Combining Texts

Ideas for 'Parmenides', 'Mathematics and Indispensibility' and 'Logic as Semiotic: Theory of Signs'

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2 ideas

7. Existence / D. Theories of Reality / 3. Reality

221	Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato]
	Full Idea: The absolute good and the beautiful and all which we conceive to be absolute ideas are unknown to us.
	From: Plato (Parmenides [c.364 BCE], 134c)

7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems

9558	All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
	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.
	From: Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics
	A reaction: This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.