http://philmat.oxfordjournals.org Philosophia Mathematica - RSS feed of articles 1744-6406 Philosophia Mathematica 0031-8019 http://philmat.oxfordjournals.org/cgi/content/short/nkq001v1?rss=1 Kurt Gödel made many affirmations of robust realism but also showed serious engagement with the idealist tradition, especially with Leibniz, Kant, and Husserl. The root of this apparently paradoxical attitude is his conviction of the power of reason. The paper explores the question of how Gödel read Kant. His argument that relativity theory supports the idea of the ideality of time is discussed critically, in particular attempting to explain the assertion that science can go beyond the appearances and ‘approach the things’. Leibniz and post-Kantian idealism are discussed more briefly, the latter as documented in the correspondence with Gotthard Günther.

]]> Fri, 29 Jan 2010 08:49:37 PST info:doi/10.1093/philmat/nkq001 Oxford University Press 2010 nkq001 2010-01-29 nkq001v1 Article http://philmat.oxfordjournals.org/cgi/content/short/nkp014v1?rss=1 This paper explores how to explain the applicability of classical mathematics to the physical world in a radically naturalistic and nominalistic philosophy of mathematics. The applicability claim is first formulated as an ordinary scientific assertion about natural regularity in a class of natural phenomena and then turned into a logical problem by some scientific simplification and abstraction. I argue that there are some genuine logical puzzles regarding applicability and no current philosophy of mathematics has resolved these puzzles. Then I introduce a plan for resolving the logical puzzles of applicability.

]]> Wed, 30 Sep 2009 09:14:25 PDT info:doi/10.1093/philmat/nkp014 Oxford University Press 2009-09-30 Article