## Elements of IntuitionismThis is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an informal but thorough introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics has been completely revised for this second edition. Brouwer's proof of the Bar Theorem has been reworked, the account of valuation systems simplified, and the treatment of generalized Beth Trees and the completeness of intuitionistic first-order logic rewritten. Readers are assumed to have some knowledge of classical formal logic and a general awareness of the history of intuitionism. From reviews of the first edition: This excellent book can be recommended to the student of mathematics or philosophy wishing to get a comprehensive and reliable introduction to modern intuitionism. Zentralblatt fur Mathematik The relevance of this book extends well beyond the confines of the philosophy of mathematics, right to the centre of debates in the philosophy of language. Philosophical Books ...a valuable and original contribution to the philosophy of mathematics. Journal of Symbolic Logic |

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### Contents

Introductory remarks | 1 |

Elementary intuitionistic mathematics | 22 |

Choice sequences and spreads | 40 |

The formalization of intuitionistic logic | 88 |

The semantics of intuitionistic logic | 119 |

Some further topics | 211 |

Concluding philosophical remarks | 250 |

Bibliography | 311 |

325 | |

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### Common terms and phrases

able appeal applied argument assert assume atomic axiom bars belongs Beth trees choice sequences classical closed completeness conception conclusion condition consider consists constructive contains continuous corresponding course decidable defined definition depends derived determined domain dual effective elements equivalent exists expressed fact finite finite sequences follows formula function give given hence holds hypothesis implies induction inference infinite instance internal interpretation intuitionistic intuitionistic logic intuitive language lattice lawless Lemma logical constants mathematical means natural numbers node notion objects obtain occur operation particular path possible predicate premiss principle proof prove quantifiers realizability reason recognize recursive relation replacing represented respect restriction result rule satisfies schema segment semantics sentence species spread stage statement suppose taken Theorem theory true truth understanding valid variables verified yield