Hi again...
In +this+ post, I am attempting to encapsulate all previous posts on
sci.logic and here.
In a nutshell, my work in FL is going to hopefully provide the
beginnings of an answer to "what is the universe" by at least making a
plausibility case for some universal fuzzy set, in conjunction with
Tegmark's (et al) MUH, as being the universe.
I would at least like to rule that possibility out, ie, settle that
question: is the universe some type of universal set?
My main dilemma is not phrasing the new or different axioms. My main
goal is that I seem to need to show that such a fuzzy set theory, one
with a "universal set," is ++consistent relative to ZFC++ or at least
prove that that's not possible (ie, prove a generalization of
Russell's "paradox"). That would make at least some of this, perhaps,
interesting to mathematicians, at least logicians, instead of just
theoretical physicists and those interested in FL. Also, if any such
fuzzy set theories actually are consistent, my problem would then be
to investigate exactly what about the axioms, or the nature of logic
itself (eg, the nature of all MV-algebras for which a set theory
'using' a logic with that MV-algebra can consistently have a universal
set), leads only some such set theories to be inconsistent, as in the
case of Russell's "paradox" and two-valued logic).
And that is why the fact that FL is a generalization of classical
logic is highly relevant. If they were unrelated, for example, a
relative consistency proof would be, I believe, completely impossible.
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Received on Sat Mar 22 2008 - 19:18:45 PDT