After Godel: Platonism and Rationalism in Mathematics and Logic

Paperback | April 24, 2013

byRichard Tieszen

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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 hisengagement 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 andCarnap, 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 theobjectivity 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.

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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 hisengagement with Kant, and supplements close rea...

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 Philosop...

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Format:PaperbackDimensions:272 pages, 9.21 × 6.14 × 0.07 inPublished:April 24, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199680612

ISBN - 13:9780199680610

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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