It's not a new idea, no. However, I find the classical logic
restriction to make set theories with a universal set as unnatural
(e.g., some automatically sacrifice choice) as one that uses FL might
seem to others. I mainly want to know if Russel type paradoxes are
completely universal, which would be interesting, in all
generalizations of classical logic or even logics without excluded
middle. W/o Em, I think no paradoxes are even paradoxes, though.
(Boring w/o Em?)
Not as interesting when one changes logic, maybe to some. But to me,
changing the logic, it's like non Euclidean geometry. Why assume (not
you, but the mathematical masses) that non-classical logic need be
uninteresting? It seems to have been quite opposed until recently
(ie, basically less than a century).
I have been mainly working on different approaches recently. Now I'm
trying to stay in classical logic and challenge your valid objections
to Tegmark-like mathematizations of physics, based on Russell-style
lines of thought. The idea is that a non-well founded set theory,
where a set could easily be an element of itself, is all I really need
to resolve (seemingly?) the objections.
This post at "project virgle" might be interesting as some of Rose's
ideas are invoked:
On Mar 27, 3:57 am, Bruno Marchal <[EMAIL PROTECTED]> wrote:
> Hi Brian,
> Your idea of a universal set, in case it works, would indeed meet one
> of the objection I often raised against Tegmark-like approaches, mainly
> that the whole of mathematical reality cannot be defined as a
> mathematical object. Of course this is debatable, and a case can been
> made that such a universal set can exist (see the Forster reference
> Nevertheless I have no clues why do you want such an universal set to
> be fuzzy, except perhaps by the analogy which can exist between the
> empirical multiverse and some sort of fuzzy physical universe. A
> problem with fuzzy set is that there are many approaches, and they do
> not seem to converge on some standard apprehension. Perhaps you know
> better. Have you written a longer text?
> Now, once you assume the computationalist hypothesis in the cognitive
> science (NOT in the physical science!) and once you are aware of the
> mind-body problem (or the first person/third person relationship
> problem) then you will be confronted with my other objections to
> Tegmark, mainly the fact that the mind-body problem is still somehow
> put under the rug. I suggest you read my texts (url below, or see the
> Archive of this list) for appreciating that a universal structure
> definitely cannot exist. Like in Plotinus or Cantor the big whole
> cannot be made first order citizen.
> Of course with comp (actually with only Church's Thesis) we do have
> some "universal structure" like the universal *machine* or the
> universal dovetailer, and those are embedded in the structure they
> deploy. That is why comp works. But of course a universal machine does
> not describe a universal set in your sense.
> For the existence of a universal set in the context of Quine New
> Foundation set theory (NF) I suggest you consult the book by
> T. E. FORSTER, Set Theory with a Universal Set. Oxford Science
> Publications, 1992. Oxford.
> Le 23-mars-08, à 05:46, Brian Tenneson a écrit :
> > 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, <[EMAIL PROTECTED]> 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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