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Which Godel statements are seen to be true by humans?

  1. Mar 10, 2015 #1
    My questions arose when reading an article about artificial intelligence, and the argument of Penrose that says that humans can see the truthfulness of statements that machines cannot. But it doesn't say what those "Godel sentences" are.

    http://en.wikipedia.org/wiki/Philosophy_of_artificial_intelligence#Lucas.2C_Penrose_and_G.C3.B6del

    "Roger Penrose expanded on this argument in his 1989 book The Emperor's New Mind and his 1994 book Shadows of the Mind. He presents a complex argument, and there are many details that need to be considered carefully. However the essence of it is that

    1. It is impossible for a Turing machine to enumerate all possible Godel sentences. Such a program will always have a Godel sentence derivable from its program which it can never discover
    2. Humans have no problem discovering these sentences and seeing the truth of them"
     
  2. jcsd
  3. Mar 10, 2015 #2

    atyy

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  4. Mar 11, 2015 #3
    Beware of Penrose's arguments: Penrose is an excellent physicist, but not much of a logician. You can find Solomon Feferman's excellent article that points out the logical errors in Penrose's arguments either by googling "Feferman Penrose", or go to math.stanford.edu/~feferman/papers/penrose.pdf . In fact, because Penrose's arguments are nothing more than those of Lucas (which were wrong) with a few smokescreens (pretending to "correct" the errors of Lucas, but not quite doing so), there is the standard term: the Penrose-Lucas fallacy (which you can also google). There are much better sources for reading both about the logical points as well as for the meta-mathematical implications.
     
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