ence

Causes, Historical Causation, Catastrophe and Uniformity, First Cause.

The controversies to which the exact fixation of these Ideas and their properties have given occasion form a large and essential part of the History of Science: but they also form an important part of the Philosophy of Science, for no Philosophy of Sci

can be complete which does not solve the difficulties, antitheses, and paradoxes on which such controversies have turned. I have given a survey of such controversies, generally carried from their earliest origin to their latest aspect; and have stated what appeared to me the best solution of each problem. This has necessarily involved me in much thorny metaphysics; but such metaphysics is a necessary part of the progress of Science. The human mind deriving its knowledge of Truth from the observation of nature, cannot evade the task of determining at every step how Truth is consistent with itself. This is the Metaphysics of Progressive Knowledge, and this is the matter of this present History.

Of the remaining part of what was formerly published as the Philosophy of the Inductive Sciences, an additional part, described in the Introduction to the present work, will shortly be published.

TRINITY LODGE,

May 24, 1858.

ERRATUM. P. 157, 1. us from top, for sciences read science.

CHAP. I. OF THE FUNDAMENTAL ANTITHESIS OF Philo-

SOPHY

23

Sect. 1. Thoughts and Things

2. Necessary and Experiential Truths

3. Deduction and Induction

4. Theories and Facts

5. Ideas and Sensations

6. Reflexion and Sensation

7. Subjective and Objective

8. Matter and Form

9. Man the Interpreter of Nature

1ο. The Fundamental Antithesis is inseparable

25

27

29

30

33

35

PAGE

54

CHAP. II. OF TECHNICAL TERMS

Art. 1. Examples.

Use of Terms.

2.

57

2.

CHAP. III. OF NECESSARY TRUTHS

Art. 1.

The two Elements of Knowledge,

Shown by necessary Truths.

3. Examples of necessary Truths in numbers.

The opposite cannot be distinctly conceived.

5. Other Examples.

6. Universal Truths.

4.

65

CHAP. IV. OF EXPERIENCE .

Art. 1. Experience cannot prove necessary Truths,

2. Except when aided by Ideas.

2.

CHAP. V. OF THE GROUNDS OF NECESSARY TRUTHS

Art. 1.

These Grounds are Fundamental Ideas.

These are to be reviewed.

3. Definitions and Axioms.

4. Syllogism,

5. Produces no new Truths.

6. Axioms needed.
7. Axioms depend on Ideas :
8. So do Definitions.
9. Idea not completely expressed.

CHAP. VI. THE FUNDAMENTAL IDEAS ARE NOT DERIVED

FROM EXPERIENCE

76

Art. 1.

No connexion observed.

Faculties implied in observation.
3. We are to examine our Faculties.

2.

1

81

CHAP. VII. OF THE PHILOSOPHY OF THE SCIENCES

Sciences arranged according to Ideas.

BOOK II.

THE PHILOSOPHY OF THE PURE SCIENCES.

PAG3

88

2.

91

CHAP. I. OF THE PURE SCIENCES

Art. 1. Geometry, Arithmetic, Algebra,

Are not Inductive Sciences :

3. Are Mathematical Sciences.

4. Mixed Mathematics.

5. Space, Time, Number.

CHAP. II. OF THE IDEA OF SPACE

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.

a

.

98

2.

CHAP. IV. OF THE DEFINITIONS AND AXIOMS WHICH

RELATE TO SPACE

Art. 1. Geometry.

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

How is Geometry hypothetical ?
What was Stewart's view?

• 107

Art. 1.

2.

PAGE

Art. l.

IO.

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
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.

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

Time an Idea not derived from Experience.

Time is a Form of Experience.

3. Number.

4. Is Timne derived from Motion ?
CHAP. VIII. OF SOME PECULIARITIES IN THE IDEA OF
TIME

134
Time is not an Abstract Notion.

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.

Art. I.

2.

.

Art. 1.

2.