A Mathematical Prelude to the Philosophy of Mathematics, 2014
Auteur : Pollard Stephen
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, 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.
Offers hundreds of exercises that are highly relevant in the teaching of philosophy of mathematics
Presents the mathematical and philosophical background to those exercises
Supplements primary texts used for philosophy of mathematics courses
Includes supplementary material: sn.pub/extras
Date de parution : 09-2016
Ouvrage de 202 p.
15.5x23.5 cm
Date de parution : 05-2014
Ouvrage de 202 p.
15.5x23.5 cm
Mots-clés :
Frege Arithmetic; Gödel Glivenko Theorem; Gödel Incompleteness; Hereditarily Finite Lists; Hierarchy of Sets; Intuitionist Connectives; Intuitionist Logic; Iterative Set Theory; Monadic Second Order Logic; Peano Arithmetic; Peregrin Logic of Inference; Primitive Recursive Arithmetic; Representability of Recursive Functions; Set Theory Axioms; Zermelian Lists
