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Crisis in mathematics

  1. Jan 10, 2008 #1
    Mathematics is meant to be a rigorous deductive discipline based upon
    sound principles

    but
    colin leslie dean showing that godels theorem - what godel did- is invalid
    as it is based on invalid axioms


    throws maths into crisis
    because it now turns out that maths is not based upon sound principles

    and ad hoc principles can be used if they apparently give the right
    result

    take the axiom of reducibility used by godel
    it is ad hoc and unjustifiable as the The Stanford Dictionary of
    Philosophy

    The Stanford Dictionary of Philosophy states that ",


    with this admission and the fact that godel used an ad hoc principle
    the foundations of maths have been destroyed for any one can now use any
    ad hoc principle to prove anything
    take Fermats last theorem
    any one can now create an ad hoc principle which will prove the theorem

    colin leslie dean has thrown mathematics into crisis by shattering its
    logical foundations
    and by showing that truth can be arrived at by any ad hoc avenue
    thus showing the myth of mathematics as a rigorous deductive discipline
    based upon sound principles


    to reiterate Godel does use the axiom of reducibility in his proof of HIS
    incompleteness theorem

    it is is his axiom 1v
    and he uses it in his formular 40



    ramsey says of the axiom

    The Stanford Dictionary of Philosophy states that
     
  2. jcsd
  3. Jan 10, 2008 #2
    Has anyone noticed how these supposed 'arguments' are simply verbal? I'd rather stick with Godel's theorem. To be verbal about it, it provides a pleasing absolution in one's study of mathematics!
     
  4. Jan 11, 2008 #3

    Gib Z

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    Your first few lines tells me that your a crackpot who knows nothing about mathematics. Axioms can not be invalid, by definition.
     
  5. Jan 11, 2008 #4
    you say

    Axioms can not be invalid, by definition.

    but
    euclids 5th axiom is invalid in non-eucluidian geometry
     
  6. Jan 11, 2008 #5

    Gib Z

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    Homework Helper

    Axioms only apply in the field that they define and are the foundations of. Perhaps if Euclid knew of non-euclidean geometry he would have been more specific, to say that his axioms only apply in Euclidean geometry.

    Euclid's axioms are the basis for Euclidean geometry, and within this geometry there are no contradictions. In non-Euclidean geometry, that axiom is not there. We have shown we can still make a mathematically consistent object though, but that doesn't make Euclidean geometry wrong.
     
  7. Jan 11, 2008 #6

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Since the OP is citing "colin leslie dean", I googled that name and found this on "Yahoo Answers" http://answers.yahoo.com/question/index?qid=20070618223613AAouaH9:

    "Who is this colin leslie dean.
    I see his name all over the net for philosophy erotic poetry science religion literary criticism. I see members post here for views on his books. So any one now anything about this colin leslie dean 6 months ago."

    "What we know about Colin Leslie Dean is that he is a self-promoting wanna-be poet from Australia who posts queries here on YA (using fictitious profiles) about his own non-celebrity."

    "Somebody who posts questions all over Y/A in the hope of being noticed. But nobody cares."

    I particularly liked this from sci.logic on Yahoo Groups:

    "Colin Leslie Dean is the only person I know of who actually has proven
    that his OWN words are meaningless.
    Dean says that words are meaningless. Yet for a man who believes words to
    be meaningless he certainly uses a lot of them.
    To make his point that words are meaningless, he commits the fallacy of
    the stolen concept. i.e. he relies on the concept that words have meaning
    to say that they DON'T have meaning.
    Hence we can conclude that Dean's words are in fact meaningless! "

    Makes me suspect that "semel" is colin leslie dean.
     
    Last edited: Jan 11, 2008
  8. Jan 11, 2008 #7
    first you say

    Axioms can not be invalid, by definition.

    when proven wrong
    you now qualify that
    you say now

    Axioms only apply in the field that they define and are the foundations of. Perhaps if Euclid knew of non-euclidean geometry he would have been more specific, to say that his axioms only apply in Euclidean geometry.

    Euclid's axioms are the basis for Euclidean geometry, and within this geometry there are no contradictions.

    now you are backtracking adding qualifications to your iniatal statement

    -goal post changing it is called when proven wrong on a point just change the point
     
  9. Jan 11, 2008 #8
    The Stanford Dictionary of Philosophy states that ", many critics concluded that the axiom of reducibility was simply too ad hoc to be justified philosophically.



    with this admission and the fact that godel used an ad hoc principle
    the foundations of maths have been destroyed
    for
    any one can now use any ad hoc principle to prove anything
    take Fermats last theorem
    any one can now create an ad hoc principle which will prove the theorem

    colin leslie dean has thrown mathematics into crisis by shattering its logical foundations
    and by showing that truth can be arrived at by any ad hoc avenue
    thus showing the myth of mathematics as a
    rigorous deductive discipline based upon sound principles
     
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