(June 16, 2020 at 10:37 am)polymath257 Wrote: Even those mathematicians that are Platonists agree that most real numbers are not computable. What Platonists would say is that these real numbers still exist in some Platonic realm.Axiomatically, there must be some other definition or description which would be equivalent to the sequence of digits referred to in the halting problem. It may be the case that we can't get there in the manner described - but there's a there to get to. Yes.
Quote:A Platonist would say that this question has a definite answer.Axiomatically, just as above, yes. Every question has a definite answer, regardless of whether we possess it.
Quote:We can construct two models of set theory: one answers the question yes, the other answers the question no.A platonist may wonder whether set theory is complete, and suggest that a definite answer which might even damage platonism in some way would still remove this objection in it's entirety.
So, whither Platonism?
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