We can construct a model where we imagine that logic being different than it is, but there isn’t a fact of the matter about how logic would be if 1+1=3 instead of 2 that exists as part of standard logic without any extensions, any more than counterfactuals exist in-universe without any extensions.
Aside from a world where “3” denoted 2, I’m unclear on any aspect of how such a model would work.
Aside from a world where “3” denoted 2, I’m unclear on any aspect of how such a model would work.