### Single Idea 10108

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory]

Full Idea

The problem with reducing arithmetic to ZFC is not that this theory is inconsistent (as far as we know it is not), but rather that is not completely general, and for this reason not logical. For example, it asserts the existence of sets.

Clarification

ZFC is Zermelo-Fraenkel set theory with Choice

Gist of Idea

As a reduction of arithmetic, set theory is not fully general, and so not logical

Source

A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)

Book Reference

George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.90

A Reaction

Note that ZFC has not been proved consistent.