Originally published in Science & Society, vol. 54, no. 2 (Summer 1990), pp. 147–66
One of the principal problems faced by dialectical materialism has been the relationship between formal logic and dialectics. A view that is often encountered among dialectical materialists is that formal logic is applicable to static situations, but since, in reality, nothing is static, formal logic is superseded by dialectical logic, which permits logical contradictions. Within the framework of this view, thought is the appropriation (in the mind) of the objectively existing material world, while dialectical logic, that is, dialectics taken as logic, must be considered to be the laws of thought (or correct thinking). Thus, in the approximation where things are viewed as static, formal logic becomes the laws of thought, equally in approximation. When, however, things are viewed in their motion, change, and development, dialectical logic becomes properly the laws of thought.
Logicians point out that if one accepts a logical contradiction, any statement can be proved to be true. Even physical scientists sympathetic to Marxism are apprehensive about using explicit dialectical approaches in their work in an atmosphere of suspicion about the logical consistency of dialectical materialism.
In an earlier work I have argued that dialectical logic does not supersede formal logic in the sense that it can accept violations of formal logic (Marquit 1981). In the Marxist classics the clearest explicit example of a logical contradiction occurs in the discussion of Zeno’s paradoxes of motion by Engels. My own attention had been turned to these paradoxes in connection with the need for a generalization of the concept of spatial motion valid for both continuous and discrete (quantized) spaces (Marquit 1978–79).
In this paper I shall argue that Engels’s acceptance of the view that dialectical contradictions can embrace logical contradictions is rooted in Hegel’s idealism.
Dialectical Contradictions as Logical Contradictions in Engels and Hegel
In a passage on contradiction in Anti-Dühring, Engels writes:
True, so long as we consider things as at rest and lifeless, each one by itself, alongside and after each other, we do not run up against any contradictions in them. We find certain qualities which are partly common to, partly different from, and even contradictory to each other, but which in the last-mentioned case are distributed among different objects and therefore contain no contradiction within. Inside the limits of this sphere of observation we can get along on the basis of the usual metaphysical mode of thought. But the position is quite different as soon as we consider things in their motion, their change, their life, their reciprocal influence on one another. Then we immediately become involved in contradictions. Motion itself is a contradiction: even simple mechanical change of position can only come about through a body being at one and the same moment of time both in one place and in another place, being in one and the same place and also not in it. And the continuous origination and simultaneous solution of this contradiction is precisely what motion is. (Engels 1947, 144)
In the first part of this excerpt, Engels is referring to contradictions that have the form of a logical contradiction, but are not contradictions in content. One such example is Marx’s statement that capital “must have its origin both in circulation and yet not in circulation” (Marx 1967, 1:166). Here Marx is referring to the fact that the source of capital is surplus value, which is produced in the sphere of production. The very act of employing wage-labor under capitalist relations of production entails the realization of surplus value by the capitalist, but surplus value in commodity form. Its transformation into monetary form so that it can serve as capital takes place in the sphere of circulation. Hence the phrase “have its origin” is being used in two distinct senses and therefore we are not dealing with a case of simultaneously A and not-A in the same respect. Engels’s example of spatial motion, however, is given in both form and content as a logical contradiction. His example is not one selected by chance. It is associated with Zeno’s paradoxes of motion and was discussed by Hegel in his Science of Logic (1947, 440). Extensive notes on this question were made by Lenin (1963, 252–63) while reading a discussion of Zeno and the Eleatic School by Hegel in the latter’s Vorlesungen über die Geschichte der Philosophie [Lectures on the History of Philosophy] (Hegel 1938, 334–38).
In his Science of Logic, Hegel writes:
External, sensuous motion itself is contradiction’s immediate existence. Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this “here,” it at once is and is not. The ancient dialecticians must be granted the contradictions that they pointed out in motion; but it does not follow that therefore there is no motion; but on the contrary, that motion is existent contradiction itself. (1969, 440)
It is important to note that Hegel is not referring to the representation of motion but to motion itself. He continues with another example: “Similarly, internal self-movement proper, instinctive urge in general . . . is nothing else but the fact that something is, in one and the same respect, self-contained and deficient, the negative of itself.” (1969, 440)
Hegel’s deliberate use of the phrase “in one and the same respect” is an obvious assertion of the presence here of a logical contradiction. Thus for Hegel the instinctive urge of hunger would be a logical contradiction. The absence of food in the stomach gives rise to the instinctive urge to eat. The urge and the absence are dialectically related in the sense that they are mutually exclusive, mutually conditioned dialectical oppositions. The consequence of this unity and interpenetration (or struggle) of opposites leads to eating. Hegel sees the absence passing over to the urge. Since this movement is not a movement in time, he views absence and urge as present simultaneously. However, he also asserts paradoxically that they are identical and in the same respect, suggesting thereby the presence of a logical contradiction. He recognizes that this identity of opposites is not readily comprehended, so he offers a further example:
If the contradiction in motion, instinctive urge, and the like, is masked for ordinary thinking, in the simplicity of these determinations, contradiction is, on the other hand, immediately represented in the determinations of relationship. The most trivial examples of above and below, right and left, father and son, and so on ad infinitum, all contain opposition in each term. That is above, which is not below; “above” is specifically just this, not to be “below,” and only is in so far as there is a “below,” and conversely, each determination implies its opposite. Father is the other of son, and son the other of father, and each only is as this other of the other; and at the same time, the one determination only is, in relation to the other; their being is a single subsistence. The father also has an existence of his own apart from the son-relationship; but then he is not father but simply man; just as above and below, right and left, are each also a reflection-into-self and are something apart from their relationship, but then only places in general. Opposites, therefore, contain contradiction in so far as they are, in the same respect, negatively related to one another, or sublate each other and are indifferent to one another. (441)
Hegel’s reference here to “at the same time” and “in the same respect” is his way of asserting father and son are in logical contradiction. Hegel is indicating here that father and son as distinct human beings are not a contradiction. He is not discussing the people, but the relationship. By saying that father is the other of son and son the other of father, Hegel is expressing the mutual conditionedness of father and son. By viewing father and son as a logical contradiction, Hegel considers them not only opposites, but also identical. The unity of opposites is at the same time their identity.
In all of the examples above, the logical contradiction lies in the notion of the unity of opposites which are distinct from one another while being identical. The identity of the opposites subsists by a self-movement in the notion whereby one passes over into the other and returns to itself.
[Ordinary thinking] holds these two determinations over and against one another and has in mind only them, but not their transition, which is the essential point and which contains the contradiction. Intelligent reflection, to mention this here, consists, on the contrary, in grasping and asserting contradiction. (441)
Hegel approaches the law of identity in formal logic in the same manner. Lawler argues that Hegel does not deny the validity of formal logic, but criticizes the failure to interpret it dialectically (Lawler 1982). Lawler cites Hegel’s criticism at merely representing the logical structure of such a statement as A = A, which, according to Hegel, would be a tautology and not serve any useful purpose. Lawler asserts that Hegel, rather than rejecting the law of identity, retains it, but only in conjunction with what Hegel refers to as “the other expression of the law of identity,” namely, the law of noncontradiction, A cannot at the same time be A and not-A, which he considers to be a higher form of the same law. “Usually,” writes Hegel, “no justification is given of how the form of negation by which this law is distinguished from its predecessor, comes to identity.” Hegel continues:
But this form is implied in the fact that identity, as the pure movement of reflection, is simple negativity which contains in more developed form the second expression of the law just quoted. A is enunciated, and not-A, the pure other of A; but it only shows itself in order to vanish. In this proposition, therefore, identity is expressed—as negation of the negation. A and not-A are distinguished, and these distinct terms are related to one and the same A. Identity, therefore, is here represented as this distinguishedness in one relation or as simple difference in the terms themselves. (1969, 416)
Hegel here is asserting that the law of identity is meaningful only if the identity is also associated with a difference. In formal logic this ordinarily would not constitute a logical contradiction, since two things can share a common property and yet differ from one another in other respects. Nevertheless, Hegel asserts the identity of the law of noncontradiction with its opposite, the law of identity, and generates, in this way, a logical contradiction. However, here, as everywhere else, he avoids drawing any conclusions on the basis of a violation of the law of noncontradiction, treating the identity of opposites in practice as separate moments in thought, never applying them simultaneously to produce a logical contradiction except in the case of offering a solution to Zeno’s paradoxes of motion. Even in the latter case, he equivocates, as we shall see shortly.
Before examining why Hegel needs to assert not only the unity, but also the identity, of opposites, let us consider two cases of dialectical oppositions.
As our first case we consider an opposition that is responsible both for stability as well as for change, as might occur in the case of a physical system whose structure is maintained stable by a relative balance in the forces of attraction and repulsion. If the balance is disturbed by the quantitative increase in one of these forces, the system can then undergo qualitative transformation. One example of such a system is a star in which the forces of repulsion are provided by radiation arising from the process of thermonuclear combustion of hydrogen into helium. The star remains relatively stable because these outwardly acting forces are offset by the attractive force of gravity. Upon depletion of the hydrogen, the balance is destroyed and a gravitational collapse (e.g., into a supernova) occurs. Repulsion and attraction are distinct from one another (mutually exclusive) and exist only in relation to one another (mutually conditioned)—therefore they are dialectical opposites. Both are physical forces and in this sense they share a mutual identity. When a physical force arises between two objects, the action of the first on the second is opposite to the reaction of the second to the first. One negates the other, but the negation arising from the passage of one to the other is movement in thought, not in time, that is, a change of aspect. Each is opposite with respect to the other so that the identity is not an identity in every respect, but only in a certain respect. No logical contradiction need be invoked.
As a second dialectical opposition consider an object undergoing change, becoming what it was not and ceasing to be what it was. When we say that an object undergoes change we are implying that the object retains some aspect of its distinctiveness from other things, so that it preserves itself in some way. This thread of continuity is what distinguishes change from chaos (unrelated occurrences). Hegel introduced the term sublation to describe this process of dialectical negation: “What is sublated is at the same time preserved; it has only lost its immediacy but is not on that account annihilated” (Hegel 1969, 107). In materialist dialectics, this type of dialectical negation is embodied by the unity of the logical and the historical. The process by which objects become distinct from one other is a historical process. They acquire their distinctiveness in time. Once a material distinction has originated, the distinction can be appropriated by thought, so that the logic of the structural distinctiveness is a mediated reflection of the historical process.
The idealist dialectics of Hegel’s logic does not share the materialist need for the unity of the logical and the historical.
The movement to which Hegel refers is movement in the notion but not in time. Therefore what is to become is already present in what was. Every object must be completely identical to itself, (A), and at the same time completely different from itself, (not-A). Consider his statement above that “identity, as the pure movement of reflection, is simple negativity. . . . A and not-A are distinguished, and these distinct terms are related to one and the same A.” He is asserting that the object contains a logical contradiction insofar as it is A and not-A at the same and in the same respect.
Hegel begins his Science of Logic with “being, pure being without further determination.” He then introduces “nothing, pure nothing: it is simply equality with itself, complete emptiness, absence of all determination and content, undifferentiatedness in itself.” He then asserts both the identity and distinctness of being and nothing:
Pure being and pure nothing are, therefore, the same. What is the truth is neither being nor nothing, but that being—does not pass over but has passed over into nothing, and nothing into being. But it is equally true that they are not undistinguished from each other, that, on the contrary, they are not the same, that they are absolutely distinct, and yet that they are unseparated and inseparable and that each immediately vanishes in its opposite. Their truth is, therefore, this movement of the immediate vanishing of the one in the other: becoming, a movement in which both are distinguished, but by a difference which has equally immediately resolved itself. (1969, 82—83)
Hegel then sees becoming as double determination: coming-to-be and ceasing-to-be. He continues:
The resultant equilibrium of coming-to-be and ceasing-to-be is in the first place becoming itself. But this equally settles into a stable unity.
. . . Becoming is the vanishing of being in nothing and of nothing in being and the vanishing of being and nothing generally. (106)
The result of this vanishing is not nothing, since this would not take us further.
It is the unity of being and nothing which has settled into a stable oneness. . . . Becoming, as this transition into the unity of being and nothing, . . . is determinate being. (106)
Proceeding in this way, Hegel can now unfold the world ahistorically in all its qualitative and quantitative distinctness from pure indeterminate being, on which he bases his concept of God. Whatever is to be is already present in pure being.
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:
Thus the whole true result which we have here before us is becoming, which is not merely the one-sided or abstract unity of being and nothing. It consists rather in this movement, that pure being is immediate and simple, and for that very reason is equally pure nothing, that there is a difference between them, but a difference which no less sublates itself and is not. The result, therefore, equally assets the difference of being and nothing, but as a merely fancied or imagined difference.
. . . Let those who insist that being and nothing are different tackle the problem of stating in what the difference consists.
. . . The challenge to distinguish between being and nothing also includes the challenge to say what, then, is being and what is nothing. Those who are reluctant to recognize either one or the other as only a transition of the one into the other, and who assert this or that about being or nothing, let them state what it is they are speaking of, that is, put forward a definition of being and nothing and demonstrate its correctness. (91–92)
In Hegel’s idealism, the starting point is the Idea, identical to pure undifferentiated being. He employs the dialectic to unfold its contents. The unfolding, as a movement in thought, needs the concept of identity of opposites, as we have seen above. Materialist dialectics, on the other hand, starts from differentiated being, that is, from the concrete material world in its motion and development. The differentiation of structures, as well as their motion and development, arises in a historical process from the interpenetration of opposites which are present in all things. Unlike idealist dialectics, which focuses its attention on being overcoming nonbeing, materialist dialectics focuses its attention on how one form of being overcomes another form of being. In materialist dialectics, the identity of opposites is a shared property, and changes in matter result from the interaction of these oppositions (dialectical contradictions). In Hegel’s idealist dialectics, qualitative changes emerge as reflections of transition in thought from distinctness to identity without the passage of time so that one thing is at the same time different and identical to itself, that is, from the “asserting and grasping [formal-logical] contradiction.” I have put the phrase “formal-logical” in brackets because this is clearly what Hegel is implying, although he does not state this, probably because he does not consider formal logic to be applicable to movement in thought.
In the “notes and fragments” section of Dialectics of Nature, however, Engels echoes Hegel in relation to the identity of opposites:
Abstract identity (a = a); and negatively, (a cannot be simultaneously equal and unequal to a) is likewise inapplicable in organic nature. The plant, the animal, every cell is at every moment of its life identical with itself and yet becoming distinct from itself, by absorption and excretion of substances, by respiration, by cell formation and death of cells.
. . . The law of identity in the old metaphysical sense is the fundamental law of the old outlook: a = a. Each thing is equal to itself. Everything was permanent, the solar system, stars, organisms. This law has been refuted by natural science bit by bit in each separate case, but theoretically it still prevails and is still put forward by the supporters of the old in opposition to the new: a thing cannot simultaneously be itself and something else. And yet the fact that the true, concrete identity includes difference, change, has recently been shown in detail by natural science. (1954, 214–15)
Engels’s statement that an object undergoing change is remaining “identical with itself and yet becoming distinct from itself” is, among other things, a reference to the thread of continuity uniting the object in its previous state to its new or changed state, so that the object retains its integrity while in some respects it changes. There is no need to assert the identity of opposites in the sense of Hegel. We have seen above how Hegel gave the law of identity a dialectical content by showing its connection to the law of noncontradiction as identity in difference. This is also the sense of Engels’s assertion that “identity includes difference, change.” Hegel, and Engels after him, criticized the metaphysical outlook of Leibniz and his pupil Christian Wolff, who interpreted the law of identity, A = A, as an expression of the unchanging essence of things. Hegel derived the changeability of essence through dialectical negation. Engels, in accepting Hegel’s concept of identity of opposites, did not consider the limited character of the identity and therefore accepted Hegel’s view that dialectical negation embodied logical contradictions.
Let us consider one more example from Engels:
Another opposition in which metaphysics is entangled is that of chance and necessity. What can be more sharply contradictory than these two thought determinations? How is it possible that both are identical, that the accidental is necessary and the necessary is also accidental?
. . . Hegel came forward with the hitherto quite unheard-of propositions that the accidental has a cause because it is accidental, and just as much has no cause because it is accidental; that the accidental is necessary, that necessity determines itself as chance, and, on the other hand, this chance is rather absolute necessity. (217–20)
Is it a logical contradiction to assert that the accidental is necessary and the necessary is also accidental? Quantum physics gives statistical laws that govern interactions in the microworld. If a beam of high-energy particles is aimed at a vessel containing liquid hydrogen, a variety of particles emerge from the collisions of the incident particles with the hydrogen nuclei. We can predict statistically how many particles of each type will be produced in each collision. The law-governed character of the resulting products of the interaction is a consequence of the fact that the result of each individual collision is a random occurrence, completely independent of all previous and subsequent collisions. Thus a particular experimental arrangement necessarily produces chance events. The chance events necessarily give rise to a predictable statistical distribution. Chance gives rise to necessity. With respect to the individual collisions, the result is necessarily accidental. With respect to the ensemble of collisions, the resulting statistical distribution is a necessary outcome if the ensemble is sufficiently large for the statistical law to assert itself. The individual collision is identical to the ensemble of collisions in the same respect as the individual in formal logic is identical to the general. The individual collisions yield chance behavior, while the behavior of the ensemble is necessary echoes the statistical law. The individual need not have the same properties as the ensemble. The individual collision is a product of the statistical law, but a single collision does not itself possess the resulting statistical distribution. No logical contradiction need be asserted to account for this two-fold dialectical character of chance and necessity.
We can now return to what can be considered to be the most explicit expression of a logical contradiction in the classics of Marxism, Engels’s statement on spatial (mechanical) motion, which was cited in the opening pages of this paper. My statement above that materialist dialectics focuses its attention on how one form of being overcomes another form of being is not without its logical problems, because it implies primacy to the existence of states rather than to the transition between them. The relation between states and transitions between them lies at the heart of Zeno’s paradoxes of motion. We can only represent a state by stopping its motion. Motion is then viewed as a succession of states of stopped motion. Materialist dialectics can solve these paradoxes by asserting the primacy of motion over state of being, so that a state of being is always transitory and approximate. Modern physics now accepts the approximate character of the representation of motion in terms of trajectories, that is, the representation of motion in terms of a succession of uniquely defined positions, so that the physical basis of Zeno’s paradoxes of motion has vanished. I have discussed this in detail in an earlier article (Marquit 1978–79). But we have no way of embracing motion by thought in any other terms than a succession of states, like the succession of frames projected on the screen in a cinema. Hegel recognized this difficulty and Lenin drew special attention to it in his Philosophical Notebooks in which he cited Hegel’s words: “What makes the difficulty is always thought alone, since it keeps apart the moments of an object which in their separation are really united.” In recognizing this difficulty, Hegel, in effect, acknowledges the practical impossibility of representing motion in a logically contradictory manner (something moves “because at one and the same moment it is here and not here”), so that his assertion that motion embodies a logical contradiction is without practical consequence. Lenin expressed this difficulty more dramatically than Hegel:
We cannot imagine, express, measure, depict movement without simplifying, coarsening, dismembering, strangling that which is living. The representation of movement by means of thought always makes coarse,--and not only by means of thought, but also by sense-perception, and not only of movement, but every concept. (259–60)
The problem of representing spatial motion came to the fore in connection with quantum physics. In classical physics, the state of a particle is represented by its position and momentum (the latter being the product of the mass and velocity) at a given instant. The succession of positions occupied by a particle in motion is called a trajectory. In quantum physics, however, a particle does not go from here to there by passing through a succession of positions. For example, consider a beam of electrons directed toward a phosphorescent screen such as occurs in the picture tube of a television set. Assume that the beam impinges evenly over a region of an obstacle that includes two small closely spaced openings. The pattern of flashes of light that appears on the screen as the electrons strike it cannot be explained by the assumption that some electrons passed through one of the two openings while others passed through the other opening. Rather, it would be more accurate to say that each electron in the beam interacted with the system consisting of an obstacle with two openings. This can be clearly demonstrated as follows. Keeping the intensity of the beam unchanged, expose a photographic plate to the light from the screen for five seconds with one of the openings covered. Then, expose the photographic plate for another five seconds with this opening uncovered and the other opening covered. In this way each opening is accessible to the beam for five seconds. Now replace the photographic plate with a fresh one and let the beam impinge on the obstacle for five seconds with both openings uncovered. When the two photographic plates are developed, it will turn out that the two resulting patterns are quite different, so that it cannot be said that the electrons passed through either one or the other opening when the two openings were uncovered. In other words, the description of the motion in terms of the electrons passing through a succession of uniquely defined positions (which is what the term trajectory implies) is an inadequate representation of this process. Hence, Engels’s example of spatial motion as logical contradiction is not physically realizable.
It has also turned out that one cannot, in general, assign unique values at every instant to states of matter that are undergoing transformation. In fact, one has to assign a range of mass values rather than a unique value to the mass of any radioactive particle. This is the basic content of one form of Heisenberg uncertainty relations. If we accept the concept of motion as a transition between states in which the transition is taken as primary, as leaving one state and the entering another, then we encounter no logical contradiction as long as recognize the states between which the transition occurs as approximate and transitory. No logical contradiction need arise.
Recent Contributions to the Discussion
The position presented here, that materialist dialectics does not need the concept of identity of opposites, and, consequently, does not need to consider dialectical contradictions to be logical contradictions, is disputed, among others, by Graham Priest (1989). It will be of interest to this discussion to consider the examples of dialectical contradictions he gives to illustrate such logical contradictions. It will facilitate an understanding of the discussion to note that Marx often used the word value to denote exchange value.
Priest refers to Marx’s discussion of the contradictions in what Marx called the “elementary or accidental form of value.” Among the examples given by Marx of this form is “20 yards of linen are worth 1 coat” (Marx 1967, 48–49). Marx stressed the differences in the roles of the two commodities. “The value of the linen is represented as relative value, or appears in relative form. The coat officiates as equivalent, or appears in equivalent form.” Marx then notes their dialectical interconnection:
The relative form of the value of the linen pre-supposes, therefore, the presence of some other commodity--here the coat--under the form of an equivalent. On the other hand, the commodity that that figures as the equivalent cannot at the same time assume the relative form
Marx them notes that if the expression were reversed to state that 1 coat is worth 20 yards of linen, the linen becomes the equivalent instead of the coat. Marx then concludes that
a single commodity cannot, therefore, simultaneously assume, in the same expression of value, both forms. The very polarity of these forms makes them mutually exclusive.
Priest, considers this last state of Marx to be one side of what will be a logical contradiction. He summarizes the content of this last statement of Marx as “an object, a, may be a use value, Ua, or an (exchange value), Va. but not both, ~(Ua&Va).” Priest then adds: “But in the exchange of a commodity, the commodity is related to another as both use and (exchange) value; it is therefore both: Ua&Va.”
Marx does not state that one commodity is related to another simultaneously as both a use value and exchange value. In the statement “20 yards of linen are worth 1 coat,” the linen displays its exchange value, while the coat displays its use value. To be a commodity, an object must have the potential to serve as a use value or an exchange in the expression of the elementary form of value. Its exchange value (expressible quantitatively), as Marx showed, is determined by the socially necessary labor-time embodied in its production. It use-value is associated with one of its many qualitative sides, the ability to satisfy a need.1 Prior to the exchange the owner of the linen views the linen as a use value, its use value being that it is a commodity, that it can serve (quantitatively) as an exchange value in an exchange for a coat, which the owner of the linen views (qualitatively) as a use value. In the exchange, displays only one of its twofold aspects to its owner. The dialectical contradiction is not a logical one, since it refers to two different aspects of the properties of a commodity. Marx makes this clear explicitly: “While, therefore, with reference to use-value, the labour contained in a commodity counts only qualitatively, with reference to value it counts only quantitatively. (1967, 45).
Priest gives other examples of dialectical contradictions that he considers to be logical contradictions, but acknowledges that “the accusation may be leveled that these states are not literally contradictory, since the contradictory predicates are true in different respects.” “The charge may have some justice;” he adds, “but to suppose that this is always so is just wishful thinking” (408). He then gives what he obviously considers to be a case of an unquestionable logical contradiction: Marx’s analysis of the inseparability of the freedom of wage-laborers from their bondage. This example, however, is also readily shown to be noncontradictory in the formal-logical sense. Marx, criticizing Adam Smith writes:
It seems quite far from Smith’s mind that the individual, “in his normal state of health, strength, activity, skill, facility,” also needs a normal portion of work. . . . The external aims become stripped of the semblance of merely external natural urgencies, and become posited as aims which the individual himself posits—hence as self-realisation, objectivification of the subject, hence real freedom, whose action is, precisely labour. [Smith] is right, of course that in its historic forms as slave-labour, serf-labour, and wage-labour, labour always appears as repulsive, always as external forced labor; and not labour, by contrast, as “freedom and happiness.” (cited in Priest 1989, 408)
Priest then adds, “This forced but self-creating nature of wage-labour is not the only critical tension existing in this contradiction. There is also that between the legal position and the harsh reality of the laborer’s situation.” Again he offers a citation, from Marx in which we read in part:
The contract by which [the worker] sold his labour power to the capitalist proved in black and white, so to speak, that he was free to dispose of himself. But when the transaction was concluded, it was discovered that he was no “free agent,” that the period of time for which he is free to sell his labour-power is the period of time for which he is forced to sell it. . . . For “protection” against the serpent of their agonies, the workers have to put their heads together, and, as a class, compel the passing of a law, an all-powerful social barrier by which they can be prevented from selling themselves and their families into slavery and death by voluntary contract with capital.
Despite Priest’s conviction to the contrary, there are no logical contradictions here. Participation in conscious labor is a necessary condition for the continuation of human existence (self-realization). Historical materialism establishes the dialectical connection between freedom and necessity by considering freedom to be the ability to act to satisfy one’s needs on the basis of knowledge of those needs. Under conditions bound labor, be it slave-, serf-, or wage-labor, the laborers are satisfying one of their many needs, the self-realization discussed above. But with respect to the meeting of other needs—adequate diet, housing, rest, education, etc.—the laborers are not free and cannot be free without the power to appropriate the product of the labor, including the determination of the conditions under which their labor is being performed. In the case of wage-labor, the worker are free only in respect to the choice of entering or not entering into a contract to labor, but are not free with respect to the choice of the conditions of labor as long as they do not have the means of production at their disposal. Priest has not succeeded in demonstrating that dialectical contradictions are logical contradictions.
Sean Sayers, in his article “Contradiction and Dialectic in the Development of Science” (1981–82), comes to the defense of dialectics in what he identifies as negative and positive ways. His negative way is essentially to question the universal applicability of the law of noncontradiction. The problem with this negative approach is twofold. Sayers does not present any concrete evidence of a violation of the law of noncontradiction other than a rather general reference to Zeno’s paradoxes of motion. I have already indicated that the usefulness of Zeno’s paradoxes in this matter is questionable. The second problem with this negative approach is the impossibility of disproving the general applicability of the law of noncontradiction, since the law does not arise from a specific proof. The law of noncontradiction is a fundamental law of classical logic. Fundamental laws in any field are not derivable from other laws, otherwise they would not be considered fundamental; they must be postulated on the basis of extensive human experience with the material world from which these experiences emerge. Laws once considered to be fundamental may prove to be unnecessary as fundamental laws, in which case they can be discarded. Some logicians, for example, raise questions about the necessity of one of the laws of classical logic, namely, the law of the excluded middle. Nevertheless, although modern formal logic is not formulated in classical terms, it still retains the essential content of the law of noncontradiction.
Sayers’ positive way is to show the necessity of taking dialectical contradictions into account in order to understand processes in the spheres of nature, society, and thought. To this I would add the importance of demonstrating the dialectical content of the contributions made by scholars in different fields who were not consciously aware of the dialectical character of their solutions to problems in their fields. The work of Charles Darwin is well known in this respect; Isaac Newton’s success in establishing the quantitative relationship between force and the change in spatial motion of a physical body was based on his introduction of two dialectically connected forces as a phenomenal manifestation of the mass (Marquit 1990b); Richard Dedekind succeeded in establishing the mathematical concept of continuity of points on a line through the introduction of a discontinuity in the line (now known as the Dedekind cut). Marxist scholars have barely begun to elaborate the dialectical character of the major scientific breakthroughs.
The most influential Soviet philosopher to deal with the problem of the relationship between formal and dialectical logic in the postwar period was probably the late E. V. Il’yenkov. A summary of his views on the subject can be found in his work Dialekticheskaya Logik, published in 1974, and subsequently published in English under the title Dialectical Logic. Il’yenkov discusses some of the same examples from Marx that Priest discusses. His approach is similar to Priest’s, but with a subtle difference. Il’yenkov, like Hegel, does not state explicitly that dialectical contradictions are logical ones, but, like Hegel, repeatedly stresses that they occur simultaneously in the same respect. As an example, he takes Marx’s discussion of the elementary form of value (already considered above), namely, “20 yards of linen are worth 1 coat.” Il’yenkov considers the fact that “each of the two commodities—linen and coat—mutually measures the other’s value and also mutually serves as the material in which it is measured.” He considers this as “one concrete objective relation, a mutual relation” and concludes that “each of the commodities is simultaneously and, moreover, within one and the same relation in both mutually exclusive forms of the expression of value” (1977, 332–33, emphasis in original). Marx, however, stresses precisely the opposite:
No doubt, the expression 20 yards of linen = 1 coat, or 20 yards of linen are worth 1 coat, implies the opposite relation: 1 coat = 20 yards of linen, or 1 coat is worth 20 yards of linen. But, in that case, I must reverse the equation, in order to express the value of the coat relatively; and, so soon as I do that, the linen becomes the equivalent instead of the coat. A single commodity cannot, therefore, simultaneously assume, in the same expression of value, both forms. (Marx 1967, 49.)
Here Marx is, in fact, rejecting I1’yenkov’s formulation as an unacceptable logical contradiction.
In another argument, Il’yenkov utilizes the dialectic of phenomena and essence, according to which the phenomena are external manifestations of the internal essence. Thus the exchange of twenty yards of linen for one coat is the external manifestation of the inner essence of the commodity, that is, the dialectical opposition of exchange and use value. In his view, the internal contradictions occur simultaneously and in the same respect, but manifest themselves externally in different respects, but “the metaphysician” (i.e., the nondialectical thinker), “always strives to reduce the internal relation to an external one . . . to a contradiction ‘in different relations,’ denying it objective significance” (1977, 335). According to Il’yenkov, the elementary form of value embraced by the equation 20 yards of linen = 1 coat expresses the contradiction in the absolute content of each of the commodities—the inner contradiction between value and use value (1977, 333–34). I have already shown above that this inner contradiction between exchange value and use value is not also a logical contradiction. This is why its external manifestation is not also a logical contradiction.
I1’yenkov’s avoidance of the characterization of dialectical contradictions as logical contradictions is obviously deliberate. It is connected with his acceptance of Hegel’s concept of identity of opposites in face of the need to employ formal logic in scientific investigations:
If a contradiction arises of necessity in the theoretical expression of reality from the very course of the investigation, it is not what is called a logical contradiction, though it has the formal signs of such but is a logically correct expression of reality. On the contrary, the logical contradiction, which there must not be in a theoretical investigation, has to be recognised as a contradiction of terminological, semantic origin and properties. . . . Strictly speaking it relates to the use of terms and not to the process of the movement of a concept. The latter is the field of dialectical logic. But there another law is dominant, the law of the unity or coincidence of opposites, a coincidence, moreover, that goes as far as their identity. (342–43.)
Il’yenkov thus recognizes that the concept of identity of opposites is necessary for the acceptance of contradictions that exist simultaneously in the same respect.
In my view, the association of dialectical logic with motion in the material and mental spheres must also include its association with relatively stable systems of matter and thought as a particular case of motion (Marquit 1990a), just as Newton considered a state of rest as a particular case of uniform straight-line motion. Therefore, it is incorrect to separate formal logic from dialectical logic by asserting that the former applies to unchanging situations, while the latter to changing ones. It was one of Hegel’s great achievements that he demonstrated the dialectical content of formal logic (Hegel 1969, 416). Moreover, as I1’yenkov himself acknowledges, logical contradictions are not permissible in theoretical investigations. Movements in thought are part of theoretical investigations and constitute a shift of aspect and only in this sense is a concept transformed into its opposite. The concept of identity of opposites need not be invoked.
We have seen that Hegel, and Engels after him, considered dialectical contradictions to be logical contradictions. Hegel’s need for logical contradictions was rooted in his dialectical idealism, in which the world unfolds from the Idea as movements in thought in a process of dialectical negation from one opposite to another, rather than in the historical evolutionary development of matter, in which the process of dialectical negation unfolds in time. Hegel’s dialectical unfolding, in essence being ahistorical, required the acceptance of logical contradictions as a consequence of its need to regard the identity of opposites as an absolute identity in every respect. Materialist dialectics has no such need. Hegel illustrated the need for accepting logical contradictions by using one to resolve Zeno’s paradoxes of motion. Engels’ repetition of this solution in Anti-Dühring is the only clear case of the application of a logical contradiction in the classics of Marxism. The paradox raised by Zeno is that motion (of any kind) is always represented by a succession of states, in which each state is viewed as motionless. Zeno argued that motionless states could not be connected to one another and therefore motion was impossible. Materialist dialectics can resolve this paradox without invoking a logical contradiction by considering motion to be a transition between states, whereby the state is considered only transitory and its static description approximate.
University of Minnesota,
1. One of its other important qualitative sides is, of course, the fact that it is an embodiment of socially necessary labor time, and, therefore, possesses an exchange value.
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