> Does 2+2=4 describe anything outside of mathematics?
Yes, but only to the extent that the isomorphism is correct. And the
isomorphism in the point (mine at least) and the subjective part of the
equation. If you say the numbers stand for atoms, the isomorphism holds.
But if, for instance, you say that the numbers stand for molecules, 2+2
may or may not equal 4 molecules. Two hydrogen and two oxygen molecules
can just as easily add up to two molecules (one H2O and one hydrogen) as
four.
> What you said about possible contradictions is like saying that maybe
> 2+2 doesn't equal 4 under 12,000 lbs of atmospheric pressure.
You were right. We are talking about two different things. You're saying
the mathematics/logic holds up under all possible conditions, and I agree
with that. I'm saying that the isomorphism may not be that stable. And
that we must keep that in mind when we say that anything *other than*
mathematics or logic is as consistent as they are.
-Prof. Tim