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The Skolem paradox destroys the incompleteness of ZFC

  1. Jan 25, 2008 #1
    The Australian philosopher colin leslie dean argues that
    The Skolem paradox destroys the incompleteness of ZFC

    Crackpot link removed

    The Skolem pardox shows ZFC is inconsistent
    Undecidability of ZFC is based on the assumption that it is consistent
    therefore
    the presence of the Skolem paradox shows ZFC is not consistent
    so all those proofs that show the incompleteness of ZFC are destroyed
    undermined and complete rubbish
     
    Last edited by a moderator: Jan 25, 2008
  2. jcsd
  3. Jan 25, 2008 #2
    from colin leslie dean

    Crackpot link removed

    The paradox is seen in Zermelo-Fraenkel set theory. One of the earliest results, published by Georg Cantor in 1874, was the existence of uncountable sets, such as the powerset of the natural numbers, the set of real numbers, and the well-known Cantor set. These sets exist in any Zermelo-Fraenkel universe, since their existence follows from the axioms. Using the Löwenheim-Skolem Theorem, we can get a model of set theory which only contains a countable number of objects. However, it must contain the aforementioned uncountable sets, which appears to be a contradiction


    "At present we can do no more than note that we have one more reason here to entertain reservations about set theory and that for the time being no way of rehabilitating this theory is known." – (John von Neumann)

    "Skolem's work implies 'no categorical axiomatisation of set theory (hence geometry, arithmetic [and any other theory with a set-theoretic model]...) seems to exist at all'." – (John von Neumann)

    "Neither have the books yet been closed on the antinomy, nor has agreement on its significance and possible solution yet been reached." – (Abraham Fraenkel)

    "I believed that it was so clear that axiomatization in terms of sets was not a satisfactory ultimate foundation of mathematics that mathematicians would, for the most part, not be very much concerned with it. But in recent times I have seen to my surprise that so many mathematicians think that these axioms of set theory provide the ideal foundation for mathematics; therefore it seemed to me that the time had come for a critique." – (Skolem)
     
    Last edited by a moderator: Jan 25, 2008
  4. Jan 25, 2008 #3
    The Australian "philosopher" colin leslie dean seems to have been extremely drunk when he wrote this paper.
     
  5. Jan 25, 2008 #4

    HallsofIvy

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    I suspect that any one who publishes through something called the "gamahucher press" spends a fair amount of time drunk.

    I also suspect, though not as surely, that "gamel" is "The Australian philosopher colin leslie dean" and runs that press.
     
  6. Jan 25, 2008 #5
    WHAT DOES gamahucher MEAN i wonder
     
  7. Jan 25, 2008 #6

    Hurkyl

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    CLD is a crackpot, and you were banned once already for this.
     
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