Before I go further, I should like to give a few more biographical facts concerning Plato and Aristotle. Plato was born in Athens in 429 B.C., and came from a distinguished aristocratic family. His main works are put in the form of dialogues or conversations. He was a student of Socrates. Aristotle, in his turn, was a student of Plato.He was born in 384 B.C. He was not a native Athenian, but he lived the greater part of his life in Athens and there set up his own school of philosophy. Aristotle was the teacher of Alexander the Great, the son of Philip of Macedonia. He left many voluminous writings. Not only was he the greatest philosopher of Greek antiquity, but he was also a great natural scientist and the founder of a whole range of sciences. Aristotle was ascientific genius of the first rank, the greatest mind in all antiquity. His influence on the subsequent period was sogreat that we can say that two thousand years, until the beginning of modern times, were under his sway.
We previously stressed the reactionary role of the philosophy of Plato and Aristotle. Now we shall speak of its great progressive role. This resides in the fact that the ruling classes of Athens at that time believed the aim of the exploitation of slave labor and their class rule to be the free development of human capacities, above all, the development of reason. This is closely connected with the fact that this slave production was not ultimately and predominantly commodity production, not production for the sake of surplus value like capitalist production. Its chief aim was production for individual use, production of use values. From this it followed that the ruling class was not absorbed in business or industry, but conceived its ideal to be the development of art and of science. Thus arose the extraordinary great interest in the investigation of human reason, in the discovery of the laws of thought. Through this activity the Greeks created a new epoch in the general development of history. As represented by Aristotle they built up the doctrine of the forms and laws of thought, known as formal logic. They also laid the foundation for what is called dialectics. Wherein dialectics and formal logic differ, we shall soon see. The science of the laws of thought, formal logic, reached its highest point with Aristotle. It was here developed so broadly and fully that it was not until the beginning of the 19th century that the German philosopher, Hegel, could make a significant and decisive advance over it.
I will now briefly explain what formal logic is and how it differs from dialectics. Formal logic can be defined as the theory of the laws of thought without regard to the content of thought. The theory of thinking or logic describes how concepts are built and wherein the different concepts differ from each other in regard to form. It deals with the different kinds of propositions and, ultimately, with the different kinds and forms of inferences, of syllogisms. Logic seeks to teach how to think correctly.
Ordinarily man thinks about nature without having need for any special art of thinking. This generally suffices for everyday life. But as soon as relations and things become more difficult, as soon as man concerns himself with conclusions drawn from a great number of premises, as soon as he becomes involved in long abstract processes of thought, then the possibility of error grows, and it becomes necessary to control and to ascertain the correctness of thought. Therefore logic has a far-reaching significance for science.
The laws of logic are based on two main propositions. The first is that of identity or of self-conformity. The proposition very simply states: "A is A," that is, every concept is equal to itself. A man is a man; a hen is a hen; a potato is a potato. This proposition forms one basis of logic. The second main proposition is the law of contradiction, or as it is also called, the law of the excluded middle. This proposition states: "A is either A or not A." It cannot be both at the same time. For example: Whatever is black is black; it cannot at the same time be black and white. A thing - to put it in general terms - cannot at the same time be itself and its opposite. In practice it therefore follows that if I draw certain conclusions from a given starting point and contradictions arise, then there are errors in thinking or my starting point was wrong. If from some correct premises I come to the conclusion that 4 is the same as 5, then I deduce from the law of contradiction that my conclusion is false.
So far all appears to be clear and certain. What can be a clearer law than that man is man, a rooster a rooster, that a thing is always the same thing? It even appears to be absolutely certain that a thing is either large or small; either black or white, that it cannot be both at the same time, that contradictions cannot exist in one and the same thing.
Let us now consider the matter from the standpoint of a higher doctrine of thought, from the standpoint of dialectics. Let us take the first law which we have developed as the foundation of logic: A is A. A thing is always the same thing. Without testing this law, let us consider another one which we have already mentioned, the law of Heraclitus which says "Everything is in flux," or "One cannot ascend the same river twice." Can we say that the river is always the same? No, the law of Heraclitus says the opposite. The river is at no moment the same. It is always changing. Thus one cannot twice nor, more exactly, even once ascend the same river. In short: the law "A is A" in the last analysis is valid only if I assume that the thing does not change. As soon as I consider the thing in its change, then A is always A and something else; A is at the same time not-A. And this in the last analysis holds for all things and events. Moreover, the seemingly changeless is established by science as changeful. One takes as a symbol of changelessness, for example, rocks or great mountains. But these rocks, as the history of geography shows, come into being and pass away; the changes, however, take so long in relation to the span of man's life that man does not notice them without special study. They are eroded by wind and by moisture; under the influence of heat and cold they are in motion. These are changes which occur so slowly that their process cannot be seen with the eye. They become visible only after long intervals. Or let us take plants. Plants change, grow. This cannot be seen with the naked eye either. It is today possible to see how a plant grows by means of moving pictures. We knew today that various kinds plants have charged. We know, for example, that wheat, rye, and rice were not always what they are today and that these plants have developed from simpler ones. This also applies to all types of animals and to human beings. Perhaps the planetary system and the sun are permanent and changeless? But astronomy teaches us that this planetary system must have emerged and that it must again ultimately disappear. Thus even here there is change, unceasing, boundless change. Man had long believed - until very recent times - that the primordial matter to which all things could be reduced, the chemical elements, were changeless, that this primordial matter was the one thing that did not change. Today it is known that this also is not the case. Elements are known - radium, etc. - which change. We suspect that all matter has emerged from still simpler parts, from electrons, that under certain conditions of temperature and pressure they became integrated and that they will eventually disintegrate and be transformed. When we know this, now does the famous fundamental law of logic stand up - the law that, "A thing is always the same"? Evidently this law is in least not unconditionally correct. It has only a limited significance. It is only valid for certain limited periods of time, or in abstraction; that is, when I ignore the changes of a thing and consider it for the moment as invariable. When I thus control a thing, making it invariable and changeless for a certain length of time, I can operate without falling into great error. But if I generalize and propound without qualifications I fall into grave errors. Then this law of formal logic does not hold good. I must turn to a higher system, to dialectics; that is, I say that difference is bound up with all identity. Thus in no object can I absolutely separate identity and difference. The object remains the same, and at the same time it changes. Both attributes exist at the same time.
A modern bourgeois philosopher, the Frenchman, Bergson, fell into the error of overlooking the identity in universal change, and came to the conclusion that the true nature of all things is unknowable since the understanding can only work with fixed, changeless concepts. Here the error committed is the reverse of the assumption that the law of the self-conformity of things is exclusively and unconditionally valid. If I extend the change between two states of a thing so far that no identity at all remains between them, then I cannot establish any change. I am utterly unable to say that they represent two states of one thing. To establish change I need a single common reference. The quantitative difference between two things or two states of one thing is only possible to determine when I can consider them in some way alike. If there is no identity without difference, it is also true that there is no difference without identity.
Let us now examine the second basic law of thought, the law of contradiction. According to this law a thing cannot at the same time be itself and its opposite. A figure is either round or angular; a line is either straight or curved. If we consider what we previously discovered regarding the law of identity, we see that not only is contradiction not impossible, but that everything that changes must at every moment represent a contradiction. We have already said that a thing which changes is identical with itself and is different from itself. It is identical and different; identical and not identical. Within the same thing there exists a contradiction. And this law holds generally for all things which change - all things which are identical and not identical, the same and not the same. Let us apply, this, for example, to the proposition: "A line is either straight or curved." What do the mathematicians say? They consider the smallest part of a circle as straight. Within certain limits they make straight and curved identical. This allows much more precise and certain calculations than if one absolutely separates straight and curved. A figure is either round or angular, but mathematicians consider a circle as a figure with an infinite number of angles. In this relation they thus make round and angular identical, and an entire section of mathematics is built upon this basic law which is full of contradictions.
In place of the law of contradiction which simple, traditional logic sets up, we can set up the opposite law, the law that everything contains a contradiction within itself, is composed of opposites. We have already verified this in the concept of change which obtains for all things. We have still to verify it in connection with certain propositions of the ancient Greeks, the concept of locomotion, for example. The Eleatic philosophers showed that all locomotion represents a contradiction and is therefore impossible. They concluded, therefore, that there is no actual motion, that motion is an illusion. And they proved this with two famous examples. The first is the proposition of the arrow, the other is the proposition of Achilles and the tortoise. The proposition of the arrow runs thus: It is asserted that if I shoot an arrow from a point, it never can reach a distant point. For if I shoot an arrow from a point which I designate A, and this arrow should reach point B, then it is certain that it must have previously traversed the intervening space. From A it must have reached C. Further, it is certain that still before that it must have covered half the distance A-C, that is, it must have travelled from A to D. If it was to reach D, it must have previously traversed half that distance, that is, to F. One can continue this division to infinity. The arrow must always have attained a previous point and thus ad infinitum. It consequently can never depart from A, since the number of distances is infinitely large. In a finite time it cannot go from A to B. Consequently motion is impossible.
Perhaps even clearer is the example of Achilles and the tortoise. Achilles was reputed to be the most swift-footed of the Greeks. The tortoise is a slow-moving animal. Yet if the tortoise has any head start at all, Achilles can never catch up with the tortoise. Let us say that the tortoise has a head start of a hundred yards. In one second Achilles runs ten yards, the tortoise one yard. What will be the outcome? While Achilles covers a distance of one hundred yards which separates him from the tortoise, the tortoise goes ten yards farther. While Achilles runs these ten yards which still separate him from the tortoise, the tortoise goes one yard farther. While Achilles runs the one yard, the tortoise goes one tenth of a yard, and so on ad infinitum. There always remains a certain distance between them. While Achilles runs through this distance, the tortoise each time covers a distance one-tenth as great. It therefore follows that Achilles will never catch up with the tortoise.
These two stories are of course not merely jokes; there is a deeper meaning within them. In both cases it is demonstrated that a certain finite distance can be infinitely divided and for this very reason it follows that a finite distance cannot be put together out of infinite) many parts; it follows, in other words, that a finite distance cannot consist of infinite parts. Now in notion it is demonstrated that from infinitely small distances I can put together a finitely large distance; that is, what is here set forth in the form of a story is the dialectical law which we have previously mentioned. It is shown that a distance can be finite as well as infinite, that it can be both, in fact, at the same time. Thus it is true, as can easily be calculated, that the arrow can travel from A to B, and it is just as true that Achilles will overtake the tortoise.
Let us take the tortoise: While Achilles has traversed the handicap of one hundred yards, the tortoise has gone ahead ten yards, etc. Thus we have 100 + 10 + 1 + 1/10 + 1/100 . . . = 111.11 or 111 1/9 yards. At this point he will overtake the tortoise. He consumes ten seconds for 100 yards, 1 second for the next 10 yards, 1/10 of a second for the 1 yard, etc. Together, 10 + 1 + 1/10 ... = 11.1, or 11 1/9 seconds. Thus the question is solved. And at the same time we have another verification of our proposition that motion is contradictory.
Now, in order to clarify the matter, I will return to the first example, in which a distance which we designate 1 is composed of 1/2's; half of the distance is again divided into equal parts of 1/4, which in turn are divided into equal parts of 1/8, etc. Thus we have the series 1/2 + 1/4 + 1/8 + 1/16 + 1/32. . . . If we add them, we find that their sum more and more closely approaches 1. The sum of the infinitely many fractions, 1/2 + 1/4 + 1/8, etc., is the finite total 1. This is perfectly accurate.
From my statement that contradictions occur in things, we must not conclude inversely that I always utter a truth when I contradict myself. The matter is not so simple; rather these contradictions which appear in concepts are only appropriate and correct if they reflect actual changes in things.
Thus there are meaningful and meaningless contradictions, and dialectics is not the art of meaningless, but of meaningful contradictions. Wherein lies the difference between formal logic and dialectics? If you look closely, you will find that it lies in the following: Formal logic considers all things as motionless and changeless, each as separate from all others, isolated in itself. Dialectics is a higher form of thought, since it considers them also in their motion and in their interconnection. What is the reciprocal relation of formal logic and dialectics? The use of formal logic is limited, restricted. It is a restricted, inferior approach to phenomena. It is admissible so far as I can consider things as unchanged and rigidly demarcated from each other. Dialectics is a superior, more universal, more exact, and more profound approach to phenomena. As soon as I consider things as moved, as changeable, or in their reciprocal connection, I get nowhere with formal logic and I must turn to dialectics. I wish to add that the dialectics of both Plato and Aristotle had an idealistic character; that is, both assume that contradictions have their origin in the mind and that the contradictions in actual things derive from the mind. We materialistic dialecticians say that the contradictions in concepts are only a reflection of the motion of things.
To put this even more simply: Idealistic dialecticians believe that motion of bodies occurs because a contradiction is present in the concept of motion. The materialistic dialecticians say the opposite: The actual motion of things is the prototype, and the contradictions which appear in the concept are reflections of this actual motion.
Let us inquire into the sources of dialectics in antiquity. Why was it that in antiquity man had already come upon the foundations of the dialectical method of thinking? 1. The old philosophers of nature, Heraclitus, Anaximander, etc., investigated the emergence and decline of the world. They thus had to arrive at the concept of the universal change and the universal motion of all things. I refer to Heraclitus especially. 2. Social relations, meditation on the form of the State, on religion, etc., stimulated the consideration of all things as changeful and self-contradictory. (This applies especially to Socrates, Plato, etc.) The immediate stimulus was that in public life contradictory viewpoints clashed one with another. Public life in Athens was a very lively affair. In the market-place discussions were constantly taking place concerning what is good and what is evil, how the State should be constituted, etc. One said A, another Not-A. This was true of all things in public and private life. From this there ultimately developed an art of conversation, and this art of conversation became the source of the art of dialectics. Dialectics was originally called the art of discourse because it grew out of discourse.
This ancient dialectics as developed by Plato and Aristotle was not yet the modern dialectics which is characteristic of dialectical materialism. It was still an undeveloped dialectics. This is consistent with the social relations from which this manner of thinking emerged. The aim of these ancient thinkers, Plato and Aristotle, was to find amidst the change of social and political matters something permanent, constant, secure, to create an ideal State, an ideal society. They did not seek absolute change; their aim, on the contrary, was a changeless, constant state of affairs. They did not favor revolution, but rather the suppression of the revolution which had taken place in the social order. This is why Plato constructed a political utopia, an ideal State. And thus is explained the limited and undeveloped form of dialectics in antiquity. In ancient times there were two stages in the development of dialectics: the first was simply the dialectics of change, of the one-after-the-other. This was the dialectics developed by Heraclitus. The second is dialectics as developed particularly by Plato and Aristotle. This is a dialectics not of one-after-the-other, but a dialectics of one-beside-the-other, of the simultaneous; the dialectics which is present in the relation of the parts of a motionless whole to each other. This second form of dialectics is the highest developed in antiquity. But it is a limited form. The higher form of dialectics is that which takes into consideration the dialectics of the simultaneous as well as the dialectics of one-after the-other. This dialectics is called historical dialectics. This historical dialectics embraces the law of the changes of a whole as well as the law of the simultaneous existence of a whole which is composed of many parts. You have an example of this if from your study of political economy you remember the way Marx describes capital. You there learned a number of economic laws which show how capitalism can exist as a whole and how individual phenomena within it are related to each other. Finally, you learned how this whole system emerges from another system, that of simple commodity production, and further, how the laws of the capitalist mode of production are changed in the course of time into other laws which lead from capitalism into another, opposed system, that of socialist economy. The most highly developed form of dialectics is Marxian or historical dialectics, which developed from the limited and restricted form of antiquity into a higher form.
This ancient dialectics is. in the last analysis, limited and restricted because it is the dialectics of a ruling class which rests on slave labor. Neither Plato nor Aristotle, the most advanced thinkers of this society, could imagine a change in social relations such that slave labor would disappear and the distinction between freeman and slave be abolished.
Therefore, it follows that their concept of the change of things had a completely determined social mold, namely, the mold wherein domination over slaves must always be changeless and eternal. Accordingly, they could not develop dialectics in its full universality, since this universality presupposes that no molds can be imposed upon change. But as usufructuaries of slave ownership they were unable to pre-suppose the abolition of slavery. This is the ultimate reason why they could not develop dialectics in its full universality, why it was restricted and idealistic - and not materialistic.