Historical Origins of the Logic of Classification and the Logic of Genesis
Dr. Harry K. Wells
Associate Professor of Psychology and Philosophy
Oneonta, New York
The body of this work is based on Chapters Six and Seven of the Author's book Process and Unreality, published in 1950 by Columbia University Press, and now out of print.
TABLE OF CONTENTS
Introduction: Stages in the Science of Logic
Chapter 1: Logical and Ontological Principles: Laws of Thought and Laws of Being
Chapter 2: Plato and Heraclitus
Chapter 3: Aristotle's Logic of Classification
Chapter 4: Hegel and Aristotle
Chapter 5: Hegel's Logic of Genesis
Conclusion: The Logic of Genesis and the Twentieth Century Crisis in Thought
STAGES IN THE SCIENCE OF LOGIC
For over two thousand years the science of logic has concerned itself with the formal aspects of classification. It has sought to discover the general laws and facts of the relations between classes in their most abstract aspects, irrespective, that is, of the specificity of any concrete, existential interpretations. In doing this, the so‑called formal logic made incalculable contributions to science, the first great historic task of which was to classify the phenomena of the solar system, of the world, of life and of man and his society. So long as science remained in the classificatory stage logic was fully justified in its exclusive concern with the formal structure of classification.
In the past 150 years however, most of the sciences, beginning with geology, astronomy and biology and ending with physics, chemistry and psychology, have passed over from the stage of classification to the stage of genesis. They have moved that is, from concern with space, simultaneity, external relations and locomotion, to concern as well with time, succession, internal reactions and development. Logic, on the other hand, has stuck stubbornly to its original subject‑matter, refusing to move with the other sciences and thereby has forfeited its original role as leader in scientific method. While it should rightfully have pioneered the advance of science into the uncharted territory of genesis, it was in fact content to rest on its classificatory laurels. Science, deserted by logic, was forced to push into the frontier without the aid of its previously most advanced phalanx. The cost to science has been dear, and today, the price is being paid in the hard cash of theoretical crisis in field after field of human knowledge.
The culminating irony in this critical situation lies in the historic truth that logic was in fact the first science to concern itself with genesis, in the very opening decade of the 19th century. Hegel is to the logic of genesis as Aristotle was to the logic of classification, namely the initial discoverer, founder and formulator. Why then was Hegel' dialectical logic, the logic of genesis, and disregarded over the past century and a half, when it could have provided the scientific method which would have enabled the sciences to move into their new stage under the leadership of the science of the general, abstract structure of succession, time, internal relations and development?
The historical causes of the neglect of dialectical logic are in all probability many and highly complex. But there appears to be one overriding reason. Dialectical logic was by no means completely ignored. It was adopted and adapted almost from its inception by two systems of thought that were widely held to be antithetical to the best interests of "the Western world". Marxism and Existentialism gave dialectical logic a central position in their respective set of doctrines. On the one hand, Marx and Engels mated dialectical logic with classical French and German materialism and British political economy to develop a particular approach to history. On the other, Soren Kierkegaard mated dialectical logic with subjectivist philosophy, early Christian teachings and Eastern mystical concepts to develop a paradoxical approach to individual psychological and religious experience.
Marx, Engels and Kierkegaard heard Hegel lecture and carefully studied his Science of Logic. The two tendencies represented by these three men repudiated Hegel's system as speculative and fantastic, but accepted his method, his dialectical logic, as a great advance in human thinking. By and large, apart from scattered individuals here and there, the rest of the intellectual world at best disregarded and at worst ridiculed Hegel's logical discoveries. The two theoretical tendencies that had from the beginning recognized the cognitive power of dialectical logic remained outside the mainstream of Western thought. Both Marxist historically‑inevitable socialism and Existentialist sickness‑unto‑death mysticism were incompatible with the pluralism and practicalism of the advanced industrial nations of the West. Neither was taken very seriously until the Russian Revolution in 1917 brought Marxism dramatically to the attention of the world and until the Post‑World‑War II disillusionment especially in France and Germany rediscovered Kierkegaard and launched Existentialism on its present spectacular career. But even today, with all the attention that is currently being given to Marxism and to Existentialism, the Western world disregards the dialectical logic of genesis as it is embedded in these two movements, and concentrates rather on the features of the Marxist system and of the Existentialist system. It is the same fate that was reserved for Hegel's thought. It was Hegel's system, his world view, that was emphasized in Western thought, rather than his method, his dialectical logic.
Because dialectical logic has been employed for purposes, both socialist and mystical, of which the Western World as a whole does not approve, and because it has been used by theories, systems and political movements of which Western thought disapproves, it has been repudiated and reviled. The Hegelian dialectic is by and large not considered to be either a proper subject of academic study or an acceptable topic of investigation for research projects. To all extents and purposes, dialectical logic does not exist, and never did.
The de facto basis of this situation is its identification in the first place with anathemetized Marxism and secondly with subjectivized mysticism.
This raises some serious questions. Is the adoption of a science by a given political movement sufficient reason for the rejection of that science? Or is this not a case of "throwing the baby out with the bathwater"? Can a science rightfully become the exclusive property of a political theory, party, nation or group of nations? Or is it not a fact that science, any science belongs to mankind and should be employed by all peoples for the human good?
The answer to the latter question has of course to be in the affirmative. The real question, however, is to determine whether or not the logic of genesis, dialectical logic, constitutes in fact a new stage in the development of the science of logic. We in America and the Western World will never know the answer until we accept the legitimacy of the question and make a serious investigation of it.
The present paper is an attempt to initiate such a discussion by indicating the place of dialectical or genetic logic in the history of philosophy. If it leads to further investigation of this too‑often, tabooed subject, and in particular to the study of Hegel's Science of Logic, it will have succeeded in its primary objective.
PART I: THE LOGIC OF CLASSIFICATION
LOGICAL AND ONTOLOGICAL PRINCIPLES: LAWS OF THOUGHT AND LAWS OF BEING
Traditional method is based on the principles of identity, contradiction, and excluded middle. In short, it can be called the method or logic of classification, sometimes called "formal logic". The cornerstone of the method is the principle of identity, with the other two principles being taken as corollaries, which delineate its meaning.
The three principles are usually referred to as "the laws of thought" in textbooks on logic. Among logicians there is considerable disagreement about the status of these principles, whether they are ontological or logical, laws of being or laws of thought and discourse. But from Plato and Aristotle to Cohen and Nagel, they are generally regarded as both.
W. Stanley Jevons says: "These laws describe the very simplest truths, in which all people must agree, and which at the same time apply to all notions which we can conceive."  Here the first phrase refers to the principles as laws of being, and the second to them as laws of thought. He goes on to say that "it is impossible to think correctly and avoid evident self‑contradiction loss we observe what are called the three primary laws of thought."  Having referred to them as logical, he goes on to state them in ontological terms: “1. The Law of Identity. Whatever is, is. 2. The Law of Contradiction. Nothing can both be and not be. 3. The Law of Excluded Middle. Everything must either be or not be." 
In his elaboration of the principles, Jevons treats them on both levels. Of the principle of identity he says that it is "the best definition we can give of identity or sameness" and that its meaning is "everything is identical with itself."  Presumably the "everything" refers to concepts as well as existential "things". Of the principle of contradiction he says: "Its meaning is that nothing can have at the same time and at the same place contradictory and inconsistent qualities."  Here the reference is obviously to ontological meaning. He continues on the same level: "No quality can both be present and absent at the same time; and this seems to be the most simple and general truth which we can assert of all things.”  And he adds the explicitly ontological statement: "It is the very nature of existence that a thing cannot be otherwise than it is."  In the next phrase he changes to the logical level: "and it may be safely said that all fallacy and error arise from unwittingly reasoning in a way inconsistent with this law."  Continuing in this vein, he says: "All statements or inferences which imply a combination of contradictory qualities must be taken as impossible and false."  On what grounds do we know they are false? Jevons answers: "The breaking of this law is the mark of their being false."  This line of argument would indicate that the laws of thought are derivative from the laws of being. It is this position which is in the classic tradition of logic.
Of the principle of excluded middle Jevons says: "Its meaning may be best explained by saying that it is impossible to mention any thing and any quality or circumstance, without allowing that the quality or circumstance either belongs to the thing or does not belong."  The law "expresses the fact that there is no third or middle course; the answer must be Yes or No."  As an example, he cites a rock. A rock must be either hard or not‑hard. Here two levels are involved: ontologically the rock must be either hard or not‑hard; and for thinking, writing, or discourse a definite answer must be given, yes or no. If there is doubt as to which quality is present, judgment must simply be withheld. The point is that there is nothing which is both hard and not‑hard at the same time. In this connection, Jevons makes the usual distinction between contraries, which he calls "opposites," and contradictories. In the above example, hard and not‑hard would be contradictories, and hard and soft would be contraries. The law of excluded middle refers only to contradictories.
It is clear that Jevons treats the principles as both laws of thought and laws of being. Of them he says: "these three laws then, being universally true to whatever things they are applied, become the foundation of reasoning." Now "true" here refers to correspondence with existential things. The laws correspond to, or are a true representation of, the nature of things in the world. But they are also the criterion of rational thought. If we are to think about the world, we must think in terms of the content of our thought, or the subject‑object of our thought. Such subject-object content, in its most general aspects, is traditionally expressed in the three principles. The general aspects of the world expressed by the principles are concerned with the separate "things" at an unextended instant of time. The emphasis is not on change, but rather on identification, definition, comparison, and classification. Thus Jevons says: “All acts of reasoning proceed from certain judgments, and the act of judgment consists in comparing two things or ideas together and discovering whether they agree or differ, that is to say whether they are identical in any qualities."  Thought is primarily concerned with the agreement or difference of things (or ideas), and for what purpose if not for classification. Jevons is in the classic tradition of logic, namely, that to think is to classify. And to classify requires that a thing (or idea) be just what it is and not at the same time something else. It must be either this or that. Without such principles, classification would break down, or be impossible in the first place. If the content of thought is assumed to be static, then these laws are inherent both in the content and in the thinking about the content. The objective of thinking about such a content will be to classify it. Here we are talking about "content" rather than the existential nature of things. We do this for a definite reason. If the world is conceived as being primarily static, then this is the content of thought. The form of thinking is adapted to the content of thinking; the laws of the content ("being") are the same as the laws of thought. We can then say that the three principles are at once "laws of thought" and "ontological" laws. In this case, "ontological" refers to a particular conception of the nature of the world.
There are two fundamental questions involved here: One is the question about the principles as laws of thought; the other is the question about the nature of the world. Is it possible that our conception of the nature of the world can change without a corresponding change in the "laws of thought"? More specifically if our conception of the world is transformed from a primarily static one to a primarily dynamic one, one in which the world is characterized as process—that is, as constantly changing qualitatively—can we retain the identification of rational thought with the three principles? Similarly, can our conception of the world change without a corresponding change in the general aspects of existence as formulated in the three principles in their role of ontological laws?
Cohen and Nagel, in their textbook, An Introduction to Logic and Scientific Method, give two formulations of the laws of thought, one propositional and the other ontological. In the propositional formulation they say: "The principle of identity asserts that: if any proposition is true, it is true. The principle of contradiction asserts that: no proposition can be both true and false. The principle of excluded middle states that: any proposition must be either true or false."  Here the principles are formulated as laws of thought. The ontological formulation is, for the principle of identity, that "if anything is A it is A"; for the principle of contradiction "nothing can be both A, and not A"; and for the principle of excluded middle that "anything must be either A or not A."  Of this ontological formulation, Cohen and Nagel state that it is "an obvious counterpart of the propositional formulation," and they go on to say that "it expresses, perhaps even more clearly, that their subject matter is certain general or generic traits of all things whatsoever.”  They conclude that "as principles of being, logical principles are universally applicable,"  and "as principles of inference, they must be accepted by all, on pain of stultifying all thought." 
It is clear that Cohen and Nagel accept the principles as both laws of thought and laws of being. They are careful to assert, though, that "the principle of identity does not deny the possibility of change,” meaning by "change" qualitative change.  In truth the logic of classification may not deny change, but it does not stress change, and more important, it has trouble with change, as is seen in the treatment of it at the hands of Plato and Aristotle. The latter were acutely aware of the threat to the principles of formal logic posed by the fact of qualitative change. For one thing they were aware of the difficulties because they were constantly struggling against the doctrines of the Ionians, and in particular against Heraclitus. The Principles may not deny change, and I say may not advisably, but at the same time they do not provide a method for dealing with it.
PLATO AND HERACLITUS
The first primitive philosophical method was a crude and rudimentary logic of genesis developed by Anaximander and Anaximenes and more particularly by Heraclitus in pre‑Socratic Greece. This genetic philosophical method was so embedded and widespread in Sixth, Fifth and Fourth century Greek philosophy that Plato was forced to direct his main theoretical fire against it in his attempt to establish the basic principles of classificatory logic, centering on the principle of static identity or logical harmony, as opposed to the dynamic conflict of opposites espoused by Heraclitus and his contemporaries and followers, the Sophists.
Plato won this great battle of ideas so completely that the works of the early Greek partisans of the logic of genesis were, to put it mildly, not preserved. Even the name of the philosophical school, "the sophists", became a caustic derogatory epithet, and for that matter still is.
Plato, in the Republic, has a very interesting reference to the principles of classificatory logic. Socrates is trying to establish the point that the soul is composed of distinct parts. In the course of the argument, he says: "Let us approach the problem whether these elements are distinct or identical in this way. It is clear that the same thing cannot act in two opposite ways or be in two opposite states at the same time, with respect to the same part of itself, and in relation to the same object."  Here we have the assertion that a thing must be just what it is, and not at the same time something contrary or contradictory. To be a separate determinate something it must exclude contradictions or opposites. From this Socrates concludes: "So if we find such contradictory actions or states among the elements concerned, we shall know that more than one must have been involved.”  But with followers of Heraclitus still at large in Athens, Plato must introduce at least an appearance of argument against the principles. He offers two obviously powerless objections in the form of examples: one, the case of a man standing still but waving his arms; and the other a top spinning with its peg fixed at one spot. Such objections are patently "sophistical,” and have nothing to do with the internal contradictions advanced by Heraclitus. Socrates draws the conclusion that: "No objection of that sort, then, will disconcert us or make us believe that the same thing can ever act or be acted upon in two opposite ways, or be two opposite things, at the same time, in respect of the same part of itself, and in relation to the same object."  The assumption is that a thing cannot be one distinct entity if it contains internal contradictions. If such contradictions are found it will be concluded that there are present more than one thing.
It is this assumption that individual and distinct entities must be non‑contradictory that lies at the heart of the traditional method. Identity means non‑contradictory. Heraclitus did not deny that separate things exist. On the contrary, he insisted that they did. But he maintained that there could be separate things only through internal contradictions. Not only could it be stated that identity is the strife of opposites but that there would be no identity without such strife within the entity. In fact there would be no entity. Plato assumes that logical harmony is the precondition for being, that is, being demands the exclusion of contradictions. Finally Socrates is made to say: "Well, anyhow, as we do not want to spend time in reviewing all such objections to make sure they are unsound, let us proceed on this assumption, with the understanding that, if we ever come to think otherwise, all the consequences based upon it will fall to the ground."  Here is a recognition of Plato's part of the absolutely fundamental nature of the three principles. Together they constitute an assumption about the nature of things which lies at the foundation of both his conception of the world and his rational method. It is the assumption that logical harmony is the precondition for being as well as for thinking. Essentially it is the assumption that identity, as individual, separate, and identifiable things, requires non‑contradiction. Heraclitus made precisely the opposite assumption.
For Heraclitus, becoming, in the form of qualitative change, was the most essential character of the world. He uses "fire" as a symbol of such continual change. "This world," he says, "which is the same for all, no one of gods or men has made; but it was ever, is now, and ever shall be an ever‑living Fire, with measures of it kindling, and measures going out."  He speaks of "the transformation" of "Fire" into "Earth," "Air," and “Water.”  The latter are kinds of things, but they are forever in the process of becoming their opposites. Thus he says: "Cold things become warm, and what is warm cools; what is wet dries, and the parched is moistened."  It is impossible to catch qualities or kinds of things without their passage, for they are always transforming themselves into their opposites. Heraclitus concluded that no thing is just what it is at any given moment, but that on the contrary is a strife of "opposite tensions." What a thing is, as an individual entity, then, is nothing over and above the strife. Strife is paramount. "Homer was wrong," Heraclitus says, "in saying: 'Would that strife might perish from among gods and men!' He did not see that he was praying for the destruction of the universe; for, if his prayer were heard, all things would pass away."  His meaning becomes clearer when he says: "Men do not know how what is at variance agrees with itself. It is an attunement of opposite tensions, like that of the bow and the lyre."  What are the "opposite tensions" without which a bow would not be a bow, a lyre not a lyre? Obviously they are the tensions of opposite forces, one directed out and the other in. If these tensions were not present, there would be no such weapons or musical instruments. The bow and the lyre are brought into being by the utilization of the strife between the two opposite tensions. But by the same token, the moment the individual entity is thus established, the tension begins to break down. Strife is the beginning and the end of all things. To Heraclitus it was clear "that all things come into being and pass away through strife."  The very existence of separate, individual things depends on strife within them. Hence, for Heraclitus, logical harmony and non‑contradiction far from being the precondition for "being," are inimical to it. To think, for Heraclitus, is to think opposition, because the subject‑object of thought, the world, is itself oppositional. Thus he says: "We step and do not step into the same rivers; we are and are not." 
It is important to emphasize the fact that Heraclitus is not denying identity, where the term refers to identifiable, individual things. What he is denying is that the exclusion of oppositions is the essence of identity. He leaves no room for doubt that for him identity means the internal coexistence and strife of opposites. Without the latter there would be no identity, and in fact there would be no things; there would be nothing.
We can see that the "objections" raised by Plato through the medium of Socrates in the Republic have nothing to do with the very real objections which Heraclitus himself would raise However, in the Theaetetus Plato makes a more sincere attempt to come to grips with the problem.
Socrates proposes to "give the truth of the universal flux a ring," and he asks the question: "Is the theory sound or not?"  Referring to Heraclitus and his followers as "the river‑gods," he asks what they mean when they say that all things are in motion. The answer involves a distinction between two types of motion: one, "when a thing changes from one place to another, or goes round in the same place"; two, "when a thing grows old, or becomes black from being white, or hard from being soft, or undergoes any other change, while remaining in the same place."  Socrates is referring to "two kinds" of motion: the first is mechanical motion or change of place, which is here called "motion in place"; the second is qualitative change, here called simply "Change." It is concluded, in the dialogue, that the doctrine of the flux refers to both kinds of motion. All things are in flux means that "they move and are also changed."  Socrates remarks: "If they only moved, and were not changed, vie should be able to say what are the kinds of things which are in motion and flux.”  There are two interesting points in this hypothetical statement. In the first place, we notice that Plato is concerned with the problem of definition of "the kinds of things." The tacit assumption is that it is impossible to say what kind of a thing something is, if it is in the process of becoming something other—that is, if it is at once both this and that (and moreover the strife of the two), rather than this or that. For Plato, knowledge tends to be the enumeration of qualities of a thing and its classification as this or that kind. While for Heraclitus, the objective of knowledge is more the direction of the development of a thing, development being the strife of opposites, and direction being determined by that strife.
In the second place, we notice in the above quotation that Plato would have no difficulty with the concept of motion in the form of change of place. For in that case the thing itself does not change; it merely moves from one place to another. This will serve to remind us that mechanistic materialism, against the presuppositions of which Whitehead is inveighing, raises no such problem as does Heraclitus. The mechanists reduced all motion to mechanical motion, so that there is no question of the applicability of the principle of identity. Plato recognizes that the problem arises only with the qualitative type of change. Keeping this point in mind will help us to understand how it was possible for the three principles to be retained as the foundation of rational method, as well as of the general nature of reality, right down to the present time. The mechanistic outlook is still dominant, though it is most certainly in the process of being transformed.
Plato continues with his investigation of the theory of the universal flux. He reveals his primary concern when he asks: “But now, since not even white continues to flow white, and the very whiteness is a flux or change which is passing into another colour, and will not remain white, can the name of any colour be rightly used at all?"  If white is forever in the process of becoming not‑white, how can we speak of white or any other quality? At the very moment we speak of it it is becoming something else. Thus Theodorus answers: "How is that possible, Socrates, either in the case of this or of any other quality‑‑if while we are using the word the object is escaping in the flux?”  Here we see again the underlying assumption that to be a given quality involves noncontradiction. If white is simply white, without any conflict of opposing tensions, how can the transformation of white into another color be accounted for? This problem involves also, of course, the problem of the internal relation between qualities and the thing which is white, for example. The predicament indicated by Socrates and Theodorus does not exist for Heraclitus. He is not, as we have seen, denying that there is a separate thing which is white. What he is denying is that the white thing is non‑contradictory. To be white, for him, is the name of a strife of opposites which makes the quality what it is, but which also brings about its transformation into another quality. To say that a thing changes while we talk about it does not mean it is lost in the flux. If the same contradictory tensions are present, it is the same thing in a very real sense, even though the relations between the opposites may have changed to some extent. Only when the opposite tension breaks down is there a transformation. And then the change is a qualitative one; there is a different kind of thing or a different quality. Here again Plato is not dealing with Heraclitus in his own terms. He understands by "flux," sheer change or motion; whereas Heraclitus did not stop at such an assertion, but went on to try to understand the inner nature of change. For him, identity is the identity of opposites in their relation of strife; and change is the various stages of the development of the conflict. When the conflict develops to a certain stage, there is a change to a different conflict, which in turn is a different quality or kind of thing.
But Plato does not understand this, for he talks about the quality disappearing in the flux at the very moment we see or hear it. He concludes that “if nothing is at rest, every answer upon whatever subject is equally right" and that “we must not speak of seeing any more than of not seeing, nor of any other perception more than of any non‑perception."  In the last analysis, what Plato is doing is equating identity with non‑contradiction or non-opposition, and non‑contradiction with rest, that is, with the exclusion of qualitative change. With him we see the recognition that qualitative change involves opposition. But having equated rationality with non‑contradiction, he is led to deny continuous qualitative change as a fundamental character of the world. Barring that, he would have to conclude that reason could not know the world; or he would have had to change his conception or rational method.
What has come down to us as Platonism, the doctrine of ideas, is one attempt to rationalize the method with the experiential fact that things in the world are in constant process of becoming. The hypostatization of ideas or qualities as eternal and unchanging, while matter or the "receptacle" contributes the element of becoming, is one resolution of the contradiction between method and observation. We turn now to Aristotle to see how he deals with the principles and how he attempts to deal with qualitative change or process.
ARISTOTLE'S LOGIC OF CLASSIFICATION
In the Metaphysics, Aristotle says: "There is a science which investigates being as being and the attributes which belong to this in virtue of its own nature."  This science is philosophy, which "will examine not only substances but also their attributes," together with "the truths which are in mathematics called axioms."  The latter refer in particular to the first principles both of the syllogism and being qua being. The philosopher is concerned with the first principles of being and demonstration. Thus Aristotle says; "Evidently then it belongs to the philosopher, i.e., to him who is studying the nature of all substance, to inquire also into the principles of syllogism."  These principles are not those required in each science separately, but are rather "the most certain principles of all things."  What is meant by "most certain principles"? Aristotle explains that "the most certain principle of all is that regarding which it is impossible to be mistaken."  It is both "the best known (for all men may be mistaken about things which they do not know)," and "non‑hypothetical (for a principle which everyone must have who understands anything that is, is not a hypothesis).” 
It is the task of the philosopher to investigate the most certain principle of syllogism and being, and the most certain principle is "that which everyone must know who knows anything” and which he must already have when he comes to a special study."  Aristotle, after this introduction, is ready to say "which principle this is"  which meets the definition of "the most certain." "It is," he says "that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect."  Elsewhere he leaves no doubt about the dual status of this principle, as a principle of demonstration and being. Thus, speaking of "the starting points of demonstration" as "the common beliefs, on which all men base their proofs," he states the principle in two ways: "that everything must be either affirmed or denied, and that a thing cannot at the same time be and not be."  This most certain principle is the spelling out of the meaning of identity, namely, that it involves the exclusion of contradiction and the affirmation of logical harmony. Such is the function of the principle of contradiction, namely to eliminate contradiction.
Referring to the principle of contradiction, Aristotle says, "This, then, is the most certain of all principles. . . . For it is impossible for any one to believe the same thing to be and not to be as some think Heraclitus says";  and he adds that this principle is "an ultimate belief" for it is "naturally the starting‑point even for all the other axioms."  Admitting that "many writers about nature use this language," he nevertheless concludes "but we have now posited that it is impossible for anything at the same time to be and not to be, and by this means have shown that this is the most indisputable of all principles.” 
The difficulty is that the principle cannot be demonstrated, but is itself the ground of demonstration. It is a fundamental assumption on two levels; on the one hand, it is an assumption about the nature of "being," i.e., that it is non‑contradictory; on the other, it is an assumption about the nature of rational thought, i.e. that it is impossible to think in terms of contradiction. In other words, the assumption is concerned with both the ontological and logical levels. Both content and method are assumed to involve non-contradiction.
For Aristotle, as for most philosophers who make the assumption, it is meaningless to ask for demonstration of the principle which is the very starting point for all demonstration. Thus he says: "Some indeed demand that even this shall be demonstrated, but this they do through want of education, for not to know of what things one should demand demonstration, and of what one should not, argues want of education."  Education would lead these people to see that "it is impossible that there should be demonstration of absolutely everything (there would be an infinite regress, so that there would still be no demonstration)."  Aristotle's conclusion is: "But if there are things of which one should not demand demonstration, these persons could not say what principle they maintain to be more self‑evident than the present one.” 
In contrast to modern philosophers who are for the most part unaware of any challenge of the assumption, Aristotle is keenly aware of the opposing position held by the natural philosophers, He returns to the problem over and over again. Thus in Book IV (Gamma) of the Metaphysics, speaking of those who hold that a thing can both be and not be at the same time, he charges that "in general those who say this do away with substance and essence."  They do away with them because "denoting the substance of a thing means that the essence of the thing is nothing else," which in turn means that "contradictories cannot be predicated at the same time."  But this is a circular argument which simply shows that what he means by substance is that which has an essence, and that essence is non‑contradictory. He could not conceive, as Heraclitus apparently could, that the essence of a thing might be rooted in opposition, rather than harmony; indeed, that if things are always in process of becoming, then opposition, not harmony, is the essential category.
And yet it is not quite true to say that Aristotle could not conceive of opposites existing at one and the same time in the same thing. For, in speaking of those who “think that contradictories or contraries are true at the same time," he remarks that "in a sense they speak rightly and in a sense they err.” They "speak rightly" in that "the same thing can be potentially at the same time two contraries, but it cannot actually."  By the concept of potentiality and actuality, Aristotle minimizes the difficulty involved in dealing with qualitative change.
But Aristotle is not satisfied with the elimination of contradiction or opposition in qualitative change through the mechanism of potentiality and actuality. He, too, is searching for something which does not change. Thus he says: "And again we shall ask them to believe that among existing things there is also another kind of substance to which neither movement or destruction nor generation at all belongs." Those who talk about continual change, and hence of contradiction as of the essence of things, "have been led to this opinion by observation of the sensible world. They think that contradictories or contraries are true at the same time, because they see contraries coming into existence out of the same thing."  Of this reliance on sense experience, which presents us with a world characterized by qualitative becoming, Aristotle says: "And again it would be fair to criticize those who hold this view for asserting about the whole material universe what they saw only in a minority even of sensible things."  And he adds: "For only that region of the sensible world which immediately surrounds us is always in process of destruction and generation; but this is—so to speak—not even a fraction of the whole, so that it would have been juster to acquit this part of the world because of the other part, than to condemn the other because of this."  Acquit it and condemn it and condemn it of what? Of qualitative change, and therefore of at least apparent contradiction. Then follows immediately another appeal to the unchanging: "And again, obviously we shall make to them also the reply that we made long ago; we must show them and persuade them that there is something whose nature is changeless."  Finally, since it is sense‑experience which shows us a world of ceaseless "generation and destruction," Aristotle concludes: "Regarding the nature of truth, we must maintain that not everything which appears is true." 
Aristotle, like Plato, tends to equate identity and non-contradiction with the unchanging. But in so far as he is dealing with the sensible world, where he has to deal with qualitative charge, he minimizes the difficulties by his concept of potentiality. However, in the Physics and in the biological works, where he is dealing primarily with sensible things, he seeks for the unchanging in another direction.
In the Physics, after agreeing with the natural philosophers that the contraries are principles, he says: “Everything, therefore, that comes to be by a natural process is either a contrary or a product of contraries."  Each contrary is a principle, hence, since there are only pairs of opposites, the contraries constitute two principles. Now the question is "whether the principles are two or three or more in number."  The two contraries are: one, what it was; and two, what it is changing into. Stressing the "it," Aristotle concludes that the principles are three, since "to preserve both, we must assume a third somewhat as the substratum of the contraries."  There must always be something which becomes this from that, something which "survives through the process";  this is the substratum, substance or subject. Thus Aristotle says that "one can gather from the various cases of becoming in the way we are describing, that, as we say, there must always be an underlying something, namely, that which becomes."  Both "something which comes into existence" and "something which becomes that" from this, are "coming to be from a substratum."  What, then is a substratum? We are told that "the substratum is different from the contraries, for it is itself not a contrary."  Essentially, the substratum is that which endures through change, the self‑identical subject, which undergoes change, and which itself is not contradictory.
It is the substratum which has contraries attributed to it, but the contraries cannot be attributed to it in the same way at the same time. One can be attributed as actual while the other is potential, and vice versa. The contraries are, then, pairs of qualities, as opposites and their intermediates.
In this manner Aristotle laid the logical and ontological cornerstones for the science of classification. Upon this solid foundation he constructed the edifice which has endured for more than two thousand years and which we know under the name of "formal logic". It was this science of classificatory logic which guided all the sciences through their first stage of historical development, the classification of that particular aspect of reality or thought with which each was concerned.
For the purposes of classification it was historically and procedurally necessary to view phenomena as being just what they are and nothing else, and as simultaneously existing. In this finished, side‑by‑side existence of all things, the structure was one of classes within classes and of mutually exclusive classes. The categories, principles, laws and facts of formal logic were clustered around the concepts of genus, species and individual members. The problems of formal logic centered around classification, such as propositions concerning the class membership of any given phenomenon, whether it be a thing (noun) or action or relationship (verb) or subtle distinctions between things or actions (adjectives and adverbs).
To complete the classification of phenomena, it was absolutely indispensable for the various sciences to view them as self-identical and non‑contradictory. Each phenomenon had of necessity to be viewed as clearly definable so that it might be classified. The matter of classificatory definition required that a thing be viewed as now and forever just what it is, and not at the same time something else. This requirement could only be met by the elimination of the concept of becoming, process, evolution and qualitative transformation. Thus the struggle on the part of Plato and Aristotle against Heraclitus and the primitive logic of genesis with its stress on those very categories which were inimical to the task of classification, was scientifically necessary. It had to be successful so that science could carry out its first task, the classification of astronomical, physical, chemical, biological and social phenomena. That task, however, was completed by all the sciences during the course of the 19th century, some early some late in that one‑hundred year span.
At the very beginning of the last century, Hegel, aware of what was happening in a number of sciences, attempted to develop a new logic, one designed to deal with development and growth, transformation and evolution. One of the major influences on him were the revolutionary changes that had taken place in America and especially in France. The French Revolution, that great social transformation, brought the problem of qualitative change dramatically to the fore. Hegel set himself the gigantic problem of developing a philosophical method of thinking which would make it possible for man to deal rationally with change, process, evolution and fundamental transformation of one kind of thing into another.
It was perhaps inevitable that in pursuing his self‑appointed historic task he would be obliged to carry on a sharp critique of Aristotle and the logic of classification on the one hand, and that on the other he would resurrect the primitive logic of genesis formulated crudely by Heraclitus and his contemporaries of the sixth century, B.C.
HEGEL AND ARISTOTLE
Hegel returns to the conflict between Heraclitus on the one hand and Plato and Aristotle on the other, and sides with the former against the latter. The Hegelian criticism of Aristotle's logic is not a complete rejection of formal logic. It does not simply say "no". It is rather a "negation", in Hegel's meaning of the term of the principles of traditional logic. In this sense, "negation" is the raising and transforming of the old method at another level. For example, the principle of identity is not discarded, but is carried forward and transformed.
Hegel's central point is that whereas the content of thinking, that on which thought is employed, has changed in the course of two thousand years, the method has remained relatively unaltered. Thus he says that "up to the present day, the logic of Aristotle continues to be the received system,”  that "the form and content of Logic had remained the same that it had inherited by long tradition‑‑a tradition which in being handed down had become ever more meagre and attenuated; there are no traces in logic of the new spirit which has risen both in Learning and in Life."  He adds that "it is, however (let us say it once for all), quite vain to try to retain the forms of an earlier stage of development when the inner structure of spirit has become transformed; these earlier forms are like withered leaves which are pushed off by the new buds already being generated at the roots."  There must be a new method to fit the new content, or “spirit," as he calls it.
The old "spirit" was of the "understanding" which took things as static and isolated, with merely external relations. Corresponding to such a content was the “metaphysical method," the main characteristic of which "was to make abstract identity its principle and to try to apprehend the objects of reason by the abstract and finite categories of the understanding."  This traditional logical method conceived of "thought as the faculty of comparison and classification" and until Hegel "Logic hitherto had no other idea of its duty than this."  And yet, as a matter of fact, the traditional method of "comparison and classification" was adequate to the traditional "spirit." A major difficulty arises only when the "spirit" changes without concomitant changes in the method. In this connection it may be well to quote Hegel at some length:
Kant considers that Logic—that is, the aggregate of Definitions and Propositions which are called Logic in the ordinary sense—is fortunate in that it has fallen to its lot to attain so early to completion, before the other sciences; for Logic has not taken any step backwards since Aristotle,—but also it has taken no step forwards—the latter because to all appearance it was already finished and complete.—If Logic has undergone no change since Aristotle—and in fact when one looks at modern compendiums of Logic the changes consist to a large extent merely in omissions—what is rather to be inferred from this is, that Logic is all the more in need of a thorough overhaul; for when Spirit has worked on for two thousand years, it must have reached a better reflective consciousness of its own thought and its own unadulterated essence. A comparison of the forms to which Spirit has risen in the worlds of Practice and Religion, and of Science in every department of knowledge Positive and Speculative,—a comparison of these with the form which Logic—that is, Spirit's knowledge of its own pure essence—has attained, shows such a glaring discrepancy that it cannot fall to strike the most superficial observer that the latter is inadequate to the lofty development of the former, and unworthy of it. 
He concludes: "As a matter of fact the need of a transformation of Logic has long been felt."  It will be noted that what he is calling for is not a reform of logic, but its transformation, which means that its basic underlying assumptions must be transformed because no amount of pruning will save the tree. What he is demanding is a new method for philosophy. He leaves no doubt of his meaning when he says: "The essential point of view is, that we have to do altogether, with a new concept of philosophical method." 
The old logical method of the understanding is a "moment' in the development of human knowledge. It is first necessary to analyze things in their aspect of static isolation, noting that there are separate things different from one another. “Knowledge begins," says Hegel, by apprehending existing objects in their specific differences," and he adds that "the merit and rights of the mere understanding should unhesitatingly be admitted."  In the development of the child, as of the human race, thought must first "distinguish matters, forces, genera and the like, and stereotype each in its isolation."  In doing so, it bases itself on the principles of identity, contradiction and excluded middle for the purposes of comparison and classification. "Thought is here acting," Hegel says, "in its analytic capacity, where its canon is identity, a simple reference of each attribute to itself. . . and what is this but to proceed on the principle of identity." 
It is the principle of identity, which, together with the two principles which spell out its meaning, must be criticized if thought is to proceed beyond understanding to reason. Reason for Hegel, is the procedure for thinking the internal interconnections of the development of things and concepts.
For Hegel, the principles of identity and contradiction are formal. Rather than being concerned with truth, they are merely rules for "epistemological correctness." They are important for consistency of definition and meaning in thought and discourse. They are not reflections of ontological reality; they are not concerned with truth. Thus he says:
The simple basic or common determination of all these forms is Identity, which as the Law of Identity as A equals A, and as the maxim of contradiction, is maintained in the Logic of this collection of forms. Common sense has so thoroughly lost its reverence for the school which is in possession of these laws of truth and still fosters them, that it derides the school on account of the laws, and would regard anyone as insufferable who, in accordance with these laws, made true statements such as, "the plant is—a plant," "Science is—Science," and so ad infinitum. . . . However, truth may be determined—that they are unserviceable for higher Truth—that, broadly, they are merely a matter of epistemological correctness and not of Truth itself. The inadequacy of this way of regarding thought, which leaves Truth on one side, can only be supplemented when in the contemplation of Thought, Content is included as well as that which is habitually reckoned as belonging to external form. 
The old content and method are "empty and lifeless."  Their "determinations are assumed to stand immovably rigid and are brought into a merely external relation with one another."  Isolation, immovable rigidity, external relations are the categories on which the old logic bases its laws of thought and being. For it, "everything rests on an external difference, on mere comparison, and becomes a wholly analytic procedure, a matter of merely mechanical calculation."  Such a method "is not much better than a manipulation of rods of unequal length in order to sort and arrange them according to size—like the child's game of trying to fit into their right places the various pieces of a picture puzzle."  This is the method of "defining and classifying,"  which is a stage in the development of thought, but only the beginning, the early stage, and must be transcended, if there is to be further progress. The method of thinking must be brought into line with the new content which is concerned with development and internal relations.
The above constitutes in essence the Hegelian criticism of Aristotle's traditional method of classification or formal logic. Hegel points to the fact that whereas our knowledge of the world has made gigantic strides, logic has remained relatively unaltered, at least in regard to its basic principles. To remedy this situation, Hegel developed the logic of genesis, sometimes called "dialectical logic".
HEGEL'S LOGIC OF GENESIS
Hegel's problem is how is logical method to be transformed so that there will be no absolute opposition between it and its new, dynamic, developmental content? The first thing to note is that traditional logic bases itself on non‑contradiction, but finds itself in opposition to the content on which it is to be employed. This new content involves qualitative development which according to Hegel is itself "contradictory."
Here we must pause to consider what Hegel means by the term "contradiction" or "contradictory." Much confusion has arisen through his use of this traditional term. Obviously, he cannot mean by it the intention of the term as defined in formal logic. The latter defines it as two propositions which cannot be true of the same thing at the same time." Hegel could not accept such a definition simply because he holds that contradictory opposites can and must be asserted as true of the same thing at the same time. The difficulty arises from the different meaning of "opposites." Formal logic defines contradictory opposites as A and not‑A, in which A denotes a specific thing and not‑A denotes everything which is not that thing. It is clear that opposites so defined cannot be asserted of the same thing at the same time. What, then, does Hegel mean by "opposites"'?
By "contradictory opposites" Hegel means, not a specific and a general, but two specific traits in the form of tendencies. These tendencies, in their simplest form are the specific past and the specific future of the thing in question. In short, they refer to what the thing was and what it is becoming, to what is passing away and what is arising. Thus by contradictory opposites Hegel means two tendencies within the process of becoming which are in irreconcilable opposition. Irreconcilable opposition means that the tendencies cannot be harmonized, but it does not mean that the opposition is unresolvable. It is resolvable however, only through one abolishing the other through the gradual or quantitative development of the opposition. The point of abolition of the opposites is the nodal point of qualitative change, at which the opposition is transformed at a different level. By employing the term "contradiction" in this new meaning, Hegel has occasioned much misunderstanding of his dialectic.
For Hegel, a thing in the process of development is not simply a logical harmony; it is not related to itself as a tautology. Rather, its self‑relation is both negative and positive. It is related both to its past and its future. The past and future exist in a sense, in the present thing. They exist in the present in the form of what was and what is becoming, what is perishing and what is arising. And the relationship between the two tendencies is one of opposition or negation. The result is that the new concept of method must reconstruct the principle of identity. The latter can no longer be tautological and non-contradictory. On the contrary, identity is to be conceived as self‑relation involving essential and specific opposition or "contradiction." It is not identity as such that is negated, but identity as harmonious or tautological. The new method is the affirmation of internal opposition or "contradiction" as of the essence of identity. Identity is self‑relation but the self‑relation is not simple; it is complex. With the emphasis on development from one kind of thing into another kind of thing, rather than on classification of static entities, it is important to know what a thing was and what it is becoming, and the relationship between these two aspects in the present stage of development of the thing.
There are two fundamental problems in the new method proposed by Hegel: one is how qualitative change occurs; and the second is how two tendencies, fundamentally opposed, exist in the same thing at the same time. The two problems are closely related, and cannot be answered in isolation one from another. If one thing changes into its opposite, in the process going through various stages of transformations into contraries, as Aristotle had indicated, it must mean that the new exists along side of the old. The latter is what is perishing, the former what is arising. Now through the quantitative development of both, a point is reached at which any further quantitative development will lead to the transformation of the essence of the thing. The problem then becomes: What is the relation between what is arising and what is passing away? Hegel answers that they are in conflict, and that this conflict is fundamental in determining the nature of the given thing at any given stage. As a matter of fact, the essence of a thing is the opposition, and there is nothing over and above it. The two basic principles of the new method then are: the transformation of quantitative changes into qualitative changes and vice versa, and the identity and opposition of opposites, what Hegel calls "the unity of opposites."
In the Introduction to The Science of Logic, Hegel indicates the lines on which the new method must be developed:
We have here modes of consciousness each of which in realizing itself abolishes itself, has its own negation as its result,—and thus passes over into a higher mode. The one and only thing for securing scientific progress (and for quite simple insight into which, it is essential to strive)—is knowledge of the logical precept that Negation is just as much affirmation as Negation, or that what is self‑contradictory resolves itself not into nullity, into abstract Nothingness, but essentially only into the negation of its particular content, that such negation is not an all‑embracing Negation, but is the negation of a definite somewhat which abolishes itself, and thus is a definite negation; and that thus the results, the negation, is a definite negation, it has a content. It is a new concept, but a higher, richer concept than that which preceded; for it has been enriched by the negation or opposite of that preceding concept, and thus contains it, but contains also more than it, and is the unity of it and its opposite. 
This is the dialectical method, the logic of genesis, in which each thing contains its negation in itself, is self‑related in the form of a unity of opposites. The conflict of the opposites is the source of self‑motion, and is the cause of the quantitative development which leads to qualitative transformation.
Of the method, Hegel says: "I could not of course imagine that the Method which in this System of Logic I have followed—or rather which this System follows of itself—is not capable of much improvement, of much elaboration in detail but at the same time I know that it is the only true Method."  He knows it is "the only true Method" because it eliminates the opposition between method and the world of becoming and perishing inherent in traditional formal logic; because, as he says: "the Method is no ways different from its object and content;—for it is the content in itself, the dialectic which it has in itself, that moves it on."  He concludes: It is clear that no expositions can be regarded as scientific which do not follow the course of this Method, and which are not conformable to its simple rhythm, for that is the course of the thing itself.”  Implicit in this flat assertion is the recognition that "the thing itself," which is a process of perishing and becoming, involves opposition, and that this is at last taken into account and made the basis of method. What he is saying is that this is the true line of development of method as conformable to content. In this sense, such a method alone is scientific, namely, can give rise to truth.
The most important aspect of the dialectic, for Hegel, is "the Unity of Opposites" or "the Positive in the Negative." "That by means of which the Concept forges ahead," Hegel says, "is the above mentioned Negative which it carries within itself: it is this that constitutes the genuine dialectical procedure."  The heart of the dialectic is opposition, which Hegel calls "contradiction." It is clear that he is employing a traditional term which historically has meant mutually exclusive propositions. Hegel's use of the term "contradiction"' has led to many misunderstandings of his method. His essential position, however, is that it is the identity of opposites in and through their opposition, which is the nature of a thing at any stage of development. Here we see the transformation of the principle of identity, from "non‑opposition" to "opposition," or from "non‑contradiction" to "contradiction." Not only can things be in internal opposition, be "contradictory," not only can things be said to be contradictory,'' but there would be no separate distinguishable things without such internal opposition. Therefore, opposition, far from being anti‑rational, is itself the ground of rationality. For without internal opposition there would be no identity. Traditional logic recognizes that this is true, at least implicitly, when in stating that A is A, it indicates in the next breath that A is not non‑A. But this is an external opposition, namely, A is opposed to and different from all that is not itself. The Hegelian dialectic carries it another step in showing that A is self‑related in the same way because it is not static.
Opposition or "contradiction" is central in the dialectic, so central that Hegel states it as a law. "It should be annunciated," he says, "that all things are contradictory in themselves, in this meaning, that this proposition as opposed to the others expresses the truth and essence of things.”  Wherever there is movement, activity, change, life, there is "contradiction," or opposition; and, conversely, only what is abstract "dead Being" is non‑contradictory, non‑oppositional, harmonious, or self‑identical in the traditional meaning of identity. But where is there not movement and change and activity? For Hegel everything is moving, changing, and active; therefore, everything is in essence self‑oppositional or "contradictory."
Hegel states as a law that "all things are contradictory in themselves." By "contradictory in themselves," we know that he means to indicate that all things are within themselves a conflict of opposites in the form of what is arising and what is passing away. This law is in Hegelian language, "the unity of opposites." Now the unity between opposites is precisely, for Hegel, their opposition or strife or conflict. In short, the tie which binds opposites together into one identity, is their opposition. It is clear that in this sense, then, there would be no identity without internal opposition. Tautology for Hegel is not the precondition either for thought or being. To be an identity, a thing must be not a tautology, but an opposition between what is arising and what is passing away. It follows that to think about such unities of opposites requires that thinking be able to deal with internal oppositions rather than with tautologies. The term “contradiction" means, for Hegel, just that—that is, internal opposition.
Now in calling this "Unity of opposites" a law, Hegel is asserting that there are permanences—namely, the laws of "being." In so far as he assigns these laws as eternal laws of "Absolute Being," he is asserting something which is in absolute and unresolvable opposition to his postulate that everything is changing. In short, he too is going beyond process in giving an eternal structure of process. This absolute opposition in Hegel could only be overcome through a recognition that the laws of nature are themselves only relatively permanent, that they are relative to space‑time systems and epochs. This would allow not only for changing "permanences," in relation to objective changes, but also to changes brought about through our developing understanding of the world.
Traditional logic abhors self‑opposition or "contradiction." If a "contradiction" is encountered, it is the result of faulty reasoning. For Hegel, however, thought would know it was not dealing with real things if it did not find a "contradiction." Of these antithetical positions Hegel says:
But it has been a fundamental prejudice of hitherto existing logic and of ordinary imagination that Contradiction is a determination having less essence and immanence than identity; but indeed, if there were any question of rank, and the two determinations had to be fixed as separate, Contradiction would have to be taken as the profounder and more fully essential. For as opposed to it Identity is only the determination of the simple immediate, or of dead Being, while Contradiction is the root of all movement and life, and it is only in so far as it contains a Contradiction that anything moves and has impulse and activity. 
The conditional clause above, "if there were any question of rank, and the two determinations had to be fixed as separate," would not be granted by Hegel. The position that "all thing things are contradictory in themselves" requires a transformation of the principle of identity, and will not allow for the separate and side‑by‑side coexistence of the principles of the "old" and “new" methods. Difference and contradiction are not to be taken as external to identity, rather they are internal to it. Identity and "contradiction" are internally related, namely, identity is identity of opposites; the identity is the particular opposition. Thus Hegel says: 'The contemplation of everything that is shows, in itself, that in its self-identity it is self‑contradictory and self‑different, and in its variety or contradiction, self‑identical."  This is the case "because each in itself is its own opposite."  One of the basic difficulties with formal logic is that it relates identity and contradiction only externally. They are reduced to absolute opposites which cannot coexist, which cannot be true of the same thing at the same time in the same respect. Identity and "contradiction," once completely separated, the former is affirmed as of the essence of things, while the latter is repudiated as an abomination. In this connection Hegel says:
Ordinarily Contradiction is removed, first of all from things, from the existent and the true in general; and it is asserted that there is nothing contradictory. Next it is shifted into subjective reflection, which alone is said to posit it when it relates and compares. But really‑‑it is said‑‑it does not exist even in this reflection, for it is impossible to imagine or to think anything contradictory. Indeed, Contradiction, both in actuality and in thinking reflection, is considered an accident, a kind of abnormality or paroxysm of sickness which will soon pass away. 
Of the assertion "that there is nothing contradictory," Hegel says "we may disregard this statement" because "at least there are a number of contradictory things about, contradictory arrangements and so forth."  In other words, there are at least some contradictory things. But he is not satisfied with such a partial affirmation of "contradiction." He adds:
But it must further not be taken only as an abnormality which occurs just here and there: it is the Negative in its essential determination, the principle of all self‑movement, which consists of nothing else but an exhibition of Contradiction, External, sensible motion is itself its immediate existence. Something moves, not because it is here at one point of time and there at another, but because at one and the same point of time it is here and not here, and in this here both is and is not. must grant the old dialecticians the contradictions which they prove in motion; but what follows is not that there is no motion but rather that motion is existent Contradiction itself.
And similarly internal or self‑movement, or impulse in general. . . is nothing else than the fact that something is itself and is also deficiency or the negative of itself, in one and the same respect. Abstract self‑identity has no life; but the fact that Positive in itself is negativity causes it to pass outside itself and to change. Something therefore has life only in so far as it contains Contradiction, and is that force which can both comprehend and endure contradiction. 
Imagination and understanding are Hegel's terms for that stage of thinking which limits itself to the mere external relation of opposites. At this stage identity and non‑contradiction are adequate principles. But when thinking rises to the level of reason, it passes beyond concern with external relation to concern with transition from one opposite into the other, which involves their internal relation. Such internally related transition is inherently oppositional since it involves self‑relation to two different qualities. The thinking of transition or qualitative change, therefore, requires the thinking of internal opposition of two qualities. An internal opposition of this kind is called a "contradiction". A contradiction is a unity and conflict between two qualities, one representing what a thing was and the other what it is becoming. Reason, for Hegel, signifies that type of thinking which is able to encompass the simultaneous existence within any thing or concept of both the past and the future, The present of anything is then said to be the opposition between what that thing was in the past and what it is becoming in the future. The central feature of genetic logic or the dialectic is what Hegel calls "the understanding and enunciating of Contradiction".  Reason is concerned with understanding the structure of development or internal change; it is concerned therefore with the transformation of one thing into another, one quality into another; as a result reason must proceed in terms of contradiction or in other words the opposition between the old thing or quality and the new. The terms "opposite” and "opposition" refer to the old and new qualities and to the fact that a new quality comes in to being only with the elimination of the old. For example, an infant is at one and the same time both the infant that it was and the child that it is in the process of becoming. The identity which is called infancy must according to Hegel be understood in terms of the opposition or contradiction between past infancy and future childhood. The study of child development would be concerned with the course of development of this specific contradiction.
With his emphasis on development or internal transformation of one kind of thing into another, Hegel found it necessary to transform the principle of non‑contradiction as the basis of identity into the principle of contradiction as the basis of identity. Instead of excluding contradiction, as the principle of identity in classificatory logic does, he found it imperative that identity include or be founded in contradiction. For Hegel, identity becomes the identity of opposites. This is itself the opposite of the concept of identity in classic Aristotelian logic which is rooted in non‑contradiction. Hegel's concept of identity posits the conflict of opposites or contradiction as of its essence. In fact it could be stated negatively as: no internal opposition, no identity, no quality, no thing. Here Hegel reaffirms the position taken by Heraclitus in his statement about Homer praying for the end of all strife, for if strife were to cease "all things would pass away".
Hegel transformed the logic of classification into the logic of genesis, formal logic into dialectical logic. He characterized the former as thinking statically about a world conceived as being essentially static. In such a world the function of thought is limited to definition, comparison, description and classification. Hegel characterizes genetic logic as thinking dynamically about a world conceived as being essentially dynamic, one in which process and change are basic features. So long as the world was conceived as static and so long as the task of science was to classify the phenomena of such a world, just so long was there congruence between world view and the method of reasoning about it, between, that is, subject‑matter and logic. Now, however, all this is radically changed. Modern science in all its branches today pictures the world as forever in the process of development and becoming. To retain the old static method of classificatory logic while our concept of the world is dynamic is to condemn human reason to impotence. In this case there is an absolute, not a dialectical opposition between subject‑matter and method of reasoning. It is this situation which Hegel recognized to be in the process of becoming already at the beginning of the nineteenth century. He saw It as comprising a crisis at that time. Since then the crisis has sharpened until it is of gigantic proportions cutting across all areas of human thought and activity.
Hegel transformed classificatory logic into genetic logic but he did so within the context of an impossibly involved philosophical system. The intermeshing of the logic and the system make the study of Hegel's logic an exceedingly difficult task. It is particularly difficult because his system is in open and absolute conflict with the logic. The latter is concerned with the structure of change, while his system is wholly static and unchanging. The system is rooted in a concept of the self-development of the Absolute unfolding itself. Thus the end is already contained in the beginning, and nothing really changes at all. His system is essentially mystical and becomes hopelessly enmeshed in all kinds of metaphysical speculations. His logic of genesis is developed as the way in which the Absolute unfolds itself from conception to conception. The intellectual task is to extract the logic from the system, to take it out of the context of unfolding Absolutes and allow it to stand on its own feet, as a separate science, the science of the structure of change and interconnection, of the world and of thought.
When this disengagement is accomplished, Hegel's logic is found to be highly effective as a method for dealing rationally with the new categories of process. Genetic logic, it turns out, has three general principles, just as classificatory logic has. The three principles of classificatory logic are the laws of identity, noncontradiction and excluded middle. In effect these laws state that for classificatory purposes a thing must be conceived as being just what it is, not at the some time something else and as either this or that but not both at once. The laws of genetic logic, on the other hand, include as we have already seen the identity of opposites but in addition the law of the unity and transformation of quantitative and qualitative changes and the law of the temporal and spatial interconnection of things. In effect, these laws state that a thing must be viewed as being in the process of becoming something else; that the something else must be viewed as already existing in embryonic form within the old thing; that a thing exists only as a unity of the old and the new; that the new can come into being as a thing in its own right only by eliminating the old; that a thing can remain the same only by gradually changing and eventually changing to a point at which any further change in degree will bring about a change in kind; that a thing is interconnected on the one hand with its own past and the past extending behind itself to previous things which had given rise to it, and on the other to things existing spatially outside itself, namely, the environment.
The principles of genetic logic are far more complex than those of classificatory logic. But the world viewed as process is likewise far more complex than the world viewed as static. The fact is that we require a more delicate and intricate method of thinking than did our ancestors of a century and a half ago. To use classificatory login on developmental subject‑matters is like using a meat-cleaver in brain surgery.
Within the science of logic itself, genetic logic leads to synthesis of what has for two thousand years been subject to fragmentation through analysis. It means, among other things, that the many pairs of categories which have been separated into self-contained isolation must be brought back together again as interconnected opposites which cannot be separated without woeful distortion. Such pairs of concepts as relative and absolute, form and content, concrete and abstract, particular and general, continuity and discontinuity, past and future, space and time, objective and subjective, finite and infinite, quality and quantity, magnitude and measure, beginning and end and a host of others, are examples.
A primary task of logic, of a logic of genesis, that is, is to explore the unity and conflict, the mutual transformations and interconnections of these pairs of concepts, and the interrelations between the pairs. The results of such an exploration should prove to be of inestimable service to the other sciences, those dealing not with the most abstract features of the structure of process but with specific aspects of the world of nature, man and society. It should also be of great service to the arts and technical disciplines, and especially to education. The understanding that a developed genetic logic could bring to the thought and knowledge of man, the common abstract frame of reference thereby gained, would go a long way toward breaking down the compartmentalization of learning and research and toward the integration of the sciences, the arts and technology. It would help likewise in overcoming the deep‑seated disillusionment with science, reason, art and life so prevalent today. Such a development of genetic logic would constitute a powerful instrument for resolving the current crisis in all intellectual pursuits.
Hegel's philosophical method, his logic of genesis, his dialectics, is pregnant with significance for modern thought in all fields. It is by no means a fully developed science, but it does furnish the foundation on which a mature logic of genesis can be constructed. An indispensible prerequisite for this, however, first of all the study of Hegel's logic. Short of that, we have not even begun to plan, much less to build.
THE LOGIC OF GENESIS AND THE 20th CENTURY CRISIS IN THOUGHT
The logic of genesis has had a long history, as old as itself. In the opening centuries of Western philosophy it represented, in Heraclitus and his followers, the dominant trend. Only with the separation of certain sciences from philosophy in Ancient Greece did the genetic logic cease to be immediately relevant. During the entire period of the classification stage of the sciences the logic of genesis played a secondary role, subsidiary to the logic of classification. It was limited to a form of reasoning, in which thesis, antithesis and synthesis was the mode of argumentation. Beginning with Socrates and continuing through a number of Greek and Roman schools of philosophy and extending into the scholastic philosophy of the medieval period and on to Bruno in the Renaissance and Diderot in the pre‑French Revolutionary thinkers, the logic of genesis was kept very much alive. Thus when in the opening decades of the 19th Century the sciences began to emerge from their respective stages of classification, Hegel had ready at hand a long and rich tradition on which to build his science of genetic logic. He called his logic of genesis "dialectics", a term which had for two milleniums been used to designate the Socratic‑Scholastic method of argument: the ultimate union of two opposite points of view on a "higher" more inclusive level. By "dialectical logic", however, Hegel meant to designate not only a form of reasoning but also the general structure of process and becoming in the phenomenal world as a whole and in all its details. He thus returned to the original position of Heraclitus, assigning to the logic of genesis ontological as well as logical status.
There is therefore both continuity and discontinuity in the origin and development of genetic logic. The continuity exists in the fact that change and interconnection, transformation and time are always present to man's consciousness and must be dealt with in daily life and in the life of the intellect. The discontinuity in genetic logic, the partially filled hiatus, that is, between Heraclitus and Hegel, is accounted for by the primary and historically constituted classificatory task of science during that extended epoch.
The two‑thousand‑year epoch dominated by the logic of classification was characterized by the stress on the categories of space, external relations, locomotion, permanence and simultaneity. Phenomena if they were to be classified had to be viewed as permanently existing side‑by‑side with no organic interconnection, transformation or evolution.
Today no sciences are concerned solely with spatial, simultaneous classification of phenomena, but are concerned primarily with their genesis, evolution, transformation and temporal and spatial internal interconnections. In Botany and Biology, for example, the classification of the flora and fauna of the earth has to all extents and purposes been completed. The foremost problem in these sciences is now not classification but genesis, evolution, the origin, development and transformation of species and genii. For this task the logic of classification cannot give guidance. A logic of genesis is required. The same is true in geology in which today the evolution of the earth's crust, not its classification, is being investigated. Astronomy is concerned with the origin and evolution of the solar system, galaxies, and universes. Physics is preoccupied with the transformation and internal organization and relations of atomic and sub‑atomic elements. In Psychology the two main questions are the origin and development of human nature in the species from animal to man and in the individual from conception to maturity.
At whatever science one looks, the overall problem is the same: to investigate the relevant phenomena in terms of process, becoming, evolution, internal structure and relations, transformation and the like. Time and development have become categories at least equal in importance to the categories of space and simultaneity. To deal effectively and rationally with the newer set of categories and with their interconnection with that set of categories stressed during the classificatory stage of the sciences, the logic of genesis is required.
In this view, logic is defined as the science of structure. This science has two branches: one, the science of the structure of classification; and two, the science of the structure of genesis and interconnection, The first branch of logic met the needs of science during the classificatory epoch. The second can, according to the present contention, meet the needs of the current epoch, that concerned with becoming, interconnection and process.
The need for such a genetic logic is not limited to the sciences, but is equally required by the various arts and by such practical and applied fields as engineering, architecture, medicine and education. The disease of "professionalism" with its exclusive "compartmentalization" is a hallmark of our era. This era is one of intellectual crisis in part at least due to the fact that reason, rationality and scientific method are identified with the traditional logic of classification. When this logic is found, as it inevitably is, to be inadequate to deal with the conflicts of old and. new, with transformations, with interactions, with evolving phenomena, the conclusion is drawn that reason and science are inadequate to deal with them. The limitations of a particular type of logical reasoning is identified with the limit of reason as such. The result is the current widespread disillusionment with reason and science and the consequent painfully apparent movement toward irrationalism, pessimism, cynicism and defeatism.
Obviously the lack of a logic of genesis is not the sole or perhaps even the chief cause of the 20th century crisis in science and reason. There are social and historical causes which no doubt underlie all others. It is however the contention here that the lack of a genetic logic is at least a contributing cause and that an investigation of the foundation laid by Hegel for such a logic would be a step in the right direction. Such an investigation should include not only a serious study of Hegel's Science of Logic and his Shorter Logic of the Encyclopedia, but also the significance a genetic logic could have for the crises in the various sciences and arts, in reason and in the applied fields, especially education. The first requires the difficult task of separating Hegel's logic from his system, while the second presupposes a mastery of the logic of genesis in addition to familiarity with a wide range of human knowledge, scientific, artistic and applied.
No matter how difficult the task we cannot fail to undertake it, for to so fail would mean to surrender by default the future of these fields to that "Eastern" third of the intellectual world which is now busily at work both in mastering the logic of genesis and in applying it in many sciences and related fields, including education. Simply because the socialist world is doing it is no sufficient or rational reason why we should not. We are already a hundred years behind in this area. At least a scholarly and serious investigation of genetic logic is in order and can not, save at our own deadly intellectual peril, be further postponed.
1. Jevons, W. Stanley, Elementary Lessons In Logic. London, 1946. P. 117. [—> main text]
2. Ibid. [—> main text]
3. Ibid. [—> main text]
4. Ibid., p. 118. [—> main text]
5. Ibid. [—> main text]
6. Ibid. [—> main text]
7. Ibid. [—> main text]
8. Ibid. [—> main text]
9. Ibid. [—> main text]
10. Ibid. [—> main text]
11. Ibid., p. 119. [—> main text]
12. Ibid. [—> main text]
13. Ibid., p. 121. [—> main text]
14. Cohen and Nagel, An Introduction To Logic And Scientific Method, New York, 1934. P. 181. [—> main text]
15. Ibid. [—> main text]
16. Ibid. p. 185. [—> main text]
17. Ibid., p. 186. [—> main text]
18. Ibid. [—> main text]
19. Ibid. [—> main text]
1. Plato, The Republic, Cornford, trans. New York, 1945. P. 132. [—> main text]
2. Ibid. [—> main text]
3. Ibid., p. 133. [—> main text]
4. Ibid. [—> main text]
5. John Burnet, Early Greek Philosophy, London, 1930. p. 134. [—> main text]
6. Ibid., p. 135. [—> main text]
7. Ibid., p. 136. [—> main text]
8. Ibid. [—> main text]
9. Ibid. [—> main text]
10. Ibid., p. 137. [—> main text]
11. Ibid., p. 139. [—> main text]
12. Plato, Theaetetus in the Dialogues Of Plato, Jowett, trans., Oxford, 1875. p. 330. [—> main text]
13. Ibid., p. 332. [—> main text]
14. Ibid., p. 333. [—> main text]
15. Ibid. [—> main text]
16. Ibid. [—> main text]
17. Ibid. [—> main text]
18. Ibid., p. 334. [—> main text]
1. Aristotle, The Basic Works Of, New York, 1941. p. 731. [—> main text]
2. Ibid., p. 736. [—> main text]
3. Ibid. [—> main text]
4. Ibid. [—> main text]
5. Ibid. [—> main text]
6. Ibid. [—> main text]
7. Ibid. [—> main text]
8. Ibid. [—> main text]
9. Ibid. [—> main text]
10. Ibid., p. 719. [—> main text]
11. Ibid., p. 737. [—> main text]
12. Ibid. [—> main text]
13. Ibid. [—> main text]
14. Ibid. [—> main text]
15. Ibid. [—> main text]
16. Ibid. [—> main text]
17. Ibid., p. 739. [—> main text]
18. Ibid., p. 740. [—> main text]
19. Ibid., p. 744. [—> main text]
20. Ibid. [—> main text]
21. Ibid., p. 746. [—> main text]
22. Ibid. [—> main text]
23. Ibid. [—> main text]
24. Ibid. [—> main text]
25. Ibid., p. 227. [—> main text]
26. Ibid., p. 228. [—> main text]
27. Ibid., p. 229. [—> main text]
28. Ibid., p. 230. [—> main text]
29. Ibid. [—> main text]
30. Ibid., p. 231. [—> main text]
31. Ibid., p. 232. [—> main text]
1. The Logic Of Hegel, William Wallace, trans., Oxford, 1892. p. 41. [—> main text]
2. Hegel, Science Of Logic, Macmillan, New York, 1929. Vol. I, pp. 34‑35. [—> main text]
3. Ibid., p. 35. [—> main text]
4. The Logic Of Hegel, p. 75. [—> main text]
5. Ibid., p. 34. [—> main text]
6. Science Of Logic, I, p. 62. [—> main text]
7. Ibid. [—> main text]
8. Ibid., p. 36. [—> main text]
9. Logic of Hegel, p. 144. [—> main text]
10. Ibid. [—> main text]
11. Ibid. [—> main text]
12. Science Of Logic, I, p. 47. [—> main text]
13. Ibid., p. 63. [—> main text]
14. Ibid. [—> main text]
15. Ibid. [—> main text]
16. Ibid. [—> main text]
17. Ibid., p. 64. [—> main text]
1. Science Of Logic, I, p. 66. [—> main text]
2. Ibid. [—> main text]
3. Ibid. [—> main text]
4. Ibid. [—> main text]
5. Ibid., p. 66. [—> main text]
6. Ibid., II, p. 66. [—> main text]
7. Ibid., pp. 66‑67. [—> main text]
8. Ibid. [—> main text]
9. Ibid., p. 38. [—> main text]
10. Ibid., p. 67. [—> main text]
11. Ibid., p. 66. [—> main text]
12. Ibid., pp. 67‑68. [—> main text]
13. Ibid., p. 69. [—> main text]
SOURCE: Wells, Harry K. "Historical Origins of the Logic of Classification and the Logic of Genesis." Oneonta, New York, Dept. of Philosophy, Hartwick College. October 1961. 53 pp. Based on chapters 6 & 7 of the author's 1950 dissertation "Process and Unreality."
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