Prior Analytics/Table of Contents
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.
- 2. Of syllogisms per impossibile there is the same method.
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.
- 2. How to assume propositions as to these, in order to inference.
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 καθ’οὑ τὸ Β κατὰ παντὸς τὸ A λεγεσθαι, though not per se identical with καθ’οὕ 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.
Chap. 1. Recapitulation.—Of the Conclusions of certain Syllogisms.
- 1.1. Reference to the previous observations. Universal syllogisms infer many conclusions.
- 1.2. So also do particular affirmative, but not the negative particular.
- 1.3. Difference between universals of the first and those of the second figure.
Chap. 2. On a true Conclusion deduced from false Premises in the first Figure.
- 2.1. Material truth or falsity of propositions, is not shared by the conclusion.
- 2.2. We may infer the true from false premises, but not the false from true premises. Proof—(Vide Aldrich general rules of syllogism.)
- 2.3. Instance of a false proposition.
- 2.4. When the major is wholly false, but the minor is true, the conclusion is false; but when the whole is not false, the conclusion is true.
- 1. Affirmative
- 2. Negative
- 2.5. If the major is true wholly, but the minor wholly false, the conclusion is true.
- 1. Affirmative
- 2. Negative
- 2.6. In particulars with a major false, but a minor true, there may be a true conclusion.
- 1. Affirmative
- 2. Negative
- 2.7. If the major is partly false, the conclusion will be true.
- 1. Affirmative
- 2. Negative
- 3. Major true, minor false.
- 4. Major negative.
- 5. Major partly, minor wholly, false.
- 6. Negative.
- 7. Both false.
- 8. Major negative.
Chap. 3. The same in the middle Figure.
- 3.1. In this figure we may infer the true from premises, either one or both wholly or partially false.
- 1. Universals.
- 2. One wholly false, the other wholly true.
- 3. One partly false.
- 4. Minor or negative.
- 5. Affirmative partly false.
- 6. Both partly false.
- 2. Particulars.
- 1. Major negative.
- 2. Major affirmative.
- 3. Univ. true, part. false.
- 4. Univ. affirm.
- 5. Case of both premises false.
- 1. Universals.
Chap. 4. Similar Observations upon a true Conclusion from false Premises in the third Figure.
- 4.1. The case the same as with the preceding figures.
- 1. Both univ. affirm.
- 2. One negative.
- 3. One partly false.
- 4. Negatives
- 5. One wholly false, the other true.
- 7. Both affirm.
- 4.2. Particulars follow the same rule, i.e. those with one universal and one particular premise.
- 4.3. Also negatives.
- 4.4. If the conclusion is false there must be falsity in one or more of the premises—but this does not hold good vice versâ. Reason of this.
Chap. 5. Of Demonstration in a Circle, in the first Figure.
- 5.1. Definition of this kind of demonstration—and example.
- 5.2. A demonstration of this kind not truly made, except through converted terms, and then by assumption "pro concesso," only.
- 5.3. Case of negatives.
- 5.4. In particulars the major is not demonstrated, but the minor is.
Chap. 6. Of the same in the second Figure.
- 6.1. In universals of the second figure an affirmative proposition is not demonstrated.
- 6.2. But the negative is.
- 6.3. In particulars the particular proposition alone is demonstrated when the universal is affirmative.
Chap. 7. Of the same in the third Figure.
- 7.1. In this figure, when both propositions are universal there is no demonstration in a circle.
- 7.2. There will be demonstration where the minor is universal and the major particular.
- 7.3. When the affirmative is universal there is demonstration of the particular negative.
- 7.4. Not when the negative is universal (exception).
- 7.5. Recapitulation of the preceding chapters.
Chap. 8. Of Conversion of Syllogisms in the first Figure.
- 8.1. Definition of conversion of syllogism
- 8.2. Difference whether this is done contradictorily or contrarily. The distinction between these shown.
- 8.3. In particulars, of the first figure when the conclusion is converted contradictorily both propositions are subverted, if contrarily, neither.
Chap. 9. Of Conversion of Syllogisms in the second Figure.
- 9.1. In universals we cannot infer the contrary to the major premise, but we may the contradictory—the minor dependent upon the assumption of the conclusion.
- 9.2. In particulars, if the contrary of the conclusion is assumed, neither proposition is subverted; if the contradictory, both are.
Chap. 10. Of the same in the third Figure.
- 10.1. In this figure, if the contrary to the conclusion is assumed, neither premise is subverted, but if the contradictory, both.
- 1. Universals.
- 10.2. Particulars the same.
- 10.3. Recapitulation.
Chap. 11. Of Deduction to the Impossible in the first Figure.
- 11.1. How syllogism διὰ τοῦ ἀδυνατοῦ is shown, and its distinction from conversion (ἄντιστοφὴ).
- 11.2. The universal affirm. in the first figure not demonstrable per impossibile.
- 11.3. But the par. affir. and univ. nega. may be demonstrated, when the contradictory of the conclusion is assumed.
- 11.4. Also the par. neg. is demonstrated, but if the sub-contrary to the conclusion is assumed, what was proposed is subverted.
- 11.5. Summary and reason of the above assumption.
Chap. 12. Of the same in the second Figure.
- 12.1. In the second figure A is proved per absurdum, if the contradictory is assumed, not if the contrary.
Chap. 13. Of the same in the third Figure.
- 13.1. In this figure both affirmatives and negatives are demonstrable per absurdum.
- 13.2. Recapitulation.
Chap. 14. Of the difference between the Ostensive, and the Deduction to the Impossible.
- 14.1. Difference between direct demonstration and that per impossible.
- 14.2. What is demonstrated per absurdum in the first figure, is proved in the second, ostensively, if the problem be negative, and in the third figure if it be affirmative.
- 14.3. What is demonstrable per absurdum is so also ostensively and vice versâ.
Chap. 15. Of the Method of concluding from Opposites in the several Figures.
- 15.1. Of the various figures from which a syllogism is deducible from opposite propositions, the latter (κατα τὴν λεξιν) of four kinds, (cf. Herm. 7,) but κατὰ τὴν ἀληθειαν, of three.
- 15.2. No conclusion from opposites if either kind in the first figure.
- 15.3. But from both in the second.
- 15.4. In the third no affirmative is deduced.
- 15.5. Opposition six-fold
- 15.6. No true conclusion deducible from such propositions.
- 15.7. From contradictories a contradiction to the assumption is inferred.
- 15.8. To infer contradiction in the conclusion, we must have contradiction in the premises. (Vide Whately, b. ii. c. 2 and 3.)
Chap. 16. Of the "Petitio Principii," or Begging the Question.
- 16.1. What the "petitio principii" is—ἐν ἀρχῇ αἰτεισθαι.
- 16.2. How this fallacy is effected. See Hill's Logic, p. 331, et seq. Rhet. ii. 24.
- 2. Example given of mathematicians.
- 5. Beg the question.
- 16.3. This fallacy may occur in both the 2nd and 3rd figures, but in the case of an affirmative syllogism by the 3rd and first.
Chap. 17. A Consideration of the Syllogism, in which it is argued, that the false does not happen—"on account of this," παρὰ τοῦτο συμβαίνειν, τὸ ψεῦδος
- 17.1. This happens in a deduction to the impossible, which is contradicted not in ostensive demonstration.
- 17.2. The perfect example of this is when the prop. of which the syllo. consists do not concur.
- 17.3. Another mode.
- 17.4. Necessity of connecting the impossible with the terms assumed from the first.
- 17.5. This not to be employed as if a deduction to the impossible arises from other terms.
Chap. 18. Of false Reasoning.
- 18.1. False conclusion arises from error in the primary propositions.
Chap. 19. Of the Prevention of a Catasyllogism.
- 19.1. Rule to prevent the advancement of a catasyllogism is to watch against the same term being twice admitted in the prop.
- 19.2. Necessity and method of masking our design in argument—two ways of effecting this.
Chap. 20. Of the Elenchus.
- 20.1. The elenchus (redargutio) is a syllogism of contradiction, to produce which there must be a syllogism—though the latter may subsist without the former (Conf. Sop. Elen. 6.)
Chap. 21. Of Deception, as to Supposition—κατὰ τὴν ὑπόληψιν
- 21.1. This kind of deception twofold.
- 21.2. Case of the middles in Barbara and Celarent, not being subaltern.
- 21.3. Distinction between universal and particular knowledge.
- 21.4. Our observation of particulars, derived from our knowledge of universals, a peculiarity noticed. (Met. book vi. 9.) Locke's Ess. vi. 4, v. 5, and vi. 2.
- 21.5. A deception from knowing one prop. and being ignorant of the other.
- 21.6. Scientific knowledge is predicated triply.
- 21.7. From a deception of this kind, a person may imagine that a thing concurs with its contrary.
Chap. 22. On the Conversion of the Extremes in the first Figure.
- 22.1. If the terms connected by a certain middle are converted, the middle must be converted with both.
- 22.3. The mode of converting a negative syllogism, begins from the conclusion, as in Barbara.
- 22.4. Case of election of opposites.
- 22.5. The greater good and less evil preferable to the less good and greater evil.
- 22.6. The desire of the end, the incentive to the pursuit (Eth. b. 1, c. 7.)
Chap. 23. Of Induction.
- 23.1. Not only dialectic and apodeictic syllogisms, but also rhetorical, and every species of demonstration, are through the above-named figures.
- 23.2. Induction is proving the major term of the middle by the minor.
- 23.3. Induction is occurrent in those demonstrations, which are proved without a middle.
Chap. 24. Of Example
- 24.1. παράδειγμα, or example, is proving the major of the middle by a term resembling the minor.
- 24.3. Example subsists as part to part, (ὡς μέρος προς μέρος,) wherein it differs from induction. (Vide note above.)
Chap. 25. Of Abduction.
- 25.1. Ἀπαγωγὴ a syllogism with a major prem. certain, and the minor more credible than the conclusion.
- 25.2. Moreover when the minor is proved by the interposition of few middle terms.
Chap. 26. Of Objection.
- 26.1.Ἐνστασις (Instantia,) a proposition contrary to a proposition, it differs from a proposition in that it may be either καθόλου or ἐπὶ μέρος.
- 26.2. Method of alleging the ἐιστασισ.
- 26.3. Rule for the καθολου ἐνστασις.
- 26.4. And for that ἐν μερει. Vide note.
- 26.5. Objection adduced in the first and third figures alone.
- 26.6. Objections of other kinds to be noticed, vide not. 1, supra; Rhet. ii. 25.
Chap. 27. Of Likelihood, Sign, and Enthymeme.
- 27.1. Εἰκὸς consentaneum argumentum, Buhle and Taylor; "verisimile" and "verisimilitudo," Averrois, Waitz; "probablile," Cicero; "likelihood," Sir W. Hamilton;—is a probable proposition. Σημείον is a demonstrative proposition, either necessary or probable. Enthymeme is a syllogism drawn fron either of these. Cf. Rhet. b. i. c. 2. Soph. Œd. Col. 292 and 1199.
- 27.2. A sign assumed triply, according to the number of figures.
- 27.3. If one prop. be enunciated, there is only a sign.
- 27.4. Syllogism, if it be true, is incontrovertible in the 1st fig., but not so in the last or 2nd fig.
- 27.5. τεκμηριον. (indicium,) a syllogism in the first figure. (Cf. Quintilian, lib. v. c. 9, sec. 8.)
- 27.6. By the example of physiognomy Aristotle shows that signs especially probable belong to the 1st figure.
- 27.7. The first physiognomic hypothesis is that natural passion changes at one time the body and soul. The 2nd, that there is one sign of one passion. The 3rd, that the proper passion of each species of animal may be known.
- 27.8. Whatever is inferred in this respect is collected in the 1st figure.