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.
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