> > I'd say they are *less* than models of reality. They are just consistency
> > conditions on our models of reality. They are attempts to avoid talking
> > nonsense. But note that not too long ago all the weirdness of quantum
> > mechanics and relativity would have been regarded as contrary to logic.
> I guess we could agree that they are "other" than models of reality?
What do you mean by "reality", by the way, since it's seems to be confounding
so many here?
> It still strikes me as paradoxical: ultimately we have learned our
> intuitions about mathematics and logic from reality, via the mechanisms
> of evolution and also our own individual learning experiences.
That's exactly right!
> And yet it seems that at some level a degree of logic, and certain
> mathematical assumptions, are necessary to get learning off the
> ground in the first place, and that they should not depend on reality.
"In the first place?" What does that mean? It sounds like you're using
English tenses and even English time-ordering adjectives.
If so, then that takes us, by the hand, back before the big bang,
and I'm not so sure that our English temporal vocabulary and grammar
are really of much use there.
Yes, there indeed are mysteries about the relationship between physics
and mathematics. But a lot of the math is now in our genes, because it
turns out that it really is a feature of the real physical universe.
And it had to be learned if we wanted to survive.
On a much more abstruse level are our philosophical meanderings about
Tegmark and Tipler universes. I'm just writing this so that we keep
the basics firmly in mind as we explore.