> I would've thought that the incompleteness theorems would be taken as evidence against Platonism, but clearly this didn't happen
I don't think they really are evidence against it. The first incompleteness theorem says (to put it simply) there are truths about the natural numbers you can't prove, and (if we equate proof with knowledge) can't know. I don't know why a Platonist would find that objectionable. I mean, naïve materialism would imply there are lots of facts about the material world we are never going to be able to know (e.g. the particular arrangement of rocks on a lifeless planet in a distant galaxy right now, or as close to right now as relativity permits). If unknowable truths isn't evidence against materialism, why would it be evidence against Platonism?
Really, Gödel's theorems were a much bigger problem for formalism than Platonism. Formalists wanted to identify mathematical truth with provability, and Gödel shattered that dream. Platonists never dreamt the dream, so its destruction didn't discourage them.
I don't think they really are evidence against it. The first incompleteness theorem says (to put it simply) there are truths about the natural numbers you can't prove, and (if we equate proof with knowledge) can't know. I don't know why a Platonist would find that objectionable. I mean, naïve materialism would imply there are lots of facts about the material world we are never going to be able to know (e.g. the particular arrangement of rocks on a lifeless planet in a distant galaxy right now, or as close to right now as relativity permits). If unknowable truths isn't evidence against materialism, why would it be evidence against Platonism?
Really, Gödel's theorems were a much bigger problem for formalism than Platonism. Formalists wanted to identify mathematical truth with provability, and Gödel shattered that dream. Platonists never dreamt the dream, so its destruction didn't discourage them.