2017-12-24
9783319058160
3319058169
Sciences humaines
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9783319058153
3319058150
Printed edition:
Pollard
Stephen
Stephen Randall
Stephen Randall Pollard
2014
en
A mathematical prelude to the philosophy of mathematics
880689138
880689138
Preface -- Chapter 1: Recursion, Induction -- Chapter 2: Peano Arithmetic, Incompleteness -- Chapter 3: Hereditarily Finite Lists -- Chapter 4: Zermelian Lists -- Chapter 5: The Hierarchy of Sets. Chapter 6: Frege Arithmetic -- Chapter 7: Intuitionist Logic -- Chapter 8. Solutions of Odd-Numbered Exercises -- Index.
This book is based on two premises: one cannot understand philosophy of mathematics without understanding mathematics and one cannot understand mathematics withoutdoing 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 ofmathematics. Topics include primitive recursive arithmetic, Peano arithmetic, GĂ¶del's theorems, interpretability, the hierarchyof sets, Frege arithmetic, and intuitionist sentential logic. The book is intended for readers who understand basic properties of the natural and realnumbers and have some background in formal logic.
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Mathematics--Philosophy