A Mathematical Prelude to the Philosophy of Mathematics

Softcover Nachdruck of the original 1. Auflage 2014
ISBN: 978-3-319-34833-9
Verlag: Springer International Publishing

Buch, Englisch, 202 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 3343 g

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.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Pollard, Stephen

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik

Inhaltsverzeichnis

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.

Über Autor(innen)

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.