After godel: platonism and rationalism in mathematics and lo gic

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Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Godels writings on the philosophy and foundations of mathematics and logic. Tieszen structures the a...
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Richard Tieszen presents an analysis, development, and defense of a number of central ideas in Kurt Godels writings on the philosophy and foundations of mathematics and logic. Tieszen structures the argument around Godels three philosophical heroes - Plato, Leibniz, and Husserl - and his engagement with Kant, and supplements close readings of Godels texts on foundations with materials from Godels Nachlass and from Hao Wangs discussions with Godel. As well as providing discussions of Godels 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 Godels critique of Hilbert and Carnap, and of his subsequent turn to Husserls 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.
Uitgever Oxford University Press
ISBN/EAN 9780199606207
Auteur Tieszen, r.l.
Vakken Wiskunde

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