>
>Day Brown was probably misquoted, but here goes anyway...
>
 DB> On 01-02-98 William Elliot wrote to David Martorana... 
 WE> Nihilism is a philosophic notion of a limit to knowledge.   
 WE> 'Cannot', again another negative implication.  You'd like  
 WE> Godel Incompleteness Theorem from mathematical logic.  He  
 WE> proved that there existed statements such that neither the  
 WE> statement itself nor its negation could ever be proved.   
 WE> That there are statements that can neither be proven nor  
 WE> disproved.  How's that for enforced ignorance. -)  Tho  
 WE> nihilism asserts that human knowledge is incomplete,  
 WE> mathematicians have proven that it is.   
 
 DB> Lemmee see if I got this: 
 DB> A: this statement does not exist. 
 DB> B: Statement A is wrong. 
 
 Godel's Incompleteness Theorem is best summarized by using this classic
 sentence as an example:  "This sentence is false."  
 
 Please note the self-referent in the sentence.  Is the sentence true?
 If it is, then the sentence is false.  If the sentence is false, then
 the sentence is true.  No other sentence in the Universe so succinctly
 portrays the classic Incompleteness Theorem as this, and it was used
 by Godel himself.
 
 Furthermore, Godel's Incompleteness Theorem in no way argues that there
 are _no_ functions which cannot be proved, as you apparently took for
 granted.  Several functions _can_ be proved, but their proof is not
 _complete_, in that there are infinite possible contingencies upon any
 proof.  For example, if we did not exist to formulate a premise or
 an argument, or a conclusion...?  Therefore, something _apart_ from
 the equation must provide a context, thus making it impossible to 
 _complete_ a function without an external contextual predesignator.
 And you can't do that with "This sentence is false", because no matter
 what, there is no complete contextual basis for proving the sentence
 one way or the other.  Thus, all functions, alone, are incomplete and
 cannot prove themselves to be either true or false.  This entire 
 theorem is used to discount circular reasoning as well, not as 
 _impossible_, but as being _incomplete_.  There is a difference, and
 it would do well for us to take note of that difference.  Godel did
 not set out to discount proving anything, rather he demonstrated that
 to prove anything, there must be _more_ than simply the equation itself
 to prove it.  The equation is always _imcomplete_ for one of several
 reasons: one being there must be a "prover" - some entity outside of 
 the equation itself to evaluate the equation, or else there is no
 equation at all.  Or, put another way, there must be some contextual 
 designator external to the equation to complete any function.  Therefore,
 for _any_ function (F), (F) cannot prove itself.  That is the first of
 the three premises of Godel's Incompleteness Theorem.  
 
 WE> Recent focus has been on problems which, tho theoretically  
 WE> solvable, cannot actually be done even with supercomputers.  
 WE>  They haven't actually proved the existence of such, but it  
 WE> has been proven that the whole bunch of such problems are  
 WE> equivalent in the sense that if one is actually solvable,  
 WE> they all are. 
 
 DB> And, if they all are? 
 
 They all _are_.  But who is the evaluator?  Who will be the contextual
 designator external to every equation possible?  Not us puny humans, 
 I bet.
 
... I do what my Rice Krispies tell me to do.
--- GEcho 1.11++TAG 2.7c
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