The Principles of Mathematics (1903)

Part II. Number
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Part II. Number

Table of Contents

  1. Chapter XI. Definition of Cardinal Numbers

    1. § 107. Plan of Part II
    2. § 108. Mathematical meaning of definition
    3. § 109. Definitions of numbers by abstraction
    4. § 110. Objections to this definition
    5. § 111. Nominal definition of numbers

  2. Chapter XII. Addition and Multiplication

    1. § 112. Only integers to be considered at present
    2. § 113. Definition of arithmetical addition
    3. § 114. Dependence upon the logical addition of classes
    4. § 115. Definition of multiplication
    5. § 116. Connection of addition, multiplication, and exponentiation

  3. Chapter XIII. Finite and Infinite

    1. § 117. Definition of finite and infinite
    2. § 118. Definition of a0
    3. § 119. Definition of finite numbers by mathematical induction

  4. Chapter XIV. Theory of Finite Numbers

    1. § 120. Peano's indefinables and primitive propositions
    2. § 121. Mutual independence of the latter
    3. § 122. Peano really defines progressions, not finite numbers
    4. § 123. Proof of Peano's primitive propositions

  5. Chapter XV. Addition of Terms and Addition of Classes

    1. § 124. Philosophy and mathematics distinguished
    2. § 125. Is there a more fundamental sense of number than that defined above?
    3. § 126. Numbers must be classes
    4. § 127. Numbers apply to classes as many
    5. § 128. One is to be asserted, not of terms, but of unit classes
    6. § 129. Counting not fundamental in arithmetic
    7. § 130. Numerical conjunction and plurality
    8. § 131. Addition of terms generates classes primarily, not numbers
    9. § 132. A term is indefinable, but not the number 1

  6. Chapter XVI. Whole and Part

    1. § 133. Single terms may be either simple or complex
    2. § 134. Whole and part cannot be defined by logical priority
    3. § 135. Three kinds of relation of whole and part distinguished
    4. § 136. Two kinds of wholes distinguished
    5. § 137. A whole is distinct from the numerical conjunctions of its parts
    6. § 138. How far analysis is falsification
    7. § 139. A class as one is an aggregate

  7. Chapter XVII. Infinite Wholes

    1. § 140. Infinite aggregates must be admitted
    2. § 141. Infinite unities, if there are any, are unknown to us
    3. § 142. Are all infinite wholes aggregates of terms?
    4. § 143. Grounds in favour of this view

  8. Chapter XVIII. Ratios and Fractions

    1. § 144. Definition of ratio
    2. § 145. Ratios are one-one relations
    3. § 146. Fractions are concerned with relations of whole and part
    4. § 147. Fractions depend, not upon number, but upon magnitude of divisibility
    5. § 148. Summary of Part II
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