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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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20130
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It is absurd to think you can change your own essence, like a garment [Nietzsche]
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Full Idea:
Man is necessity down to his last fibre, and totally 'unfree', that is if one means by freedom the foolish demand to be able to change one's 'essentia' arbitrarily, like a garment.
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From:
Friedrich Nietzsche (Philosophy in the Tragic Age of the Greeks [1873], p.7), quoted by Brian Leiter - Nietzsche On Morality 2 'Realism'
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A reaction:
This is the big difference between the existentialism of Nietzsche and the more famous Sartrean approach, where the idea of being able to remake your essence is the most exciting and glamorous proposal. I'm with Nietzsche.
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