Graham Priest vs Erwin Marquit on Contradiction

by Ralph Dumain

Priest, Graham. 'Dialectic and Dialetheic', Science and Society 53 (1990): 388-415.

Priest is an odd duck. He illustrates the problem of combining two disparate enterprises: the pursuit of logic as a pure formal enterprise (in his case paraconsistent logic, which admits of true contradictions, whose attendant doctrine is dialetheism), and the substantive engagement with philosophical issues and ultimately the real world. While logic was practically developed to study the nature of inference, valid and invalid argument (without larger philosophical claims), its formal form has never neatly meshed with the messiness of the real world nor with the structuring the categories of its fundamental understanding. Furthermore, mixing up logic with metaphysics has, historically, more often served the cause of mysticism than science.

In his 1995 (with additions in 2002) book Beyond the Limits of Thought, Priest bravely reviews the history of western philosophy (with Nagarjuna thrown in in 2002) and attempts to unify all paradoxes in his Inclosure Schema. Paradoxically, paradoxically, by the time he has accomplished this task, he has left the philosophical content of all these philosophies embodying these paradoxes behind. In other words, the bare formal structure he seeks to generalize does not do justice to the nature of the philosophical issues involved.

In a later paper on philosophy in the 21st century, Priest predicts that Asian philosophy will be the next big thing. Perhaps this ties in to his interest in Nagarjuna, Taoism, and the martial arts. About Marxism he seems to throw up his hands and suggest that somehow it drowned in the Sea of Ilyenkov. I'll review this article more extensively at a later date.

However, back in 1989, Priest aggressively attempts to prove that Hegel, Marx, and Engels were adherents of dialetheism. What this amounts to may prove instructive.

(1) That Hegel's dialectics is dialetheism should be a no-brainer, Priest argues. Hegel states that the very nature of motion embodies contradiction. (You will be familiar with the issue from Zeno's paradox.) But others have denied that Hegel affirms contradiction in the formal logical sense.

Marxist philosophers have made similar denials about the Marxist view of dialectical contradiction. Sometimes contradiction is characterized as the co-existence of conflicting forces, which is hardly a logical interpretation. Priest cites a few to that effect. After the Stalin era (in which contradiction hazily covered a variety of meanings), a growing number of Soviet philosophers dissociated the notion of dialectical contradiction from any taint of logical contradiction (Sheptulin, Narskii), and some maintain that contradictions hold in thought but not in reality (Narskii).

(2) The arguments against this position: In Hegel's time, the only logic extant was Aristotle's logic, which Hegel deemed inadequate from a dialectical perspective. But Frege/Russell logic is far more sophisticated, and is the gold standard now. Contradiction is even more taboo. Note Priest's quotation of Popper on dialectic. Most Marxists, who know little of formal logic, have been browbeaten into retreating from dialetheism. But now we have paraconsistent logic to the rescue.

(3) Dialetheic logic: Priest outlines the principles of paraconsistent logic, which may assign truth values of both true and false. He also discusses its semantics. He also introduces an operator ^ to nomialize sentences, e.g. ^A means "that A" (e.g. 'that Sam went to the store' is true). Further discussion.

(4) Motion: an illustration. Priest claims that paraconsistent logic can easily render Hegel's notion of the paradox of motion into logical form. He also deals with an argument based on a distinction between extensional and intensional contradiction. In extensional contradiction, there is no intrinsic connection between the conjuncts. But for intensional (putatively dialectical) contradictions, there is an internal relation between the conjuncts not captured by a mere extensional conjunction (A & not-A). Priest treats this latter qualification by way of example (with reference to Grice's conversational implicature), but leaves us hanging, and promises to pick up the argument again in section 8.

(5) The history of Hegel's dialectic: This section is quite interesting, and appears to be remote from the realm of paraconsistent logic. Hegel draw on his predecessors Kant and Fichte as well as the medieval Neo-Platonists who held that the One embodies contradictions. Priest quotes Hegel's analysis of Kant's antinomies of reason. Hegel objects to Kant's banishing contradiction from the world and relegating it to the Reason claiming that "reason falls into contradiction only by applying the categories". The postulation of the not-ego by the ego as argued by Fichte is also summarized. Art the end of this review, Priest claims to have firmly established Hegel as a dialetheist.

(6) Contradiction in Hegel's dialectic: There is a lengthy treatment of Hegel's view of Geist, with reference to Fichte, that segues into the master/slave dialectic and Sartre's notion of freedom. Then Priest takes up the argument that all these 'contradictions' do not refer to the same thing in the same respect, which he considers a dodge. (In his later book he calls this parameterization.)

(7) Contradiction in Marx's dialectics: In his youthful Feuerbachian phase, Marx transmutes Hegel's geist into Humanity and takes up the theme of alienated labor and self-development. Priest briefly characterizes the structural logic at work here. Then he skips to the mature Marx, on use-value and exchange-value, and the forces and relations of production.

Then he moves on to Engels, who states his views more plainly. We are back to the contradiction of motion. While impatient with the tendency to abuse Engels, Priest concedes that Engels saw contradiction where it doesn't exist, e.g. in his infamous claim about the square root of minus one.

(8) Identity in difference: Hegel's notion is for Priest the essential form of dialectical contradiction. Here Priest translates Hegel's argument about the identity of opposites into logical notation. The only example cited is the paradox of motion.

Priest thinks he has proved his case, as promised in section 4. Now if my abstract of the overall argument seems disjointed, this is just how I see the original. There is a schizoid tendency plainly evident to me that escapes Priest's attention:

(a) Priest qua logician can talk about logic;

(b) Priest is capable of discussing the substance of philosophical doctrines;

(c) yet, when he attempts to combine the two, he is a complete idiot. Mixing up the metaphysician in him and the logician yields only the most philistine product: the logician superficially wins out by trivially rendering some formal property in logical notation, totally evading the substantive philosophical content in the zeal to prove that A and not-A are simultaneously predicated. This is neither fish nor fowl, merely a foul fish or a fishy foul. To paraphrase Lenny Bruce, this is so obtuse, it's thrilling.

(9) Dialectics and epistemology: Priest admits that there is much more to dialectics than these formal considerations, i.e the analysis of concrete contradictory situations. He takes up the example of being-in-itself and being-in-consciousness. He then contrasts the positions of dualists (Locke), non-dialectical monists: idealists (Berkeley), traditional materialists (cf. central state materialism). Presumably, the dialectical monist resolves this conundrum. True to form (pun intended), Priest illustrates the resolution with logical notation. Miraculously, he fails to see the triviality of such a treatment, as he fails to illuminate any of the ideas involved, nor does he add anything by using the symbols c and not-c.

(10) Conclusion: Priest's bête noir is the pussyfooting around in fear of acknowledging a contradiction. Priest indeed concludes with the statement that his paper at least calls a spade a spade. (There seems to be a subtle Tarskian allusion here. It would have been more obvious—and funnier!—if he wrote: "a 'spade' is a spade" iff a 'spade' is a spade.)

It is truly remarkable that such sophisticated means should be marshalled to such an unsophisticated end. It is also most telling that throughout the essay Priest favorably refers to Sean Sayers, with whom he even shared a draft of his paper. He also references this debate, published in a book:

Norman, Richard and Sean Sayers. Hegel, Marx and Dialectic. Harvester Press, 1980.

My long-term readers will recognize this title and recall that I wrote an exhaustive analysis of this debate in the mid-'90s. Very briefly: Sayers took the most philistine position, defending the most intellectually sloppy version of dialectical materialism (clogged up with fudge on the nature of logic, which even the Soviets abandoned after the Stalin era), adding further offense by citing Mao. Norman defends Engels' general effort to formulate a nonreductive materialism while criticizing his logical confusions and Sayers' shoddy reasonings. But there was never a Maoist anywhere who was not a moron, and Norman's analysis fell on deaf ears (or blind eyes). That Priest could embrace Sayers as he does is truly a prodigious feat for a logician. Here we have an example of not only the troubled relation between logic and reality, but the vexed relation between their intermediary—philosophy—and logic. Logic as a self-contained formal enterprise is one thing; engagement with philosophical issues another, and the reality beyond yet something else. Aside from the historical fact that philosophy and logic were done by the same people (in China and India as well as in what is called the West), in my opinion they make very poor bedfellows.

11 September 2005


Priest, Graham. 'Was Marx a Dialetheist?', Science and Society, 54 (1991): 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, 54, no. 2 (Summer 1990): 147-166.

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 three 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.

11 September 2005

Postscript (response to complaint)

My review is part of a much larger project, which has to do with the relation of logic and reality, and beyond that, the fragmentation of knowledge under conditions of alienation. That would be the "Marxist" angle that interests me, rather than advocacy of 'Marxism' per se. Graham Priest is far more interesting than Sean Sayers was at the time of the debate in question. But let's review the logic of my intervention.

Priest's book (1995, 2002) Beyond the Limits of Thought doesn't mention Marx or Marxism, though Hegel emerges as the hero of the book. We also know from Priest's earlier two essays in Science and Society that he is a Marxist or has a keen interest in Marxism. Furthermore, he is one of those rare individuals in the English-speaking world with an interest in both dialectics and formal logic. So it is important to see how he seeks to unite the two. But oddly—and this part of my larger purview—he doesn't seem to have a whoe lot to say about dialectics (or about the vcarious philosophies he treats later) except to make his one big pitch for paraconsistent logic which offers a formalism for incorporating contradictions. But what good is this formalism in terms of modeling reality in a substantive fashion? I can't tell. And this, it seems to me, Priest merely reproduces the conditions of alienated theoretical labor and fails to overcome fragmentation and to unify an understanding of how logic relates to other philosophical issues and to objective reality itself. His grasp of formal logic should make him far more sophisticated than the dialectical materialists of old, but he seems bent on making the same trivial points.

15 September 2005


Erwin Marquit's articles in Science and Society offset the two articles by Graham Priest previously described.

Marquit, Erwin. "Dialectics of Motion in Continuous and Discrete Spaces," Science and Society, vol. 42, Winter 1978-79, 410-425.

Marquit, Erwin. "Contradictions and Dialectics and Formal Logic," Science and Society, vol. 45, no. 3, Fall 1981, 306-323.

Marquit, Erwin. "A Materialist Critique of Hegel's Concept of Identity of Opposites," Science and Society, vol. 54, no. 2, Summer 1990, 147-166.

See also Marquit's article in Nature, Society and Thought:

Marquit, Erwin. "Distinctions Between the Spheres of Action of Formal Logic and Dialectical Logic," Nature, Society and Thought, vol. 3, no. 1, 1990, 31-37.

Both Marquit (1981) and Priest (1990-91) refer to Marquit (1978-79). Marquit also refers to Marquit (1981) and Marquit's article in NST. Marquit (1990) reacts to Priest (1989-90), and Priest (1990-91) reacts to Marquit (1990).

There, now that we've cleared that up . . .

Marquit (1981) endeavors to clarify the three 'laws of dialectics' beginning with a formulation of what he calls "law zero", the law of universal interconnection. He then clarifies the logic of the famed three laws and their relation one to one another. His next step is to clarify objective and subjective dialectics and their relation to one another. Taking examples of antinomial statements which seem to embody logical contradictions, Marquit then argues that dialectical contradictions are not logical contradictions. (319). Examples chosen from Hegel, Engels, and quantum mechanics can be expressed in the form: "A changing object exists in a given state and not in the given state at the same time." Other views are brought in from Ilyenkov, F.F. Vyakkerev, Gottfired Stiehler, and D.P. Gorskii. Marquit's main inspiration is Igor S. Narski.

While I have not really described Marquit's argument, I will give him credit for treating this matter in an uncommonly precise and sophisticated manner, which Priest (the logician!) unaccountably shortchanges. I don't recall what I've seen by Narski, though I am familiar with the name. Also in evidence is the increasing professionalism and sophistication of Soviet philosophers following the death of Stalin.

17 September 2005


Marquit, Erwin. "A Materialist Critique of Hegel's Concept of Identity of Opposites," Science and Society, vol. 54, no. 2, Summer 1990, 147-166.

Marquit details the treatment by Hegel and Engels of dialectical contradictions as logical contradictions. Marquit claims that materialist dialectics, in contradistinction to idealist dialectics, "dialectical negation is embodied by the unity of the historical and the logical." (152) "Hegel's need for the identity of opposites is made clear by his insistence that one must begin with the identity of pure being and pure nothing " (154) and is tied up with the changeability of essence. But materialist dialectics "starts from differentiated being". Marquit treats of an example from quantum mechanics, and returns to Zeno's paradox (the clearest case offered by Engels). The paradox arises from viewing motion as a succession of stopped states. While this is a necessary procedure of analysis, we must recognize that the paradox arises from just this cognitive act. (157) Both Hegel and Lenin recognized this problem. Marquit then returns to another example from quantum mechanics, and explains how the dialectical contradiction does not yield a logical contradiction. (158-9)

Marquit then criticizes Priest (1989/90) and takes up the noted example of Marx's 20 yards of linen, then proceeds to other examples. Marquit then criticizes Sean Sayers, and suggests that Marxists have barely begun to elaborate the dialectical character of major scientific and mathematical breakthroughs (163). Marquit then turns to Ilyenkov, who tends to avoid any postulation of logical contradictions and who provides a much subtler analysis than Priest. (163-5)

The upshot, I think, is that even if Priest can prove Marquit wrong in arguing for contradictions in 'the same respect', that one point does not render his analysis of the issues involved any subtler, nor does it lead to interesting arguments and conclusions. The argument is to one point only—the admission of contradictions into formal logic. And so?

17 September 2005


Graham Priest, Paraconsistent Logic, and Philosophy, Or, Logic and Reality
by R. Dumain

Graham Priest's Inclosure Schema

Dialectics Bout: Richard Norman vs. Sean Sayers by R. Dumain

What is the Relationship Between Logic and Reality? by R. Dumain

Philosophy of Paraconsistency & Associated Logics (Web Guide)

Salvaging Soviet Philosophy (1)

Marx and Marxism Web Guide

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Paraconsistency and Dialectical Consistency by Jindrich Zelený


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