A Mathematical Prelude to the Philosophy of Mathematics

  • Stephen Pollard

Table of contents

  1. Front Matter
    Pages i-xi
  2. Stephen Pollard
    Pages 1-33
  3. Stephen Pollard
    Pages 35-53
  4. Stephen Pollard
    Pages 55-83
  5. Stephen Pollard
    Pages 85-100
  6. Stephen Pollard
    Pages 101-121
  7. Stephen Pollard
    Pages 123-159
  8. Stephen Pollard
    Pages 161-197
  9. Back Matter
    Pages 199-202

About this book

Introduction

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.

Keywords

Frege Arithmetic Gödel Glivenko Theorem Gödel Incompleteness Hereditarily Finite Lists Hierarchy of Sets Intuitionist Connectives Intuitionist Logic Iterative Set Theory Monadic Second Order Logic Peano Arithmetic Peregrin Logic of Inference Primitive Recursive Arithmetic Representability of Recursive Functions Set Theory Axioms Zermelian Lists

Authors and affiliations

  • Stephen Pollard
    • 1
  1. 1.Truman State University Dept. Philosophy & ReligionKirksvilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-05816-0
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Humanities, Social Sciences and Law
  • Print ISBN 978-3-319-05815-3
  • Online ISBN 978-3-319-05816-0
  • About this book