After Godel: Platonism and Rationalism in Mathematics and Logic

by Richard Tieszen

Overview

Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Godel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Godel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Godel's texts on foundations with materials from Godel's Nachlass and from Hao Wang's discussions with Godel. As well as providing discussions of Godel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed-up theorems, and independence proofs, Tieszen furnishes a detailed analysis of Godel's critique of Hilbert and Carnap, and of his subsequent turn to Husserl's transcendental philosophy in 1959. On this basis, a new type of platonic rationalism that requires rational intuition, called 'constituted platonism', is developed and defended. Tieszen shows how constituted platonism addresses the problem of the objectivity of mathematics and of the knowledge of abstract mathematical objects. Finally, he considers the implications of this position for the claim that human minds ('monads') are machines, and discusses the issues of pragmatic holism and rationalism.

Product Details

ISBN-13:	9780199606207
Publisher:	Oxford University Press
Publication date:	06/20/2011
Edition description:	New Edition
Pages:	258
Product dimensions:	6.40(w) x 9.30(h) x 1.00(d)

About the Author

Richard Tieszen is the author of Phenomenology, Logic, and the Philosophy of Mathematics and Mathematical Intuition, along with numerous papers and reviews on the philosophy of mathematics, philosophy of logic, and phenomenology. He co-edited Between Logic and Intuition: Essays in Honor of Charles Parsons, and is Professor of Philosophy at San Jose State University in California.

Table of Contents

Preface1. Setting the Stage2. Consistency, and the Ascent to Platonic Rationalism3. Godel's Path From Hilbert and Carnap to Husserl4. A New Kind of Platonism5. Consciousness, Reason, and Intentionality6. Constituted Platonism, Reason, and Mathematical Knowledge7. Minds and Machines8. Reason, Science, and EvidenceBibliographyIndex

Editorial Reviews

"Tieszen has long been one of the bridge builders in contemporary philosophy, who is engaged by the philosophical issues and studies them with a broad background and an open mind. There is much to be learned by this, and I am eagerly looking forward to Tieszen's continuation of this interesting and very valuable work." — Philosophia Mathematica

"The book also presents in a very readable way the main sources of Gödel's speculations, in particular, Leibniz' rationalism and Husserl's phenomenology. It has been clear for some years that Gödel did not hold the caricatured platonism that has often been attributed to him. But Tieszen certainly gives the most extensive analysis of Gödel's texts on the question of platonism and, in my eyes, definitely establishes the depth and qualifications of Gödel's reflections upon the question of mathematical objectivity. The time is over when Gödel's name could be attached to the scarecrow of an unmitigated Platonism that one sets aside at the beginning of a paper." —Pierre Cassou-Noguès, History and Philosophy of Logic

From the Publisher