logical systems (Query about symbolic logic)

Jim Farmelant farmelantj at juno.com
Thu Jul 10 19:44:16 MDT 2003

On Thu, 10 Jul 2003 20:24:11 -0400 Les Schaffer <schaffer at optonline.net>
> Jim Farmelant:
> > Was Zwicky's logic a three-value logic like Reichenbach's?  In
> that
> > case we might have an issue of priority over who developed it
> > first. Reichenbach's 1944 book *Philosophic Foundations of Quantum
> > Mechanics* makes no mention of Zwicky.
> here's what i know so far:
> 1921   Lukasiewicz    3-valued
>        E L Post       m-valued
> 1930   Lukasiewicz    more m-valued
>          & Tarski
> 1932   Reichenbach    inifinite-valued
> 1933   Zwicky         suggests 3-valued for QM
> a footnote in Eves' book:
>    As a mater of historical interest, in 1936 K. Michalsi discovered
>    that three-valued logics had actually been anticipated as wearly
> as
>    the fourteeth century by the medieval schoolman, WIlliam of
>    Occam. The possibility of a three-valued logic had also been
>    considered by the philospher Hegel and, in 1896, by Hugh
>    MacColl. These speculations, however, had little effect on
>    subsquent thought and so cannot be considered as decisive
>    contributions.

Lukasiewicz is generally given credit for the discovery
of three-value and n-value logics within the context
of mathematical logic.  Many scholars, however,
believe that the notion of such logics goes back
much further, with some attributing this notion
to William of Ockam, while some go further,
tracing three-value logics back to the Stoics.

> i'll check the library soon and see what's up with Zwicky. one of
> his
> bios on the web described him as an eccentric astronomer. if you
> read
> that as academi speak, it could mean he threw lots of interesting
> ideas around "haphazardly", and Eves just happened to come across
> it.

Maybe he talked about these ideas with fellow scientists
without bothering to publish them.  As I said before,
Reichenbach uses three-value logic in his treatment
of QM in *Philosophic Foundations of Quantum Mechanics*,
but he makes no mention of Zwicky, so as far as I can
tell, attribution is usually made to Reichenbach.

> > I remember years ago reading some papers by Patrick Heelan on
> > quantum lattice logics.  Heelan is a Jesuit
> > priest/physicist/philosopher.
> i couldnt find anything on lattices listed on his web page at
> georgetown u.

I think some of the papers in which he discusses
quantun logics as lattice logics include:

"Quantum Logic and Classical Logic: Their Respective Roles," in
Logical and Epistemological Studies in Contemporary Physics.
Ed. by Robert S. Cohen and Marx Wartofsky.  Boston Studies in the
Philosophy of Science Series, vol. 13.  The Hague: Reidel, 1974.
Pp. 318-349.

"Quantum Logic and Classical Logic: Their Respective Roles,"
Synthese, 22 (1970), 3-33.

 "Complementarity, Context-Dependence and Quantum Logic,"
Foundations of Physics, 1 (1970), 95-110.

His argument as I recall is that such quantum logics form
non-distributive lattices.

> > Well Priest's point is that classical logic is explosive, in that
> if
> > we try to assert both A and not-A simultaneously, then their
> > conjunction will logically (via material implication) imply
> > anything.  Priest contends that certain scientific theories (such
> as
> > QM) are not explosive in his sense, and so therefore dialetheism
> and
> > paraconsistent logics can be quite legitimately applied to such
> > theories.
> well, here's a case:
>      A            ~A               B
> -------------------------------------------
>    Lassie is    Lassie is        Lassie is
>    a dog        not a dog        a good
> 		                 junkyard
>                                  guard
> now the conjunction:
> if {   (Lassie is a dog) and (Lassie is not a dog)  }
>   then  (Lassie is a good junkyard guard)
> then is always true regardless of whether Lassie makes a good
> guard!!!
> but what is it saying?!?!?!?!?!?!?!
> classical material implication is strange. maybe john enyang has
> time
> to pitch something in here.
> ok. how about giving a short description now of dialetheism.

A dialetheist system is one in which the Aristotelian Law
of Non-Contradiction is denied or relaxed such that
it is possible to have both a statement A and its negation,
~A both be true at once, without this entailing all propositions.

BTW the philosopher Peter Suber after discussing both
paraconsistent logics and intuitionist logics (in which
the Law of the Excluded Middle is denied) goes on to
define what he calls "dialectical logics" in which both the
Law of Non-Contradiction and the Law of the Excluded Middle
are denied.

> les 'is, is not' schaffer

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