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A mathematical prelude to the philosophy of mathematics

Author: Stephen Pollard
Publisher: Cham : Springer, 2014.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Stephen Pollard
ISBN: 9783319058160 3319058169
OCLC Number: 880689138
Description: 1 online resource (xi, 202 pages)
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: Stephen Pollard.

Abstract:

This book draws readers into the philosophy of mathematics by having them do mathematics. Coverage includes primitive recursive arithmetic, Godel's theorems, the hierarchy of sets, Frege arithmetic  Read more...

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From the book reviews: "The aim of the book is to give students opportunities to recreate some mathematics that will illuminate important readings in the philosophy of mathematics. ... The book Read more...

 
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schema:description"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, Gödel'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."@en
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