Path: utzoo!attcan!utgpu!jarvis.csri.toronto.edu!rutgers!gatech!bloom-beacon!usc!ucsd!hub!silber From: silber@voodoo.ucsb.edu Newsgroups: comp.ai Subject: "in any case rubin's statement is still true (RE: axioms and universes) Message-ID: <2208@hub.UUCP> Date: 14 Aug 89 16:36:40 GMT Sender: news@hub.UUCP Organization: UC, Santa Barbara. Physics Computer Services Lines: 12 -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!