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It is a bit of a digression here, but 1+1=2 is a theorem that can be proven from axioms of arithmetic.ebg said:on the other hand....1+1=2 is an axiom....it can't be proven, but is accepted as being true because the probability of the outcome it being 2 is quite high. What is the possibility (not probability) of the sum of 1+1 = 11? QED is not a proof.
This is a different situation than claims made by empirical science, which are based on experimental evidence and observations about how the world works, and are evaluated based on the accuracy and generality of their predictions. A challenge to such a theory will only be taken seriously if we either produce empirical evidence showing that the predictions are incorrect, or we advance an alternative theory that produces, to the limits of experimental accuracy, the same predictions as the existing theory and also produces correct predictions outside of the range of validity of the existing theory.