A Mathematical Prelude to the Philosophy of Mathematics
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ISBN-13:
9783319348339
Veröffentl:
2016
Einband:
Paperback
Erscheinungsdatum:
03.09.2016
Seiten:
216
Autor:
Stephen Pollard
Gewicht:
335 g
Format:
235x155x12 mm
Sprache:
Englisch
Beschreibung:
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.
Offers hundreds of exercises that are highly relevant in the teaching of philosophy of mathematics
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.
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