🚀 go-pugleaf

In article <362@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:


   I think it will be difficult to build a discrete theory that
   encompasses GR and QM. The issue is not how difficult the theory is, but
   what approach gives the simplest model that accounts for experimental
   results. Arguments about countable sets have little relevance to this
   question. 

Yes! Exactly right!

   They do allow one to avoid making certain errors such as
   thinking that the continuum is a necessary mathematical element in
   any physical theory.

Did anyone ever make this claim, i.e., that it is impossible to build a
consistent physical theory without the continuum?  My impression is that
the Defenders of the Continuum (hmm...  sounds like the title for an SF
novel) in this newsgroup simply prefer continuum math to discrete math--
and also, there are well-worked continuum-based theories, with warts to be
sure, for which detailed discrete replacements have yet to be offered.

"We can dream, but we need not deliberately court nightmares."  For some,
getting rid of R looks like a nightmare.

Personally, I am not fond of the Brouwer-Heyting-Bishop approach to
mathematics.  On the other hand, I think it would be delightful if someone
created a new physical theory out of some strange-smelling brew of math
logic, model theory, and who know what else (braids too, gotta have
braids!), that at one blow "solved" quantum gravity, gave a new resolution
to all the old QM koans, and predicted new, experimentally verified,
physics.  However, I'm not holding my breath.