On Apr 24, 12:08 pm, "Brian Tenneson" <tenn....domain.name.hidden> wrote:
> I was attempting to -invalidate- that argument against the existence of the
> universe, actually, by saying that in three truth values, which the
> Physicists can't rule out as being the more accurate logic of their
> universe, the argument "reductio ad absurdum" is not a tautology and,
> therefore, can't necessarily be applied.
>
> However, in binary logic, the Physicist's universe (or whatever Everything
> means) can't exist.
I take your point about the reductio not working in three valued
logic.
I am not convinced that the problem you are attempting to solve is
necessarily a problem since I haven’t been able to construe the
proposed reductio ad absurdum argument in a way that seems coherent to
my way of thinking.
However, you may be on to something with the general program that you
have embarked upon. Maybe there is a need for a mathematics to
describe the everything ensemble. Something along those lines is
likely the only way to define the everything with any sort of rigor. I
think it is a good idea.
Set theory does seem to be too rich for the job. Determining what type
of formalism is apropriate is a task. I think that such a mathematical
formalism may be precisely what is called for in order to define the
everything, as well as analyze it any useful sort of way.
I am still confused by what you mean by certain terms. What is meant
by the Physicist’s universe? Even more to the point, what is meant by
saying that it cannot exist in binary logic? The propositional
calculus, for example, does not even satisfy the conditions the Godel
theorems, i.e. there are no undecidable propositions possible in it.
To think that the axioms of any two valued logic could be sufficient
to produce a physical existence for self-aware substructures is
distinctly overstepping what Max Tegmark suggests in his metaphysical
theory.
>
> I doubt self-reference is inherently the problem in light of things like
> Tarski's fixed point theorems which provide concrete examples of wffs that
> are self-referencing, in terms of Godel numbers, if I recall. That proof I
> was exposed to was not an existence proof of self-referencing wffs merely by
> "logical flamboyancy" but by the providing an example of an actual -class-
> of self-referencing wffs. Obviously, the above argument does not explicitly
> involve wffs (it does, however, implicitly), and I am -only- making a case
> for plausibility at this particular moment.
>
> I see no problems with the argument given that in binary logic, their
> universe can't exist; this, to me, convinces me that the Physicist's
> universe can't operate on binary logic by Occam's Razor as -none- of the
> data in any experiment would fit the result that confirms their speculation
> that their universe exists.
>
> Ergo, the Physicist's universe must operate on at least three truth values.
> (Consequently, it exists.) This to me is a more elegant solution to the
> argument than citing self-referencing issues as automatically damning. If
> natural language can be used to prove the Heine-Borel theorem, without the
> need for wffs, then why must a statement about Everything be formalized in
> machine-level code with wffs?
>
> If there is further objection to my line of thinking, -please- point it out
> to Everyone (which I hope is well-defined or else no one would know what I
> mean, right?) ;)
>
> Thank you for your remarks; I find all input extremely productive!!
I too appreciate the chance to talk about such interesting ideas.
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Received on Sat Apr 26 2008 - 00:52:07 PDT