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Philosophy

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  • While I agree with most of your points (+1), I feel compelled to point out that we have no evidence that humans are better theorem-solvers than Turing machines. We have come up with clever ways to solve individual problems (and classes thereof) that would naively be out of reach of a Turing machine, but there is no proof that a Turing machine could not implement the same clever approaches that we use, nor can we demonstrate that we are universal solvers (though it's tempting to assume we are!).
    – Rex Kerr
    Commented Oct 3, 2012 at 21:43
  • @RexKerr There are good reasons to believe that all (present, past and future) human minds together (including the tools they will invent) are better problem solvers than any given Turing machine using sound reasoning, at least with respect to their creativity. They won't use only sound reasoning, and they have the "game theoretic" privilege to always have the last word.
    – Thomas Klimpel
    Commented Oct 20, 2012 at 21:15
  • 1
    @ThomasKlimpel - Waving your hands about creativity is waving your hands. Do you have any theoretical basis for assuming that one cannot compute creativity? Or that various unproven alternatives cannot be explored in depth by an algorithm? (Chess programs already do the latter.) Does having the last word make one's truth-statements any more true?
    – Rex Kerr
    Commented Oct 20, 2012 at 21:39
  • Rex: I do not mean to agree with Lucas or Penrose (I don't), I just wanted to point out that an understanding of their argument requires a fairly deep understanding of logic.
    – Xodarap
    Commented Oct 20, 2012 at 21:42