Single Idea 9570

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

Full Idea

Field commits himself to a Platonic view of mathematics. The theorems of set theory are held to imply or presuppose the existence of things that don't in fact exist. That is why he believes that these theorems are false.

Gist of Idea

In Field's Platonist view, set theory is false because it asserts existence for non-existent things


report of Hartry Field (Science without Numbers [1980]) by Charles Chihara - A Structural Account of Mathematics 11.1

Book Reference

Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.318

A Reaction

I am sympathetic to Field, but this sounds wrong. A response that looks appealing is that maths is hypothetical ('if-thenism') - the truth is in the logical consequences, not in the ontological presuppositions.