Combining Philosophers

Ideas for Lynch,MP/Glasgow,JM, Wilfrid Hodges and Jackson/Pargetter/Prior

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2 ideas

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.
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
     Full Idea: A 'set' is a mathematically well-behaved class.
     From: Wilfrid Hodges (First-Order Logic [2001], 1.6)