I would tend to think that most mathematicians and even more
physicists and even more engineers and even more laymen would say that
'just' is a huge, huge understatement.
However, from the perspective of Non-Classical logic (be it
paraconsistent or fuzzy), that sentence was perfectly formulated, in
my humble opinion, and that article was not written with all forms of
non-classical logic in mind.
What I need to show is that the answer is different or the same in all
MV-Algebras. My guess is looking at just [0,1], as proofs done in
[0,1] can sometimes be carried over to all MV-algebras using Chang's
theorems, mentioned above, which connect just [0,1] to all of these
types of fuzzy logics, would be a big step towards settling my
investigation for all MV-algebras.
In other words, I want to investigate Russell's "paradox" for as many
types of logic that already have been developed, to determine how
"true" Russell's "paradox" is for any logic that is not binary logic.
I don't know, it could be false in +all+ logics that could be
reasonably called logics or, more interestingly to me, true in some
but not all. Then, in that event, the investigation would be to find
out in which logics Russell's Theorem (ie, no universal set exists in
that logic-set-theory combo) is true and in which is false. Then I'd
like to know why Russell's Theorem is true sometimes and why not
sometimes. Or why it's always true. Why being the main question for
me. I think the physicist would mainly be interested in whether any
universal (fuzzy) sets can consistently exist, and the logician more
interested in why it exists. However, why it exists is, I think, also
interesting to the philosopher in that it is like asking "why does the
universe exist" assuming the MUH and that any universal sets can
consistently exist.
On Mar 22, 9:30 pm, <dfzone-everyth....domain.name.hidden> wrote:
> > Does 'any theory' in the following quote include theories that
> > involve
> > logics with every MV-algebra as their truth set and every set of
> > syntactical axioms or is this just any theory using binary logic?
>
> my guess is: just any theory using binary logic.
>
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Received on Sun Mar 23 2008 - 00:46:25 PDT