RD,
Sorry not to respond earlier, but between writing up on Ilyenkov (it turns
out to be a review and justification of Lenin's concept of real with a
couple of surprising - to me at least - twists) and working full-time
corresponding is a luxury.
About an age ago (a year or so) I developed something of an interest in
Paraconsistent Logic (mostly from the general systems point of view). Was
reading works by a number of Czech systems people who were and apparently
still are trying to model it by a modification of fuzzy logic programming
(probably x-students of my professor of general systems Georg Klir at
SUNY-Binghamton). I wasn't terribly impressed, probably because of its
extremely formalist and mechanist modelling of the reasoning process. Like
Andy Blunden, I find set theory, even fuzzy set theory, inadequate to
describe the dialectical deduction of the concrete from the abstract.
Another logical system, Sheldon Klein's 'Appositional Transformational
Operator' from "Analogy and Mysticism and the Structure of Culture 1983
Current Anthropology vol 24, pg 151, was much more interesting because
unlike paraconsistency and dialetheism it incorporates essence (significance
or meaning) as an integral part of the logical system. SK based his model
on the dialectical categorizing system of the I Ching and then expanded the
abstract formal method to other similar categorical systems, e.g. the
directional logic of pre-Columbian Americans, some Buddhist imagery and so
on.
One of the interesting features of ATO systems is that the entire conceptual
space of the universals they process are described by them in the form of a
bifurcating genetic tree which is reminiscent of and, indeed, related to the
dendritic mappings of genetic algorithms. Moreover, the routing process
whereby one deduces, (going from the top, abstract root of the tree to its
branches) concretes from abstractions or induces (going from the bottom, the
branches to the top, root, of the tree) abstractions from the concretes in
ATO systems is similar to the genetic algorithm. As a past-time diversion
I've experimented with several ways to remodel SK's ATO system to represent
Hegelian dialectics. I think I figured out how to do this about 2 or 3
months ago. The basic difference between the I Ching /SK ATO model and
Hegelian dialectics is that though carried out diachronically they produce
what is in essence a synchronic model, while GH's dialectics are diachronic
in execution and in representation. Also, while the path making algorithm of
the ATO model simply follows a continuous genetic line, the Hegelian
system's algorithm must jump back and forth between "lineages" (the
negation and the negation of the negations of Hegelian dialectics) thereby
producing all the lineages/branches of the tree in one blow. So, while the
I Ching /SK ATO the algorithm generates each lineal path in turn, the
algorithm of the GH model, based on the triadic structure of the dialectic,
simultaneously builds all the branches simultaneously.
Unfortunately, ATO systems suffer from the same bias as does GH's
dialectics; the incorporation of essence as an integral part of the logical
system limits the degree to which it can be described by mechanical forms,
i.e. numbers, hence they are described as mystical and uninteresting by
mathematically inclined academic logicians. It's really hard to get much
information on them, but if you're interested you can check out
http://www.journals.uchicago.edu/cgi- for the Sheldon Klein article and
http://portal.acm.org/citation.cfm?id=1056663.1056733 for the only
other on-line article Propositional & analogical generation of coordinated
verbal, visual & musical texts: U. of Wisconsin ACM SIGART Bulletin Issue 79
(January 1982) SPECIAL ISSUE: Special section-Natural Language Pages: 104 -
104 Year of Publication: 1982 ISSN:0163-5719 on the subject of ATO's
(You have to pay for both)
Regards,
Victor
----- Original Message -----
From: "Ralph Dumain" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Sunday, September 11, 2005 22:01
Subject: [Marxism-Thaxis] Graham Priest: Dialetheism & Marx
Priest, Graham. 'Was Marx a Dialetheist?', Science and Society, 1991, 54,
468-75.
While I don't expect everyone to be held spellbound by this question, it
is illustrative of a recurring problem in intellectual history (and also
in popular intellectual culture, which is another story. Priest's views
on dialetheism (logic which admits contradictions) is controversial among
his fellow logicians, and he responds to objections in his book. Probably
his fellow logicians (except those interested in Marx, among which there
are more than a few) are not terribly concerned about his views on Marx,
and in fact he says nothing about Marx in his book. However he did get a
response to his earlier article on dialectics and dialetheism:
Marquit, Erwin. "A Materialist Critique of Hegel's Concept of Identity of
Opposites," Science and Society, Summer 1990, 54, no. 2, 147-166.
I haven't yet reviewed this article, so I'll move directly to Priest's
response. Marquit himself is a Marxist (and a physicist, I believe) who
maintains that logical contradictions are unacceptable. Priest counters
this by reaffirming the existence of formal logics not susceptible to this
limitation. Moreover, Marquit is wrong to claim that contradiction is
intolerable in theoretical investigations, citing Dirac's early
formulation of quantum mechanics and teh early infinitesimal calculus as
examples. However, as all theories get replaced eventually,
inconsistencies or no, one can't argue much on this basis. (Am I missing
something, or is Priest undermining himself here?)
Then there is Marquit's argument as to the difference between idealism and
materialism. While Hegel's idealism requires an identity of opposites,
materialism does not. Priest argues that the substantive differences
between Hegel and Marx are irrelevant to the question of whether the
entities in question have formally contradictory properties. Marquit
argues that a succession of states in time (state A and state not-A) are
contradictory or not depending on whether Hegel's or Marx's logical and
historical dialectics are temporal or not. I'm not going to reproduce the
confusing paragraph in question, but suffice it to say that Priest
counters this argument. Finally, Priest claims that since Marx says that
he took over his dialectic from Hegel, we should take his word for it,
along with the criticisms he explicitly makes of Hegel's dialectic. Oy!
In his earlier article, Priest cites three alleged examples of Marx's
dialetheism; Marquit addresses only one, with the familiar ploy of
reinterpreting a situation in which A & not-A are both true as being so in
DIFFERENT RESPECTS. The example in question is a famous one from Marx on
the nature of the commodity, its use value, exchange value, and
equivalency. Priest analyzes this example from CAPITAL as well as another
one from A CONTRIBUTION TO POLITICAL ECONOMY to counter Marquit's
argument.
Priest segues to the contradictory nature of wage labor, both free and
unfree. Here too he counters Marquit's attempt to weasel out of a
contradiction in the same respect.
Next Priest discusses the nature of motion, beginning with Zeno's paradox.
Here I am confused about Priest's argument about the unsatisfactoriness of
the Russellian argument, about which he claims to agree with Marquit.
Then he throws quantum mechanics into the mix, and I can't make sense out
of the argument anymore, as we move into paragraphs on the uncertainty
principle and the two-slit experiment. Priest concludes that he is not
"suggesting that quantum mechanical descriptions are descriptions of an
inconsistent reality. My point is just that it is premature to claim
quantum mechanics as an ally against dialetheism."
I don't know whether you can make any sense out of my summary of this
article, but to me the article itself is an awful mess. I offer a few
observations:
(1) Priest treats disparate examples as if they are alike:
(a) the nature of motion (implying, firstly, the nature of the continuum).
There is a philosophical dimension, a scientific dimension, and a
mathematical dimension to this problem. The ancient Greeks, lacking the
calculus (though I'm told that Archimedes came close), could not handle
the mathematical dimension, but they dealt with both the logical
(philosophical) and scientific dimension of the problem as best they
could. The strictly logical dimension--i.e. the nature of the
continuum--involves the question of infinite divisibility of the line into
points. If I remember correctly, already Aristotle challenged Zeno by
denying that motion should be considered as a succession of states of
rest, and that the line, while potentially infinitely divisible, should
not be considered as a collection of points (or actual infinity of real
numbers, a nondenumerable infinite set as Cantor proved it to be).
Then there is the relation between the mathematical idealization and the
physical. In his book Priest recounts Aristotle's struggle with the
concept of the atom on the one hand and on the other the (im)possibility
of the physical infinite divisibility of matter and space. This is
already an issue more than two millennia before the worse problems
introduced by quantum mechanics. Curiously, in this article, Priest
acknowledges that quantum mechanics complicated matters, but otherwise
remains simplistic in his indifference toward other distinctions.
Interestingly, Marx had a hobby in the last decade of his life, writing
about the various explanations of the calculus in the old textbooks he
read and evaluating their relative (in)adequacies. These manuscripts have
been published and analyzed, (I think they were analyzed before they were
published.) Priest does not mention them or compare them to other
treatments, such as those of Engels. While I do vaguely recall Dirk
Struik's treatment of Marx's analysis of 3 approaches to the calculus (all
before Weierstrauss et al straightened out the mess), I don't recall Marx
making any of the claims or arguments that Engels does (Van Heijenoort
exonerates Marx of the intellectual sins he finds in Engels), let alone
linking them in any way to his social theory.
(b) the nature of the commodity and the money economy: how do the alleged
contradictions here relate in any way to the nature of the continuum.
True, motion in time as well as space also involves a measurement along
the continuum, and thus raises the question of nature of the "instant"
(both at rest and in motion?), but how does this abstract property of the
time continuum relate to Marx's social theory and substantive critique of
political economy? There is an abstract question of the viewpoint of
stasis vs. that of motion (development), but can it be stated as baldly
identical to the apparent paradox of the continuum (of time)? We can
continue to argue philosophically over the nature of the instant and
whether motion should or should not be considered as a succession of
states of rest, or rather, inversely, that the paradox emerges from the
artifact of freezing motion as hypothetical point-instants. But in the
meanwhile we do have the calculus to address the question mathematically.
We even now have nonstandard analysis. What analog do we have in
approaching the relation of use-value and exchange-value according to
Marx? (OK, Marx used math in his critique of political economy, but is
this some sort of axiomatizable theory?) How is it possible to switch
from one example to the other as if one is engaging an identical argument
in both cases?
(c) freedom and unfreedom: here we have a categorial pair far removed from
the nature of the continuum and simple physical motion, and no math to
resort to. The mutual (dialectical) interrelation of these categories, or
other pairs (indeterminism-determinism, chance-necessity,
freedom-necessity) raises a whole different question from that of the
nature of motion and the continuum. Priest briefly addresses the question
of internal relations in his previous essay, which as far as I can tell
just gets lost even where he promises to nail it. Priest is so obsessed
with showing that A & not-A are both predicated in all of his examples, he
fails to note not only their substantive differences but whether or not
this formula tells us anything meaningful about the relation of A and
not-A, or about the examples in question.
(2) Is there any meaningful way that paraconsistent logic can be applied
to illuminate any higher-level philosophical questions, or for that matter
the nature of use-value and exchange-value according to Marx? What is the
point of such an exercise? Does it add anything to our understanding of
the matter at hand, or does it even formally capture its logical
structure?
(3) Priest's argumentation is truly remarkable to me. One would think
that as a person versed in both contemporary formal logic (unlike the
average Marxist) and Hegel and Marx (unlike the average logician or
analytical philosopher) that he would escape the recurrent pattern of
simplistic arguments. Yet, for all his delving into substantive
philosophical ideas and theories, all he cares about in the end is
validating dialetheism, i.e. establishing the existence of formal
contradictions, just as if he were another simpleton regurgitating the bad
arguments of Stalinists, Trotskyists, and Maoists, his more sophisticated
qualifications notwithstanding. What does Dr. Paraconsistency have to
offer in relation to the contributions of Ilyenkov, Zeleny, Tony Smith,
Uno, Arthur, and scores of others? Where is the synthesis of the
achievements of modern logic and analytical philosophy and the
Hegelian-Marxist heritage? All I got was this lousy T-shirt.
_______________________________________________
Marxism-Thaxis mailing list
Marxism-Thaxis@lists.econ.utah.edu
To change your options or unsubscribe go to:
http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis
_______________________________________________
Marxism-Thaxis mailing list
Marxism-Thaxis@lists.econ.utah.edu
To change your options or unsubscribe go to:
http://lists.econ.utah.edu/mailman/listinfo/marxism-thaxis
