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To: snarks_when_bored
Thanks for the ping.

Yourgrau's appears to be the more accurate account of what Gödel was attempting to accomplish with his two great Incompleteness theorems

Would this be it? From the link:

Finally, Gödel's incompleteness theorem… set a permanent limit on our knowledge of the basic truths of mathematics: The complete set of mathematical truths will never be captured by any finite or recursive list of axioms that is fully formal. Thus, no mechanical device, no computer, will ever be able to exhaust the truths of mathematics. It follows immediately, as Gödel was quick to point out, that if we are able somehow to grasp the complete truth in this domain, then we, or our minds, are not machines or computers.

7 posted on 09/19/2005 2:43:19 AM PDT by D-fendr
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To: D-fendr
I find nothing to criticize in that quote from Yourgrau as far as what Gödel accomplished, but I do point out that he ends by saying this: "...if we are able somehow to grasp the complete truth in this domain, then we, or our minds, are not machines or computers." That 'if' is huge. I see nothing that leads me to believe that we're capable of grasping the complete truth in mathematics.
9 posted on 09/19/2005 2:52:30 AM PDT by snarks_when_bored
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