If mathematicians could define a workable alternate universe defined by different principles I suppose they could then argue that our universe is defined by the maths we know. Not sure if anyone has tried.
There are mathematical models of alternate universes where math and logic don't work, in the sense that a person living in those universes would easily prove that 1 = 0 from the Peano axioms (and would presumably give up on either the Peano axioms or first-order logic as a result). These mathematical models are uncomputable (so we can't actually simulate one like we can with the Game of Life), but they can be defined unambiguously and could even be simulated if we had access to a halting oracle. But even these alternate universes where math doesn't work are still built out of math - it's hard to even imagine a model of something which isn't built out of math.