Mark van Atten

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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)
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)
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)
David Hilbert opened 'Axiomatic Thought' [15] 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)
I argue that Brouwer's general philosophy cannot account for itself, and, a fortiori, cannot lend justification to mathematical principles derived from it. Thus it cannot ground intuitionism, the job Brouwer had intended it to do. The strategy is to ask whether that philosophy actually allows for the kind of knowledge that such an account of itself would(More)