Hi(adsbygoogle = window.adsbygoogle || []).push({});

I'm reading some stuff about proof theory and set theory right now and one question comes to my mind.

Set theory is defined in terms of FOL (First Order Logic). Nevertheless, when we "define" first order logic we already have the notion of a "domain of discourse", which is basically the same as a set. We also can't say "everything" is the domain of discourse because then we would need a universal set in set theory which doesn't exist (at least not in ZFC)

But then, we are defining one thing in terms of the other without knowing what the other is.

Isn't that sort of circular reasoning?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The Foundation of mathematics

**Physics Forums | Science Articles, Homework Help, Discussion**