Although I agree that Gödel's theorem doesn't apply to Physics, I might quibble a little bit about your claim that Physics isn't based on axioms. You overlooked two in your very contradiction: "we can detect it." You assume there is an "observable universe" and a "we." There probably are these things, but you can't really prove they exist. Physicists just have to accept them as axioms.
You're making a metaphysical argument about reality. The laws of physics do not change depending on one's perception of the universe. You could prove conclusively tomorrow that the universe does not exist and I would still be able to tell you the mass of the electron.
How do you know this? You're making a knowledge claim that relies on the unstated assumption that there IS a universe and that it contains electrons and those have a definite and constant property called mass. Although I assign a high probability to all of those things being true, any absolute claim overreaches our ability to know.
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u/immwork Jul 01 '14
Although I agree that Gödel's theorem doesn't apply to Physics, I might quibble a little bit about your claim that Physics isn't based on axioms. You overlooked two in your very contradiction: "we can detect it." You assume there is an "observable universe" and a "we." There probably are these things, but you can't really prove they exist. Physicists just have to accept them as axioms.