Mathematical Prelude to the Philosophy of Mathematics

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, American pragmatism and the philosophy of science. Pollard is the author of Philosophical Introduction to Set Theory (Notre Dame, 1990), co-translator of The Continuum by Herman Weyl (Dover, 1994), co-author of Closure Spaces and Logic (Kluwer, 1996) and translator/editor of Essays on the Foundations of Mathematics by Moritz Pasch (Springer, 2010). His papers have appeared in Analysis, Erkenntnis, Logique et Analyse, The Monist, Notre Dame Journal of Formal Logic, Noûs, Philosophical Studies, Philosophia Mathematica, Synthese and other journals.

"This book provides some mathematical background for undergraduate students of philosophy who want to study philosophy of mathematics. It provides mathematical training using a lot of elementary exercises." (Reinhard Kahle, Mathematical Reviews, January, 2016) "There have been many books on the philosophy of mathematics, but I do not think that many books aim to prepare students properly for the subject, which is what Pollard wants to do. ... For readers like me, who know some basic number theory and analysis, as well as basic logic and computability theory, Pollard's book will be a stimulating and novel experience." (John Stillwell, Studia Logica, Vol. 104, 2016) "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 contains 298 exercises in the mentioned areas supported by explanatory materials. Each chapter ends by solutions of odd-numbered exercises as well as references. ... The book can serve as a supplement to primary texts chosen by instructors." (Roman Murawski, zbMATH, Vol. 1294, 2014)

• 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.