Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, Pierre Duhem and Wilfrid Hodges

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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

10480	First-order logic can't discriminate between one infinite cardinal and another [Hodges,W]
	Full Idea: First-order logic is hopeless for discriminating between one infinite cardinal and another.
	From: Wilfrid Hodges (Model Theory [2005], 4)
	A reaction: This seems rather significant, since mathematics largely relies on first-order logic for its metatheory. Personally I'm tempted to Ockham's Razor out all these super-infinities, but mathematicians seem to make use of them.