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Ideas for 'fragments/reports', 'Prior Analytics' and 'Philosophy of Logic'

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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

18959	Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam]
	Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example) should today be investigated in an 'if-then' spirit.
	From: Hilary Putnam (Philosophy of Logic [1971], Ch.7)
	A reaction: This attitude goes back to Hilbert, but it fits with Quine's view of what is indispensable for science. It is hard to see a reason for the cut-off, just looking at the logic of expanding sets.