Tieszen Richard (EN) — After Gödel: Platonism and Rationalism in Mathematics and Logic

After Gödel: Platonism and Rationalism in Mathematics and Logic краткое содержание

After Gödel: Platonism and Rationalism in Mathematics and Logic - описание и краткое содержание, автор Tieszen Richard (EN), читать бесплатно онлайн на сайте электронной библиотеки Lib-King.Ru.

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