数学の基礎の哲学的説明<br>The Search for Certainty : A Philosophical Account of Foundations of Mathematics

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数学の基礎の哲学的説明
The Search for Certainty : A Philosophical Account of Foundations of Mathematics

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  • 製本 Hardcover:ハードカバー版/ページ数 298 p.
  • 言語 ENG
  • 商品コード 9780198752448
  • DDC分類 510.1

基本説明

New in paperback. Hardcover was published in 2001.

Full Description

The nineteenth century saw a movement to make higher mathematics rigorous.
This seemed to be on the brink of success when it was thrown into confusion
by the discovery of the class paradoxes. That initiated a period of intense
research into the foundations of mathematics, and with it the birth of
mathematical logic and a new, sharper debate in the philosophy of
mathematics.
The Search for Certainty examines this foundational endeavour from the
discovery of the paradoxes to the present. Focusing on Russell's logicist
programme and Hilbert's finitist programme, Giaquinto investigates how
successful they were and how successful they could be. These questions are
set in the context of a clear, non-technical exposition and assessment of
the most important discoveries in mathematical logic, above all Gödel's
underivability theorems.
More than six decades after those discoveries, Giaquinto asks what our
present perspective should be on the question of certainty in mathematics.
Taking recent developments into account, he gives reasons for a
surprisingly positive response.

Contents

1. Setting ; 2. The Class Paradoxes and Early Responses ; 3. The Language Paradoxes and Principia Mathematica ; 4. Axiomatic Set Theory and Hilbert's Programme ; 5. Godel's Underivability Theorems ; 6. Aftermath ; Bibliography, Index