Chapter II: Book II: Of Knowledge

CHAP. I. OF TWO PRINCIPAL PROCESSES BY WHICH SCIENCE IS
CONSTRUCTED 27

CHAP. II. OF THE EXPLICATION OF CONCEPTIONS 30
_Sect._ I. _The Historical Progress._
_Art._ 1. The Explication of Conceptions,
2. Has taken place historically by discussions.
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_Art._ 3. False Doctrines when exposed appear impossible:
4. But were plausible before
5. Men's Minds gradually cleared.
_Sect._ II. _Use of definitions._
_Art._ 6. Controversies about Definitions.
7. Not arbitrary Definitions.
8. Attention to Facts requisite.
9. Definition is not essential.
10. The omission of Definition not always blameable.
_Sect._ III. _Use of Axioms._
_Art._ 11. Axioms serve to express Ideas.
_Sect._ IV. _Clear and appropriate Ideas._
_Art._ 12. We must see the Axioms clearly.
13. Inappropriate Ideas cannot lead to Truth.
14. The fault is in the Conceptions.
15. Rules cannot teach Discovery;
16. But are not useless.
17. Discussion as well as Facts needed.
_Sect._ V. _Accidental Discoveries._
_Art._ 18. No Scientific Discovery is accidental.
19. Such accidents do not happen to common Men.
20. Examples.
21. So far Explication of Conceptions.

CHAP. III. OF FACTS AS THE MATERIALS OF SCIENCE 50
_Art._ 1. Facts must be true.
2. Facts not separable from Ideas.
3. The Ideas must be distinct.
4. Conceptions of the Intellect only to be admitted.
5. Facts are to be observed with reference to
Space and Time:
6. And also to other Ideas.
7. The Decomposition of Facts.
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_Art._ 8. This step is not sufficient.
9. It introduces Technical Terms,
10. And Classification.
11. The materials of Science.

CHAP. IV. OF THE COLLIGATION OF FACTS 59
_Art._ 1. Facts are colligated by Conceptions.
2. Science begins with common Observation.
3. Facts must be decomposed.
4. What Ideas first give Sciences.
5. Facts must be referred to Ideas.
6. Sagacity needed.
7. Discovery made by Guesses.
8. False Hypotheses preluding to true ones.
9. New Hypotheses not mere modifications of old ones.
10. Hypotheses may have superfluous parts.
11. Hypotheses to be compared with Facts.
12. Secondary Steps.

CHAP. V. OF CERTAIN CHARACTERISTICS OF SCIENTIFIC INDUCTION 70
_Sect._ I. _Invention a part of Induction._
_Art._ 1. Induction the source of Knowledge.
2. Induction involves a New Element.
3. Meaning of Induction.
4. The New Element is soon forgotten.
5. Induction includes a Definition and a Proposition.
_Sect._ II. _Use of Hypotheses._
_Art._ 6. Discoveries made by Guesses,
7. Which must be compared with Facts.
8. Hypotheses are suspected.
9. Hypotheses may be useful though inaccurate.
_Sect._ III. _Tests of Hypotheses._
_Art._ 10. True Hypotheses foretel Phenomena,
11. Even of different kinds.--Consilience of Inductions.
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_Art._ 12. True Theories tend to Simplicity.
13. Connexion of the last Tests.

CHAP. VI. OF THE LOGIC OF INDUCTION 97
_Art._ 1. Steps of Generalization,
2. May be expressed by _Tables_.
3. Which exhibit Inductive Steps;
4. And the Consilience of Inductions;
5. And the tendency to Simplicity;
6. And the names of Discoverers;
7. And the Verifications of Theory;
8. By means of several easy steps.
9. This resembles Book-keeping.
10. The Logic of Induction.
11. Attention at each step required.
12. General Truths are not mere additions of
particulars:
13. But a new view is introduced.
14. Formula of Inductive Logic:
15. May refer to Definition.
16. Formula inadequate.
17. Deductive Connexion of Steps.
18. Relation of Deductive and Inductive Reasoning.
19. The Criterion of Truth.
20. Theory and Fact.
21. Higher and Lower Generalizations.

CHAP. VII. OF LAWS OF PHENOMENA AND OF CAUSES 118
_Art._ 1. Knowledge of Laws of Phenomena.
2. _Formal_ and _Physical_ Sciences.
3. Causes in Astronomy.
4. Different Mechanical Causes in other Sciences.
5. Chemical and Vital Forces as Causes.
6. Difference of these kinds of Force.
7. Difficulty of conceiving new Causes.
8. Men willingly take old Causes.
9. Is the Magnetic Fluid real?
10. Are Causes to be sought? (Comte's Doctrine.)
11. Both Laws and Causes to be studied.
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CHAP. VIII. OF ART AND SCIENCE 129
_Art._ 1. Art precedes Science.
2. Contrast of Art and Science.
3. Instinct and Insight.
4. Difference of Art and Instinct.
5. Does Art involve Science?
6. Science unfolds Principles.
7. Science may improve Art.
8. Arts not classified with Sciences.

CHAP. IX. OF THE CLASSIFICATION OF SCIENCES 136
_Art._ 1. Use and Limits of such Classification.
2. Classification depends on the Ideas.
3. This points out Transitions.
4. The Classification.

INDUCTIVE TABLE OF ASTRONOMY 140

INDUCTIVE TABLE OF OPTICS 140