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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15456
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Extrinsic properties, unlike intrinsics, imply the existence of a separate object [Kim, by Lewis]
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Full Idea:
Kim suggest that 'extrinsic' properties are those that imply 'accompaniment' (coexisting with some wholly distinct contingent object), whereas 'intrinsic' properties are compatible with 'loneliness' (being un-accompanied).
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From:
report of Jaegwon Kim (Psychophysical supervenience [1982], 9th pg) by David Lewis - Extrinsic Properties II
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A reaction:
The aim of Kim and Lewis is to get the ontological commitment down to a minimum - in this case just to objects (and mysterious 'implications'!). I like nominalism, but you can't just deny properties. 'Loneliness' is extrinsic!
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