Re: Cantorian pseudomathematics

Keith Ramsay said:
My point is that by this criterion the set theory on which
he heaps so much abuse makes predictions that do not follow
without using it. My secondary point is that I don't arrive
at this conclusion by mindlessly defending the status quo; I
agree that insisting upon the two criteria above is plausible
and would have consequences for how we do mathematics if we
were to agree to it. In particular, it would entail dropping
the axioms that, whether coincidentally or not, also happen
to be the nonconstructive ones (in the more common usage of
the term). But he's not happy with just that, for reasons
that as far as I'm concerned have nothing to do with wanting
mathematics to make computational predictions.

Keith Ramsay

Hey Keith -

I have really enjoyed your expounding on this subject. I think you go right to
the heart of the matter. Maybe David Petry has more of a restriction in mind,
but I think it's no coincidence that elimination of AC and LEM can bring one
closer to something more quantitative and constructive, and it's interesting to
hear this explained.

Eliminating LEM would seem to entail a new logistical system, wouldn't it, like
a probabilistic one? I guess intuitionistic logic is more of a three state,
rather than continuous, aalternative to Boolean logic. What do you think of a
probabilistic logistical system as a foundation for such a theory? Can that
give more of a computational potential from the ground up?

I also wonder about the Axiom of Choice. Does it really add nothing to the
predictive power of the theory? Wouldn't one want to replace it with something,
perhaps a more explicit construction that serves the same purpose without the
vaguaries? Somehow I see the description of the dimensional system in terms of
set concept as being what AC is really all about, and maybe this could be
addressed ina slightly different manner?

I am not sure my questions ultimately make sense, but however you respond, I am
sure it will be interesting. Thanks so far.

--
Smiles,

Tony
.