> > > Same sort of logical limitation. Of course it's possible that the Pythagorean Theorem *isn't* true, but that for some reason or by some incredible chance every person who has thought about the problem has made some fundamental flaw. Then God could make said non-conforming triangle and amaze us all, I guess. But I doubt this would happen. It would seem to be against God's nature to deceive us that way.
> >
> > Of course, this is a very bad example as there are places in this universe where Pythagoras' Theoram doesn't work. In fact, even the Earth's gravity distorts space enough that it's only approximatly true here. Like most geometric "laws", it assumes that Universe is flat.
> >
> > wintermute
>
> If your space is not flat, you're not even referring to the same geometry as I am (which is flat). I was referring to geometrical truth based on Euclidean axioms, not "real-world" geometry. Perhaps you are confused by the same thing as uselessness. When I say that the truth of Pythagorean theorem is absolute, it is with reference to a set of geometric axioms and further logical axioms to make deductions, and *independent* of the physical universe. It has NOTHING TO DO with physical experiment.

So when you say that you couldn't create a universe in which Euclidian geometry doesn't hold, you're ignoring the fact that it doesn't hold in this Universe? I don't understand...

wintermute