A Mathematical Prelude to the Philosophy of Mathematics [Paperback]

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, G?del'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.

This book draws readers into the philosophy of mathematics by having them do mathematics. Coverage includes primitive recursive arithmetic, G?del's theorems, the hierarchy of sets, Frege arithmetic and intuitionist sentential logic. Includes 298 exercises.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.

A Mathematical Prelude to the Philosophy of Mathematics is an easy-to-read book with a variety of helpful exercises covering a range of topics in the foundations of mathematics, with chapters focussing on set theory, arithmetic, and intuitionistic logic. & students interested in contemporary issues in the philosophy of mathematics would likely still find these useful, as many of the issues raised by these results remain live in the literature to this day. (Audrey Yap, Philosophia Mathematica, Vol. 24 (2), June, 2016)?

This book provides some mathemalƒ˜