Full Idea
The main philosophical problem with the position of platonism or realism is the epistemic problem: of explaining what perception or intuition consists in; how it is possible that we should accurately detect whatever it is we are realists about.
Gist of Idea
The big problem for platonists is epistemic: how do we perceive, intuit, know or detect mathematical facts?
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], 2.5)
Book Reference
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.36
A Reaction
The best bet, I suppose, is that the mind directly perceives concepts just as eyes perceive the physical (see Idea 8679), but it strikes me as implausible. If we have to come up with a special mental faculty for an area of knowledge, we are in trouble.
Related Idea
Idea 8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]