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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 Michčle Friend - Introducing the Philosophy of Mathematics 2.4
Book Ref
Friend,Michčle: '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.
| 9942 | Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam] |
| 10868 | The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg] |
| 13517 | If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD] |
| 18062 | Set-theory paradoxes are no worse than sense deception in physics [Gödel] |
| 8679 | We perceive the objects of set theory, just as we perceive with our senses [Gödel] |
| 10271 | Basic mathematics is related to abstract elements of our empirical ideas [Gödel] |