In Reply to: Re: Nerdier to Nerdiest :-) posted by Nerdier than thou on November 04, 2006 at 21:47:10:
Godel's incompleteness theorem I:
Statement: "God cannot be proven true"
God = G
If G were proven true under the theory's axioms, then the theory would have a theorem, G, which contradicted itself. A similar contradiction would occur if G could be proven false. So we are forced to conclude that G cannot be proven true or false, but is true because of this very fact.
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Godel's incompleteness theorem 2:
Statement: "Thank God I am an atheist" = oxymoron
Godels theorem requires the use of axioms which is another name for an assumption, something you take into the calculation. God or atheist or "I am" = axiom (something you take as true without proof, an assumption) therefore result is oxymoron.
Statement: "Thank God I am an atheist correct in everything, even this false statement"
To prove this is incorrect, you have to prove that it doesn't add up, requiring the use of axioms, the assumption that at least one of the factors is true: God, atheist, correct, everything, false statement.
If atheist correct, no God to thank.
If God exists then atheist incorrect.
If atheist incorrect, then statement is false.
If statement is false, then "this false statement" is correct.
If false statement, then atheist correct.
You can go in an endless loop, even after you change one of the factors: if the atheist is not correct about everything, but only some things, and so on. To me that would be basically a statement being neither provable nor refutable, in some specified deductive system.