Pre-Logic, Formal Logic, Dialectical Logic

by Mustafa Cemal

Logic is the result of mind's thinking on itself. What is thinking itself, and howis mind able to think on itself? Thinker and being thought which is itself thought, oppose in the thinking process but are at the same time inseparable. My aim in this essay, by putting preliminary ideas, is to enlarge the method and system discussion. Andy Blunden's article 'System and Method' is an admirable introduction to the subject matter (system1.htm, 3 April 1997). He writes:

"The method is the subjectivity, the system the objectivity. Method is the inner, system is the external. The method is manifested in the system, but the method must be true to the system. The method is the "germ" of the system."

I have, continually, tried to show that logic itself bears methodological character in its historical development.

Pre-Logic Thought

Researches on cognitive processes reveal that there is a great difference between everyday reasoning and the logical system devised by logicians. A great deal of everyday thinking is practical, intuitive and emotional. Thinking in formal logical terms requires explicit training, but it is still difficult for highly educated people, even those trained in logic. Wason and Johnson-Laird had made an experiment called card-tuning to test the ability of adults in formal thinking. The results are so striking that the vast majority of adults including trained logicians not only had got the given problem wrong, but usually had given the same logically incorrect answers (1972. Psychology of Reasoning. Batsford, London.)

We find the similar distinction in the anthropology. Lévy-Bruhl, disciple of Durkheim, argued that the mode of thought of preliterate people was so different from the formal logic that it can only be mystical and expressive of emotions. Sociologist Vilfredo Pareto (like Freud), following the way Lévy-Bruhl opened, considered almost all religion, art and morality as essentially non-logical. The observation that led Lévy-Bruhl to deduce preliterate people's thought is their personalisation of the universe, that is feeling their life in unity with plants and animals that means violation of the law of identity (or law of non-contradiction). Anthropologist Radcliffe-Brown expresses two distinct modes of thought explicitly when he suggested that,

"In every human society there inevitably exist two different and in a certain sense conflicting conceptions of nature. One of them, the naturalistic, is implicit everywhere in technology, and, in our twentieth-century European culture, has become explicit and preponderant in our thoughts. The other which might be called the mythological or spiritualistic conception, is implicit in myth and in religion, and often becomes implicit in philosophy." ([1952], Structure and Function in Primitive Society, p. 130)

We find a similar distinction in the writings of Freud between dreams, neurotic symptoms and their cultural manifestations in religion, myths (primary process), and logical thought and science (secondary process). Piaget also differentiates concrete thought from formal operational thought. In the same vein direction Vygotsky has written:

"Primitive peoples also think in complexes, and consequently the word in their languages does not function as the carrier of a concept but as a 'family name' for groups of concrete objects belonging together, not logically, but factually. Storch has shown that the same kind of thinking is characteristic of schizophrenics, who regress from conceptual thought to a more primitive level of mentation, rich in images and symbols. He considers the use of concrete images instead of abstract concepts one of the most distinctive traits of primitive thought. Thus the child, primitive man, and the insane, much as their thought process may differ in other important respects, all manifest participation a symptom of primitive complex thinking and of the function of words as family names." ([1934]. Thought and Language, p.72)

Lévi-Strauss facing this dilemma tried to explain the structure of non-logic thought. Contrary to Malinowsky's reduction of ideology to the instinct, desire and need and his denying any internal logic, Lévi-Strauss emphasised that there was a symbolic order. He recognised that,

"The savage mind deepens its knowledge with the help of imagines mundi. It builds mental structures that facilitate an understanding of the world in as much as they resemble it. In this sense savage thought can be defined as analogical thought." "Mythical thought always progresses from the awareness of opposition toward their resolution." ([1962]. The Savage Mind, p.263.)

Leaving aside his pseudo-dialectics, he successfully revealed that myth, magic or totemic representations are constructed by metaphorical and metonymical representations. Metaphor operates by selection, metonym on the other hand, substitutes contiguous terms for one another resulting combination of linguistic units in the chain of a given verbal message. Let me give and example from a hunter-gatherer society:

"In the Northern tribes it is believed that a woman can tell the sex of her unborn child. If she feels it on the left side it is a male, because men hold the bow (the typical masculine implement) in the left hand. If she feels it on the right side it is a female, because it is in her right hand that a woman holds her fishing net." (Radcliffe-Brown, A. R., [1932], The Andaman Islanders, 90)

Here, the right side that a pregnant woman feels is related with right arm. Since in these societies distribution of instruments of production is made specific to sex in accordance with sexual division of labour, and because the right arm is the effective arm of a woman in her specific labour process, it is decided that sexuality of born baby will be a girl. Metonymically, 'side' stands for 'sexuality'; 'right' becomes girl, 'left' becomes boy. On the other hand, labour process and pregnancy are related metaphorically, such that it is asserted that the side the pregnant woman felt manifests the sexuality.

Pre-logic thought is the unity of metaphor and metonymy. It makes possible some kind of explanation about the world in a mythical form. Conceptions are complexes in Vygotsky's sense, but not random aggregation of meaning, metonymic and metaphoric constitution.

Logic is not given naturally, but is the achievement during a long historical process. Logic is the self-reflection of the mind on itself, therefore it was only possible after the invention of writing. Nevertheless, pre-logical thought certainly has the potential of logic, as it is obvious from the connectives like 'but', 'because', 'if', 'then' which we find in all the preliterate people's languages.

Logical Thought

Formal Logic

Logic is the taming of "savage mind", making the concepts well defined, univocal and constant in time. Every concept, using modern terminology, must represent only one set. This is in fact nothing more than the law of identity. Every concept, according to this rule, can only be defined by itself. If concept A is identical with concept B, than they both have all their elements in common. If A or B possesses at least one element that is not common, then they cannot be identical.

The identity law in logic corresponds to the identity law in Being. In being, any object can only be differentiated from another by its own specific properties. In other words, what makes A and B distinct object is that they have different properties. If object A and object Bs have all their properties in common (i.e., if A and B are indiscernible) then they are identical. In Leibniz's words:

"It is not true that two substances may be exactly alike and differ only numerically, solo numero." (Leibniz, G.W. 1951. Selections. Ed. P. Wiener.)

Formal logic, even in its most abstract forms, has an ontological claim by the identity rule. But this correspondence is valid only for an assumed world where life is at rest, and the limit between different entities (for example, between circle and polygon, pink and white) is arbitrarily drawn. According to ontological assumption of formal logic, the world is divided into independent, autonomous and self-sufficient elements, and stay so eternally. Therefore, when logic is applied to movement directly, it collapses into nonsense, as Zeno's paradoxes had proved. The so-called paradoxes or dilemmas are in fact real contradictions. In the domain of formal logic, what Hegel had said, are still true:

"Zeno's dialectic of matter has not been refuted to the present day; even now we have not got beyond it, and the matter is left in uncertainty." (Lectures on the History of Philosophy, 265)

Secondly, logical reasoning is making inference by syllogism:

In syllogism result is implicit in major premise. For any logical inference, you need at the outset a definite axiom which is assumed without justification. It must, otherwise, be included in a larger category, such that definition of any genus requires a more comprehensive genus, in relation to which former is its kind. As the ladder is climbed every larger category become more impoverished, therefore at the top there is not any defining genus. The most comprehensive category is Being, which in fact does not contain any determination in it, hence has not capacity of explanation.

Thirdly, every proposition (premise) is the combination of concepts. Every concept (determination) can be defined by many other concepts which they are in turn are defined by another set of concepts and this continue infinitely. There is no pure concept which gets its meaning only by itself. Every concept is mediated by other concepts. As a result, formal logic gets into trouble both horizontally and vertically.

Fourthly, since the corollary of the identity law is "A is not non-A", whenever any proposition refers to itself or a set itself is the subset of itself, there occurs contradiction (Russell paradoxes). Solution is possible only if you accept "A is also non-A." All these are enough to show that formal logic is not simply our natural ability to think, but a tool we use to understand the world. Similarly it can be said that dialectical logic is also, but more developed tool.

Dialectical Logic

Contrary to formal logic, the law of dialectical logic is that everything is mediated therefore everything is itself and at the same time not itself. "A is non-A." A is negated. For Hegel, identity is the unity of different terms, and difference is the difference of united terms, namely, negation of negation. To claim for two different things are the same at one and the same moment is contradiction.

"When the difference of reality is taken into account, it develops from difference into opposition, and from this into contradiction, so that in the end the sum total of all realities simply becomes absolute contradiction within itself." (Logic, p. 442)

The law of dialectical logic is contradiction. This, however, is not destructive; on the contrary, the opposites constitute a whole. The whole is not only different from its contradictory moments, but also more than them. It is another, third thing in which opposites are in a systematic relation with each other. If only A is for B and B is for A there is systematicity in their unity.

"... Notion is to be regarded in the first instance simply as the third to being and essence, to the immediate and to reflection." (Logic, 576)

What in motion or change is, is both itself and other at the same time. Motion is therefore, contradiction. Since opposites constitute a unity they are related to each other systematically, that is, systematicity is result of contradiction. Hence, the concepts are in motion. Dialectics can begin only if there is contradiction, motion is always in contradiction. Everything is the result of prime mover and everything is in motion. Unity is the first step of constituting system, for that reason motion is the key to find the opposite of any concepts.

I think the concepts of contradiction replace the concept of time, leaving it as a quantity, or magnitude of number of oscillation of a pendulum. Lenin writes: "Motion is the essence of space and time." ([1914-1916]. Philosophical Notebooks, p. 256). The Notion of time is contradiction.

Secondly, again contrary to linear character of formal logic, dialectical logic is circular. Something is explained by Other, and Other is explained by Something.

"Finite things, therefore, in their indifferent multiplicity are simply this, to be contradictory and disrupted within themselves and to return into their ground." (Logic, 443)

On the other hand, the first category of being can be understood fully only at the end, but this end is relative to the precedent level. Dialectical logical system formation is an open-ended process. At every level it is necessary to return back such that precedent category is included and at time same time better explained.

Thirdly, every concept is mediated by other concepts. Therefore, every proposition by itself lacks truth; truth is whole. Truth, dialectically, cannot be isolated within propositions. If true is whole, there is always the problem of beginning and end. Beginning cannot be a priori arbitrary proposition or principle by the same reason. To begin it is necessary to find the most abstract category of the subject-matter. That means from the start we assume almost nothing, the first category must be the most meagre of truth. We must start from the most abstract and indeterminate to those that are more concrete and complex. It is only for philosophy necessary to start from Being, because philosophy different from science can not presume. But for sciences it is always Something (Etwas). This Something must be analysed beginning from the Being of the subject matter. If I exemplify from Hegel, while his first category in Logic is Being, he starts with "sense-certainty" in Phenomenology of Mind. I think the most beautiful example can be given from Marx. His starting point is commodity, but he begins analysis from abstract labour.

Fourthly, according to nominalism only concrete individual things exist and qualities, universals and relations are merely mind's own production. On the opposite pole, realism, pointing to the transitory character of individuals, claimed that universals were not only independent of the mind, but they exist in themselves. The concepts of force, mass, abstract labour may help us to understand the objectivity of universals. Kant, on the other hand, putting the universal side to the subject claimed that reason knows the individual in the universal by means of a priori Notions, but understanding reaches categories from individuals by means of perception. Hegel unites these two contradictory poles;

"In speaking of some definite animal we say it is (an) animal. Now, the animal, qua animal, cannot be shown; nothing can be pointed out excepting some special animal. Animal, qua animal, does not exist: it is merely the universal nature of the individual animals, while each existing animal is a more concretely defined and particularised thing. But to be an animal - the law of kind which is the universal in this case - is the property of the particular animal, and constitutes its definite essence. Take away from the dog its animality, and it becomes impossible to say what it is. All things have a permanent inward nature, as well as an outward existence. They live and die, arise and pass away; but their essential and universal part is the kind; and this means much more than something common to them all." (Lesser Logic, §24n)

In this way Hegel describes how we apply Notions to the things which have corresponding universal features. Therefore, in contrast to formal logic that treats Notion as abstract generality, for Hegel it has three moments; universality, particularity, individuality. A new syllogism!

Lastly, there is a similarity between formal logic and dialectical logic, they both assume definable concepts whether by itself or through other. But for dialectical logic concepts are intellectual as well as empirical, social as well as historical. Experiment is just an abstraction made from production. There is only one category that completely units historical and social, and, conceptual and empirical, it is production:

"If we are able to prove the correctness of our conception of a natural process by making it ourselves, bringing it into being out of its conditions and making it serve our own purposes into the bargain, then there is an end to the Kantian ungraspable "thing-in-itself"." (Engels, Ludwig Feuerbach and the End of Classical German Philosophy, Part III.)