Organon (Owen)/The Posterior Analytics/Book 1

Chap. 1. Upon the Nature of Demonstration.
 * 1.1. All dianœtic discipline is produced from previous knowledge, possessed in a two-fold respect. (Cf. Mag. Moral. lib. i. 18, and Eth. Eud. lib. v. c. 1, 2, 3)
 * 1.2. What we know universally and generally we may not know singly, although not in the same manner.

Chap. 2. Of Knowledge, and Demonstration, and its Elements.
 * 2.1. Scientific knowledge is possessed, when we know the necessary connexion between a thing and its cause. Definition of Demonstration. (Vide Ethics, vi. 3, 4.)
 * 2.2. Specified elements of true demonstrative science.
 * 2.2.1. True.
 * 2.2.2. First and indemonstrable.
 * 2.2.3. Causes of the conclusion.
 * 2.2.4. Prior and more known, in a two-fold respect.
 * 2.2.5. Immediate.
 * 2.3. Distinction of proposition.
 * 2.4. Definition of thesis, considered by Pacius and Waits as synonymous with.
 * 2.5. Of axiom.
 * 2.6. Of hypothesis.
 * 2.7. The necessity of knowing principles and their opposites, in order to possess science by demonstration.

Chap. 3. Refutation of certain opinions as to Science and Demonstration.
 * 3.1. Refutation of those who deny the existence of science.
 * 3.2. Also of those who declare all things capable of demonstration.
 * 3.3. We cannot demonstrate in a circle things which do not reciprocate.
 * 3.4. Example.

Chap. 4. Upon the terms "every," "per se," and "universal."
 * 4.1. Definition of demonstration.
 * 4.2. Of predication "de omni.".
 * 4.3. Of "’," "per se."
 * 4.4. Of accidents. . (Cf. Phys. lib. ii, et Metap. lib. v.)
 * 4.5. "Per se," recapitulation.
 * 4.6. What is a contrary.
 * 4.7., "quatenus ipsum," and , explained.

Chap. 5. Of Errors about the primary Universal.
 * 5.1. Sources of error in effecting universal demonstration. Example.

Chap. 6. Demonstration consists of Principles per se; and of a necessary Medium.
 * 6.1. Recapitulation; true demonstration only from necessary propositions.
 * 6.2. Proof of this.
 * 6.2.1. Reply to objection.
 * 6.3. If the conclusion be necessary, the premises need not be so, but when the latter are so the conclusion must be necessary.
 * 6.4. The non-necessary, not to be neglected in disputation.
 * 6.5. Necessity of the minor and major propositions being "per se."

Chap. 7. That we may not demonstrate by passing from one Genus to another.
 * 7.1. Three things in demonstration, viz. a demonstrated conclusion, axioms, and the subject genus.
 * 7.2. That the extremes and media must be of the same genus.

Chap. 8. Things which are subject to Change are incapable of Demonstration per se.
 * 8.1. That there is no demonstration nor definition "per se" of mutable natures, because of the universal being non-existent.

Chap. 9. That the Demonstration of a thing ought to proceed from its own appropriate Principles: these last indemonstrable.
 * 9.1. That true demonstration only results from principles appropriate to the subject of demonstration: the terms must either be homogeneous, or from two genera, of which one is contained in the other.
 * 9.2. That the appropriate principles of each thing are themselves incapable of demonstration. What is the especial science.
 * 9.3. Difficulty of deciding whether a thing is really known.

Chap. 10. Of the Definition and Division of Principles.
 * 10.1. Definition of principles, their existence to be assumed.  Example.
 * 10.2. What are peculiar to each science, and what common.
 * 10.3. All demonstration conversant with three things, of which we sometimes may neglect two.
 * 10.4. Of the difference between, , and.
 * 10.5. That definition is not hypothesis.

Chap. 11. Of certain Common Principles of all Sciences.
 * 11.1. Demonstration may exist without, but not without an universal conception.
 * 11.2. Of the use of what is called the principle of contradiction in demonstration.
 * 11.3. Of the common principles of the several sciences.

Chap. 12. Of Syllogistic Interrogation.
 * 12.1. Method of deciding what proposition belongs to each science.
 * 12.2. Of discovering the science to which each false syllogism appertains.
 * 12.3. When an objection is not to be made.
 * 12.4. Instance of a syllogistic argument, by employing a syllogism with both prop. affirm. in the 2nd figure.
 * 12.5. Mathematical demonstrations rarely prove the same, by many media.

Chap. 13. The difference between Science, "that" a thing is, and "why" it is.
 * 13.1. A two-fold difference if the syllogism be not through things immediate: next, if it be, but not through cause, in the same science.
 * 13.2. Where the media do not reciprocate the is demonstrated, also where the middle is externally placed.
 * 13.3. Another difference between a syllogism of the and the, in respect of each belonging to a different science.
 * 13.4. The knowledge of the belongs to the perceptive, of the  to the mathematical arguer.

Chap. 14. The first Figure most suitable to Science.
 * 14.1. Mathematical demonstrations effected through this figure.
 * 14.2. Also the syllogism of the . Cf book 2nd.
 * 14.3. Also the science of.
 * 14.4. The other figures condensed by this one.

Chap. 15. Of immediate negative Propositions.
 * 15.1. That one thing may possibly not be individually present with another. Examples.

Chap. 16. Of Ignorance, according to corrupt position of the Terms, where there are no Media.
 * 16.1. Definition of, and its kinds.
 * 16.2. Examples of affirmative deception.
 * 16.3. Negative deception instanced in the first and middle figures.
 * [16.3.1. First fig.]
 * 16.3.2. Middle fig.

Chap. 17. Continuation of the same with Media.
 * 17.1. Syllogism of the false produced in mediates, when the major is false.
 * 17.2. Case of both propositions being false.
 * 17.3. Both prop. cannot be wholly false in the middle figure, when deception is produced.
 * 17.4. Affirmative deception.

Chap. 18. Of the Dependence of Universals upon Induction, and of the latter upon Sense.
 * 18.1. Universals from which demonstration proceeds, depend upon induction, the latter upon sense. (Cf. Eth, b. vi. ch. 3; Rhet. b. i. ch. 2, and b. ii. ch. 23.

Chap. 19. Of the Principles of Demonstration, whether they are Finite or Infinite.
 * 19.1. By those who syllogize it is to be considered whether the syllogisms arise from propositions especially probable.
 * 19.2. An inquiry whether a stated series of terms proceeds to infinity.
 * 19.3. The same as to negatives.
 * 19.4. The doubt does not exist in the case of reciprocals.

Chap. 20. Of Finite Media.
 * 20.1. Media not infinite where the predications stop—Explanation and example.

Chap. 21. It is shown that there are no Infinite Media in Negative Demonstration.
 * 21.1. That there is not an infinity of media in negative demonstration, proved in the several figures.

Chap. 22. That there are no Infinite Media in Affirmative Demonstration.
 * 22.1. Of predications, as to what a thing is, there cannot be infinity—a difference of predication pointed out.
 * 22.2. True predications either define what the subject is, or are accidents.
 * 22.3. In either case there cannot be an infinite series shown from the nature of category.
 * 22.4. Hypothesis that a mediate proposition may be proved.
 * 22.5.1. If there is an infinity of predication, demonstration cannot exist.
 * 22.5.2. The same proved analytically from the nature of those things which are predicated ’.
 * 22.6. That there is not infinity of media.

Chap. 23. Certain Corollaries
 * 23.1. Case where no common ground of inherency subsists.
 * 23.2. Cases of propositional demonstration, when a certain medium is granted.
 * 23.3. What position the connecting term should occupy in an affirmative and negative proposition.

Chap. 24. The superiority of Universal to Particular Demonstration proved.
 * 24.1. The question stated.
 * 24.2. Reasons why particular demonstration may appear eligible.
 * 24.3. Reply to the above.
 * 23.4.3. Universal alone is cognizant of cause.
 * 24.4. It is true "non per aliud," but "per se."
 * 24.5. Universals tend to the simple and finite hence are more scientific.
 * 24.6. They come closer in demonstration to the principle.
 * 24.7. The universal is above all superior, in that it comprehends the particular, and is more intellectual.

Chap. 25. The Superiority of Affirmative to Negative Demonstration proved.
 * 25.1. That the demonstration which is through fewer postulates, etc., is, "cæteris paribus," the better—proved by example, and applied to affirmatives.
 * 25.2. The negative requires the affirmative, but the latter does not need the former.
 * 25.3. Affirmative comes nearer than negative to the nature of a principle.

Chap. 26. The Superiority of the same to Demonstration ad impossible proved.
 * 26.1. The difference proved by example, between direct demonstration and that which leads "ad absurdum."
 * 26.2. Scale of demonstrative superiority.

Chap. 27. Upon the Nature of more Accurate Science.
 * 27.1. That one science is more subtle and accurate than another.

Chap. 28. What constitutes one, and what different Sciences.
 * 28.1. Whatever things are demonstrated from principles of a common genus, these constitute one science. Nature of diverse sciences.

Chap. 29. That there may be several Demonstrations of the same thing.
 * 29.1. The same thing demonstrable in many modes, both when the middles are taken from the same, or from a different genus.

Chap. 30. That there is no Science of the Fortuitous.
 * 30.1. This class does not come under the proper subjects of demonstration.

Chap. 31. That we do not possess Scientific Knowledge through Sensation.
 * 31.1. The perception of the senses is not science.
 * 31.2. Though there are certain things unknown, from the deficiency of sensible perception.

Chap. 32. On the Difference of Priniciples according to the Diversity of Syllogisms.
 * 32.1. The impossibility of principles of all syllogisms being identical, proved.
 * 32.2. Reply to objection founded upon mistaken identity.
 * 32.3. Principles two-fold,  and.

Chap. 33. Upon the Difference between Science and Opinion.
 * 33.1. Science is universal, and subsists through things necessary: intellect the principle of science.
 * 33.2. Opinion conversant with the non-necessary.
 * 33.3. Solution of an inquiry why in certain cases opinion may not be science.
 * 33.4. We cannot, at one and the same time, know, and opine.

Chap. 34. Of Sagacity.
 * 34.1. Definition of sagacity, : instances.

