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A Mathematical Prelude to the Philosophy of Mathematics

Author: Stephen Pollard; SpringerLink (Online service)
Publisher: Cham : Springer International Publishing : Imprint: Springer, 2014.
Edition/Format:   Downloadable article : EnglishView all editions and formats
Publication:Springer eBooks
Summary:
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  Read more...
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Material Type: Internet resource
Document Type: Internet Resource, Article
All Authors / Contributors: Stephen Pollard; SpringerLink (Online service)
ISBN: 9783319058160 3319058169
OCLC Number: 918961779
Description: XI, 202 p. : online resource
Contents: 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.
Responsibility: by Stephen Pollard.

Abstract:

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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