## Outlines of a Formalist Philosophy of Mathematics |

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### Contents

Chapter I Introduction | 1 |

Chapter II The problem of mathematical truth | 3 |

Chapter III Idealistic views of mathematics | 5 |

Chapter IV Definition and structure of a formal system | 8 |

Chapter V Examples of formal systems | 17 |

Chapter VI Ontological discussion of a formal system | 28 |

Chapter VII Reduction of a formal system | 34 |

Chapter VIII Formal systems and syntax | 38 |

Chapter IX Metatheory | 50 |

Chapter X The formalist definition of mathematics | 56 |

Chapter XI Truth and acceptability | 59 |

Chapter XII Mathematics and logic | 65 |

Appendix | 70 |

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### Common terms and phrases

abstract acceptability assumptions autonymous axiom schemes beweisbar binary operation binary predicate Carnap category of terms Chapter character Church-Rosser Theorem classical analysis completely formalized consider considerations consistency proof constant constructive defined definition of mathematical derived discussion elementary algebra elementary propositions elementary theorems essentially Example 9 expressions fact finite formal system formalist definition Godel green cheese Hilbert idealistic intuitionism intuitionist intuitive evidence involved let us call linguistic mathe mathematical induction mathematical truth mathematicians matics meaning metaphysical metaproposition mode of speech Moreover morphological nature notions noun number of arguments O-expressions O-language O-sentence O-symbols object language occurs free paper parentheses philosophical PHILOSOPHY OF MATHEMATICS point of view polynomials postulates primitive frame primitive ideas priori quasi-quotes recursive definitions reduction reference regard relation replace representation rules of procedure sense sentence specifications subject matter Subst symbols syntactical syntax language system of logic theory tokens unary variables word