Chapter I: Book II: The Philosophy of the Pure Sciences

CHAP. I. OF THE PURE SCIENCES 88

_Art._ 1. Geometry, Arithmetic, Algebra,
2. Are not Inductive Sciences:
3. Are Mathematical Sciences.
4. Mixed Mathematics.
5. Space, Time, Number.

CHAP. II. OF THE IDEA OF SPACE 91

_Art._ 1. Space is an Idea,
2. Not derived from Experience,
3. As Geometrical Truth shows.
4. Space is a Form of Experience.
5. The phrase not essential.

CHAP. III. OF SOME PECULIARITIES OF THE IDEA OF SPACE 95

_Art._ 1. Space is not an Abstract Notion.
2. Space is infinite.
3. Space is real.
4. Space is a Form of Intuition.
5. Figure.
6. Three Dimensions.

CHAP. IV. OF THE DEFINITIONS AND AXIOMS WHICH RELATE TO SPACE 98

_Art._ 1. Geometry.
2. Definitions.
3. Axioms.
4. Not Hypotheses.
5. Axioms necessary.
6. Straight Lines.
7. Planes.
8. Elementary Geometry.

CHAP. V. OF SOME OBJECTIONS WHICH HAVE BEEN MADE TO THE
DOCTRINES STATED IN THE PREVIOUS CHAPTER 107

_Art._ 1. How is Geometry hypothetical?
2. What was Stewart's view?
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3. 'Legitimate filiations' of Definitions.
4. Is a Definition a complete explanation?
5. Are some Axioms Definitions?
6. Axiom concerning Circles.
7. Can Axioms become truisms?
8. Use of such.

CHAP. VI. OF THE PERCEPTION OF SPACE 117

_Art._ 1. Which Senses apprehend Space?
2. Perception of solid figure.
3. Is an interpretation.
4. May be analysed.
5. Outline.
6. Reversed convexity.
7. Do we perceive Space by Touch?
8. Brown's Opinion.
9. The Muscular Sense.
10. Bell's Opinion.
11. Perception includes Activity.
12. Perception of the Skyey Dome.
13. Reid's Idomenians.
14. Motion of the Eye.
15. Searching Motion.
16. Sensible Spot.
17. Expressions implying Motion.

CHAP. VII. OF THE IDEA OF TIME 131

_Art._ 1. Time an Idea not derived from Experience.
2. Time is a Form of Experience.
3. Number.
4. Is Time derived from Motion?

CHAP. VIII. OF SOME PECULIARITIES IN THE IDEA OF TIME 134

_Art._ 1. Time is not an Abstract Notion.
2. Time is infinite.
3. Time is a Form of Intuition.
4. Time is of one Dimension,
5. And no more.
6. Rhythm.
7. Alternation.
8. Arithmetic.
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CHAP. IX. OF THE AXIOMS WHICH RELATE TO NUMBER 138

_Art._ 1. Grounds of Arithmetic.
2. Intuition.
3. Arithmetical Axioms,
4. Are Conditions of Numerical Reasoning
5. In all Arithmetical Operations.
6. Higher Numbers.

CHAP. X. OF THE PERCEPTION OF TIME AND NUMBER 141

_Art._ 1. Memory.
2. Sense of Successiveness
3. Implies Activity.
4. Number also does so.
5. And apprehension of Rhythm.
Note to Chapter X. 145

CHAP. XI. OF MATHEMATICAL REASONING 147

_Art._ 1. Discursive Reasoning.
2. Technical Terms of Reasoning.
3. Geometrical Analysis and Synthesis.

CHAP. XII. OF THE FOUNDATIONS OF THE HIGHER MATHEMATICS 151

_Art._ 1. The Idea of a Limit.
2. The use of General Symbols.
3. Connexion of Symbols and Analysis.

CHAP. XIII. THE DOCTRINE OF MOTION 156

_Art._ 1. Pure Mechanism.
2. Formal Astronomy.

CHAP. XIV. OF THE APPLICATION OF MATHEMATICS TO THE INDUCTIVE
SCIENCES 159

_Art._ 1. The Ideas of Space and Number are clear from
the first.
2. Their application in Astronomy.
3. Conic Sections, &c.
4. Arabian Numerals.
5. Newton's Lemmas.
6. Tides.
7. Mechanics.
8. Optics.
9. Conclusion.
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