🚀 go-pugleaf

In article <1992Nov22.230633.12855@galois.mit.edu>, jbaez@riesz.mit.edu (John C. Baez) writes:
> In article <1992Nov22.002703.5865@CSD-NewsHost.Stanford.EDU> pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
> >In article <368@mtnmath.UUCP> paul@mtnmath.UUCP (Paul Budnik) writes:
> 
> >>The discussion on L-S has apparently misled you. I believe that the
> >>space-time manifold is discrete, i. e. not continuous. There are many
> >>ways to discriminate between a continuous and discrete model and this
> >>has nothing to do with countability.
> >
> >So why this raging debate about how many reals, then?
> 
> Typically, issues which have no practical significance generate more
> raging debates on sci.physics than those which do.

The question of how many reals, is significant
even though it does not have a direct effect on the
mathematics that physicists use. The way mathematicians extend logic
today is by postulating the existence of large cardinals.
These abstractions are so far removed from the computational roots of
mathematics that there is no intuitive basis for deciding between them.
However these large cardinal axioms have combinatorial implications.
For example they allow us to decide the halting problems for a wider
class of Turing Machines. It is my contention that if one focused
on understanding these combinatorial implications and forgot about the
Platonic heaven of completed infinite totalities, real progress could
be made in extending logic.

Follow ups are directed to `sci.logic'.

Paul Budnik