9558
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All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
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Full Idea:
If mathematical statements are part of every competing hypothesis, then no matter which hypothesis comes out best in the light of observations, they will be part of the best hypothesis. They are not tested, but are a background assumption.
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From:
Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics
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A reaction:
This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.
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12742
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A whole is just its parts, but there are no smallest parts, so only minds and perceptions exist [Leibniz]
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Full Idea:
The whole, if it is assumed to be body or matter, is nothing other than all of its parts; but this is absurd, since there aren't any smallest parts. Therefore there really exist only minds and their perceptions.
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From:
Gottfried Leibniz (Calculus Ratiocinator [1679], A6.4.279), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 7
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A reaction:
Leibniz is sometimes labelled as an 'idealist', but this text is unusual in being so explicit, and he was mainly concerned to explain the reality of individual bodies. Monads were his final attempt to do this, not an attempt to escape into pure minds.
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