Comment by Anonymous56 on The Pascal's Wager Fallacy Fallacy · 2009-03-18T02:18:15.000Z · LW · GW

Johnicholas:

I agree with your sentiment, however:

There is a perfectly good description of the real numbers that is not ugly. Namely, the real numbers are a complete Archimedean ordered field.

To actually construct them, I think using (Cauchy) convergent sequences of rational numbers would be much less ugly than using Dedekind cuts.

Also, the Löwenheim–Skolem theorem only applies to first-order logic, not second-order logic. Why are you constraining me to use only first-order logic? You have to explain that first.