ παντὸς τὸ A λεγεσθαι, though not per se identical with καθοὕ παντὸς τὸ Β κατὰ τοῦτοῦ παντὸς καὶ το A, is equivalent to A being predicated of every thing of which B is predicated.
41.2. Certain expressions used for illustration.

Chap. 42. That not all Conclusions in the same Syllogism are produced through one Figure.

42.1. The conclusion an evidence in what figure the inquiry is to be made.

Chap. 43. Of Arguments against Definition, simplified.

43.1. For brevity's sake the thing impugned in the definition, and not the whole definition itself, is to be laid down.

Chap. 44. Of the Reduction of Hypotheticals and of Syllogisms ad impossibile.

44.1. Reason for our not reducing hypotheticals.
44.2. Nor syllogisms per impossibile.
44.3. Further consideration of hypotheticals deferred.

Chap. 45. The Reduction of Syllogisms from one Figure to another.

45.1. Whatever syllogisms are proved in many figures, may be reduced from one figure to another—case of universal and particular in the first and second figures.
45.2. Universals in the second are reducible to the first, but only one particular.
45.3. Of those in the third figure, one only, when the negative is not universal, is not reducible to the first.
45.4. The conversion of the minor premise necessary for reduction.
45.5. Those syllogisms not mutually reducible into the other figures which are not into the first.

Chap. 46. Of the Quality and Signification of the Definite, and Indefinite, and Privative.

46.1. Difference in statement arising from "not to be" and "to be not,"—with the reason. (Cf. Herm. 6.)
46.2. Order of affirmation and negation.
46.3. Relation between (ἁι στηρῆσεις) privatives and attributes (κατηγορίαι).
46.4. The difference of the character of assertion shown by the difference in the mode of demonstration.
46.5. Relative consequence proved in certain cases.
46.6. Fallacy arising from not assuming opposites properly.


Chapter 1Edit

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.

Chapter 2Edit

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."

Chapter 3Edit

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.

Chapter 4Edit

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.

Chapter 5Edit

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, for since M was truly asserted not to be with some certain O, even if it is present with no O; yet being present with no O, there was not a syllogism, it is evident, that neither now will there be one. Again, let them be affirmative, and let the universal be similarly assumed, e. g. let M be present with every N, and with a certain O, N may happen therefore to be present, both with every and with no O, let the terms of being present with none, be "white," "swan," "snow;" but we cannot assume the terms of being present with every, for the reason which we have before stated, but it may be shown from the indefinite. But if the universal be joined to the minor extreme, and M is present with no O, and is not present with some certain N, it is possible for N to be present with every and with no O; let the terms of presence be "white," "animal," "crow," but of absence, "white," "stone," "crow." But if the propositions are affirmative, let the terms of absence be "white," "animal," "snow," of presence, "white," "animal," "swan." Therefore it is evident, when the propositions are of the same quality, and the one universal, but the other particular, that there is by no means a syllogism. Neither, however, will there be one, if a thing be present to some one of each term, or not present, or to the one, but not to the other, or to neither universally, or indefinitely, let the common terms of all be "white," "animal," "man;" "white," "animal," "inanimate."

Wherefore it is evident, from what we have stated, that if the terms subsist towards each other, as has been said, there is necessarily a syllogism, and if there be a syllogism, the terms must thus subsist. It is also clear that all syllogisms in this figure are imperfect, for all of them are produced from certain assumptions, which are either of necessity in the terms, or are admitted as hypotheses, as when we demonstrate by the impossible. Lastly, it appears that an affirmative syllogism is not produced in this figure, but all are negative, both the universal and also the particular.

Chapter 6Edit

When with the same thing one is present with every, but the other with no individual, or both with every, or with none, such I call the third figure; and the middle in it, I call that of which we predicate both, but the predicates the extremes, the greater extreme being the one more remote from the middle, and the less, that which is nearer to the middle. But the middle is placed beyond the extremes, and is last in position; now neither will there be a perfect syllogism, even in this figure, but there may be one, when the terms are joined to the middle, both universally, and not universally. Now when the terms are universally so, when, for instance, P and R are present with every S, there will be a syllogism, so that P will necessarily be present with some certain R, for since an affirmative is convertible, S will be present to a certain R. Wherefore since P is present to every S, but S to some certain R, P must necessarily be present with some R, for a syllogism arises in the first figure. We may also make the demonstration through the impossible, and by exposition. For if both are present with every S, if some S is assumed, (e. g.) N, both P and R will be present with this, wherefore P will be present with a certain R, and if R is present with every S, but P is present with no S, there will be a syllogism, so that P will be necessarily inferred as not present with a certain R; for the same mode of demonstration will take place, the proposition R S being converted; this may also be demonstrated by the impossible, as in the former syllogisms. But if R is present with no S, but P with every S, there will not be a syllogism; let the terms of presence be "animal," "horse," "man," but of absence "animal," "inanimate," "man." Neither when both are predicated of no S, will there be a syllogism, let the terms of presence be "animal," "horse," "inanimate," but of absence "man," "horse," "inanimate," the middle "inanimate." Wherefore also in this figure it is evident, when there will, and when there will not, be a syllogism, the terms being universal, for when both terms are affirmative, there will be a syllogism, in which it will be concluded that extreme is with a certain extreme, but when both terms are negative there will not be. When however one is negative and the other affirmative, and the major is negative but the other affirmative, there will be a syllogism, that the extreme is not present with a certain extreme, but if the contrary there will not be.

If indeed one be universal in respect to the middle, and the other particular, both being affirmative, syllogism is necessarily produced, whichever term be universal. For if R is present with every S, but P with a certain S, P must necessarily be present with a certain R, for since the affirmative is convertible, S will be present with a certain P, so that since R is present to every S, and S with a certain P, R will also be present with a certain P, wherefore also P will be present with a certain R. Again, if R is present with a certain S, but P is present with every S, P must necessarily be present with a certain R, for the mode of demonstration is the same, and these things may be demonstrated like the former, both by the impossible, and by exposition. If however one be affirmative, and the other negative, and the affirmative be universal, when the minor is affirmative there will be a syllogism; for if R is present with every S, and P not present with a certain S, P must also necessarily not be present with a certain R, since if P is present with every R, and R with every S, P will also be present with every S, but it is not present, and this may also be shown without deduction, if some S be taken with which P is not present. But when the major is affirmative there will not be a syllogism, e. g. if P is present with every S, but R is not present with a certain S; let the terms of being universally present with be "animate," "man," "animal." But it is not possible to take the terms of universal negative, if R is present with a certain S, and with a certain S is not present, since if P is present with every S, and R with a certain S, P will also be present with a certain R, but it was supposed to be present with no R, therefore we must assume the same as in the former syllogisms. As to declare something not present with a certain thing is indefinite, so that also which is not present with any individual, it is true to say, is not present with a certain individual, but not being present with any, there was no syllogism, (therefore it is evident there will be no syllogism). But if the negative term be universal, (yet the particular affirmative,) when the major is negative, but the minor affirmative, there will be a syllogism, for if P is present with no S, but R is present with a certain S, P will not be present with a certain R, and again there will be the first figure, the proposition R S being converted. But when the minor is negative, there will not be a syllogism; let the terms of presence be "animal," "man," "wild," but of absence, "animal," "science," "wild," the middle of both, "wild." Nor will there be a syllogism when both are negative, the one universal, the other particular: let the terms of absence when the minor is universal as to the middle, be "animal," "science," "wild," (of presence, "animal," "man," "wild)." When however the major is universal, but the minor particular, let the terms of absence be "crow," "snow," "white;" but of presence we cannot take the terms, if R is present with some S, and with some is not present, since if P is present with every R, but R with some S, P will also be present with some S, but it was supposed to be present with no S, indeed it may be proved from the indefinite. Neither if each extreme be present or not present with a certain middle, will there be a syllogism; or if one be present and the other not; or if one be with some individual and the other with not every or indefinitely. But let the common terms of all be, "animal," "man," "white," "animal," "inanimate," " white." Wherefore it is clear in this figure also, when there will and when there will not be a syllogism, and that when the terms are disposed as we have stated, a syllogism of necessity subsists, and that there should be a syllogism, it is necessary that the terms should be thus. It is also clear that all syllogisms in this figure are imperfect, for they are all perfected by certain assumptions, and that an universal conclusion either negative or affirmative, cannot be drawn from this figure.

Chapter 7Edit

In all the figures it appears that when a syllogism is not produced, both terms being affirmative, or negative, (and particular,) nothing, in short, results of a necessary character; but if the one be affirmative and the other negative, the negative being universally taken, there is always a syllogism of the minor extreme with the major. For example, if A is present with every or with some B, but B is present with no C, the propositions being converted, C must necessarily not be present with some A; so also in the other figures, for a syllogism is always produced by conversion: again, it is clear that an indefinite taken for a particular affirmative, will produce the same syllogism in all the figures.

Moreover it is evident that all incomplete syllogisms are completed by means of the first figure, for all of them are concluded, either ostensively or per impossibile, but in both ways the first figure is produced: being ostensively completed, (the first figure is produced,) because all of them were concluded by conversion, but conversion produces the first figure: but if they are demonstrated per impossibile, (there will be still the first figure,) because the false being assumed, a syllogism arises in the first figure. For example, in the last figure, if A and B are present with every C, it can be shown that A is present with some B, for if A is present with no B, but B is present with every C, A will be present with no C; but it was supposed that A was present with every C, and in like manner it will happen in other instances.

It is also possible to reduce all syllogisms to universal syllogisms in the first figure. For those in the second, it is evident, are completed through these, yet not all in like manner, but the universal by conversion of the negative, and each of the particular, by deduction per impossibile. Now, particular syllogisms in the first figure are completed through themselves, but may in the second figure be demonstrated by deduction to the impossible. For example, if A is present with every B, but B with a certain C, it can be shown that A will be present with a certain C, for if A is present with no C, but is present with every B, B will be present with no C, for we know this by the second figure. So also will the demonstration be in the case of a negative, for if A is present with no B, but B is present with a certain C, A will not be present with a certain C, since if A is present with every C, and with no B, B will be present with no C, and this was the middle figure. Wherefore, as all syllogisms in the middle figure are reduced to universal syllogisms in the first figure, but particular in the first are reduced to those in the middle figure, it is clear that particular will be reduced to universal syllogisms in the first figure. Those, however, in the third, when the terms are universal, are immediately completed through those syllogisms; but when particular (terms) are assumed (they are completed) through particular syllogisms in the first figure; but these have been reduced to those, so that also particular syllogisms in the third figure (are reducible to the same). Wherefore, it is evident that all can be reduced to universal syllogisms in the first figure; and we have therefore shown how syllogisms de inesse and de non inesse subsist, both those which are of the same figure, with reference to themselves, and those which are of different figures, also with reference to each other.

Chapter 8Edit

Since however to exist, to exist necessarily, and to exist contingently are different, (for many things exist, but not from necessity, and others neither necessarily, nor in short exist, yet may happen to exist,) it is evident that there will be a different syllogism from each of these, and from the terms not being alike; but one syllogism will consist of those which are necessary, another of absolute, and a third of contingent. In necessary syllogisms it will almost always be the same, as in the case of absolute subsistences, for the terms being similarly placed in both absolute existence, and in existing, or not of necessity, there will and there will not be a syllogism, except that there will be a difference in necessary or non-necessary subsistence being added to the terms. For a negative is in like manner convertible, and we assign similarly to be in the whole of a thing, and to be (predicated) of every. In the rest then it will be shown by the same manner, through conversion, that the conclusion is necessary, as in the case of being present; but in the middle figure, when the universal is affirmative, and the particular negative, and again, in the third figure, when the universal is affirmative, but the particular negative, the demonstration will not be in the like manner; but it is necessary that proposing something with which either extreme is not present, we make a syllogism of this, for in respect of these there will be a necessary (conclusion). If, on the other hand, in respect to the proposed term, there is a necessary conclusion, there will be also one (a necessary conclusion) of some individual of that term, for what is proposed is part of it, and each syllogism is formed under its own appropriate figure.

Chapter 9Edit

It sometimes happens also that when one proposition is necessary, a necessary syllogism arises, not however from either proposition indifferently, but from the one that contains the greater extreme. For example, if A is assumed to be necessarily present or not present with B, but B to be alone present with C, for the premises being thus assumed, A will necessarily be present or not with C; for since A is or is not necessarily present with every B, but C is something belonging to B, C will evidently of necessity be one of these. If, again, A B (the major) is not necessary, but B C (the minor) is necessary, there will not be a necessary conclusion, for if there be, it will happen that A is necessarily present with a certain B, both by the first and the third figure, but this is false, for B may happen to be a thing of that kind, that A may not be present with any thing of it. Besides, it is evident from the terms, that there will not be a necessary conclusion, as if A were "motion," B "animal," and C "man," for "man" is necessarily "an animal," but neither are "animal" nor "man" necessarily "moved;" so also if A B is negative, for there is the same demonstration. In particular syllogisms, however, if the universal is necessary, the conclusion will also be necessary, but if the particular be, there will not be a necessary conclusion, neither if the universal premise be negative nor affirmative. Let then, in the first place, the universal be necessary, and let A be necessarily present with every B, but B only be present with a certain C; it is necessary therefore that A should of necessity be present with a certain C, for C is under B, and A was of necessity present with every B. The same will occur if the syllogism be negative, for the demonstration will be the same, but if the particular be necessary, the conclusion will not be necessary, for nothing impossible results, as neither in universal syllogisms. A similar consequence will result also in negatives; (let the terms be) "motion," "animal," "white."

Chapter 10Edit

In the second figure, if the negative premise be necessary, the conclusion will also be necessary, but if the affirmative (be necessary, the conclusion) will not be necessary. For first, let the negative be necessary, and let it not be possible for A to be in any B, but let it be present with C alone; as then a negative proposition may be converted, B cannot be present with any A, but A is with every C, hence B cannot be present with any C, for C is under A. In like manner also, if the negative be added to C, for if A cannot be with any C, neither can C be present with any A, but A is with every B, so neither can C be present with any B, as the first figure will again be produced; wherefore, neither can B be present with C, since it is similarly converted. If, however, the affirmative premise be necessary, the conclusion will not be necessary; for let A necessarily be present with every B, and alone not be present with any C, then the negative being converted, we have the first figure; but it was shown in the first, that when the major negative (proposition) is not necessary, neither will the conclusion be necessary, so that neither in these will there be a necessary conclusion. Once more, if the conclusion is necessary, it results that C is not necessarily present with a certain A, for if B is necessarily present with no C, neither will C be necessarily present with any B, but B is present necessarily with a certain A, if A is necessarily present with every B. Hence, it is necessary that C should not be present with a certain A; there is, however, nothing to prevent such an A being assumed, with which universally C may be present. Moreover, it can be shown by exposition of the terms, that the conclusion is not simply necessary, but necessary from the assumption of these, e. g. let A be "animal," B "man," C "white," and let the propositions be similarly assumed: for it is possible for an animal to be with nothing "white," then neither will "man" be present with any thing white, yet not from necessity, for it may happen for "man" to be "white," yet not so long as "animal" is present with nothing "white," so that from these assumptions there will be a necessary conclusion, but not simply necessary.

The same will happen in particular syllogisms, for when the negative proposition is universal and necessary, the conclusion also will be necessary, but when the affirmative is universal and necessary, and the negative particular, the conclusion will not be necessary. First, then, let there be an universal and necessary negative, and let A not possibly be present with any B, but with a certain C. Since, therefore, a negative proposition is convertible, B can neither be possibly present with any A, but A is with a certain C, so that of necessity B is not present with a certain C. Again, let there be an universal and necessary affirmative, and let the affirmative be attached to B, if then A is necessarily present with every B, but is not with a certain C, B is not with a certain C it is clear, yet not from necessity, since there will be the same terms for the demonstration, as were taken in the case of universal syllogisms. Neither, moreover, will the conclusion be necessary, if a particular necessary negative be taken as the demonstration is through the same terms.

Chapter 11Edit

In the last figure, when the terms are universally joined to the middle, and both premises are affirmative, if either of them be necessary, the conclusion will also be necessary; and if one be negative, but the other affirmative, when the negative is necessary, the conclusion will be also necessary, but when the affirmative (is so, the conclusion) will not be necessary. For first, let both propositions be affirmative, and let A and B be present with every C, and let A C be a necessary (proposition). Since then B is present with every C, C will also be present with a certain B, because an universal is converted into a particular: so that if A is necessarily present with every C, and C with a certain B, A must also be necessarily present with a certain B, for B is under C, hence the first figure again arises. In like manner, it can be also demonstrated if B C is a necessary (proposition), for C is converted with a certain A, so that if B is necessarily present with every C, (but C with a certain A,) B will also of necessity be present with a certain A. Again let A C be a negative (proposition), but B C affirmative, and let the negative be necessary; as therefore an affirmative proposition is convertible, C will be present with some certain B, but A of necessity with no C, neither will A necessarily be present with some B, for B is under C. But if the affirmative is necessary, there will not be a necessary conclusion; for let B C be affirmative and necessary, but A C negative and not necessary; since then the affirmative is converted C will also be with a certain B of necessity; wherefore if A is with no C, but C with a certain B, A will also not be present with a certain B, but not from necessity, for it has been shown by the first figure, that when the negative proposition is not necessary, neither will the conclusion be necessary. Moreover this will also be evident from the terms, for let A be "good," B "animal," and C "horse," it happens therefore that "good" is with no "horse," but "animal" is necessarily present with every "horse," but it is not however necessary that a certain "animal" should not be "good," for every "animal" may possibly be "good." Or if this is not possible, (viz. that every animal is good,) we must assume another term, as "to wake," or "to sleep," for every "animal" is capable of these. If then the terms are universal in respect to the middle, it has been shown when there will be a necessary conclusion.

But if one term is universally but the other particularly (predicated of the middle), and both propositions are affirmative, when the universal is necessary the conclusion will also be necessary, for the demonstration is the same as before, since the particular affirmative is convertible. If therefore B is necessarily present with every C, but A is under C, B must also necessarily be present with a certain A, and if B is with a certain A, A must also be present necessarily with a certain B, for it is convertible; the same will also occur if A C be a necessary universal proposition, for B is under C. But if the particular be necessary, there will not be a necessary conclusion, for let B C be particular and necessary, and A present with every C, yet not of necessity, B C then being converted we have the first figure, and the universal proposition is not necessary, but the particular is necessary, but when the propositions are thus there was not a necessary conclusion, so that neither will there be one in the case of these. Moreover this is evident from the terms, for let A be "wakefulness," B "biped," but C, "animal;" B then must necessarily be present with a certain C, but A may happen to be present with every C, and yet A is not necessarily so with B, for a certain "biped" need not "sleep" or "wake." So also we may demonstrate it by the same terms if A be particular and necessary. But if one term be affirmative and the other negative, when the universal proposition is negative and necessary, the conclusion will also be necessary, for if A happens to no C, but B is present with a certain C, A must necessarily not be present with a certain B. But when the affirmative is assumed as necessary, whether it be universal or particular, or particular negative, there will not be a necessary conclusion, for we may allege the other same (reasons against it), as in the former cases. But let the terms when the universal affirmative is necessary be "wakefulness," "animal," "man," the middle "man." But when the particular affirmative is necessary, let the terms be "wakefulness," "animal," "white," for "animal" must necessarily be with something "white," but "wakefulness" happens to be with nothing "white," and it is not necessary that wakefulness should not be with a certain animal. But when the negative particular is necessary, let the terms be "biped," "motion," "animal," and the middle term, "animal."

Chapter 12Edit

It appears then, that there is not a syllogism de inesse unless both propositions signify the being present with, but that a necessary conclusion follows, even if one alone is necessary. But in both, the syllogisms being affirmative, or negative, one of the propositions must necessarily be similar to the conclusion; I mean by similar, that if (the conclusion) be (simply) that a thing is present with, (one of the propositions also signifies simply) the being present with, but if necessarily, (that is, in the conclusion, one of the propositions is also) necessary. Wherefore this also is evident, that there will neither be a conclusion necessary nor simple de inesse, unless one proposition be assumed as necessary, or purely categorical, and concerning the necessary, how it arises, and what difference it has in regard to the de inesse, we have almost said enough.

Chapter 13Edit

Let us next speak of the contingent, when, and how, and through what (propositions) there will be a syllogism; and to be contingent, and the contingent, I define to be that which, not being necessary, but being assumed to exist, nothing impossible will on this account arise, for we say that the necessary is contingent equivocally. But, that such is the contingent, is evident from opposite negatives and affirmatives, for the assertions—"it does not happen to be," and, "it is impossible to be," and, "it is necessary not to be," are either the same, or follow each other; wherefore also the contraries to these, "it happens to be," "it is not impossible to be," and, "it is not necessary not to be," will either be the same, or follow each other; for of every thing, there is either affirmation or negation, hence the contingent will be not necessary, and the not-necessary will be contingent. It happens, indeed, that all contingent propositions are convertible with each other. I do not mean the affirmative into the negative, but as many as have an affirmative figure, as to opposition; e. g. "it happens to exist," (is convertible into) "it happens not to exist," and, "it happens to every," into "it happens to none," or, "not to every," and, "it happens to some," into "it happens not to some." In the same manner also with the rest, for since the contingent is non-necessary, and the non-necessary may happen not to exist, it is clear that if A happens to be with any B, it may also happen not to be present, and if it happens to be present with every B, it may also happen not to be present with every B. There is the same reasoning also in particular affirmatives, for the demonstration is the same, but such propositions are affirmative and not negative, for the verb "to be contingent," is arranged similarly to the verb "to be," as we have said before.

These things then being defined, let us next remark, that to be contingent is predicated in two ways, one that which happens for the most part and yet falls short of the necessary—(for instance, for a man to become hoary, or to grow, or to waste, or in short whatever may naturally be, for this has not a continued necessity, for the man may not always exist, but while he does exist it is either of necessity or for the most part)—the other way (the contingent is) indefinite, and is that which may be possibly thus and not thus; as for an animal to walk, or while it is walking for an earthquake to happen, or in short whatever occurs casually, for nothing is more naturally produced thus, or in a contrary way. Each kind of contingent however is convertible according to opposite propositions, yet not in the same manner, but what may naturally subsist is convertible into that which does not subsist of necessity; thus it is possible for a man not to become hoary, but the indefinite is converted into what cannot more subsist in this than in that way. Science however and demonstrative syllogism do not belong to indefinites, because the middle is irregular, but to those things which may naturally exist; and arguments and speculations are generally conversant with such contingencies, but of the indefinite contingent we may make a syllogism, though it is not generally investigated. These things however will be more defined in what follows, at present let us show when and how and what will be a syllogism from contingent propositions.

Since then that this happens to be present with that may be assumed in a twofold respect,—(for it either signifies that with which this is present, or that with which it may be present, thus the assertion, A is contingent to that of which B is predicated, signifies one of these things, either that of which B is predicated, or that of which it may be predicated; but the assertion that A is contingent to that of which there is B, and that A may be present with every B, do not differ from each other, whence it is evident that A may happen to be present with every B in two ways,)—let us first show if B is contingent to that of which there is C, and if A is contingent to that of which there is B, what and what kind of syllogism there will be, for thus both propositions are contingently assumed. When however A is contingent to that with which B is present, one proposition is de inesse, but the other of that which is contingent, so that we must begin from those of similar character, as we began elsewhere.

Chapter 14Edit

When A is contingent to every B, and B to every C, there will be a perfect syllogism, so that A is contingent to every C, which is evident from the definition, for thus we stated the universal contingent (to imply). So also if A is contingent to no B, but B to every C, (it may be concluded) that A is contingent to no C, for to affirm that A is contingent in respect of nothing to which B is contingent, this were to leave none of the contingents which are under B. But when A is contingent to every B, but B contingent to no C, no syllogism arises from the assumed propositions, but B C being converted according to the contingent, the same syllogism arises as existed before, as since it happens that B is present with no C, it may also happen to be present with every C, which was shown before, wherefore if B may happen to every C, and A to every B, the same syllogism will again arise. The like will occur also if negation be added with the contingent (mode) to both propositions, I mean, as if A is contingent to no B, and B to no C, no syllogism arises through the assumed propositions, but when they are converted there will be the same as before. It is evident then that when negation is added to the minor extreme, or to both the propositions, there is either no syllogism, or an incomplete one, for the necessity (of consequence) is completed by conversion. If however one of the propositions be universal, and the other be assumed as particular, the universal belonging to the major extreme there will be a perfect syllogism, for if A is contingent to every B, but B to a certain C, A is also contingent to a certain C, and this is clear from the definition of universal contingent. Again, if A is contingent to no B, but B happens to be present with some C, it is necessary that A should happen not to be present with some C, since the demonstration is the same; but if the particular proposition be assumed as negative, and the universal affirmative, and retain the same position as if A happens to be present to every B, but B happens not to be present with some C, no evident syllogism arises from the assumed propositions, but the particular being converted and B being assumed to be contingently present with some C, there will be the same conclusion as before in the first syllogisms. Still if the major proposition be taken as particular, but the minor as universal, and if both be assumed affirmative or negative, or of different figure, or both indefinite or particular, there will never be a syllogism; for there is nothing to prevent B from being more widely extended than A, and from not being equally predicated. Now let that by which B exceeds A, be assumed to be C, to this it will happen that A is present neither to every, nor to none, nor to a certain one, nor not to a certain one, since contingent propositions are convertible, and B may happen to be present to more things than A. Besides, this is evident from the terms, for when the propositions are thus, the first is contingent to the last, and to none, and necessarily present with every individual, and let the common terms of all be these; of being present necessarily "animal," "white," "man," but of not being contingent, "animal," "white," "garment." Therefore it is clear that when the terms are thus there is no syllogism, for every syllogism is either de inesse, or of that which exists necessarily or contingently, but that this is neither de inesse, nor of that which necessarily exists, is clear, since the affirmative is subverted by the negative, and the negative by the affirmative, wherefore it remains that it is of the contingent, but this is impossible, for it has been shown that when the terms are thus, the first is necessarily inherent in all the last, and contingently is present with none, so that there cannot be a syllogism of the contingent, for the necessary is not contingent. Thus it is evident that when universal terms are assumed in contingent propositions, there arises always a syllogism in the first figure, both when they are affirmative and negative, except that being affirmative it is complete, but if negative incomplete, we must nevertheless assume the contingent not in necessary propositions, but according to the before-named definition, and sometimes a thing of this kind escapes notice.

Chapter 15Edit

If one proposition be assumed to exist, but the other to be contingent, when that which contains the major extreme signifies the contingent, all the syllogisms will be perfect and of the contingent, according to the above definition. But when the minor (is contingent) tney will all be imperfect, and the negative syllogisms will not be of the contingent, according to the definition, but of that which is necessarily present with no one or not with every; for if it is necessarily present with no one, or not with every, we say that "it happens" to be present with no one and not with every. Now let A be contingent to every B, and let B be assumed to be present with every C, since then C is (included) under B, and A is contingent to every B, A is also clearly contingent to every C, and there is a perfect syllogism. So also if the proposition A B is negative, but B C affirmative, and A B is assumed as contingent, but B C to be present with (simply), there will be a perfect syllogism, so that A will happen to be present with no C.

It appears then that when a pure minor is assumed the syllogisms are perfect, but that when it is of a contrary character it may be shown per impossibile that there would be also syllogisms, though at the same time it would be evident that they are imperfect, since the demonstration will not arise from the assumed propositions. First, however, we must show that if A exists, B must necessarily exist, and that if A is possible, B will necessarily be possible; let then under these circumstances A be possible but B impossible, if therefore the possible, since it is possible to be, may be produced, yet the impossible, because it is impossible, cannot be produced. But if at the same time A is possible and B impossible, it may happen that A may be produced without B; if it is produced also, that it may exist, for that which has been generated, when it has been so generated, exists. We must however assume the possible and impossible, not only in generation, but also in true assertion, and in the inesse, and in as many other ways as the possible is predicated, for the case will be the same in all of them. Moreover (when it is said) if A exists B is, we must not understand as if A being a certain thing B will be, for no necessary consequence follows from one thing existing; but from there being two at least, as in the case of propositions subsisting in the manner we have stated in syllogism. For if C is predicated of D, but D of F, C will also necessarily be predicated of F; and if each be possible, the conclusion will be possible, just as if one should take A as the premises, but B the conclusion; it will not only happen that A being necessary, B is also necessary, but that when the former is possible, the latter also will be possible.

This being proved, it is manifest that when there is a false and not impossible hypothesis, the consequence of the hypothesis will also be false and not impossible, e. g. if A is false yet not impossible, but when A is, B also is,—here B will also be false yet not impossible. For since it has been shown that A existing, B also exists, when A is possible, B will be also possible, but A is supposed to be possible, wherefore B will be also possible, for if it were impossible the same thing would be possible and impossible at the same time. These things then being established, let A be present with every B, and B contingent to every C, therefore A must necessarily happen to be present with every C; for let it not happen, but let B be supposed to be present with every C, this is indeed false yet not impossible; if then A is not contingent to C, but B is present with every C, A is not contingent to every B, for a syllogism arises in the third figure. But it was supposed (that A was) contingently present with every (B), therefore A must necessarily be contingent to every C, for the false being assumed, and not the impossible, the consequence is impossible. We may also make a deduction to the impossible in the first figure by assuming B to be present with every C, for if B is with every C, but A contingent to every B, A will also be contingent to every C, but it was supposed not to be present with every C. Still we must assume the being present with every, not distinguishing it by time, as "now" or "at this time," but simply; for by propositions of this kind, we also produce syllogisms, since when a proposition is taken as to the present it will not be syllogism, since perhaps there is nothing to hinder "man" from being present some time or other with every thing moved, viz. if nothing else is moved, but what is moved is contingent to every "horse," yet "man" is contingent to no "horse." Moreover, let the first term be "animal," the middle, "that which is moved," and the last, "man;" the propositions will then be alike, but the conclusion necessary, and not contingent, for "man" is necessarily "an animal," so that it is evident that the universal must be taken simply and not deprived by time.

Again, let the proposition A B be universal negative, and let A be assumed to be present with no B, but let B contingently be present with every C; now from these positions A must necessarily happen to be present with no C, for let it not so happen, but let B be supposed to be present with C, as before; then A must necessarily be present with some B, for there is a syllogism in the third figure, but this is impossible, wherefore A can be contingent to no C, for the false and not the impossible being assumed, the impossible results. Now this syllogism is not of the contingent according to the definition, but of what is necessarily present with none, for this is a contradiction of the given hypothesis, because A was supposed necessarily present with some C, but the syllogism per impossibile is of an opposite contradiction. Besides, from the terms it appears clearly that there is no contingent conclusion, for let "crow" stand for A, "that which is intelligent" for B, and "man" for C; A is therefore present with no B, for nothing intelligent is a "crow;" but B is contingent to every C, since it happens to every "man" to be "intelligent," but A is necessarily present with no C, wherefore the conclusion is not contingent. But neither is the conclusion always necessary, for let A be "what is moved," B "science," and C "man," A will then be present with no B, but B is contingent to every C, and the conclusion will not be necessary, for it is not necessary that no "man" should be "moved," but also it is not necessary that a certain man should be moved; therefore it is clear that the conclusion is of that which is necessarily present with no one, hence the terms must be assumed in a better manner. But if the negative be joined to the minor extreme, signifying to be contingent, from the assumed propositions there will be no syllogism, but there will be as in the former instances, when the contingent proposition is converted. For let A be present with every B, but B contingent to no C, now when the terms are thus, there will be nothing necessary inferred, but if B C be converted, and B be assumed to be contingent to every C, a syllogism arises as before, since the terms have a similar position. In the same manner, when both the propositions are negative, if A B signifies not being present, but B C to be contingent to no individual, through these assumptions no necessity arises, but the contingent proposition being converted, there will be a syllogism. Let A be assumed present to no B, and B contingent to no C, nothing necessary is inferred from these; but if it is assumed that B is contingent to every C, which is true, and the proposition A B subsists similarly, there will be again the same syllogism. If however B is assumed as not present with C, and not that it happens not to be present, there will by no means be a syllogism, neither if the proposition A B be negative nor affirmative; but let the common terms of necessary presence be "white," "animal," "snow," and of non-contingency "white," "animal," "pitch." It is evident, therefore, that when terms are universal, and one of the propositions is assumed, as simply de inesse, but the other contingent, when the minor premise is assumed contingent, a syllogism always arises, except that sometimes it will be produced from the propositions themselves, and at other times from the (contingent) proposition being converted; when, however, each of these occurs, and for what reason, we have shown. But if one proposition be assumed as universal, and the other particular, when the universal contingent is joined to the major extreme, whether it be affirmative or negative, but the particular is a simple affirmative de inesse, there will be a perfect syllogism, just as when the terms are universal, but the demonstration is the same as before. Now when the major is universal, simple, and not contingent, but the other (the minor) particular and contingent, if both propositions be assumed affirmative or negative, or if one be affirmative and the other negative, there will always be an incomplete syllogism, except that some will be demonstrated per impossibile, but others by conversion of the contingent proposition, as in the former cases. There will also be a syllogism, through conversion, when the universal major signifies simply inesse, or non-inesse, but the particular being negative, assumes the contingent, as if A is present, or not present, with every B, that B happens not to be present with a certain C; for the contingent proposition B C being converted, there is a syllogism. Still when the particular proposition assumes the not being present with, there will not be a syllogism. Now let the terms of presence be "white," "animal," "snow," but of not being present "white," "animal," "pitch," for the demonstration must be assumed through the indefinite. Yet if the universal be joined to the less extreme, but particular to the greater, whether negative or affirmative, contingent or pure, there will by no means be a syllogism, nor if particular or indefinite propositions be assumed, whether they take the contingent, or simply the being present with, or vice versâ, will there thus be a syllogism, and the demonstration is the same as before; let however the common terms of being present with from necessity be "animal," "white," "man;" and of not being contingent "animal," "white," "garment." Hence it is evident, that if the major be universal, there is always a syllogism, but if the minor be so, (if the major be particular,) there will never be.

Chapter 16Edit

When one is a necessary proposition simple, de inesse, or non-inesse, and the other signifies being contingent, there will be a syllogism, the terms subsisting similarly, and it will be perfect when the minor premise is necessary; the conclusion however, when the terms are affirmative, will be contingent, and not simple, whether they are universal or not universal. Nevertheless, if one proposition be affirmative, and the other negative, when the affirmative is necessary, the conclusion will in like manner signify the being contingent, and not the not-existing or being present with; and when the negative is necessary, the conclusion will be of the contingent non-inesse, and of the simple non-inesse, whether the terms are universal or not. The contingent also in the conclusion, is to be assumed in the same way as in the former syllogisms, but there will not be a syllogism wherein the non-inesse will be necessarily inferred, for it is one thing "inesse" not necessarily, and another "non-inesse" necessarily. Wherefore, it is evident that when the terms are affirmative, there will not be a necessary conclusion. For let A necessarily be present with every B, but let B be contingent to every C, there will then be an incomplete syllogism, whence it may be inferred that A happens to be present with every C; but that it is incomplete, is evident from demonstration, for this may be shown after the same manner as in the former syllogisms. Again, let A be contingent to every B, but let B be necessarily present with every C, there will then be a syllogism wherein A happens to be present with every C, but not (simply) is it present with every C, also it will be complete, and not incomplete, for it is completed by the first propositions. Notwithstanding, if the propositions are not of similar form, first, let the negative one be necessary, and let A necessarily be contingent to no B, but let B be contingent to every C; therefore, it is necessary that A should be present with no C; for let it be assumed present, either with every or with some one, yet it was supposed to be contingent to no B. Since then a negative proposition is convertible, neither will B be contingent to any A, but A is supposed to be present with every or with some C, hence B will happen to be present with no, or not with every C, it was however supposed, from the first, to be present with every C. Still it is evident, that there may also be a syllogism of the contingent non-inesse, as there is one of the simple non-inesse. Moreover, let the affirmative proposition be necessary, and let A be contingently present with no B, but B necessarily present with every C: this syllogism then will be perfect, yet not of the simple, but of the contingent non-inesse, for the proposition (viz. the contingent non-inesse) was assumed from the major extreme, and there cannot be a deduction to the impossible, for if A is supposed to be present with a certain C, and it is admitted that A is contingently present with no B, nothing impossible will arise therefrom. But if the minor premise be negative when it is contingent, there will be a syllogism by conversion, as in the former cases, but when it is not contingent, there will not be; nor when both premises are negative, but the minor not contingent: let the terms be the same of the simple inesse "white," "animal," "snow," and of the non-inesse "white," "animal," "pitch."

The same will also happen in particular syllogisms, for when the negative is necessary, the conclusion will be of the simple non-inesse. Thus if A is contingently present with no B, but B contingently present with a certain C, it is necessary that A should not be present with a certain C. since if it is present with every C, but is contingent to no B, neither will B be contingently present with any A. So that if A is present with every C, B is contingent with no C, but it was supposed contingent to a certain C. When however in a negative syllogism the particular affirmative is necessary, as for example B C, or the universal in an affirmative syllogism, e.g. A B, there will not be a syllogism de inesse, the demonstration however is the same as in the former cases. But if the minor premise be universal, whether affirmative or negative and contingent, but the major particular necessary, there will not be a syllogism, let the terms of necessary presence be "animal," "white," "man," and of the non-contingent "animal," "white," "garment." But when the universal is necessary, and the particular contingent, the universal being negative, let the terms of presence be "animal," "white," "crow," and of non-inesse "animal," "white," "pitch."

But when (the universal) affirms let the terms of presence be "animal," "white," "swan," but of the non-contingent be "animal," "white," "snow." Nor will there be a syllogism when indefinite propositions are assumed or both particular, let the common terms, de inesse, be "animal," "white," "man," de non-inesse "animal," "white," "inanimate;" for "animal" is necessarily and not contingently present with something "white," and "white" is also necessarily and not contingently present with something "inanimate;" the like also occurs in the contingent, so that these terms are useful for all.

From what has been said then it appears that when the terms are alike both in simple and in necessary propositions, a syllogism does and does not occur, except that if the negative proposition be assumed de inesse there will be a syllogism with a contingent (conclusion), but when the negative is necessary there will be one of the character of the contingent and of the non-inesse, but it is clear also that all the syllogisms are incomplete, and that they are completed through the above-named figures.

Chapter 17Edit

In the second figure, when both premises are assumed contingent, there will be no syllogism, neither when they are taken as affirmative, nor negative, nor universal, nor particular; but when one signifies the simple inesse, and the other the contingent, if the affirmative signifies the inesse, there will never be a syllogism, but if the universal negative (be pure, there will) always (be a syllogism). In the same manner, when one premise is assumed as necessary, but the other contingent; still in these syllogisms we must consider the contingent in the conclusions, as we did in the former ones. Now in the first place, we must show that a contingent negative is not convertible, e.g. if A is contingent to no B, it is not necessary that B should also be contingent to no A. For let this be assumed, and let B be contingently present with no A, therefore since contingent affirmatives, both contrary and contradictory, are convertible into negatives, and B is contingently present with no A, it is clear that B may be contingently present with every A; but this is false, for if this is contingent to all of that, it is not necessary that that should be contingent to this, wherefore a negative (contingent) is not convertible. Moreover, there is nothing to prevent A being contingent to no B, but B not necessarily present with a certain A, e.g. "whiteness" may happen not to be present with every "man," (for it may also happen) to be present; but it is not true to say, that man is contingently present with nothing "white," for he is necessarily not present with many things (white), and the necessary is not the contingent. Neither can it be shown convertible per impossibile, as if a man should think, since it is false that B is contingently present with no A, that it is true that it (A) is not contingent to no one (B), for these are affirmation and negation; but if this be true B is necessarily present with a certain A, therefore A is also with a certain B, but this is impossible, since it does not follow if B is not contingent to no A, that it is necessarily present with a certain A. For not to be contingent to no individual, is predicated two ways, the one if a thing is necessarily present with something, and the other if it is necessarily not present with something. For what necessarily is not present with a certain A, cannot be truly said to be contingently not present with every A; as neither can what is necessarily present with a certain thing, be truly said to be contingently present with every thing; if, then, any one thinks that because C is not contingently present with every D, it is necessarily not present with a certain D, he would infer falsely, for, perchance, it is present with every D; still because a thing is necessarily present with certain things, on this account, we say that it is not contingent to every individual. Wherefore the being present necessarily with a certain thing, and the not being present with a certain thing necessarily, are opposed to the being contingently present with every individual, and in like manner, there is a similar opposition to the being contingent to no individual. Hence it is evident, that when the contingent and non-contingent are taken, in the manner we first defined, not only the necessarily being present with a certain thing, but also the necessarily not being present with it, ought to be assumed; but when this is assumed, there is no impossibility to a syllogism being produced, whence it is evident, from what we have stated, that a negative contingent is not convertible.

This then being demonstrated, let A be assumed contingent to no B, but contingent to every C; by conversion, therefore, there will not be a syllogism, for it has been said that a proposition of this kind is inconvertible, neither, however, will there be by a deduction per impossibile. For B being assumed contingently present with every C, nothing false will happen, for A may contingently be present with every and with no C. In short, if there is a syllogism, it is clear that it will be of the contingent, (because neither proposition is assumed as de inesse,) and this either affirmative, or negative; it is possible, however, in neither way, since, if the affirmative be assumed, it can be shown by the terms, that it is not contingently present; but if the negative, that the conclusion is not contingent, but necessary. For let A be "white," B "man," and C "horse," A therefore, i.e. "whiteness," is contingently present with every individual of the one, though with no individual of the other, but B is neither contingently present, nor yet contingently not present, with C. It is evident that it is not contingently present, for no "horse" is "a man," but neither does it happen not to be present, for it is necessary that no "horse" should be "a man," and the necessary is not the contingent, wherefore there is no syllogism. This may be also similarly shown, if the negative be transposed, and if both propositions be assumed affirmative, or negative, for the demonstration will be by the same terms. When one proposition also is universal, but the other particular, or both particular or indefinite, or in whatever other way it is possible to change the propositions, for the demonstration will always be through the same terms. Hence it is clear that if both propositions are assumed contingent there is no syllogism.

Chapter 18Edit

If one proposition signifies inesse, but the other the contingent, the affirmative proposition being simple, but the negative contingent, there will never be a syllogism, neither if the terms be assumed universally, or partially, still the demonstration will be the same, and by the same terms, yet when the affirmative is contingent, but the negative simple, there will be a syllogism. For let A be assumed present with no B, but contingent with every C, then by conversion of the negative, B will be present with no A, but A is contingent to every C, therefore there is a syllogism in the first figure, that B is contingent to no C. So also if the negative be added to C; but if both propositions be negative, and one signifies the simple, but the other the contingent non-inesse, from these assumed propositions nothing necessary is inferred, but the contingent proposition being converted, there is a syllogism, wherein B is contingently present with no C, as in the former, for again there will be the first figure. If, however, both propositions be assumed affirmative, there will not be a syllogism: let the terms of presence be "health," "animal," "man," but of not being present with "health," "horse," "man." The same will happen in the case of particular syllogisms, for when the affirmative is pure, taken either universally, or particularly, there will be no syllogism, and this is shown in like manner through the same terms as before. But when the negative is simple, there will be a syllogism by conversion, as in the former cases. Again, if both premises be taken negative, and that which signifies simply the non-inesse be universal; from these propositions no necessity will result, but the contingent being converted as before there will be a syllogism. If however the negative be pure but particular, there will not be a syllogism, whether the other premise be affirmative or negative. Neither will there be one, when both propositions are assumed indefinite, whether affirmative, negative, or particular, and the demonstration is the same and by the same terms.

Chapter 19Edit

If however one premise signifies the being present necessarily, but the other contingently, when the negative is necessary there will be a syllogism, wherein not only the contingent but also the simple non-inesse (may be inferred), but when the affirmative (is necessary) there will be no syllogism. For let A be assumed necessarily present with no B, but contingent to every C, then by conversion of the negative neither will B be present with any A, but A was contingent to every C, wherefore there is again a syllogism in the first figure, so that B is contingently present with no C. At the same time it is shown that neither is B present with any C, for let it be assumed to be present, therefore if A is contingent to no B, but B is present with a certain C, A is not contingent to a certain C, but it was supposed contingent to every C, and it may be shown after the same manner, if the negative be added to C. Again, let the affirmative proposition be necessary, but the other negative and contingent, and let A be contingent to no B, but necessarily present with every C; now when the terms are thus, there will be no syllogism, for it may happen that B is necessarily not present with C. Let A be "white," B "man," C "a swan;" "whiteness," then, is necessarily present with "a swan," but is contingent to no "man," and "man" is necessarily present with no "swan;" therefore that there will be no syllogism of the contingent is palpable, for what is necessary is not contingent. Yet neither will there be a syllogism of the necessary, for the latter is either inferred from two necessary premises, or from a negative (necessary premise); besides, from these data it follows that B may be present with C, for there is nothing to prevent C from being under B, and A from being contingent to every B, and necessarily present with C, as if C is "awake," B "animal," and A "motion;" for "motion" is necessarily present with whatever is "awake," but contingent to every "animal," and every thing which is "awake" is "an animal." Hence it appears that neither the non-inesse is inferred, since if the terms are thus the inesse is necessary, nor when the enunciations are opposite, so that there will be no syllogism. There will be also a similar demonstration if the affirmative premise be transposed, but if the propositions are of the same character, when they are negative, a syllogism is always formed, the contingent proposition being converted, as in the former cases. For let A be assumed necessarily not present with B, and contingently not present with C, then the propositions being converted, B is present with no A, and A is contingent with every C, and the first figure is produced; the same would also occur if the negation belongs to C. But if both propositions be affirmative, there will not be a syllogism, clearly not of the non-inesse, nor of the necessary non-inesse, because a negative premise is not assumed, neither in the simple, nor in the necessary inesse. Neither, again, will there be a syllogism of the contingent non-inesse, for necessary terms being assumed, B will not be present with C, e.g. if A be assumed "white," B "a swan," and C "man;" nor will there be from opposite affirmations, since B has been shown necessarily not present with C, in short, therefore, a syllogism will not be produced. It will happen the same in particular syllogisms, for when the negative is universal and necessary, there will always be a syllogism of the contingent, and of the non-inesse, but the demonstration will be by conversion; still, when the affirmative (is necessary), there will never be a syllogism, and this may be shown in the same way as in the universals, and by the same terms. Nor when both premises are assumed affirmative, for of this there is the same demonstration as before, but when both are negative, and that which signifies the non-inesse is universal, and necessary; the necessary will not be concluded through the propositions, but the contingent being converted, there will be a syllogism as before. If however both propositions are laid down indefinite, or particular, there will not be a syllogism, and the demonstration is the same, and by the same terms.

It appears then, from what we have said, that an universal, and necessary negative being assumed, there is always a syllogism, not only of the contingent, but also of the simple non-inesse; but with a necessary affirmative, there will never be a syllogism; also that when the terms subsist in the same manner, in necessary, as in simple propositions, there is, and is not, a syllogism; lastly, that all these syllogisms are incomplete, and that they are completed through the above-mentioned figures.

Chapter 20Edit

In the last figure, when both premises are contingent, and when only one is contingent, there will be a syllogism, therefore when the premises signify the contingent, the conclusion will also be contingent; also if one premise signifies the contingent, but the other, the simple inesse. Still when one premise is assumed necessary, if it be affirmative, there will not be a conclusion either necessary or simple, if on the contrary it is negative, there will be a syllogism of the simple non-inesse as before; in these however the contingent must be similarly taken in the conclusions. First then let the premises be contingent, and let A and B be contingently present with every C; since therefore a particular affirmative is convertible, but B is contingent to every C, C will also be contingent to a certain B, therefore if A is contingent to every C, but C is contingent to a certain B, it is necessary also that A should be contingent to a certain B, for the first figure is produced. If again A is contingently present with no C, but B with every C, A must also of necessity be contingently not present with a certain B, for again there will be the first figure by conversion; but if both propositions be assumed negative from these the necessary will not result, but the propositions being converted there will be a syllogism as before. For if A and B are contingently not present with C, if the contingently not present be changed, there will again be the first figure by conversion. If however one term be universal but the other particular, when they are so, as in the case of simple inesse, there will, and will not, be a syllogism; for let A be contingently present with every C, and B present with a certain C, there will again be the first figure by conversion of the particular proposition, since if A is contingent to every C, and C to a certain B, A is also contingent to a certain B, and in like manner if the universal be joined to B C. This also will be produced in a similar way if A C be negative, but B C affirmative, for again we shall have the first figure by conversion, if however both are negative, the one universal and the other particular, by the assumed propositions there will not be a syllogism, but there will be when they are converted as before. Lastly, when both are indefinite or particular, there will not be a syllogism, for A must necessarily be present with every and with no B, let the terms de inesse be "animal," "man," "white," and de non-inesse "horse," "man," "white," the middle term "white."

Chapter 21Edit

If however one premise signifies the inesse, but the other the contingent, the conclusion will be that a thing is contingent to, and not that it is present with (another), and there will be a syllogism, the terms subsisting in the same manner as the previous ones. For, first, let them be affirmative, and let A be in every C, but B contingent with every C; B C then being converted there will be the first figure, and the conclusion will be that A is contingently present with a certain B, for when one premise in the first figure signifies the contingent, the conclusion also was contingent. In like manner if the proposition B C be of the simple inesse, but the proposition A C be contingent, and if A C be negative, but B C affirmative, and either of them be pure; in both ways the conclusion will be contingent, since again there arises the first figure. Now it has been shown that where one premise in that figure signifies the contingent, the conclusion also will be contingent; if however the negative be annexed to the minor premise, or both be assumed as negative, through the propositions laid down themselves, there will not indeed be a syllogism, but by their conversion there will be, as in the former cases.

Nevertheless if one premise be universal and the other particular, yet both affirmative, or the universal negative but the particular affirmative, there will be the same mode of syllogisms; for all are completed by the first figure, so that it is evident there will be a syllogism of the contingent and not of the inesse. If however the affirmative be universal and the negative particular, the demonstration will be per impossibile; for let B be with every C and A happen not to be with a certain C, it is necessary then that A should happen not to be with a certain B, since if A is necessarily with every B, but B is assumed to be with every C, A will necessarily be with every C, which was demonstrated before, but by hypothesis A happens not to be with a certain C.

When both premises are assumed indefinite, or particular, there will not be a syllogism, and the demonstration is the same as in universals, and by the same terms.

Chapter 22Edit

If one premise be necessary, but the other contingent, the terms being affirmative there will be always a syllogism of the contingent; but when one is affirmative but the other negative, if the affirmative be necessary there will be a syllogism of the contingent non-inesse; if however it be negative, there will be one both of the contingent and of the absolute non-inesse. There will not however be a syllogism of the necessary non-inesse, as neither in the other figures. Let then, first, the terms be affirmative, and let A be necessarily with every C, but B happen to be with every C; therefore since A is necessarily with every C, but C is contingent to a certain B, A will also be contingently, and not necessarily, with some certain B; for thus it is concluded in the first figure. It can be similarly proved if B C be assumed as necessary, but A C contingent.

Again, let one premise be affirmative, but the other negative, and let the affirmative be necessary; let also A happen to be with no C, but let B necessarily be with every C; again there will be the first figure; for the negative premise signifies the being contingent it is evident therefore that the conclusion will be contingent, for when the premises were thus in the first figure, the conclusion was also contingent. But if the negative premise be necessary, the conclusion will be that it is contingent, not to be with something, and that it is not with it; for let A be supposed necessarily not with C, but contingent to every B, then the affirmative proposition B C being converted, there will be the first figure, and the negative premise will be necessary. But when the premises are thus, it results that A happens not to be with a certain C, and that it is not with it; wherefore it is necessary also that A should not be with a certain B. When however the minor premise is assumed negative there will be a syllogism, if that be contingent by the premise being converted as in the former cases, but if it be necessary there will not be, for it is necessary to be with every, and happens to be with none; let the terms of being with every individual, be "sleep," a "sleeping horse," "man;" of being with none "sleep," a "waking horse," "man."

It will happen in the same way, if one term be joined to the middle universally, but the other partially, for both being affirmative there will be a syllogism of the contingent, and not of the absolute, also when the one is assumed as negative but the other affirmative, and the affirmative is necessary. But when the negative is necessary, the conclusion will also be of the not being present with; for there will be the same mode of demonstration, whether the terms are universal or not universal, since it is necessary that the syllogisms be completed by the first figure, so that it is requisite that the same should result, in these, as in those. When however the negative, universally assumed, is joined to the less extreme, if it be contingent, there will be a syllogism by conversion, but if it be necessary there will not be, and this may be shown in the same mode as in universals, and by the same terms. Wherefore in this figure it it is evident, when and how there will be a syllogism, and when of the contingent, and when of the absolute, all also it is clear are imperfect, and are perfected by the first figure.

Chapter 23Edit

That the syllogisms then in these figures are completed by the universal syllogisms in the first figure, and are reduced to these, is evident from what has been said; but that in short every syllogism is thus, will now be evident, when it shall be shown that every syllogism is produced by some one of these figures.

It is then necessary that every demonstration, and every syllogism, should show either something inesse or non-inesse, and this either universally or partially, moreover either ostensively or by hypothesis. A part however of that which is by hypothesis is produced per impossibile, therefore let us first speak of the ostensive (syllogisms), and when these are shown, it will be evident also in the case of those leading to the impossible, and generally of those by hypothesis.

If then it is necessary to syllogize A of B either as being with or as not being with, we must assume something of something, if then A be assumed of B, that which was from the first (proposed) will be assumed (to be proved), but if A be assumed of C, but C of nothing, nor any thing else of it, nor of A, there will be no syllogism, for there is no necessary result from assuming one thing of one, so that we must take another premise. If then A be assumed of something else, or something else of A, or of C, there is nothing to hinder a syllogism, it will not however appertain to B from the assumptions. Nor when C is predicated of something else, and that of another, and this last of a third, if none of these belong to B, neither thus will there be a syllogism with reference to B, since in short we say that there never will be a syllogism of one thing in respect of another unless a certain middle is assumed, which refers in some way to each extreme in predication. For a syllogism is simply from premises, but that which pertains to this in relation to that, is from premises belonging to this in relation to that, but it is impossible to assume a premise relating to B, if we neither affirm nor deny any thing of it, or again of A in relation to B, if we assume nothing common, but affirm or deny certain peculiarities of each. Hence a certain middle of both must be taken, which unites the predications, if there shall be a syllogism of one in relation to the other; now if it is necessary to assume something common to both, this happens in a three-fold manner, (since we either predicate A of C, and C of B, or C of both or both of C,) but these are the before-mentioned figures—it is evident that every syllogism is necessarily produced by some one of these figures, for there is the same reasoning, if A be connected with B, even through many media, for the figure in many media will be the same.

Wherefore that all ostensive syllogisms are perfected by the above-named figures is clear, also that those per impossibile (are so perfected) will appear from these, for all syllogisms concluding per impossibile collect the false, but they prove by hypothesis the original proposition, when contradiction being admitted some impossibility results, as for instance that the diameter of a square is incommensurate with the side, because, a common measure being given, the odd would be equal to the even. They collect then that the odd would be equal to the even, but show from hypothesis that the diameter is incommensurate, since a falsity occurs by contradiction. This then it is, to syllogize per impossibile, namely, to show an impossibility from the original hypothesis, so that as by reasonings leading to the impossible, an ostensive syllogism of the false arises, but the original proposition is proved by hypothesis; and we have before said about ostensive syllogisms, that they are perfected by these figures—it is evident that syllogisms also per impossibile will be formed through these figures. Likewise all others which are by hypothesis, for in all there is a syllogism of that which is assumed, but the original proposition is proved by confession, or some other hypothesis. Now if this is true, it is necessary that every demonstration and syllogism should arise through the three figures before named, and this being shown, it is manifest that every syllogism is completed in the first figure, and is reduced to universal syllogisms in it.

Chapter 24Edit

Moreover it is necessary in every syllogism, that one term should be affirmative and one universal, for without the universal there will not be a syllogism, or one not pertaining to the thing proposed, or the original (question) will be the subject of petition. For let it be proposed that pleasure from music is commendable, if then any one should require it to be granted that pleasure is commendable, and did not add all pleasure, there would not be a syllogism, but if that a certain pleasure is so, if indeed it is a different pleasure, it is nothing to the purpose, but if it is the same it is a petitio principii, this will however be more evident in diagrams, for instance, let it be required to show that the angles at the base of an isosceles triangle are equal. Let the lines A B be drawn to the centre of a circle, if then he assumes the angle A C to be equal to the angle B D, not in short requiring it to be granted that the angles of semicircles are equal, and again that C is equal to D, not assuming the whole (angle) of the section, if besides he assumes that equal parts being taken from equal whole angles, the remaining angles E F are equal, he will beg the original (question), unless he assume that if equals are taken from equals the remainders are equal. Wherefore in all syllogism we must have an universal; universal is also shown from all universal terms, but the particular in this or that way, so that if the conclusion be universal, the terms must of necessity be universal, but if the terms be universal, the conclusion may happen not to be universal. It appears also that in every syllogism either both premises or one of them must be similar to the conclusion, I mean not only in its being affirmative or negative, but in that it is either necessary, or absolute, or contingent; we must also have regard to other modes of predication.

In a word then it is shown when there will and will not be a syllogism, also when it is possible, and when perfect, and that when there is a syllogism it must have its terms according to some one of the above modes.

Chapter 25Edit

It appears that every demonstration will be by three terms and no more, unless the same conclusion should result through different arguments, as E through A B, and through C D, or through A B, A C, and B C, for there is nothing to prevent many media subsisting of the same conclusions). But these being (many), there is not one syllogism, but many syllogisms; or again, when each of the propositions A B is assumed by syllogism, as A through D E, and again B through F G, or when the one is by induction, but the other by syllogism. Thus in this manner indeed there are many syllogisms, for there are many conclusions, as A and B and C, and if there are not many but one, it is thus possible, that the same conclusion may arise through many syllogisms, but in order that C may be proved through A B, it is impossible. For let the conclusion be E, collected from A B C D, it is then necessary that some one of these should be assumed with reference to something else, as a whole, but another as a part, for this has been shown before, that when there is a syllogism, some of the terms should necessarily thus subsist; let then A be thus with reference to B, from these there is a certain conclusion, which is either E or C or D, or some other different from these. Now if E is concluded, the syllogism would be from A B alone, but if C D are so as that the one is universal, and the other particular, something also will result from these which will either be E or A or B, or something else different from these, and if E is collected, or A or B, there will be either many syllogisms, or, as it was shown possible, the same thing will happen to be collected through many terms. If, however, any thing else different from these is collected, there will be many syllogisms unconnected with each other; but if C is not so with respect to D, as to produce a syllogism, they will be assumed to no purpose, except for the sake of induction or concealment, or something of the sort. Still if from A B, not E, but some other conclusion is produced, and from C D, either one of these, or something different from these, many syllogisms arise, yet not of the subject, for it was supposed that the syllogism is of E. If, again, there is no conclusion from C D, it will happen that they are assumed in vain, and the syllogism is not of the primary problem, so that it is evident that every demonstration and every syllogism will be through three terms only.

This then being apparent, it is also clear that a syllogism consists of two premises and no more; for three terms are two premises, unless something is assumed over and above, as we observed at first, for the perfection of the syllogisms. Hence it appears, that in the syllogistic discourse, in which the premises, through which the principal conclusion is collected, are not even,—(for it is requisite that some of the former conclusions should be premises,)—this discourse is either not syllogistically constructed, or has required more than is necessary to the thesis.

When then the syllogisms are taken according to the principal propositions, every syllogism will consist of propositions which are even, but of terms which are odd for the terms exceed the premises by one, and the conclusions will be half part of the premises. When, however, the conclusion results through pro-syllogisms, or through many continued middles, as A B through C D, the multitude of terms, in like manner, will exceed the premises by one, (for the term interpolated will be added either externally or in the middle; but in both ways it will happen that the intervals are fewer than the terms by one,) but the propositions are equal to the intervals, the former, indeed, will not always be even, but the latter odd, but alternately, when the propositions are even the terms are odd, but when the terms are even the propositions are odd; for together with the term, one proposition is added wherever the term is added. Hence, since the propositions were even, but the terms odd, it is necessary they should change when the same addition is made; but the conclusions will no longer have the same order, neither with respect to the terms, nor to the propositions, for one term being added, conclusions will be added less than the pre-existent terms by one, because to the last term alone there is no conclusion made; but to all the rest, e.g. if D is added to A B C, two conclusions are immediately added, the one to A and the other to B. The same occurs in the other cases also, if the term be inserted in the middle after the same manner, for it will not make a syllogism to one term alone, so that the conclusions will be many more than the terms, and than the propositions.

Chapter 26Edit

Since we have those particulars with which syllogisms are conversant, and what is their quality in each figure, and in how many ways demonstration takes place, it is also manifest to us, what kind of problem is difficult, and what easy of proof, for that which is concluded in many figures, and through many cases, is more easy, but what is in fewer figures, and by fewer cases, is more difficult. An universal affirmative then is proved through the first figure alone, and by this in one way only; but a negative, both through the first and through the middle, through the first in one way, but through the middle in two ways; the particular affirmative again through the first and through the last, in one way through the first figure, but in three ways through the last; lastly, the particular negative is proved in all the figures, but in the first in one way, in the middle in two ways, and in the last in three ways. Hence it appears most difficult to construct an universal affirmative, but most easy to subvert it, in short, universals are easier to subvert than particulars, because the former are subverted, whether a thing is present with nothing, or is not with a certain thing, of which the one, namely, the not being with a certain thing, is proved in all the figures, and the other, the being with nothing, is proved in two. The same mode also prevails in the case of negatives, for the original proposition is subverted, whether a thing is with every, or with a certain individual, now this was in two figures. In particular problems there is one way (of confutation), either by showing a thing to be with every, or with no individual, and particular problems are easier of construction, for they are in more figures, and through more modes. In short, we ought not to forget that it is possible to confute universal mutually through particular problems, and these through universal, yet we cannot construct universal through particular, but the latter may be through the former, at the same time that it is easier to subvert than to construct is plain.

In what manner then every syllogism arises, through how many terms and premises, how they subsist with reference to each other, also what sort of problem may be proved in each figure, and what in many and in fewer modes, may be gathered from what has been said.

Chapter 27Edit

We must now describe how we may always obtain a provision of syllogisms for a proposed question, and in what way we may assume principles about each, for perhaps it is not only requisite to consider the production of syllogisms, but also to possess the power of forming them.

Of all beings then, some are of such a nature as not to be truly predicated universally of any thing else, as "Cleon," and "Callias," that which is singular, and that which is sensible, but others are predicated of these, (for each of these is man and animal); some again are predicated of others, but others not previously of these; lastly, there are some which are themselves predicated of others, and others of them, as "man" is predicated of Callias, and "animal" of man. That some things therefore are naturally adapted to be predicated of nothing is clear, for of sensibles each is almost of such a sort, as not to be predicated of any thing except accidentally, for we sometimes say that that white thing is Socrates, and that the object approaching is Callias. But that we must stop somewhere in our upward progression we will again show, for the present let this be admitted. Of these things then we cannot point out another predicate, except according to opinion, but these may be predicated of others, nor can singulars be predicated of others, but others of them. It appears however that those which are intermediate, are capable in both ways (of demonstration), for they may be predicated of others, and others of them, and arguments and speculations are almost all conversant with these.

Still it is requisite to assume the propositions about each thing thus:—In the first place, the subject, (by hypothesis,) the definitions, and such peculiarities as exist of the thing; next, whatever things are consequent to the thing, and which the thing follows; lastly, such as cannot be in it; those however which it cannot be in are not to be assumed, because of the conversion of the negative. We must also distinguish in the consequents what things belong to "what a thing is," what are predicated as properties, and what as accidents; also of these, those which are (predicated) according to opinion, and those, according to truth; for the greater number any one has of these, the quicker will he light upon a conclusion, and the more true they are, the more will he demonstrate. We must too select not those which are consequent to a certain one, but those which follow the whole thing, e.g. not what follows a certain man, but what follows every man, for a syllogism consists of universal propositions. If therefore a proposition is indefinite, it is doubtful whether it is universal, but when it is definite, this is manifest. So also we must select those things the whole of which a thing follows, for the reason given above, but the whole consequent itself need not be assumed to follow; I say for instance, (it must not be assumed) that every "animal" is consequent to "man," or every science to music, but only that they are simply consequent, as we set forth, for the other is useless and impossible, as that "every man" is "every animal," or that "justice is every thing good." To whatever (subject) a consequent is attached, the sign "every" is added; when however the ject is comprehended by a certain thing, the consequents of which we must assume, those which follow or which do not follow the universal, we are not to select in these—for they were assumed in those, since whatever are consequent to "animal," are also consequent to "man," and as to whatever things are not absolutely present with in like manner; but the properties of each thing must be taken, for there are certain properties in species not common to genus, since it is necessary that certain properties should be in different species. Nor are we to select those in regard to the universal, which the thing comprehended follows, as those which "man" follows ought not to be assumed to "animal," for it is necessary if animal follows man that it follows all these, but these more properly belong to the selection of the antecedents of "man." We must also assume those which are generally consequent and antecedent, for of general problems the syllogism also is from propositions, all or some of which are general, as the conclusion of each syllogism resembles its principles. Lastly, we are not to select things consequent to all, since there will not be composed a syllogism from them, on account of a reason which will appear from what follows.

Chapter 28Edit

Those therefore who desire to confirm any thing of a certain universal, should look to the subject matter of what is confirmed, in respect of which it happens to be predicated; but of whatever ought to be predicated, of this, he should examine the consequents; for if one of these happens to be the same, one must necessarily be in the other. But if (it is to be proved) that a thing is not present universally but particularly, he must examine those which each follows, for if any of these is the same, to be particularly present is necessary; but when the presence with nothing is necessary, as to what it need not be present with, we must look to those which cannot be present with it; or on the contrary, (as regards that) with which it is necessary not to be present, we must look to those which cannot be with it, but as to what ought not to be present, to the consequents. For whichever of these are identical, it will happen that the one is in no other, since sometimes a syllogism arises in the first and at other times in the middle figure. If however the particular non-inesse (is to be proved), that with which it ought not to be present, and those which it follows, are to be looked to; but of that which ought not to be present, those must be considered, which it is impossible can be in it, for if any of these be identical the particular non-inesse is necessary. What has been said however will perhaps be more clear thus. Let the consequents to A be B, but let those to which it is consequent be C; those again which cannot be in it, D; again, let the things present with E be F, and those to which it is consequent, G; lastly, those which cannot be in it, H. Now if a certain C and a certain F are identical, it is necessary that A should be with every E, for F is present with every E, and A with every C, so that A is with every E; but if C and G are identical, A must necessarily be with a certain E, for A follows every C, and E every G. If however F and D are identical, A will be with no E from a pro-syllogism, for since a negative is convertible and F is identical with D, A will be with no F, but F is with every E; again, if B and H are the same, A will be with no E, for B is with every A, but with no E, for it was the same as H, and H was with no E. If D and G are identical, A will not be with a certain E, for A will not be with G, since it is not present with D, but G is under E, so that neither will it be with a certain E. Moreover if B is identical with G there will be an inverse syllogism, for G will be with every A, (since B is with A,) and E with B (for B is the same as G); still it is not necessary that A should be with every E, but it is necessary that it be with a certain E, because an universal predication may be converted into a particular one.

Wherefore we must evidently regard what has been mentioned as to each part of every problem, since all syllogisms are from these; but in consequents, and the antecedents of each thing, we must look to first elements, and to those which are for the most part universal, as in the case of E we must look more to K F than only to F, but in the case of A more to K C than to C only. For if A is present with K C it is also present with F and with E, but if it is not consequent to this, yet it may be consequent to F; in like manner we must examine those which the thing itself is consequent to, for if it follows the primary, it also does those which are included under them, and if it does not follow these, yet it may those which are arranged under them.

Speculation then, plainly, consists of three terms and two propositions, and all syllogisms are through the above-mentioned figures; for A is shown present with every E, when of C and F something identical may be assumed. Now this will be the middle term, and A and E the extremes, and there is the first figure, but (presence with) a certain thing is shown when C and G are assumed identical, and this is the last figure, for G becomes the middle. Again, (presence with) none, when D and F are identical, but thus also the first figure and the middle are produced; the first, because A is with no F, (since a negative is converted,) but F is with every E; and the middle because D is with no A, but with every E. Not to be present also with a certain one, (is shown) when D and G are the same, and this is the last figure, for A will be with no G, and E with every G. Wherefore all syllogisms are evidently through the above-named figures, and we must not select those which are consequent to all, because no syllogism arises from them; as, in short, we cannot construct from sequents, nor deduce a negative through an universal consequent, for it must be in one, and not in the other.

That other modes of speculation also, as regards selection, are useless for the construction of syllogism is apparent; for instance, if the consequents to each are identical, or if those which A (the predicate) follows, and which cannot be with E (the subject), or again those which cannot concur to be with either, for no syllogism arises through these. If then the consequents are identical, as B and F, the middle figure is produced, having both premises affirmative; but if those which A follows, and which cannot be with E, as C and H, there will be the first figure having the minor premise negative; again, if those are identical which cannot be with either, as D and H, both propositions will be negative, either in the first or in the middle figure: thus, however, there will by no means be a syllogism.

We see moreover that we must assume in speculation things identical, and not what are different, or contrary; first, because our inspection is for the sake of the middle, and we must take as a middle, not what is different, but what is identical. Next, in whatever a syllogism happens to be produced, from the assumption of contraries, or of those things which cannot be with the same, all are reduced to the before-named modes, as if B and F are contraries, or cannot be with the same thing; if these are assumed there will be a syllogism that A is with no E: this however does not result from them, but from the above-named mode; for B is with every A, and with no E, so that B must necessarily be identical with a certain H. Again, if B and G do not concur to be with the same thing, (it will follow) that A will not be with a certain E, and so there will be the middle figure, for B is with every A, and with no G, so that B must necessarily be identical with some H. For the impossibility of B and G being in the same thing, does not differ from B being the same as a certain H, since every thing is assumed which cannot be with E.

From these observations, then, it is shown that no syllogism arises; but if B and F are contraries, B must necessarily be identical with a certain H, and a syllogism arises through these. Nevertheless it occurs to persons thus inspecting, that they look to a different way than the necessary, from the identity of B and H escaping them.

Chapter 29Edit

Syllogisms which lead to the impossible subsist in the same manner as ostensive, for these also arise through consequents, and those (antecedents) which each follows, and the inspection is the same in both, for what is ostensively demonstrated may also syllogistically inferred per impossibile, and through the same terms, and what is demonstrated per impossibile, may be also proved ostensively, as that A is with no E. For let it be supposed to be with a certain E, therefore since B is with every A, and A with a certain E, B also will be with a certain E, but it was present with none; again, it may be shown that A is with a certain E, for if A is with no E, but E is with every H, A will be with no H, but it was supposed to be with every H. It will happen the same in other problems, for always and in all things demonstration per impossibile will be from consequents, and from those which each follows. In every problem also there is the same consideration, whether a man wishes to syllogize ostensively, or to lead to the impossible, since both demonstrations are from the same terms, as for example, if A were shown to be with no E, because B happens to be with a certain E, which is impossible, if it is assumed that B is with no E, but with every A, it is evident that A will be with no E. Again, if it is ostensively collected that A is with no E, to those who suppose that it is with a certain E, it may be shown per impossibile to be with no E. The like will also occur in other cases, for in all we must assume some common term different from the subject terms to which there will appertain a syllogism of the false, so that this proposition being converted, but the other remaining the same, there will be an ostensive syllogism through the same terms. But an ostensive syllogism differs from that per impossibile, because in the ostensive both premises are laid down according to truth, but in that which leads to the impossible one is laid down falsely.

These things however will more fully appear by what follows, when we come to speak of the impossible, for the present let so much be manifest to us, that both he who wishes to syllogize ostensively, and per impossibile, must observe these things. In other syllogisms indeed which are hypothetical, such as those which are according to transumption, or according to quality, the consideration will be in the subject terms, not in the original ones, but in those taken afterwards, but the mode of inspection will be the same; but it is necessary also to consider, and distinguish, in how many ways hypothetical syllogisms arise.

Each problem then is demonstrated thus, and some of them we may infer syllogistically after another method, for example, universals by an hypothetical inspection of particulars, for if C and H are the same, and if E is assumed to be with H alone, A will be with every E; and again, if D and H are the same, and E is predicated of H alone, (it may be shown) that A is with no E. Wherefore the inspection must clearly be in this way after the same manner both in the necessary and contingent, for the consideration is the same, and the syllogism both of the contingent and the absolute will be through terms the same in order; in the contingent however we may assume things which are not with, but which may be, for it has been shown that by these a contingent syllogism is produced, and the reasoning is similar in the case of the other predications. From what has been said then it appears not only that it is allowable for all syllogisms to be formed in this, but that they cannot be formed in any other way, for every syllogism has been shown to originate through some one of the before-named figures, and these may not be constituted through any other than the consequents and antecedents of a thing, for from these are the premises and assumption of the middle, so that it is not admissible that a syllogism should be produced through other things.

Chapter 30Edit

The way then of proceeding in all (problems), both in philosophy and in every art and discipline, is the same, for we must collect about each of them those things which are with, and the subjects which they are with, and be provided with as many as possible of these, considering them also through three terms in one way subverting, but in another constructing according to truth (we reason) from those which are truly described to be inherent, but as regards dialectic syllogisms (we must reason) from probable propositions. Now the principles of universal syllogisms have been mentioned, how they subsist, and how we must investigate them, that we may not direct our attention to every thing which is said, nor to constructing and subverting the same things, nor both constructing universally or particularly, nor subverting wholly or partially, but look to things fewer and definite; as to each however we must make a selection, as of good or of science. The peculiar principles indeed in every science are many, hence it is the province of experience to deliver the principles of every thing, for instance, I say that astrological experience gives the principles of astrological science, for from phenomena being sufficiently assumed, astrological demonstrations have thus been invented, so also is it in every other art and science. Wherefore if things are assumed which exist in individuals, it is now our duty readily to exhibit demonstrations, for if as regards history nothing is omitted of what is truly present with things, we shall be able about every thing of which there is demonstration to discover and demonstrate this, and to make that clear which is naturally incapable of demonstration.

Universally then we have nearly shown how propositions ought to be selected, but we have discussed this accurately in the treatise on Dialectic.

Chapter 31Edit

THAT the division through genera is but a certain small portion of the method specified, it is easy to perceive, for division is, as it were, a weak syllogism, since it begs what it ought to demonstrate, and always infers something of prior matter. Now this has first escaped the notice of all those who use it, and they endeavour to show that demonstration about essence and the very nature of a thing is possible, so that they neither perceive that those who divide happen to syllogize, nor that it is possible in the manner we have said. In demonstrations therefore, when it is requisite to infer absolute presence, the middle term by which the syllogism is produced must always be less, and must not be universally predicated of the first extreme, but on the contrary, division takes the universal for the middle term. For let animal be A, mortal B, immortal C, and man of whom we ought to assume the definition D, every animal then comprehends either mortal or immortal, but this is that the whole of whatever may be A is either B or C. Again, he who divides man, admits that he is animal, so that he assumes A to be predicated of D, hence the syllogism is that every D is either B or C, wherefore it is necessary for man to be either mortal or immortal, yet it is not necessary that animal should be mortal, but this is desired to be granted, which was the very thing which ought to have been syllogistically inferred. Again, taking A for mortal animal, B for pedestrian, C without feet, and D for man, in the same manner it assumes A to be either with B or C, for every mortal animal is either pedestrian or without feet, and that A is predicated of D, for it has assumed that man is a mortal animal, so that it is necessary that man should be either a pedestrian animal or without feet, but that he is pedestrian is not necessary, but they assume it, and this again is what they ought to have proved. After this manner it always happens to those who divide, namely, that they assume an universal middle, and what they ought to show, and the differences as extremes. In the last place, they assert nothing clearly, as that it is necessary that this be a man, or that the question necessarily is whatever it may be, but they pursue every other way, not apprehending the available supplies. It is clear however, that by this method we can neither subvert nor syllogistically infer any thing of accident or property or genus, or of those things of which we are a priori ignorant as to how they subsist, as whether the diameter of a square be incommensurable, for if it assumes every length to be either commensurable or incommensurable, but the diameter of a square is a length, it will infer that the diameter is either incommensurable or commensurable, and if it assumes that it is incommensurate, it will assume what it ought to prove, wherefore that we cannot show, for this is the way, and by this we cannot do it; let however the incommensurable or commensurable be A, length B, and diameter C. It is clear then that this mode of inquiry does not suit every speculation, neither is useful in those to which it especially appears appropriate, wherefore from what sources, and how demonstrations arise, and what we must regard in every problem, appear from what has been said.

Chapter 32Edit

How then we may reduce syllogisms to the above-named figures must next be told, for this is the remainder of the speculation, since if we have noticed the production of syllogisms, and have the power of inventing them, it moreover we analyze them when formed into the before-named figures, our original design will have been completed. At the same time, what has before been said will happen to be confirmed, and be more evident that they are thus from what shall now be said, for every truth must necessarily agree with itself in every respect.

First then we must endeavour to select the two propositions of a syllogism, for it is easier to divide into greater than into less parts, and composites are greater than the things of which they are composed; next we must consider whether it is in a whole or in a part, and if both propositions should not be assumed, oneself placing one of them. For those who propose the universal do not receive the other which is contained in it, neither when they write, nor when they interrogate, or propose these, but omit those by which these are concluded, and question other things to no purpose. Therefore we must consider whether any thing superfluous has been assumed, and any thing necessary omitted, and one thing is to be laid down, and another to be removed, until we arrive at two propositions, for without these we cannot reduce the sentences which are thus the subjects of question. Now in some it is easy to see what is deficient, but others escape us, and seem to be syllogisms, because something necessarily happens from the things laid down, as if it should be assumed that essence not being subverted, essence is not subverted, but those things being subverted, of which a thing consists, what is composed of these is subverted also; for from these positions it is necessary that a part of essence should be essence, yet this is not concluded through the assumptions, but the propositions are wanting. Again, if because man exists, it is necessary that animal should be, and animal existing, that there should be essence; then, because man exists, essence must necessarily be; but this is not yet syllogistically inferred, for the propositions do not subsist as we have said they should; but we are deceived in such, because something necessary happens from the things laid down, and because also a syllogism is something necessary. The necessary, however, is more extensive than the syllogism, for every syllogism is necessary, but not every thing necessary is a syllogism; so that if any thing occurs from certain positions, we must not immediately endeavour to reduce, but first assume two propositions, then we must divide them into terms, in this manner, that term we must place as the middle which is said to be in both propositions, for the middle must necessarily exist in both, in all the figures. If then the middle predicates, and is predicated of, or if it indeed predicates, but another thing is denied of it, there will be the first figure, but if it predicates, and is denied by something, there will be the middle figure, and if other things are predicated of it, and one thing is denied, but another is predicated, there will be the last figure; thus the middle subsists in each figure. In a similar manner also, if the propositions should not be universal, for the determination of the middle is the same, wherefore it is evident, that in discourse, where the same thing is not asserted more than once, a syllogism does not subsist, since the middle is not assumed. As, however, we know what kind of problem is deduced in each figure, in what the universal, and in what the particular, it is clear that we must not regard all the figures, but that one which is appropriate to each problem, and whatever things are deduced in many figures, we may ascertain the figure of by the position of the middle.

Chapter 33Edit

It frequently happens then, that we are deceived about syllogisms, on account of the necessary (conclusion), as we have before observed, and sometimes by the resemblance in the position of the terms, which ought not to have escaped us.

Thus if A is predicated of B, and B of C, there would appear a syllogism from such terms, yet neither is any thing necessary produced, nor a syllogism. For let A be that which always is; B, Aristomenes the object of intellect; and C, Aristomenes; it is true then that A is with B, for Aristomenes is always the object of intellect; but B is also with C, for Aristomenes is Aristomenes the object of intellect, but A is not with C, for Aristomenes is corruptible, neither would a syllogism be formed from terms thus placed, but the universal proposition A B must be assumed, but this is false, to think that every Aristomenes who is the object of intellect always exists, when Aristomenes is corruptible. Again, let C be Miccalus, B Miccalus the musician, A to die to-morrow; B therefore is truly predicated of C, since Miccalus is Miccalus the musician, and A is truly predicated of B, for Miccalus the musician may die to-morrow, but A is falsely predicated of C. This case therefore is the same with the preceding, for it is not universally true that Miccalus the musician will die to-morrow, and if this is not assumed, there would be no syllogism.

This deception arises therefore from a small (matter), since we concede, as if there were no difference between saying that this thing is present with that, and this present with every individual of that.

Chapter 34Edit

Deception will frequently occur from the terms of the proposition being improperly expounded, as if A should be health, B disease, and C man, for it is true to say that A cannot be with any B, for health is with no disease, and again that B is with every C, for every man is susceptible of disease, whence it would appear to result that health can be with no man. Now the reason of this is, that the terms are not rightly set out in expression, since those words which are significant of habits being changed, there will not be a syllogism, as if the word "well" were taken instead of "health," and the word "ill" instead of "disease," since it is not true to say, that to be well cannot be present with him that is ill. Now this not being assumed, there is no syllogism except of the contingent, which indeed is not impossible, for health may happen to be with no man. Again, in the middle figure there will likewise be a falsity, for health happens to be with no disease, but may happen to be with every man, so that disease shall be with no man. In the third figure however falsity occurs by the contingent, for it is possible that health and disease, science and ignorance, in short, contraries, shall be with the same individual, but it is impossible that they should be present with each other: this, however, differs from the preceding observations, since when many things happen to be present with the same individual they also happen to be so with each other.

Evidently then in all these cases deception arises from the setting forth of the terms, as if those are changed which relate to the habits, there is no falsity, and it is therefore apparent that in such propositions, what relates to habit must always be exchanged and placed for a term instead of habit.

Chapter 35Edit

It is not always necessary to seek to expound the terms by a name, since there will oftentimes be sentences to which no name is attached, wherefore it is difficult to reduce syllogisms of this kind, but we shall sometimes happen to be deceived by such a search, for example, because a syllogism is of things immediate. For let A be two right angles, B a triangle, C an isosceles triangle. A then is with C through B, but no longer with B through any thing else, for a triangle has of itself two right angles, so that there will not be a middle of the proposition A B, which is demonstrable. The middle then must clearly not thus be always assumed, as if it were a particular definite thing, but sometimes a sentence, which happens to be the case in the instance adduced.

Chapter 36Edit

For the first to be in the middle, and the latter in the extreme, it is unnecessary to assume as if they were always predicated of each other, or in like manner, the first cf the middle, and this in the last, and also likewise in the case of noninesse. Still in so many ways as to be is predicated, and any thing is truly asserted, it is requisite to consider that we signify the inesse, as that of contraries there is one science.

For let A be, there is one science, and B, things contrary to each other, A then is present with B, not as if contraries are one science, but because it is true in respect of them, to say that there is one science of them. It sometimes occurs indeed, that the first is predicated of the middle, but the middle not of the third, as if wisdom is science, but wisdom is of good, the conclusion is that science is of good: hence good is not wisdom, but wisdom is science. Sometimes, again, the middle is predicated of the third, but the first not of the middle, e. g. if there is a science of every quality or contrary, but good is a contrary and a quality, the conclusion then is, that there is a science of good, yet neither good, nor quality, nor contrary is science, but good is these. Sometimes, again, neither the first is predicated of the middle, nor this of the third, the first indeed being sometimes predicated of the third, and sometimes not, for instance, of whatever there is science, there is genus, but there is science of good, the conclusion is that there is a genus of good, yet none of these is predicated of any. If, nevertheless, of what there is science, this is genus, but there is a science of good, the conclusion is that good is genus, hence the first is predicated of the extreme, but there is no predication of each other.

In the case of the non-inesse there must be the same manner of assumption, for this thing not being present with this, does not always signify that this is not this, but sometimes that this is not of this, or that this is not with this, as there is not a motion of motion or generation of generation, but there is (a motion and generation) of pleasure: pleasure therefore is not generation. Again, there is of laughter a sign, but there is not a sign of a sign, so that laughter is not a sign, and similarly in other cases, wherein the problem is subverted from the genus being in some way referred to it. Moreover, occasion is not opportune time, for to the divinity there is occasion, but not opportune time, because there is nothing useful to divinity, we must take as terms, occasion, opportune time, and divinity, but the proposition must be assumed according to the case of the noun, since, in short, we assert this universally, that we must always place the terms according to the appellations of the nouns, e.g. man, or good, or contraries, not of man, nor of good, nor of contraries, but we must take propositions according to the cases of each word, since they are either to this as the equal, or of this as the double, or this thing as striking, or seeing, or this one as man, animal, or if the noun falls in any other way, according to the proposition.

Chapter 37Edit

For this thing to be with that, and for one thing to be truly predicated of another, must be assumed in as many ways as the categories are divided; the latter must also be taken either in a certain respect, or simply, moreover either as simple or connected, in a similar manner also with regard to the non-inesse; these however must be better considered and defined.

Chapter 38Edit

Whatever is reiterated in propositions must be annexed to the major and not to the middle term; I mean for instance, if there should be a syllogism, that there is a science of justice "because it is good," the expression "because it is good," or "in that it is good," must be joined to the major. For let A be "science, that it is good;" B, "good;" and C, "justice;" A then is truly predicated of B, since of good there is science that it is good: but B is also true of C; for justice is what is good, thus therefore the solution is made. But if, "that it is good" be added to B, it will not be true; for A will indeed be truly predicated of B, but it will not be true that B is predicated of C, since to predicate of justice, good that it is good, is false, and not intelligible. So also it may be shown that the healthy is an object of science in that it is good, or that hircocervus is an object of opinion, quoad its nonentity, or that man is corruptible, so far as he is sensible, for in all super-predications, we must annex the repetition to the (major) term.

The position of the terms is nevertheless not the same when a thing is syllogistically inferred simply, and when this particular thing, or in a certain respect, or in a certain way. For instance, I mean, as when good is shown to be an object of science, and when it is shown to be so because it is good; but if it is shown to be an object of science simply, we must take "being" as the middle term; if (it is proved that it may be scientifically known) to be good, a certain being (must be taken as the middle). For let A be "science, that it is a certain being," B "a certain being," and C "good;" to predicate then A of B is true, for there is science of a certain being, that it is a certain being; but B is also predicated of C, because C is a certain being; therefore A will be predicated of C, hence there will be science of good that it is good, for the expression "a certain being" is the sign of peculiar or proper essence. If, on the other hand, "being" is set as the middle, and being simply and not a certain being is added to the extreme, there will not be a syllogism that there is a science of good, that it is good, but that it is being: for example, let A be science that it is being; B, being; and C, good. In such syllogisms then as are from a part, we must clearly take the terms after this manner.

Chapter 39Edit

We must also exchange those which have the same import; nouns for nouns, and sentences for sentences, and a noun and a sentence, and always take the noun for the sentence, for thus the exposition of the terms will be easier. For example, if there is no difference in saying that what is supposed is not the genus of what is opined, or that what is opined is not anything which may be supposed, (for the signification is the same,) instead of the sentence already expressed we must take what may be supposed and what may be opined, as terms.

Chapter 40Edit

Since however it is not the same, for pleasure to be good, and for pleasure to be the good, we must not set the terms alike; but if there is a syllogism that pleasure is the good, the good (must be taken as a term) if that it is good, good (must be taken), and so of the rest.

Chapter 41Edit

It is neither in fact nor in word the same thing to assert that A is present with every individual with which B is present, and to say that A is present with every individual of what B is present with, since there is nothing to prevent B from being with C, yet not with every C. For instance, let B be beautiful, but C white, if then beautiful is with something white, it is true to say that beauty is present with what is white, yet not perhaps with every thing white. If then A is with B, but not with every thing of which B is predicated, neither if B is present with every C, nor if it is alone present, it is necessary that A should not only not be present with every C, but that it should not be present (at all), but if that of which B is truly predicated, with every individual of this A is present, it will happen that A will be predicated of every individual of which B is predicated of every individual. But if A is predicated of that of which B is universally predicated, there is nothing to prevent B from being present with C with not every or with no individual of which A is present, therefore in (three terms it is evident that) the assertion that A is predicated of every individual of which B is predicated, signifies that of whatever B is predicated of all these A is predicated also, and if B is predicated of every, A will also thus be predicated, but if it is not predicated of every individual it is not necessary that A should be predicated of every individual.

Still we need not imagine that any absurdity will occur from this exposition, for we do not use the expression that this is a particular definite thing, but as a geometrician says that this is a foot in length, is a straight line, and is without breadth though it is not so, he does not however so use them, as if he inferred from these. In a word, that which is not as a whole to a part, and something else in reference to this as a part to a whole, from nothing of these can a demonstrator demonstrate, wherefore neither is there a syllogism, but we use exposition as we do sense when we address a learner, since we do not (use it) so as if it were impossible to be demonstrated without these, as (we use propositions) from which a syllogism is constructed.

Chapter 42Edit

Let us not forget that all conclusions in the same syllogism are not produced by one figure, but one through this figure, and another through that, so that clearly we must make the resolutions in the same manner, but since not every problem is proved in every figure, but arranged in each, it is evident from the conclusion in what figure the inquiry must be made.

Chapter 43Edit

With regard, however, to arguments against definition, and by which a particular thing in the definition is attacked, that term must be laid down which is attacked, and not the whole definition, for it will result that we shall be less disturbed by prolixity, e.g. if we are to show that water is humid potable, we must place potable and water as terms.

Chapter 44Edit

We must not endeavour, moreover, to reduce hypothetical syllogisms, for we cannot reduce them, from the things laid down, since they are not proved syllogistically, but are all of them admitted by consent. Thus if a man supposing that except there is one certain power of contraries, there will neither exist one science of them, it should afterwards be dialectically proved that there is not one power of contraries; for instance, of the wholesome and or the unwholesome, for the same thing will be wholesome and unwholesome at the same time—here it will be shown that there is not one power of all contraries, but that is not a science, has not been shown. We must yet acknowledge that there is, not however by syllogism, but by hypothesis, wherefore we cannot reduce this, but that, we may, viz. that there is not one power, for this perhaps was a syllogism, but that an hypothesis. The same thing happens in the case of syllogisms, which infer a consequence per impossibile, since neither can we analyze these, though we may a deduction to the impossible, (for it is demonstrated by syllogism,) but the other we cannot, for it is concluded from hypothesis. They differ nevertheless from the before-named, because we must in them indeed have admitted some thing previously, if we are about to consent, as if, for example, one power of contraries should have been shown, and that there was the same science of them, now here they admit, what they had not allowed previously on account of the evident falsity, as if the diameter of a square having been admitted commensurable with the side, odd things should be equal to even.

Many others also are concluded from hypothesis, which it is requisite to consider, and clearly explain; what then are the differences of these, and in how many ways an hypothetical syllogism is produced, we will show hereafter; at present, let only so much be evident to us, that we cannot resolve such syllogisms into figures; for what reason we have shown.

Chapter 45Edit

As many problems as are demonstrated in many figures, if they are proved in one syllogism, may be referred to another, e.g. a negative in the first may be referred to the second, and one in the middle to the first, still not all, but some only. This will appear from the following: if A is with no B, but B with every C, A is with no C, thus the first figure arises; but if the negative is converted, there will be the middle, for B will be with no A, and with every C. In the same manner, if the syllogism be not universal, but particular, as if A is with no B, but B is with a certain C, for the negative being converted there will be the middle figure.

Of syllogisms, however, in the middle figure, the universal will be reduced to the first, but only one of the particular, for let A be with no B, but with every C, then by conversion of the negative there will be the first figure, since B will be with no A, but A with every C. Now if the affirmative be added to B, and the negative to C, we must take C as the first term, since this is with no A, but A is with every B, wherefore C is with no B, neither will B be with any C, for the negative is converted. If however the syllogism be particular, when the negative is added to the major extreme, it will be reduced to the first figure, as if A is with no B, but with a certain C, for by conversion of the negative there will be the first figure, since B is with no A, but A with a certain C. When however the affirmative (is joined to the greater extreme), it will not be resolved, as if A is with every B, but not with every C, for the proposition A B does not admit conversion, nor if it were made would there be a syllogism.

Again, not all in the third figure will be resolvable into the first, but all in the first will be into the third, for let A be with every B, but B with a certain C, since then a particular affirmative is convertible, C will be with a certain B, but A was with every B, so that there is the third figure. Also if the syllogism be negative, there will be the same result, for the particular affirmative is convertible, wherefore A will be with no B, but with a certain C. Of the syllogisms in the last figure, one alone is not resolvable into the first, when the negative is not placed universal, all the rest however are resolved. For let A and B be predicated of every C, C therefore is convertible partially to each extreme, wherefore it is present with a certain B, so that there will be the first figure, if A is with every C, but C with a certain B. And if A is with every C, but B with a certain C, the reasoning is the same, for B reciprocates with C. But if B is with every C, and A with a certain C, B must be taken as the first term, for B is with every C, but C with a certain A, so that B is with a certain A; since however the particular is convertible, A will also be with a certain B. If the syllogism be negative, when the terms are universal, we must assume in like manner, for let B be with every C, but A with no C, wherefore C will be with a certain B, but A with no C, so that C will be the middle term. Likewise, if the negative is universal, but the affirmative particular, for A will be with no C, but C with a certain B; if however the negative be taken as particular, there will not be a resolution, e.g. if B is with every C, but A not with a certain C, for by conversion of the proposition B C, both propositions will be partial.

It is clear then, that in order mutually to convert these figures, the minor premise must be converted in either figure, for this being transposed a transition is effected; of syllogisms in the middle figure, one is resolved, and the other is not resolved into the third, for when the universal is negative there is a resolution, for if A is with no B, but with a certain C, both similarly reciprocate with A, wherefore B is with no A, but C with a certain A, the middle then is A. When however A is with every B, and is not with a certain C, there will not be resolution, since neither proposition after conversion is universal.

Syllogisms also of the third figure may be resolved into the middle, when the negative is universal, as if A is with no C, but B is with some or with every C, for C will be with no A, but will be with a certain B, but if the negative be particular, there will not be a resolution, since a particular negative does not admit conversion.

We see then that the same syllogisms are not resolved in these figures, which were not resolved into the first figures, and that when syllogisms are reduced to the first figure, these only are conducted per impossibile.

How therefore we must reduce syllogisms, and that the figures are mutually resolvable, appears from what has been said.

Chapter 46Edit

There is some difference in the construction or subversion of a problem, whether we suppose the expressions "not to be this particular thing," and "to be not this particular thing," have the same, or different signification, e. g. "not to be white," and "to be not white." Now they do not signify the same thing, neither of the expression "to be white," is the negation "to be not white," but, "not to be white;" and the reason of this is as follows. The expression "he is able to walk," is similar to "he is able not to walk," the expression "it is white" to, "it is not white," and "he knows good," to "he knows what is not good." For these, "he knows good," or "he has a knowledge of good," does not at all differ, neither "he is able to walk," and "he has the power of walking; wherefore also the opposites, "he is not able to walk," and "he has not the power of walking," (do not differ from each other). If then "he has not the power of walking," signifies the same as "he has the power of not walking," these will be at one and the same time present with the same, for the same person is able to walk, and not to walk, and is cognizant of good, and of what is not good, but affirmation and negation being opposites, are not at the same time present with the same thing. Since therefore it is not the same thing "not to know good," and "to know what is not good," neither is it the same thing to be "not good" and "not to be good," since of things having analogy, if the one is different the other also differs. Neither is it the same to be "not equal," and "not to be equal," for to the one, namely, "to that which is not equal," something is subjected, and this is the unequal, but to the other there is nothing subjected, wherefore "not every thing is equal or unequal," but "every thing is equal or not equal." Besides this expression, "it is not white wood," and this, "not is white wood," are not present together at the same time, for if it is "wood not white," it will be wood; but "what is not white wood" is not of necessity "wood," so that it is clear that of "it is good" the negation is not "it is not good." If then of every one thing either the affirmation or negation is true, if there is not negation, it is evident that there will in some way be affirmation, but of every affirmation there is negation, and hence of this the negation is, "it is not not good." They have this order indeed with respect to each other: let to be good be A, not to be good B, to be not good C under B, not to be not good D under A. With every individual then either A or B will be present, and (each) with nothing which is the same and C or D with every individual, and with nothing which is the same, and with whatever C is present, B must necessarily be present with every individual, for if it is true to say that "a thing is not white," it is also true to say that "not it is white," for a thing cannot at one and the same time be white and not white, or be wood not white and be white wood, so that unless there is affirmation, negation will be present.—C however is not always (consequent) to B, for in short, what is not wood will not be white wood, on the contrary, with whatever A is present D also is present with every individual, for either C or D will be present. As however "to be not white" and "to be white," cannot possibly co-subsist, D will be present, for of what is white we may truly say, that it is not not white, yet A is not predicated of every D, for, in short, we can not truly predicate A of what is not wood, namely, to assert that it is white wood, so that D will be true, and A will not be true, namely, that it is white wood. It appears also, that A and C are present with nothing identical, though B and D may be present with the same.

Privatives also subsist similarly to this position with respect to attributes, for let equal be A, not equal B, unequal C, not unequal D. In many things also, with some of which the same thing is present and not with others, the negative may be similarly true, that, "not all things are white," or "that not each thing is white;" but, "that each thing is not white," or, "that all things are not white," is false. So also of this affirmation, "every animal is white," the negation is not, "every animal is not white," for both are false, but this, "not every animal is white." Since however it is clear that "is not white," signifies something different from "not is white," and that one is affirmation and the other negation, it is also clear that there is not the same mode of demonstrating each, for example, "whatever is an animal is not white," or "happens not to be white;" and that we may truly say, "it is not white," for this is "to be not white." Still there is the same mode as to it is true to say it is white or not white, for both are demonstrated constructively through the first figure, since the word "true" is similarly arranged with "is," for of the assertion "it is true to say it is white," the negation is not, "it is true to say it is not white," but "it is not true to say it is white." But if it is true to say, "whatever is a man is a musician, or is not a musician," we must assume that "whatever is an animal is either a musician or is not a musician," and it will be demonstrated, but that "whatever is a man is not a musician," is shown negatively according to the three modes stated.

In short, when A and B are so, as that they cannot be simultaneously in the same thing, but one of them is necessarily present to every individual, and again C and D likewise, but A follows C and does not reciprocate, D will also follow B, and will not reciprocate, and A and D may be with the same thing, but B and C cannot. In the first place then, it appears from this that D is consequent to B, for since one of C D is necessarily present with every individual, but with what B is present C cannot be, because it introduces with itself A, but A and B cannot consist with the same, D is evidently a consequent. Again, since C does not reciprocate with A, but C or D is present with every, it happens that A and D will be with the same thing, but B and C cannot, because A is consequent to C, for an impossibility results, wherefore it appears plain that neither does B reciprocate with D, because it would happen that A is present together with D.

Sometimes also it occurs that we are deceived not such an arrangement of terms, because of our not taking opposites rightly, one of which must necessarily be with every individual, as if A and B cannot be simultaneously with the same, but it is necessary that the one should be with what the other is not, and again C and D in like manner, but A is consequent to every C; for B will happen necessarily to be with that with which D is, which is false. For let the negative of A B which is F be assumed, and again the negative of C D, and let it be H, it is necessary then, that either A or F should be with every individual, since either affirmation or negation must be present. Again also, either C or H, for they are affirmation and negation, and A is by hypothesis present with every thing with which C is, so that H will also be present with whatever F is. Again, since of F B, one is with every individual, and so also one of H D, and H is consequent to F, B will also be consequent to D, for this we know. If then A is consequent to C, B will also follow D, but this is false, since the sequence was the reverse in things so subsisting, for it is not perhaps necessary that either A or F should be with every individual, neither F nor B, for F is not the negative of A, since of "good" the negation is "not good," and "it is not good" is not the same with "it is neither good nor not good." It is the same also of C D, for the assumed negatives are two.