After Gödel: Platonism and Rationalism in Mathematics and Logic
Richard Tieszen
Abstract
This book contains 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, with reference to his three philosophical heroes, Plato, Leibniz, and Husserl, and to his engagement with Kant. Close readings of Gödel's texts on foundations are supplemented with materials from the Gödel Nachlass and from Hao Wang's discussions with Gödel. Gödel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed‐up theorems, and indep ... More
This book contains 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, with reference to his three philosophical heroes, Plato, Leibniz, and Husserl, and to his engagement with Kant. Close readings of Gödel's texts on foundations are supplemented with materials from the Gödel Nachlass and from Hao Wang's discussions with Gödel. Gödel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed‐up theorems, and independence proofs are discussed throughout the book. A detailed analysis of his critique of Hilbert and Carnap, and of his subsequent turn to Husserl's transcendental philosophy in 1959, is provided. On this basis, a new type of platonic rationalism that requires rational intuition, called ‘constituted platonism’, is developed and defended. It is shown how constituted platonism addresses the problem of the objectivity of mathematics and of the knowledge of abstract mathematical objects. The implications of the position for the claim that human minds (‘monads’) are machines are considered in some detail. Issues about pragmatic holism and rationalism are discussed in a final chapter.
Keywords:
Gödel,
platonism,
incompleteness,
rationalism,
intuition,
consistency,
Husserl,
undecidability,
monads,
logic
Bibliographic Information
| Print publication date: 2011 |
Print ISBN-13: 9780199606207 |
| Published to Oxford Scholarship Online: May 2011 |
DOI:10.1093/acprof:oso/9780199606207.001.0001 |
