more from Kurt Gdel

Single Idea 8679

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

Full Idea

We have something like perception of the objects of set theory, shown by the axioms forcing themselves on us as being true. I don't see why we should have less confidence in this kind of perception (i.e. mathematical intuition) than in sense perception.

Gist of Idea

We perceive the objects of set theory, just as we perceive with our senses


Kurt Gdel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michle Friend - Introducing the Philosophy of Mathematics 2.4

Book Reference

Friend,Michle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.35

A Reaction

A famous strong expression of realism about the existence of sets. It is remarkable how the ingredients of mathematics spread themselves before the mind like a landscape, inviting journeys - but I think that just shows how minds cope with abstractions.