logical systems (Query about symbolic logic / Re: marxism-digest V1 #6030)

Jim Farmelant farmelantj at juno.com
Wed Jul 2 15:10:20 MDT 2003

On Wed, 02 Jul 2003 14:54:17 -0400 Les Schaffer <schaffer at optonline.net>
> Jim F.:
> thanks for the stanford encylopedia references. will read over the
> holidays and we can talk more.
> by the way, i just found this:
>    http://groups.yahoo.com/group/paraconsistency/
> in the meantime, some things to discuss:
> 1.) quantum logic: for example, "Quantum mechanics and the particles
> of nature", by Anthony Sudbery, has a section on quantum logic, with
> comments on the "logic" of two-slit experiments, superselection
> rules,
> and the use of three valued logic to handle system states which are
> not eigenstates of observable A.

That sort of thing goes at least as far back as to Hans Reichenbach,
the physicist turned logical empiricst philosopher.  In interpreting
QM he distinguished between what he called phenomena (i.e. collsions
between elementary particles as oberved in a cloud chamber) and what
he called interphenomena (i.e. the unobervable behavior of the
particles between collisions).  Physicists must construct
theories that are capable of explaining both the observable
phenomena and the unobervable interphenomena.

Reichenbach maintained that we can have two types of
descriptive systems -(1) those where the laws of nature
are the same regardless whether the objects are observed
or not and (2) systems where the laws will vary depending
whether objects are being observed or not.

The first class of systems, Reichenbach called "normal",
while the second class, he called "nonnormal".  As an
example we could have one descriptive system, our
"normal" system, where we assume that a tree will
have the same characteristics regardless of whether
anyone is looking at it not.  But we can also have a
system where the tree might be assumed to disappear
when no one looks at it, then reappears when someone
goes to look at it.  The two descriptive systems will
be equivalent since both will predict the same observations
but the second, nonnormal system introduces what Reichenbach
called "causal anomalies."  Our choice of descriptive system
was for Reichenbach a matter of convention.

In QM both the wave and particle interpretations involve
descriptions of interphenomena.  Neither description
can escape the introduction of causal anomalies.  One
of his examples of this is in electron diffraction experiments.
Individual flashes are said to introduce a causal anomaly
into the wave description, while the diffraction pattern
introduces a causal anomaly into the particle description.
Neither the particle interpretation nor the wave interpretation
can provide us with a normal description, according to
Reichenbach.  We cannot use either the wave or the
particle interpretation to give us an exhaustive account
of the interphenomena that will satisfy the postulates
of causality.  Reichenbach understood the proponents
of the Copenhagen Interpretation of QM, Niels Bohr
and Werner Heisenberg, as holding that statements
about the interphenomena, must be understood
as being meaningless.  Reichenbach in contrast
proposed an alternative interpretation in which
statements about interphenomena would be
treated as being meaningful but indeterminate
in their truth-values.  Hence, he proposed using
a three-value logic in which statements about
physical phenomena could either be true, false,
or indeterminate.  Such a "quantum logic" would in
Reichenbach's view enable us to eliminate
causal anomalies  from our descriptive system
since the statements describing such anomalies
would be neither true nor false.

> 2.) is there a relation between fuzzy and paraconsistent logic?

According to Priest, fuzzy logic is a type of paraconsistent

> 3.) quantum logic offers an alternative interpretation of QM, but
> offers no new physics (True or false???). fuzzy logic has given us
> implementable control schemes for dynamical systems. Godel has
> triggered Godel --> Church,Turing --> Chaitin and insights into
> logic
> and computatation. has the latter (Godel --> Chaitin) given us
> anything new as in fuzzy, or is it still solely in the realm of
> meta-mathematics?
> 4.) i did some googling and found several references to the use of
> paraconsistent logic in the field of relational database systems.
> what
> are the specific computational schemes suggest by the new logic?

I wasn't aware of the use of fuzzy logic in relational databases
but please tell us more.

> 5.) paraconsistentcy and interactive computation: see:
>    http://arxiv.org/pdf/cs.LO/0207074
> which also makes some comments on physics which look worth pursuing.
> and then of course:
> 7.) bringing this all back to marx and dialectics.
> les schaffer

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