more from Wilfrid Hodges

### Single Idea 10480

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity]

Full Idea

First-order logic is hopeless for discriminating between one infinite cardinal and another.

Gist of Idea

First-order logic can't discriminate between one infinite cardinal and another

Source

Wilfrid Hodges (Model Theory [2005], 4)

Book Reference

'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.11

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.