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After Gödel
Richard L. Tieszen
其他書名
Platonism and Rationalism in Mathematics and Logic
出版Oxford University Press, 2011-05-05
主題Biography & Autobiography / Science & TechnologyMathematics / History & PhilosophyMathematics / LogicPhilosophy / GeneralPhilosophy / History & Surveys / GeneralPhilosophy / LogicPhilosophy / Metaphysics
ISBN019960620X9780199606207
URLhttp://books.google.com.hk/books?id=dQkWDAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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.