🚀 go-pugleaf

In article <1992Nov17.124233.24312@oracorp.com> daryl@oracorp.com (Daryl McCullough) writes:
>columbus@strident.think.com (Michael Weiss) writes:
>
>>In short: there may be good reasons for radically changing the foundations
>>of physics (and there may not-- pace, defenders of the status quo(ntum)!),
>>but the Loewenheim-Skolem theorem is not one of them.
>
>LS doesn't demand that we adopt Paul Budnik's discretized physics, but
>I believe it gives us permission to do so. LS shows that there can
>never be a demonstration that space-time must be continuous, because
>there is no property of an uncountable set that doesn't also hold of
>some countable set.

I object.  Lowenheim-Skolem says there are countable models of the
reals; you can go ahead and use these if you like, and I will not
object, since this does not affect what *theorems* you can prove about
the real numbers.  (Theorems, those statements that follow from the
axioms, are defined purely syntactically and are utterly independent of
a choice of model.)  So I am at a loss to think of any sense in which
using a countable model of the real numbers makes ones physics more
"discrete."