## Introduction to Mathematical Philosophy |

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### Contents

THE SERIES OF NATURAL NUMBERS I | 1 |

DEFINITION OF NUMBER II | 7 |

FINITUDE AND MATHEMATICAL INDUCTION | 20 |

16 other sections not shown

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### Common terms and phrases

a-functions aliorelative argument arithmetic assert assume asymmetrical asymmetrical relation author of Waverley axiom of infinity belongs called Cantor cardinal number chapter classes of classes commutative law complex numbers consists converse domain correlation Dedekindian deduction defined example existence fact finite follows formally equivalent fractions function f>x generalised given identical ifix inductive cardinal inductive numbers inference infinite number integers irrational less limit limiting-points logical logical constants mathematical induction means multiplicative axiom namely natural numbers not-p notion null-class number of individuals number of terms object one-many relations one-one relation ordinal Peano's philosophy of mathematics possible posterity premisses primitive ideas primitive propositions Principia Mathematica progression propositional function prove real numbers reflexive relation-numbers sense serial number series of ratios set of terms similar so-and-so Socrates sometimes true square sub-classes successor suppose symbols theory thing tion truth-functions unicorn upper section values variable words