A Mathematical Prelude to the Philosophy of Mathematics

Nonfiction, Science & Nature, Mathematics, Logic, Science, Other Sciences, Philosophy & Social Aspects
Cover of the book A Mathematical Prelude to the Philosophy of Mathematics by Stephen Pollard, Springer International Publishing
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Author: Stephen Pollard ISBN: 9783319058160
Publisher: Springer International Publishing Publication: May 12, 2014
Imprint: Springer Language: English
Author: Stephen Pollard
ISBN: 9783319058160
Publisher: Springer International Publishing
Publication: May 12, 2014
Imprint: Springer
Language: English

This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

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This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics without doing mathematics. It draws readers into philosophy of mathematics by having them do mathematics. It offers 298 exercises, covering philosophically important material, presented in a philosophically informed way. The exercises give readers opportunities to recreate some mathematics that will illuminate important readings in philosophy of mathematics. Topics include primitive recursive arithmetic, Peano arithmetic, Gödel's theorems, interpretability, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and real numbers and have some background in formal logic.

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