[Marxism] Re: [PEN-L] More Godel
rholt at planeteria.net
Wed May 18 01:02:34 MDT 2005
I don't know who's interested in this but us, but, What is Hegelian
The real world is, so far as anybody knows, composed of a finite number
of kinds of descrete particles and/or their wave packets (which is the
same thing). This is a tenent of quantum theory and long established by
experiment. Therefore, as long as we agree the universe (at any instant)
is finite in extent and mass/energy, then the number of particles is
finite , the number of states allowed are finite, and the dimension of
their vector spaces is finite and the measure of each axis consists of
descrete, ennumerable points (i.e., particles are describes as n-tuples
with a finite n and each element, a(sub i) allowed some number
(unbounded) of descrete values). Hence the whole ensemble is finite or
ennumerable at the worst. And by "ennumerable," we mean only that for an
ennumerable set there exists a rule such that the elements of the set
are placed into a 1-to-1 correspondence with the integers (or an
unbounded subset). Strictly speaking, we do not say that "there are an
infinite number of integers," only that if we need another, we can
always construct it.
? is a Real Number and a member of a non-enumerable set. 2 is also a
Real Number and a member of the same set as ?. It matters not the least.
We can construct non-ennumerable sets mentally, the simplest being the
set of all subsets of the non-negative integers. But this does not
correspond to the real world. There is no model for the Real Numbers
taken from the real world.
P.S. The Completenes Theorem for the propositional calculus was
published by E. L. Post in 1921 when Gödel was 15-years old.
Carlos A. Rivera wrote:
> ----- Original Message ----- From: "Rod Holt" <rholt at planeteria.net>
> Compelling argument you provide, and in fact it remains a "perhaps",
> either way. Again, I retain my perception, but it is nothing but that,
> a mere perception.
>> But both the consistency and completeness of number theory is close
>> to an article of faith for a materialist, because, for any particular
>> problem, the real world is a model (because, among other reasons, the
>> real world is ennumerable).
> Actually, I think this is hegelian materialism. Diamat (again correct
> me people!) actually seems to sustain that the world is *not*
> ennumerable, hence they are not articles of faith but part of the
> I think someone here (cant remember who) compared the HUP with
> Completeness in diamat terms, an analogy I digged a lot.
>> And, it is on the borderline between the "realness" of the real world
>> model and the undecidability of certain problems with ennumerable
>> models that Turing gets most interesting.
> In this we agree. Turing is more interesting, although I doubt Turing
> would have existed without Godel (And others, including physicists
> like Einstein)
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