Quote:
Originally Posted by alex_d
oh, boy, not godel...
godel isn't wrong per se, but everyone's interpretation of his proof IS.
First of all, Godel's statement isn't "I am a liar." That's just a plain old self-contradictory statement.
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Nonetheless it is a statement whose truth value cannot be decided. What Godel showed was that in any given axiom system, it is possible to construct statements whose truth value cannot be decided. Given that are physical laws are statements constructed in an axiom system, there will always be questions in that axiom system that we cannot answer, except over infinite time and I'm sorry but your analogy to Zeno's paradox is flawed. Zeno's paradox has a simple solution that comes from quantum mechanics, which imposes a fundamental length/time scale on the Universe, thus you cannot divide distances into infinitely and his paradox does not apply to our reality. There is no such resolution for Godel's Incompleteness theorem.
Rather, a Godel statement is something like "A person who says only truths will never say this sentence." Will a person who says only truths say the aforementioned sentence? If the sentence is true, he might say it. But then the sentence becomes false. If the sentence is false, he won't say it. But then the sentence becomes true.
What happens in the end? Big surprise: in the end the guy doesn't say it. The sentence is true.
However, the truth teller wouldn't have told you that. The truth teller can't even tell you what's true about his own behavior. So much for his wisdom.
And please don't go around thinking that you know what everyone's interpretation of Godel's paradox is.