History of Scientific Ideas

BOOK I.. Of Ideas in General.

OF IDEAS IN GENERAL.

CHAP. I. OF THE FUNDAMENTAL ANTITHESIS OF PHILOSOPHY 23

Sect. 1. Thoughts and Things -- 2. Necessary and Experiential Truths 25 3. Deduction and Induction 27 4. Theories and Facts 29 5. Ideas and Sensations 30 6. Reflexion and Sensation 33 7. Subjective and Objective 35 8. Matter and Form 38 9. Man the Interpreter of Nature 41 10. The Fundamental Antithesis is inseparable 43 11. Successive Generalization 49 {viii}

CHAP. II. OF TECHNICAL TERMS 54

Art. 1. Examples. 2. Use of Terms.

CHAP. III. OF NECESSARY TRUTHS 57

Art. 1. The two Elements of Knowledge, 2. Shown by necessary Truths. 3. Examples of necessary Truths in numbers. 4. The opposite cannot be distinctly conceived. 5. Other Examples. 6. Universal Truths.

CHAP. IV. OF EXPERIENCE 65

Art. 1. Experience cannot prove necessary Truths, 2. Except when aided by Ideas.

CHAP. V. OF THE GROUNDS OF NECESSARY TRUTHS 69

Art. 1. These Grounds are Fundamental Ideas. 2. 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. 2. Faculties implied in observation. 3. We are to examine our Faculties.

CHAP. VII. OF THE PHILOSOPHY OF THE SCIENCES 81

Sciences arranged according to Ideas. {ix}

BOOK II.. The Philosophy of the Pure Sciences.

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? {x} 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. {xi}

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. {xii}

BOOK III.. The Philosophy of the Mechanical Sciences.

THE PHILOSOPHY OF THE MECHANICAL SCIENCES.

CHAP. I. OF THE MECHANICAL SCIENCES 171

CHAP. II. OF THE IDEA OF CAUSE 173

Art. 1. Not derived from Observation, 2. As appears by its use. 3. Cause cannot be observed. 4. Is Cause only constant succession? 5. Other reasons.

CHAP. III. MODERN OPINIONS RESPECTING THE IDEA OF CAUSE 178

Art. 1. Hume's Doctrine. 2. Stewart and Brown. 3. Kant. 4. Relation of Kant and Brown. 5. Axioms flow from the Idea. 6. The Idea implies activity in the Mind.

CHAP. IV. OF THE AXIOMS WHICH RELATE TO THE IDEA OF CAUSE 184

Art. 1. Causes are Abstract Conceptions. 2. First Axiom. 3. Second Axiom. 4. Limitation of the Second Axiom. 5. Third Axiom. 6. Extent of the Third Axiom.

CHAP. V. OF THE ORIGIN OF OUR CONCEPTIONS OF FORCE AND MATTER 205

Art. 1. Force. 2. Matter. 3. Solidity. 4. Inertia. 5. Application. {xiii}

CHAP. VI. OF THE ESTABLISHMENT OF THE PRINCIPLES OF STATICS 212

Art. 1. Object of the Chapter. 2. Statics and Dynamics. 3. Equilibrium. 4. Measure of Statical Forces. 5. The Center of Gravity. 6. Oblique Forces. 7. Force acts at any point of its Direction. 8. The Parallelogram of Forces 9. Is a necessary Truth. 10. Center of Gravity descends. 11. Stevinus's Proof. 12. Principle of Virtual Velocities. 13. Fluids press equally. 14. Foundation of this Axiom.

CHAP. VII. OF THE ESTABLISHMENT OF THE PRINCIPLES OF DYNAMICS 235

Art. 1. History. 2. The First Law of Motion. 3. Gravity is a Uniform Force. 4. The Second Law of Motion. 5. The Third Law of Motion. 6. Action and Reaction in Moving Bodies. 7. D'Alembert's Principle. 8. Connexion of Statics and Dynamics. 9. Mechanical Principles grow more evident. 10. Controversy of the Measure of Force.

CHAP. VIII. OF THE PARADOX OF UNIVERSAL PROPOSITIONS OBTAINED FROM EXPERIENCE 263

Art. 1. Experience cannot establish necessary Truths; 2. But can interpret Axioms. 3. Gives us the Matter of Truths. 4. Exemplifies Truths. 5. Cannot shake Axioms. 6. Is this applicable in other cases?

CHAP. IX. OF THE ESTABLISHMENT OF THE LAW OF UNIVERSAL GRAVITATION 272

Art. 1. General course of the History. {xiv} 2. Particulars as to the Law. 3. As to the Gravity of Matter. 4. Universality of the Law. 5. Is Gravity an essential quality? 6. Newton's Rule of Philosophizing. 7. Hypotheses respecting Gravity. 8. Do Bodies act at a distance?

CHAP. X. OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS 279

Art. 1. Nature of the Process 2. Among the Ancients. 3. Kepler, &c. 4. Lord Monboddo, &c. 5. Schelling, &c. 6. Common usage. 7. Effect of Phrases. 8. Contempt of Predecessors. 9. Less detail hereafter. 10. Mechanico-Chemical Sciences. 11. Secondary Mechanical Sciences.

BOOK IV.. The Philosophy of the Secondary Mechanical Sciences.

THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.

CHAP. I. OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED 293

Art. 1. Of Primary and Secondary Qualities. 2. The Idea of Externality. 3. Sensation by a Medium. 4. Process of Perception of Secondary Qualities.

CHAP. II. ON PECULIARITIES IN THE PERCEPTIONS OF THE DIFFERENT SENSES 302

Art. 1. Difference of Senses.

Sect. I. Prerogatives of Sight. Art. 2. Position. 3. Distance. {xv} Sect. II. Prerogatives of Hearing. Art. 4. Musical Intervals. 5. Chords. 6. Rhythm.

Sect. III. The Paradoxes of Vision. Art. 7. First Paradox. 8. Second Paradox. 9. The same for near Objects. 10. Objections answered.

Sect. IV. The Perception of Visible Figures. Art. 11. Brown's Opinion.

CHAP. III. SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE IDEA OF A MEDIUM 322

Art. 1. Introduction. 2. Sound. 3. Light. 4. Heat.

CHAP. IV. OF THE MEASURE OF SECONDARY QUALITIES 333

Sect. I. Scales of Qualities in General. Art. 1. Intensity. 2. Quantity and Quality.

Sect. II. The Musical Scale. Art. 3. Musical Relations. 4. Musical Standard.

Sect. III. Scales of Colour. Art. 5. The Prismatic Scale. 6. Newton's Scale. 7. Scales of Impure Colours. 8. Chromatometer.

Sect. IV. Scales of Light. Art. 9. Photometer. 10. Cyanometer.

Sect. V. Scales of Heat. Art. 11. Thermometers. 12. Their progress. 13. Fixed Points. 14. Concordance of Thermometers. 15. Natural Measure. 16. Law of Cooling. {xvi} 17. Theory of Exchanges. 18. Air Thermometer. 19. Theory of Heat. 20. Other Instruments.

Sect. VI. Scales of other Quantities. Art. 21. Tastes and Smells. 22. Quality of Sounds. 23. Articulate Sounds. 24. Transition.

BOOK V.. Of the Philosophy of the Mechanico-Chemical Sciences.

OF THE PHILOSOPHY OF THE MECHANICO-CHEMICAL SCIENCES.

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