Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly… (More)
Contents 1. Introduction 426 2. G ¨ odel's position in the 1950's—a stalemate 428 2.1. Inconclusive arguments 428 2.2. Realism and rationalism 430 2.3. Epistemological parity 434 2.4. A way out? 437 3. G ¨ odel's turn to Husserl's transcendental idealism 439 3.1. Varieties of idealism 439 3.2. G ¨ odel and German Idealism 440 3.3. The turn to Husserl's… (More)
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Husserl repeatedly has claimed that (1) mathematics without a philosophical foundation is not a science but a mere technique; (2) philosophical considerations may lead to the rejection of parts of mathematical practice; but (3) they cannot lead to mathematical innovations. My thesis is that Husserl's third claim is wrong, by his own standards. To explain… (More)
Dedicated to the memory of Maurice Boffa (1940–2001) §1. The continuity principle. There are two principles that lend Brouwer's mathematics the extra power beyond arithmetic. Both are presented in Brouwer's writings with little or no argument. One, the principle of bar induction, will not concern us here. The other, the continuity principle for numbers,… (More)
David Hilbert opened 'Axiomatic Thought'  with the observation that 'the most important bearers of mathematical thought,' for 'the benefit of mathematics itself have always [.. . ] cultivated the relations to the domains of physics and the [philosophical] theory of knowledge.' We have in L.E.J. Brouwer 3 and Kurt Gödel 4 two of those 'most important… (More)