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galathaea wrote:
> much of lukasiewicz early work
> was heavily indebted to aristotle
>
> he would tell his students
> (or so i was told)
> that when a brilliant man has left so much thought exposed
> study it
> for there may be many things still undiscovered
>
> and when you disagree
> it is better to debate brilliant dead men
> than no one at all
I can agree with that.
> > Post's "cyclical" system which is just a bit later
> > than that of Lukasiewicz isn't nearly as useful for reasoning.
>
> i would disagree with this
I haven't seen what it's useful for. My thought was something that
reduces to classical logic if you eliminate the 3rd value, and Post's
cyclical negation doesn't do that.
> his system
> provides a layered refinement
> of the logics between the boolean and the heyting
> and the structural distinctions
> all have natural functional interpretations in decision theory
I'm not familiar at all with decision theory, so I can't comment on
that.
> > It's the comment that the intended application to modal logic did not
> > materialize that intrigues me. Why didn't it and where is this
> > discussed? In one of the references in the article I cited, I think
> > it's Rosser and Turquette, but it could be Ackermann or Rescher,
> > there is mention of an objection posed by Gonseth, but this objection
> > as quoted is answerable. Lewis was aware of Lukasiewicz' approach,
> > discussed it, and rejected it, but his objections are also answerable.
> > I've not been able to get easy access to the older philosophical
> > journals where this might have been further discussed.
>
> the one i have seen who most developed the modal interpretation
> was not active in the logic community
>
> hans reichenbach's three-valued quantum logic
> was lukasiewicz with a different implication
>
> in his papers and books
> the modal interpretation is clear from the reading
> recapitulating much of your page
>
> just not in a symbolism familiar to logicians
>
> others with more background
> have returned and revised reichenbach
> often returning to lukasiewicz
> though to his infinite truth-valued logics
>
> see for example
> jaroslaw pykacz
I did look at Reichenbach's logic when I was searching throug MVL to
see whether anyone had done everything I had already, and whether my
system could include any of the other 3-valued systems.
http://www.iep.utm.edu/r/reichenb.htm
I thought his "alternative implication" was too permissive, did evil
things to the contrapositive and biconditional, and could be defined as
~[]P v Q in my system if it were needed. It looked to be too narrowly
focused on application to quantum theory and wasn't sufficiently
general-purpose for me. I already had his & and v, the "standard
implication", and the standard and alternative "equivalences". I
didn't see a good use for the cyclical negation, the "complete"
negation, or the quasi-implication.
>
> >
> > The modal operators of L3 have the same effect of limiting uncertainty
> > and containing it within the more tractable 2-valued approach. That's
> > partly why I don't use the constant U, because then uncertainty would
> > tend to proliferate.
>
> what objection do you have
> against this proliferation
Partly, the first steps into this realm go through the "logic" of
irrational and obstinate denial, and proceed further through complexity
to confusion. Each new 3-valued function that can be defined in terms
of others has its own unique set of properties that has to be
investigated and explored. This is a back door into the full range of
three-valued systems as discussed, partially, at:
xyzzy.freeshell.org/trinary/">http://xyzzy.freeshell.org/trinary/
I'm more interested in keeping my focus on the extension of classical
logic.
>
> if you were to take a separateness axiom of truth values
> (any reasonably justifiable one
> like the tendency you comment on)
> and were led to a countable infinity of uncertain values
>
> what would be the down-side
> philosophically?
I don't know about philosophically. I do think it's easier and more
practical to deal with one uncertain value than a countible infinity of
them.
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