After Godel: Platonism and Rationalism in Mathematics and Logic - Hardcover

Tieszen, Richard

Hardcover

ISBN 10: 019960620X ISBN 13: 9780199606207

Publisher: OUP UK, 2011

Synopsis

Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Gödel's three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Gödel's texts on foundations with materials from Gödel's Nachlass and from Hao Wang's discussions with Gödel. As well as providing discussions of Gödel'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 Gödel'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.

About this title

Review:

"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

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 José State University in California.

About this edition

• Publisher: OUP UK
• Publication date: 2011
• ISBN 10: 019960620X
• ISBN 13: 9780199606207
• Binding: Hardcover
• Number of pages: 258