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
Source
Kurt Gödel (What is Cantor's Continuum Problem? [1964], p.483), quoted by Michèle Friend - Introducing the Philosophy of Mathematics 2.4
Book Reference
Friend,Michèle: '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.