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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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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15149
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Properties cluster together, either because of intrinsic relations, or because of an underlying process [Boyd, by Chakravartty]
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Full Idea:
Boyd analyses 'sociability' between properties in terms of 'homeostasis', as causal relations between properties that favour clustering, or underlying processes that favour coinstantiation, or both.
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From:
report of Richard Boyd (Homeostasis, Species and Higher Taxa [1999]) by Anjan Chakravarrty - Inessential Aristotle: Powers without Essences 3
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A reaction:
Chakravarty criticises this claim, by Boyd is clearly onto something. If, like me, you think natural kinds are overrated, you have to like his view.
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