8728
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Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer]
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Full Idea:
Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths.
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From:
Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2
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A reaction:
Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time!
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15877
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The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
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Full Idea:
In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
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From:
report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
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A reaction:
I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.
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