Comment by msla
2 years ago
If mathematics were the study of real objects, why didn't Platonists realize set theory was ill-founded a long time before Russell did? After all, Plato predates Russell by a few years.
2 years ago
If mathematics were the study of real objects, why didn't Platonists realize set theory was ill-founded a long time before Russell did? After all, Plato predates Russell by a few years.
The same reason it took so long to develop theories of gravity: nobody smart enough spent the time applying the tools needed to come to with it. The tools in this case being logic as the OP described.
So if Platonism doesn't give you any special insight into mathematics, what good is it?
Oh, it does give you special insight, but it doesn't make you infallible. It is easier to reach for something if you feel that it must be out there, and you just haven't got it right yet. That's how most mathematicians feel. Gödel was a Platonist, and I'd say he had really special insights.
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