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> Now for the philosophy question: in what sense do those unfindable, unverifiable answers actually exist? I don't really see anything philosophically interest
by acchow 13y ago
> Now for the philosophy question: in what sense do those unfindable, unverifiable answers actually exist?
I don't really see anything philosophically interesting here. Such a feeling probably arises from a misinterpretation of the halting problem here:
> it would let us do interesting things like solve the Halting problem! That is, of course, an impossible thing to do. This proves that there is, in fact, no such procedure.
No such procedure to do it generally.
- btilly 13y agoIf you're familiar with the history of constructivism and the corresponding foundational debates (never truly resolved) of the early 20th century, then it is clear what I am referring to. If you're not familiar with that, Constance Reid's Hilbert! contains a surprisingly readable history of this debate for non-mathematicians, disguised as a biography. For another accessible popular reference, The Mathematical Experience walks through this in a variety of levels of detail (you get out of it what you have the background to get out of it, but it is enjoyable anyways).