silber@voodoo.ucsb.edu (08/14/89)
-Message-Text-Follows- It seems that I recall that axiomatic set theory was/is critical to the foundations of modern mathematics. I still question whether, in a different possible universe where there are no discrete particles, no inhomogeneities, that mathematics will 'work' the same as here. Of course, in such a an extreme case as that, there probably are no thinking agents either, but it might be possible to relax the conditions of the example just enough to allow some structure (hence the existence of some combinational/associational/logical systems), a structure within which, however, certain sets of axioms which we find consistent HERE are inconsistent THERE!
jk3k+@andrew.cmu.edu (Joe Keane) (08/15/89)
In article <2208@hub.UUCP> silber@voodoo.ucsb.edu writes: >It seems that I recall that axiomatic set theory was/is critical to the >foundations of modern mathematics. I still question whether, in a different >possible universe where there are no discrete particles, no inhomogeneities, >that mathematics will 'work' the same as here. I agree that someone in a different universe may be interested in different kinds of mathematics. For example, someone in a very discrete universe may never have thought about eigenvalue problems. Because of this, they may base it on something other than set theory. But ours will still ``work''. >Of course, in such a >an extreme case as that, there probably are no thinking agents either, but it >might be possible to relax the conditions of the example just enough >to allow some structure (hence the existence of >some combinational/associational/logical systems), a structure within which, > however, certain sets of axioms which we find consistent HERE >are inconsistent THERE! The key is that mathematics is not based on any structure in our universe. You can talk about mathematical objects completely independent of any physical basis. Physics, on the other hand, could obviously be much different.