Organon (Owen)/Prior Analytics/Book 1

Chap. 1. Of Proposition, Term, Syllogism, and its Elements.
 * 1.1. Purport of this treatise—the attainment of demonstrative science.
 * 1.2. Definition of proposition.  It is either,
 * 1., universal,
 * 2., particular,
 * 3. or, indefinite.
 * 1.3. Difference between the demonstrative and the.
 * 1.4. The syllogistic proposition.
 * 1.5. The demonstrative.
 * 1.6. Definition of a term—.
 * 1.7. And of a syllogism.
 * 1. The latter either perfect,, or,
 * 2..
 * 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, and of —example of syllogism.
 * 4.3. Definition of, and.
 * 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. . The first figure complete, and comprehends all classes of affirmation and negation.

Chap. 5. Of the second Figure.
 * 5.1., 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. 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 —the various methods.

Chap. 8. Of Syllogisms derived from two necessary Propositions.
 * 8.1. Variety of syllogisms, viz. those —and those, and . 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 given and confirmed. (Vide Metaph. lib. v. 2,) also Interpret. 13.
 * 13.2. Contingent 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, —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. 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,.
 * 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 ’, though not per se identical with ’, 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 privatives and attributes.
 * 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.

