A Mathematical Prelude to the Philosophy of Mathematics by Stephen PollardA Mathematical Prelude to the Philosophy of Mathematics by Stephen Pollard

A Mathematical Prelude to the Philosophy of Mathematics

byStephen Pollard

Hardcover | May 22, 2014

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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.

Stephen Pollard has been on the faculty of Truman State University since 1985. He received his B.A. from Haverford College in 1979 and his Ph.D. from the University of Texas in 1983. His research and publications deal primarily with logic and the philosophy of mathematics, but his interests also include classical Greek philosophy, Amer...
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Title:A Mathematical Prelude to the Philosophy of MathematicsFormat:HardcoverDimensions:202 pagesPublished:May 22, 2014Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319058150

ISBN - 13:9783319058153

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Table of 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.