Introduction to Dialectical Logic

The Laws of Dialectical Logic

Henri Wald

V. The object of materialist-dialectical logic 99
1. Dialectical method and dialectical logic 99
2. Elementary logic and dialectical logic 06
3. The laws of dialectical logic 113

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3. THE LAWS OF DIALECTICAL LOGIC

Logical thinking is unique and universally human. Many non-dialectical philosophers mistake logical thinking for various world outlooks or for different scientiﬁc research methods. They break to pieces the indestructible unity of human reason.

Robert Lenoble considers, for instance, the magic world outlook as a kind of logic: “. . . man has always striven for reason and knowledge. To that end he had attempted many kinds of logic and many kinds of scientiﬁc explication that we see following one after the other throughout history or even opposing themselves in the same epoch” 52. Unlike R. Lenoble, the French philosopher Lucien Goldmann mistakes reason for the special methods of particular sciences, and breaks logical thinking into three kinds of thinking “As a matter of fact — he writes — there are three fundamental patterns of knowledge, that we call hypothetic-deductive, nomothetic-experimental and dialectical thinking” 53. L. Goldmann considers that logical thinking is of three kinds: mathematical thinking, materialist thinking and social thinking. Concerning dialectical thinking, Goldmann writes that: “The criterion of the truth of dialectical statements implies... action and transformation of the very laws that structure the real towards value realization" 54. Therefore, he concludes: “. . . in speaking of the thinking which refers to historical and social life,. . . statements are not, they become true or false through men’s action” 55. In fact; no matter the object it is focused on, logical thinking is the same with all people and in all times. Its two moments —the moment of elementary thinking and that of dialectical thinking — are unmediatedly linked to each other. Elementary thinking is implicitly dialectical, too, and dialectical thinking is implicitly elementary, too. Dialectical thinking renders explicit the implicit dialectical character of elementary thinking. The two moments of reason are not only implied but also consecutive.

Elementary thinking knows the object in its relatively stable identity and when it turns onto itself — through elementary logic 56 — it discovers the elementary structure of logical forms and the elementary laws according to which all these forms of correct thinking are combined. Dialectical thinking knows the object in its absolute self-movement, and when turning onto itself — through dialectical logic — it discovers the dialectical struc-

52 R. Lenoble, “Types d’explications et types logiques au cours de l’histoire des sciences”, in Actes du XIième Congrés. . ., vol. VI, pp. l2-l3.

53 Lucien Goldmann, “Remarques sur la théorie de la connaissance”, in Actes du XIième Congrés intern. de philas., p. 90.

54 Ibid., p. 92.

55 Ibid., p. 93.

56 To think is to think of the object, to do logic is to think of thinking.

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ture of logical forms and the dialectical laws according to which they are combined.

The elementary notion which reﬂects the dialectical structure of the object — that notion mirroring only the distinctive essential characteristics of a kind of things — has also a dialectical structure; but this structure becomes apparent in the light of dialectical logic, of the dialectical notion of notion, mirroring the contradictory character of the two sides of any notion: the sphere and the content. Thinking makes up the former according to the elementary laws of reason and the latter in keeping with the dialectical logical laws. The fact that elementary notions also have a dialectical structure and self—develop does not in the least mean that they are dialectical notions since, at their level, thinking is not yet aware of the dialectical character of the reﬂected object 57.

The dialectical structure of the elementary forms of logical thinking is governed by the dialectical laws of thinking, which at this level do not act only spontaneously but implicitly, too. The dialectics of thinking is something else than dialectical thinking. Elementary thinking cannot know the dialectical structure of the object or the dialectical structure of its mirroring either. Only dialectical thinking can know the dialectics of the object and of its reﬂection. Only dialectical thinking is able to reveal the dialectics of thinking.

In establishing the dialectical pattern of the logical forms of elementary thinking and in the transition process from one form to the other, the dialectical laws of logical thinking act spontaneously and implicitly. The dialectics of elementary thinking is governed spontaneously and implicitly by the dialectical laws of reason which mirror the dialectical laws of the objective world. To elementary thinking, the dialectics of its forms exists only “in se”. It becomes “per se” only at the level of dialectical thinking. From the strictest point of view of elementary logic, thinking can be rigorous only if it goes beyond tautology, the limiting expression of the law of identity. But an elementary judgment, which mirrors the objective dialectical unity between identity and difference, and which asserts that S is P, goes beyond tautology, by this very fact, and relativizes the law of identity such that, according to it, thinking can concentrate only on the identity of different things, being no longer tautological. In this way, the path to dialectical thinking is open. The relativity of the elementary laws of logical thinking is obvious in the light of the

57 As a rule, elementary notions are formed through abstracting, on passing from the sensory concrete to the logical abstraction, and through concretization, by passing from the logical abstraction to the logical concrete, dialectical notions are formed. In the former process analysis and induction prevail, in the latter synthesis and deduction.

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absolute and universal character of the dialectical laws of correct and just thinking.

The laws of dialectical thinking do not discard the laws of elementary thinking, they are founded on them. The laws of dialectical logic do not annul the laws of elementary logic, they transcend them. The laws of dialectical logic are superior to the laws of elementary logic, because, by observing them, thinking succeeds in discovering the two contradictory sides of the thing under consideration and, thus, sensibly enhance men’s power over their environment—natural and social. Moreover, while observing the laws of dialectical logic, it also observes the laws of elementary logic. A dialectical judgment does not proceed contrary to elementary logic, since the contradiction it reﬂects proceeds in a relatively stable unity; the nodal leaps it mirrors distinguish between relatively stable qualities and the connection it clears up includes relatively independent things. The universal validity of the structure of syllogism and of its rules is governed by the relative stability of the identities of things. Dialectical judgment mirrors the self-transformation and interdependence of relatively stable and relatively independent things.

The thinking which does not observe the laws of elementary logic falls into sophistics, through dissolution of ideas into the motion of ideas. The thinking which ignores the laws of dialectical logic becomes metaphysical, by absolutizing the relative stability and the relative independence of ideas. As long as it reﬂects superﬁcial extensive practice, logical thinking has a spontaneous tendency to absolutize the identity of things, to absolutize the moment of elementary thinking; when this tendency is encouraged and strengthened by the conservative interests of a reactionary social class, elementary logic is turned into the metaphysical method 58. The dynamics of thinking is not altogether alien to elementary thinking; what it overlooks is the self-dynamics of thinking.

The major law of dialectical logic is the law of contradictory predication, first formulated by Ath. Joja in a paper delivered in 1955. When the scientist discovers the fundamental categories and laws in his ﬁeld — categories and laws whereby the fundamental categories and laws of objective dialectics are rendered manifest — elementary thinking is spontaneously transcended and its implicitly dialectical structure becomes explicit, shocking most often its very discoverer, who, unarmed with dialectical logic, either denies his own discovery, or bows to the incogniz-

58 I do not think those are right when asserting that there is “a coincidence between metaphysics on the ontological level... and formal logic on the level of the science of thinking”. Elementary logic in itself is neither metaphysical, nor idealist. It does not absolutize the relative validity of its laws. Nor does it deny their correlation with objective laws. Metaphysics and idealism were added to it from the outside.

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able divine, or else he tries to mend the old logic here and there. Zeno of Elea, Kant and Russell are typical of these three attitudes 59.

In the ﬁrst half of our century, scientists were confronted with some dialectical judgments which they called paradoxical because amazing. Here are some of them: “Radiation is both corpuscular and wavy”, “Space is both continuous and discontinuous”, “Light velocity is both constantand variable”, “The cortex neuron is both active and passive”, “Life is both assimilation and disassimilation”, “A microelement is not predictable, but a class of microelements is”, etc.

Many scholars thought they were witnessing the reversal of reason, a new “fall” of man through reiteration of the same original sin: the daring to test the apple of knowledge. They did not realize that those paradoxes are many dialectical judgments, that did not in the least sin against the elementary logical law of non-contradiction, but which, relying on it, went beyond it.

Actually, the dialectical judgment: “Space is both continuous and discontinuous (non-continuous)” is not made up, as some may think, of the affirmative elementary judgment: “Space is continuous” and the negative elementary judgment: “Space is not continuous" which are, indlisputably, incompatible within correct thinking, but of the afﬁrmative elementary judgment: “Space is continuous” and the inﬁnite afﬁrmative elementary judgment_"Space is non-continuous (discontinuous)” 60.

The elementary logical law of non-contradiction forbids correct thinking to admit simultaneously and in the same relationship the truth of two opposite judgments, one of which negates what the other asserts. The dialectical logical law of contradictory predication compels correct thinking to find the two contradictory predicates, simultaneously predicable and in the same relationship about one and the same subject within the same unique afﬁrmative complex judgment. At the same time, the law of non-contradiction is strictly observed since the assertion of the judgment: “Space is both continuous and discontinuous” implies rejection of the contradictory judgment: “Space is not continuous and discontinuous”.

Any dialectical judgment is equally observant of the other elementary logical laws. The law of identity is observed in that the two contradictory predicates are ascribed simultaneously and in the same relationship to the same subject, as they mirror the two contradictory sides of the same object. The law of the excluded middle is equally observed since acceptance

59 In discovering antinomies, inner contradictions, the Buddhists held that there are a number of problems that could not be answered either in the negative or in the affirmative.

60 An inﬁnite judgment is superior to negative judgment. The affirmative judgment is always more valuable than the negative. An inﬁnite affirmative judgment points to the existence of something, whereas a negative judgment shows only what is not.

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of the former results in rejection of the latter and in the rigorous statement that a third does not exist, that it is not possible. To observe the ﬁrst law of elementary logic means to observe at the same time the law of sufficient reason within the logical identity. Since the law of non-contradiction and of the excluded middle are the corollaries of the law of identity, all being founded on the law of sufﬁcient reason, the law of contradictory predication observes and transcends them all at the same time 61.

Many contemporary scientists hold that dialectical judgments originate in the confusion of two different points of view and that to distinguish between the two so-called confused viewpoints automatically solves the paradoxes of contemporary science, which they consider only apparent.

In order to convey the correlation of two both simultaneously and successively incompatible properties of the same thing, Niels Bohr suggested that a new logical notion be adopted, viz., “complementarity”. “The epistemological lesson taught by the recent development of the physical sciences”, Bohr writes, “can also suggest some means of tackling other ﬁelds of knowledge.. . To acknowledge the relation of complementarity is no less necessary in psychology. . . Particularly. . . those situations when we prove our arbitrariness is incompatible with the psychological situation when we rightly undertake a causal analysis” 62.

Niels Bohr does not distinguish between a logical contradiction — rejected by elementary logic — and a dialectical contradiction — required by dialectical logic. That is why he confuses an affirmative dialectical judgment — where two contradictory predicates are ascribed at the same time and in the same relationship to the same subject, with two contradictory judgments -— one of which negates what the other asserts. Taking into account the law of non-contradiction which forbids correct thinking to admit that two contradictory judgments are both true at the same time, Bohr introduces the notion of complementarity, which does not violate the simultaneous incompatibility of two contradictory judgments, but admits of their successive compatibility. Piaget shares the same opinion. “That a micro-object

61 It is clear why the dialectical unity between the two diametrically opposite fundamental sides of every object and of any knowledge on it —is called “contradictory”, since language, which is used to convey elementary judgments, becomes contradictory as soon as it is compelled to formulate dialectical judgments. Those who reduce logic to elementary logic thus face a “logical scandal”. Extending the meaning, dialecticians have also termed contradictory the dialectical unity that has determined, through reﬂection, the formation of a contradictory sentence. Thus, the contradiction is not exclusively linguistic. From this point of view I cannot agree with Mircea Florian who says that: “The contradiction is not ontological or logical, it is only grammatical”, M. Florian, Curs de logică (Course in Logic), 1941-l942, vol. II, p. 258, lithographed.

62 Niels Bohr, Despre noţiunile de causalitate şi complementaritate (Concerning the Notions of Causality and Complementarity), in Dialectica, 1948, no. 7-8, pp. 317-318.

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is at times wave and at times particle, this means it can be included at times in one system of relations, at others in another system —- never in both at a time” 63.

As a matter of fact we deal here with dialectical judgments that emerged by virtue of the law of contradictory predications, which mirror through their contradictory predicates the existence of the two contradictory sides of any object. These contradictory sides exist simultaneously, even though we can ascertain them only successively. “Simultaneity is real even if we can ascertain it only relatively” 64, Roger Garaudy rightly writes. The dialectical judgment: “A micro-object is at the same time and in the same relationship both wave and particle” violates none of the elementary laws of correct thinking nor is it conﬁned to their observance.

Others try to “solve” the judgments of dialectics by revealing an alleged violation of the reference condition of this law, and not the alleged violation of the time condition of the law of non-contradiction.

As a matter of fact, dialectical judgments do not refer to things in motion, but to the very motion of things, before the “viewpoints” have been established. Dialectical judgments mirror the developing contraries and not the developed contraries. Therefore they mirror the contraries before they have been developed and, hence, before they have entered various correlations with other things.

There are some logicians who, as if foreseeing that dialectical judgments do not disconsider the law of noncontradiction, reduce dialectical judgments to the elementary judgment level.

In their opinion, the law of non-contradiction forbids only those judgments where the predicate is and is not available to the subject, at the same time and in the same relationship, but admits of judgments where two contradictory predicates are ascribable to the same subject. For instance: This pencil is yellow and non-yellow, viz., shiny, long, sharp, etc.... 65. This opinion is shared by the Polish logician Kazimierz Adjukiewicz. “For instance”, he writes, “we can say of the Polish ﬂag that it is white at the upper part and red at the lower, viz., that it is not white at the lower part. However, we do not see any reason to attack the law of contradiction” 66.

True that the law of non-contradiction is violated only by those judgments where the predicate is and is not ascribable to the same subject and it is not violated at all by dialectical judgments; still, there is a fundamental

63 J. Piaget, Introduction à l’épistémologie génétique.

64 R. Garaudy, La théorie matérialiste de la connaissance, Paris, 1953, p. 243.

65 See also Th. Ziehen, Lehrbuch der Logik, Marcus-Weber, Bonn, 1920, p. 430 and f.

66 Kazimierz Ajdukiewicz, Deutsche Zeitschrift für Philosophie, no. 3, 1956, p. 338.

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difference between the elementary judgments with contradictory predicates and the dialectical judgments. The predicates of dialectical judgments are always categories, hence both are determinate, whereas the contradictory predicates of an elementary judgment are not categories and hence the predicate is indeterminate. The negative predicate of an elementary judgment wherein two contradictory predicates are ascribable to the subject mirrors, by its substance, an inﬁnite number of outstanding or opposite, never contradictory, qualities as against the qualities mirrored by the positive predicate, and by its sphere, as soon as it is determinate, it is in a relation of coordination or contrariness at most, as against the positive predicate.

The fact that the law of non-contradiction admits of the validity of a judgment where two contradictory predicates are ascribable to the subject does not in the least mean that in mirroring the objective dialectical contradictions, elementary logic is sufﬁcient. On the contrary, a dialectical judgment is not to be contained within elementary logic. Aristotle himself — the maker of elementary logic as a science — writes about the contradictory character of motion emphasized by Heraclitus: “It is, therefore, impossible to ever conceive that the same thing is and is not, as some think Heraclitus said” 67. Aristotle, who refutes the elliptic formulation of motion, does not realize that he refutes at the same time the scientiﬁc formulation of motion: “A moving thing is and is not in the same place at the same time”. In this dialectical judgment, the afﬁrmative link is “is” and the contradictory predicates are “is” and “is not”.

For fear of dialectics, B. Russell considered Heraclitus’ famous aphorism: “We dive and do not dive in the same river” as mystical 68. However, he approves of Plato’s formulation: “You cannot dive twice in the same river since new waters keep running over you” 69. In the latter formulation, the Heraclitean dialectical judgment: “The river that we dive in is concomitantly the same and yet another” is reduced to the level of an elementary judgment, that no longer annoys the old logic.

The same is done by the Polish logician K. Ajdukiewicz, who thinks that thinking may reﬂect the contradictory character of motion only by elementary logic. “For hundreds of years already the students in mathematics have known to point out Zeno’s mistake in his argumentation. This mistake is to actually admit that the sum of the inﬁnite time intervals. . . would not be ﬁnite. With Zeno, the sum ½ + ¼ + 1/8 + 1/12 . . .

67 Aristote, La métaphysique, trans. J. Tricot, Paris, 2nd ed., 1948, vol. I, p. 122, IV, 1005 f.

68 B. Russell, op. cit., p. 9.

69 Ibid.

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cannot have a ﬁnite value. The elementary theory of the inﬁnite geometrical sequences teaches us that the sum here is ﬁnite and has exactly the value of t” 70.

While Zeno raises the problem of the quality of motion, Ajdukiewicz measures its quantitative side. From Zeno’s point of view, who refutes the very essential existence of motion, Ajdukiewicz measures only its appearance. The French philosopher Victor Brochard’s reply to some mathematicians claiming that Zeno’s aporiae have long been solved, is fully applicable to Ajdukiewicz, too “. . . to compute the exact moment when Achilles will reach the turtle is... to answer the question when? while you are being asked how?” 71.

Starting from the false idea that a judgment that observes the law of non-contradiction can no longer have two contradictory predicates what would ascribe at the same time and in the same relationship to their subject, Adam Schaff writes: “When we state the principle of the unity of contraries, we only set a polar complex structure of the objects and phenomena, or else, the contrastiveness of the various aspects of an object considered

under different relations; in every like case we can and must speak in a logical non-contradictory way” 72.

There are also people who simply hold that the dialectical method is sophistics. “. . . Hegel’s dialectical method, especially”, M. Aebi writes, “consists of two sophisms: Aristotle’s fallacia secundum quid et simpliciter (passage from A to non-A) and confusion of contrariness with contradictoriness (passage from non-A to B, before A)” 73.

The author of the above-quoted text utterly ignores the fact that the contradictory predicates of a dialectical judgment are categorial and hence, the negative predicate is not only “secundum quid" but also “simpliciter”, and the relationship between the two predicates is contradictory, since the third is impossible 74. Aristotle was right to underline that: “it is not the same thing not to be a thing and not to be absolutely” 75, but he did not even think of the existence of the two contradictory sides of any

70 K. Ajdukiewicz, op. cit., p. 322.

71 V. Brochard, Etudes de philosophic ancienne er de philosophic moderne, Paris, 1926, p. 10.

72 Adam Schaff, D. Z. für Ph., 1956, no. 3, p. 344.

73 M. Aebi, “Système naturel des sciences”, in Actes du XIième Congrés. . ., vol. II, pp. 242-243.

74 For instance, the predicate “non-red” has only a relative existence since it only means “non-red”; the predicate “non-corpuscular” has absolute existence as well, since it means wavy alone.

75 Aristote, Organon, Les réfutations sophistiques, tome VI, trans. J. Tricot, 1939, 167, a, p. 16.

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object, but only of the confusion of the two main meanings of “is”: the copulative and the existential 76.

All this clinging to the old logic only brakes the development of contemporary science, and prevents thinking from overstepping its elementary moment, from working out dialectical judgments.

From the logical law of the contradictory predication — that mirrors the objective law of the unity of contraries and of internal contradiction — derives the logical law of determinate negation — which mirrors the objective law of the transformations of quantitative changes into qualitative changes — and the logical law of the double negation — which mirrors the objective law of the negation of the negation. All these laws of dialectical logic imply the connection of all the logical forms, which mirrors the universal connection.

If, by virtue of the law of contradictory predication, thinking makes afﬁrmative dialectical judgments — that reﬂect the dialectical unity between the two diametrically opposite sides of any object — by virtue of the law of determinate negation, thinking makes negative-afﬁrmative dialectical judgments — that mirror the leap from one quality to another— and by virtue of the law of double negation, thinking formulates negative-disjunctive-affirmative dialectical judgments — which mirror the completion of a particular process 77.

The same as in objective reality the inner contradiction governs the qualitative self-transformation and completion of that process within the universal connection, so the other laws of dialectical logic necessarily derive out of the law of contradictory predication. Thinking cannot mirror the

76 To say that non-red is non-red, does not mean that non-red exists as such, but to say that the non-individual is non-individual, means that non-individual exists as such; it is the general.

77 Here are such judgments: The ﬁrst: “Every historical event is both necessary and accidental”. The second: “It is not the eminences that make history suit their needs but history makes the eminences suit its needs”. The third: “Society cannot develop unlimitedly within primitive communal relations or within the relations of exploitation either, but only within the scientiﬁcally established communist relations”. See also Fogarasi Bela, op. cit., pp. 202-203. That we are dealing here with a determinate negation is also proved by the fact that the affirmative part of the negative-affirmative judgment preserves the relation stated by the negative part; only its solution is negated and transcended in negative disjunctive-afﬁrmative judgments; the afﬁrmative part synthetizes the negated form of the object with the non-negated content of its negation. Special heed should be paid to the fact that the terms of dialectical judgments can be but categories.

Obviously, a dialectical judgment does not always assume the same linguistic form. A sentence does not only express the judgment developed in and through it. The dialectical judgment: “The future does not belong to capitalism, but to socialism” can be conveyed also by another sentence with a higher stylistic value: “All roads opened to the contemporary society lead to communism”.

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qualitative leap itself. The qualitative self-transformation of things can be reﬂected as it is manifest as a correlation between the old and the new quality. The negative-afﬁrmative judgment mirrors by its negative part the old quality and by its afﬁrmative part, the new one.

The connection of logical forms cannot be reduced to the dialectical synthesizing of the two sides of the law of sufﬁcient reason — the self-relation and hetero-relation; it also speciﬁes materialistically the primordial character of the forms to the latter, thus covering the whole diversity of possible relations 78.

Therefore, the laws of materialist dialectical logic rely on the laws of elementary logic, but they do not include them, they assume them, they do not engulf them.

Materialist dialectical logic has a research object of its own.

By observing the laws of elementary logic alone, thinking cannot go beyond the identiﬁcation of things and establishment of their elementary interrelations; by observing the laws of dialectical logic, thinking can detect the inner objective contradiction that governs the self-dynamics of things from lower to higher, leading to new possibilities and in this way considerably enhancing people’s capacity to change the environment they live in.

Deprived of idealism, which considers logic as pure fabrication of the mind, and freed from under the rule of metaphysics, which claims that elementary logic is the only possible logic, elementary logic retains its full validity and, together with dialectical logic, which deals with the logical laws of formation and development of dialectical notions, judgments and reasonings and their logical structure, ensures the correctness of human thought and action.

78 In the world of micro-objects, for instance, the statistical law comes to the fore, showing the inﬂuence of the sets, of the environment on the individual micro-object; that is why the set is predicable, whereas the individual is not.

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SOURCE: Wald, Henri. Introduction to Dialectical Logic (1959). Bucuresti: Editura Academiei; Amsterdam: B.R. Grüner B.V., 1975. (Philosophical Currents; v. 14) Chapter 5: The object of materialist-dialectical logic; 3: The laws of dialectical logic, pp. 113-122.