The Principles of Mathematics (1903)

Part III. Quantity
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Part III. Quantity

Table of Contents

  1. Chapter XIX. The Meaning of Magnitude

    1. § 149. Previous views on the relation of number and quantity
    2. § 150. Quantity not fundamental in mathematics
    3. § 151. Meaning of magnitude and quantity
    4. § 152. Three possible theories of equality to be examined
    5. § 153. Equality is not identity of number of parts
    6. § 154. Equality is not an unanalyzable relation of quantities
    7. § 155. Equality is sameness of magnitude
    8. § 156. Every particular magnitude is simple
    9. § 157. The principle of abstraction
    10. § 158. Summary
    11. Note to Chapter XIX.

  2. Chapter XX. The Range of Quantity

    1. § 159. Divisibility does not belong to all quantities
    2. § 160. Distance
    3. § 161. Differential coefficients
    4. § 162. A magnitude is never divisible, but may be a magnitude of divisibility
    5. § 163. Every magnitude is unanalyzable

  3. Chapter XXI. Numbers as Expressing Magnitudes: Measurement

    1. § 164. Definition of measurement
    2. § 165. Possible grounds for holding all magnitudes to be measurable
    3. § 166. Intrinsic measurability
    4. § 167. Of divisibilities
    5. § 168. And of distances
    6. § 169. Measure of distance and measure of stretch
    7. § 170. Distance-theories and stretch-theories of geometry
    8. § 171. Extensive and intensive magnitudes

  4. Chapter XXII. Zero

    1. § 172. Difficulties as to zero
    2. § 173. Meinong's theory
    3. § 174. Zero as minimum
    4. § 175. Zero distance as identity
    5. § 176. Zero as a null segment
    6. § 177. Zero and negation
    7. § 178. Every kind of zero magnitude is in a sense indefinable

  5. Chapter XXIII. Infinity, the Infinitesimal, and Continuity

    1. § 179. Problems of infinity not specially quantitative
    2. § 180. Statement of the problem in regard to quantity
    3. § 181. Three antinomies
    4. § 182. Of which the antitheses depend upon an axiom of finitude
    5. § 183. And the use of mathematical induction
    6. § 184. Which are both to be rejected
    7. § 185. Provisional sense of continuity
    8. § 186. Summary of Part III
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