Mathematically speaking, what is an ‘Axiom’?
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Another way to interpret an axiom is not as a statement assumed to be true, but rather as a conditional: “*If* this thing is true, *then* these other things (theorems) must also be true.” So, it’s not that anyone is claiming water is wet, it’s that *if* water is wet, *then* fish go blub blub. If water is *not* wet, we’re not making any claim at all and so we’re not wrong.
I like this interpretation because whenever I tried to explain axioms as assumptions, some wiseass would always say “but what if water actually isn’t wet?”
Mathematicians like elegance, so it’s generally preferred to keep axioms as simple as possible – anything more complicated than the equivalent of “water is wet” should probably be proven as a theorem.
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