>>12596739To illustrate my point, let's take the formal system ZFC and in it, one arithmetic statement (among many) that people claim to correspond to Con(ZFC). Ultimately it expresses the nonexistence of a certain natural number which corresponds to a proof of 0=1 under some godelnumbering.
However, what is intuitively taken to be a natural number in ZFC is nothing like an iterated successor or whatever. There are magical natural numbers from the mushroom kingdom and beyond, among the regular natural numbers like 1,2,3,4. There is for example a natural number for almost every open problem in mathematics which corresponds to the answer to almost every open problem in mathematics, and also a natural number which corresponds to the truth value of the continuum hypothesis, which we don't even know whether it's a definite question. It could be a vague, indefinite magical natural number. So ultimately, if we admit these mystical undetermined natural numbers which have no basis in reality, then there could be a proof of inconsistency of ZFC, in which case Con(ZFC) in the less naive, but still naive interpretation would be false, even though no computer would ever find a contradiction in the system.
