## The Space of Mathematics: Philosophical, Epistemological, and Historical ExplorationsJavier Echeverrķa, Andoni Ibarra, Thomas Mormann Revised versions of papers presented by philosophers, historians of science, and mathematicians at a multidisciplinary symposium on Structures in Mathematical Theories, held at the University of the Basque Country (UPV/EHU) in Donostia/San Sebastian (Basque Country, Spain), September 1990. The 23 papers are organized within four broad areas: structural dimensions; dimensions of applicability; historical dimensions; and global dimensions of knowledge--information, implementation, and intertheoretic relations. No subject index. Annotation copyright by Book News, Inc., Portland, OR |

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### Contents

The Protean Character of Mathematics | 3 |

Categories of Space and of Quantity | 14 |

Structural Analogies Between | 31 |

Reduction and Explanation Science vs Mathematics | 47 |

Reality Truth and Confirmation in Mathematics | 60 |

Tacit Knowledge in Mathematical Theory | 79 |

Structuresimilarity as a Cornerstone of | 91 |

Applying Mathematics and the Indispensibility | 115 |

Mathematics in Philosophy | 192 |

Are There Revolutions in Mathematics? | 205 |

Observations Problems and Conjectures in Number | 230 |

Historical Aspects of the Foundations of Error Theory | 253 |

A Structuralist View of Lagranges Algebraic | 280 |

Constructivism and Objects of Mathematical Theory | 296 |

Turings Oracle From Absolute to Relative | 314 |

Computers and Mathematics The Search | 349 |

Mathematical Structures and Physical Necessity | 132 |

The Role of Mathematics in Physical Science | 141 |

The Status of Settheoretic Axioms | 156 |

Suppes Predicates for Classical | 168 |

Theories and the Flow of Information | 367 |

Towards a Typology of Intertheoretical Relations | 403 |

### Common terms and phrases

Abraham Robinson abstract algebraic analytic applied approach arithmetic arithmetical mean axiomatic axioms calculus category theory Cauchy century complexity concept consider constraints defined definition differential distributive category ematical entities equations errors example exist finite formal formula foundations functor fundamental group Gauss geometry given idea intensive quantities interpretation intuitive knowledge Lagrange Lakatos language Leibniz linear logic manifold math mathematical objects mathematical theory mathematicians means mechanics method natural numbers Newton nonstandard analysis notion Number Theory observations ontological order theories partial recursive functional particular philosophy of mathematics philosophy of science physical theory possible predicates prime number principle problem procedure PROLOG proof pure question recursion theory recursive function reduction relation representation revolution scientific sense set theory set-theoretic space species of structures Suppes symbolic constructs theorem theory elements theory nets tion Turing variable