Comment by tsimionescu

I think what the poster above means is that any formal system in which, say, 1 + 1 = 75, even if internally consistent as a set of symbols, would not be considered a valid logical foundation for mathematics by Hilbert, because it directly contradicts physical reality. Of course, this is under the assumption that 1 and + and 75 are meant to have their usual meanings, not that we've redefined the + operator to mean "the 73rd successor", nor that we're operating in some exotic numerical base where 75 is just a different set of symbols to describe the number 2.