A mathematical prelude to the philosophy of mathematics

✍ Scribed by Pollard, Stephen Randall

• Publisher: Springer
• Year: 2014
• Tongue: English
• Leaves: 206
• Edition: 2014
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xi
Recursion, Induction....Pages 1-33
Peano Arithmetic, Incompleteness....Pages 35-53
Hereditarily Finite Lists....Pages 55-83
Zermelian Lists....Pages 85-100
The Hierarchy of Sets....Pages 101-121
Frege Arithmetic....Pages 123-159
Intuitionist Logic....Pages 161-197
Back Matter....Pages 199-202

✦ Subjects

Philosophy of Science; Mathematical Logic and Foundations