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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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8416
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Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley]
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Full Idea:
Reductionist accounts of causation cannot distinguish laws from accidental uniformities, cannot allow for basic uninstantiated laws, can't explain probabilistic laws, and cannot even demonstrate the existence of laws.
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From:
Michael Tooley (Causality: Reductionism versus Realism [1990], 2)
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A reaction:
I am tempted to say that this is so much the worse for the idea of laws. Extensive regularities only occur for a reason. Probabilities aren't laws. Hypothetical facts will cover uninstantiated laws. Laws are just patterns.
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5492
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How can essences generate the right powers to vary with distance between objects? [Armstrong]
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Full Idea:
In Newtonian physics the distance between two objects determines the attractive forces between them, but then the objects will have to be sensitive to the distance, in order to 'know' what forces to generate; but distance isn't a causal power.
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From:
David M. Armstrong (Two Problems for Essentialism [2001], p.170)
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A reaction:
Ellis replies that he is not troubled, because he believes in essential properties which are separate from their causal roles. Indeed, how else could you explain their causal roles? Still, distance must be mentioned when explaining gravity.
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