Dialectics: the method of logic which understands ever-changing reality

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Hegel: "Everything that exists is changing into something else." "Hegel found that the old way of thinking based on Aristotle's logic was inadequate for comprehending a changing reality, so he devised a new system of logic that he called 6 SOCIALIST ACTION DECEMBER 1991 This is the fourth is a series of articles on dialectical materialism the philosophical foundation of Marxism. The articles are based on classes given by Cliff Conner at a Socialist Action national educational conference in August 1989. In the previous articles, the author traced the history of philosophy from the time of the ancient Greeks, contrasting the outlook of materialism to that of idealism.

"It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the age of belief, it was the epoch of incredulity, it was the season of light, it was the season of darkness, it was the spring of hope, it was the winter of despair, we had everything before us, we had nothing before us, we were all going direct to heaven, we were all going direct the other way The opening lines of Charles Dickens' great novel of the French Revolution, "A Tale of Two Cities," captures the highly contradictory nature of those events. Some people might find this unsettling: "Which one was it? Was it the best of times or the worst of times? You can't have it both ways!"

But that's just the point: To understand the French Revolution you must have it both ways. And it's not simply a matter of saying that it was the best of times for some people and the worst of times for others. Not at all! For the aristocrat, it was the best of times because he was winning his political independence from the monarchy, but the worst of times because he was losing his dominant social position. For the sansculottes [the plebian supporters of the radicals] it was the best of times because they were struggling against their oppressors and winning, but the worst of times because they were being subordinated to the domination of a new ruling class, the bourgeoisie.

For the petty-bourgeois revolutionary leaders like Robespierre, it was the best of times because they were turning the world upside down, but the worst of times because they couldn't sustain the radical revolution they had initiated.

So if Dickens seemed to be contradicting himself, the paradoxes did not originate with him; the contradictions were in the material reality of the revolutionary events themselves. It is the nature of revolutions to be contradictory.

Dialectical logic

As Marxists, we are interested in understanding the processes of social revolution. To do so, it is necessary to utilize a form of logic that can take contradictory phenomena into account. And that is the topic of this article: dialectical logic, the logic of revolutionary change.

In previous articles, we talked about materialism and noted that bourgeois philosophy had culminated in the development of mechanical materialism. "Give me matter and motion," Descartes exclaimed, "and I will construct the universe."

As a general statement, there is nothing to object to here; the universe can be thought of as essentially matter in motion. The problem with mechanical materialism lies in the narrowness of its conceptions of both matter and motion. It considered matter to be made up of tiny little inert bits of material; in the words of Isaac Newton: "solid, massy, hard, impenetrable, moveable particles."

Motion was considered to be nothing more than displacement—that is, a change of location from one position to another. The mechanical materialists believed that all phenomena could in principle be explained in terms of this kind of matter in this kind of motion. Another way of saying the same thing is that everything from the stars above to the human body functions in the same way that machines do.

In the 17th century, this was a revolutionary and highly progressive way of thinking. The narrowness of its conceptions, however, left it vulnerable to criticism. The machine analogy requires that all motion be initiated by an impulse; that is, by the physical contact of two bodies. Such a concept makes it very difficult to explain why heavy bodies fall to the earth and why magnets make iron move from a distance.

Moreover, using the machine as a model of the universe and everything in it produced a static picture of reality. The mechanical materialists recognized the existence of motion, of course, but it was the repetitive motion of a machine that simply moves things around from place to place. What is missing, above all, is any explanation of development. Many processes of change cannot be reduced to displacement.

How does fire turn wood into charcoal? How does water harden into ice in cold weather? How does gunpowder explode? And, most importantly, how do living things reproduce and grow?

From Heraclitus to Hegel The German philosopher George Hegel looked at the world and saw continuous change. Like all philosophers, Hegel pondered the question "What is? What is it that exists?" This had always been understood as the question of being, but in Hegel's reformulation it was a question of becoming.

According to this way of looking at things, nothing exists in a static sense; dialectics."

everything that exists is changing into something else. Hegel found that the old way of thinking based on Aristotle's logic was inadequate for comprehending a changing reality, so he devised a new system of logic that he called "dialectics."

Hegel found a precedent for his dialectical outlook among the first philosophers—among the Ionian Greeks who we talked about in preceding articles. There was Heraclitus, who held that the universe is fire. But what qualified Heraclitus as the discoverer of dialectical logic was his statement that "everything is in flux." Everything is changing. Nothing is standing still; nothing is staying the same; everything is in the process of becoming.

Heraclitus illustrated his contention with a famous example: "You can never step in the same river iwice." Now, you could go step in the Mississippi River today and probably go back 10 years later and step in the Mississippi River again. But Heraclitus would argue that if you did, you would not be stepping in the same river twice. The name of the river would have stayed the same, but the river itself would have changed-all the old water would be gone and replaced by an entirely new quantity of water.

Even if you put your foot in, pull it out, and stick it right back in again-even then you have not stepped in the same river twice, because it is continuously flowing.

Aristotle's "formal" logic

So dialectics began with Heraclitus, but his great insight into the ever-changing nature of reality remained a philosophical curiosity for more than 2000 years until Hegel developed it into a system challenging Aristotle's logic.

Aristotle attempted to formulate the laws of thinking. He attempted to reduce the complexities of human reason to a set of formulas, and what he came up with is known as formal logic.

Aristotle did a brilliant job of it. The laws of formal logic that he derived were valid and they still retain their validity today. But they are only valid up to a point they are not sufficient for comprehending reality insofar as it is in flux-and as Heraclitus said, everything is in flux. Dialectical logic does not invalidate formal logic, but assigns it to a limited sphere of applicability.

The central principle upon which formal logic is built can be expressed in a simple formula that at first glance appears to be a self-evident truth: "A=A."

This is the law of identity that says that every individual thing is identical to itself. I am identical to myself. You are yourself. A building is identical to itself.

Beginning with this law of identity, you can derive all of formal logic. One important corollary is the law of the excluded middle. That is, if "A equals B" is a true statement, then "A is not equal to B" must be a false statement. A is either identical to B or it is not. It is one or the other; there is no middle ground It follows from this that when we sort things into categories, we can do so precisely. We can sort fruit into separate baskets of apples, oranges, bananas, and so forth, because an apple equals an apple, but an apple does not equal an orange or a banana.

In formal logic, then, the lines dividing categories are sharp and distinct and allow for no ambiguity.

The law of identity and the law of the excluded middle are so intuitively appealing that it is no wonder that they went virtually unchallenged for more than 2000 years. But wait! What about Heraclitus's point? Is the Mississippi River identical to itself or not?

Well, if you specify a given instant of time you might say, "The Mississippi River at exactly midnight last night was identical to the Mississippi River at exactly midnight last night," but that is a rather trivial case and it begs the question of whether there is such a thing as an amount of time so small that all motion is frozen within it.

But not everything flows like a river; some things are solid, like the chair you're sitting on, for example. Nevertheless, if you were to examine its microscopic structure you would find that it, too, is continuously changing.

For all practical purposes, it might be acceptable to apply the law of identity to the chair-the chair is identical to itself. Lock the chair up in a storeroom and go back next year and it will probably still be, for all practical purposes, the same chair.

So the law of identity can be useful and can be considered provisionally valid when applied to things that change relatively slowly or over relatively short time spans. But it is important to remember that in no case is it ever absolutely true.

This law of non-identity is the foundation of dialectics, but it is a very shaky foundation. You can't build a solid, eternal, unchanging structure on it. You can find recipe books that provide all the rules for using formal logic, but dialectical logic does not lend itself to that. It is built on the explicitly self-contradictory basis of the law of non-identity.

Why would anybody want to build a system of logic on a self-contradictory axiom? The point is that dialectics is not only a system of logic; that is to say: dialectics is not only a depiction of the way human beings think about things. When Heraclitus said "Everything is in flux," he was talking about the way things really exist in the the material world.

This was the point Engels made in his "Dialectics of Nature" that Hegel's laws of dialectics describe the processes of change and development as they really occur at all levels of the natural world subatomic as well as the intergalactic (continued on next page)

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Frederick Engels: His "Dialectics of Nature" used Hegel's method.

SOCIALIST ACTION DECEMBER 1991 7 ...Dialectics level—at the physical, the biological, the psychological, and social levels.

New developments in science In his "Dialectics of Nature," Engels cited the most up-to-date scientific research available to him. Since his death, of course, there has been what some have called "permanent revolution" in science. In fact, scientific developments after Engels have continued to support his contention that nature is dialectical.

Dialectical logic is the logic of changing phenomena; the logic of motion. It has been said that formal logic is to dialectical logic as a still photo is to a motion picture. The metaphor is an appropriate one. The roots of contradiction lie in change, or motion, itself.

I mentioned earlier that organic development-the growth of living things-is a more complex form of motion than mere displacement of a solid body from one place to another. A mechanical materialist might argue that even organic development can be thought of, in the final analysis, as a composite of very many small particles moving around from place to place.

But even the simplest form of motion movement from point A to point B-embodies contradiction. To update Engels' "Dialectics of Nature," we could point to the findings of quantum mechanics that show that, on the subatomic level, particles move from place to place in a very complex way. The laws of classical mechanics cannot describe the motion of electrons and neutrons and the like. These particles don't have trajectories in the classical sense.

And if you ask: "Is the electron at point A or is it not?" the answer can't satisfy the requirements of formal logic. You can't answer that question with a definite "yes" or "no;" the best you can do is give a statistical estimate of the probability of the electron's location.

And it's not just a question of the limitations of measurement, either. The electron is and is not at point A. In other words, the electron violates the law of the excluded middle. Every subatomic particle in the universe is continuously violating the law of the excluded middle.

Physicists have also finally resolved the age-old dispute over whether light is a continuous wave or made up of discrete particles. The answer is: Both!

Furthermore, it was discovered that all of the subatomic entities are also characterized by this wave-particle duality. How can anything be both continuous and discrete at the same time? This is so contradictory that it's almost impossible to conceive of what it means. We find, therefore, a profound violation of the law of the excluded middle built into the very fabric of the material world.

Quantum mechanics, then, has given a new dimension to Heraclitus's statement that everything is in flux. Motion is inseparable from matter; all matter is in a perpetual process of change. In other words, matter itself is inherently contradictory: every object is both one thing and becoming something else at the same time.

Zeno's paradoxes

The contradictions of motion were not unknown to the early Greeks. In the 5th century B.C., Zeno of Elea formulated a number of paradoxes of motion. He illustrated one with a story about a race between Achilles and a tortoise. Achilles is much faster than the tortoise, so he gives him a 100-yard head start. They take off and after Achilles has run 100 yards, the tortoise, of course, is still in the lead, Decause he has run a short distance while Achilles covered the 100 yards. So let's say that the tortoise is now at point X, and they're both still running. By the time Achilles gets to point X, the tortoise has moved ahead to point Y. Then, by the time Achilles reaches point Y, the tortoise has moved on again. You can repeat this an infinite number of times, so it would seem that Achilles can never catch up to the tortoise.

In the real world, of course, Achilles would catch up to the tortoise and blow right by him. But if you apply certain very well established rules of arithmetic to this problem, you find that Achilles never catches up.

These rules of arithmetic are based in formal logic. Zeno showed through his paradoxes that formal logic and the material world are not in agreement. So he and his followers decided to keep the logic and discard the material world. They adopted the idealist view that the material world is only an illusion.

The other conclusion that could be drawn from Zeno's paradoxes is that if mathematics doesn't adequately describe the real world, the fault must be with the mathematics. The problem, then, would be to develop new mathematical techniques that would be able to describe motion.

Zeno's paradoxes involved problems having to do with the concept of infinity, and especially with infinitely small times and distances, or "infinitesimals." To describe most forms of motion, it was necessary to develop a mathematics of infinitesimals, and that was accomplished in the 17th century by two people, independently—Newton and Leibniz. They formulated the branch of mathematics we call calculus. But this calculus proved to be very troubling to philosophically minded people who noticed that, although arithmetic seemed to be based on formal logic, calculus seemed not to be.

The best-known critique of the logical foundations of calculus was that of the idealist philosopher George Berkeley. Berkeley showed that calculus manipulated infinitesimal quantities in an ambiguous way, treating them sometimes as if they were very small but real quantities, and other times as if they were zero. He called them "ghosts of departed quantities," and demanded that the mathematicians decide whether they are something or nothing. According to the law of the excluded midale, these infinitesimals cannot be both something and nothing at the same time.

Nevertheless, mathematicians, scientists and engineers continued to use the calculus to great advantage. Although it wasn't formally logical, it could very accurately describe physical processes involving matter in motion.

Mathematicians and philosophers put a great deal of effort into trying to put mathematics on a solid, rigorous formal logical foundation. They started with arithmetic, which they thought would provide the basis for all the rest of mathematics.

Bertrand Russell and Alfred North Whitehead believed they had accomplished this feat with their "Principia Mathematica" in 1913. But in the 1930s, Kurt Godel proved that they had not succeeded and showed, in effect, that not even arithmetic, let alone calculus, can be reduced to formal-logical rules. Or, to put it another way, even arithmetic cannot be considered to be entirely free of contradictions.

The logic of computers What I have been trying to show here is that the limitations of formal logic can be demonstrated even in those fields of science usually considered most exact and most immune to contradiction. If formal logic is inadequate as a basis for physics and mathematics, how much less adequate it is for the biological, psychological, and social sciences.

But by saying formal logic is inadequate, I don't intend to give the impression that I mean it is obsolete or useless. Not by a long shot.

For formal logic, the 20th century has been the best of times and the worst of times. George Novack, in his book "The Logic of Marxism," makes the point that formal logic not only still has an important role to play in human thinking, but is still capable of further development.

Novack wrote that in 1942, and he couldn't have been more prophetic if he had seen the future in a crystal ball. Within a few years, one of the great technological revolutions in human history began to unfold-and it was based precisely on the development of formal logic. I am speaking of the formal logic machine, better known as the digital computer.

The basis of computer logic is purely formal. To a computer, "A equals A." If it tries to contemplate "A is not equal to A," it generally goes into an endless loop. The fundamental unit of computer logic is the "bit" of binary information, which is capable of only two mutually exclusive states. In binary terms, it must be either zero or one. It has been described as a sort of tiny switch that can be turned off or on. It must always be one or the other; it can't be halfway in between. In other words, it obeys the law of the excluded middle.

There are other kinds of computers, but the computers that we are familiar with today are binary digital computers, and that makes them formal-logic machines. As powerful as they are, their formal-logic limitations are evident. That is most clearly indicated by work carried out in the field known as "AI"-artificial intelligence.

Contradictions confuse computers Just a few years ago, some artificial intelligence researchers believed they were on the verge of a breakthrough that would produce computers capable of genuine thinking; capable of carrying out human mental tasks better than we could do ourselves. This has long been a major theme of science fiction, the best known example probably being HAL in the film "2001."

Today, that optimism has been considerably muted. It has proven very tricky to construct a machine that can routinely accept the proposition that "A is not equal to A"-that is, a machine that can handle contradiction.

The first attempts to deal with this problem were strictly mechanical. If the machine were confronted with a contradiction, rather than going into an endless loop its program would instruct it to stop and move to a second level, wherein it might reexamine the same problem from another angle. If it runs into a contradiction on the second level, the program would "pop up" to a third level, and so on.

The ability of such a machine to resolve contradictions is limited to the number of levels built into its program. It is still, in principle, a formal-logic machine.

Other attempts have been made in a different direction. Rather than increasing the raw power of the standard program, the aim is to mimic human thought processes. The most interesting attempt so far has been the development of "fuzzy logic."

An article in the New York Times in 1989 reported: "The idea behind fuzzy logic is to allow computers to behave more like people. And people, unlike computers, are not precise." The point is to give computers the "ability to handle ambiguity." The main advocate of fuzzy logic says: "We have to come to terms with the pervasive imprecision of the real world."

The concept of fuzzy logic illustrates the key difference between human logic and digital computer logic. The computer organizes its information into absolute categories with rigid boundary lines; the human mind is capable of processing a great deal of contradictory information without breaking down. It is somewhat ironic that the human mind's capacity for fuzzy thinking is its greatest asset.

Let me hasten to assure you that I'm not recommending fuzzy thinking as a general method. But it is important to guard against overly formalistic thinking, especially in politics. Those who demand absolutely unambiguous political situations before they will take action will wind up never taking action. That is a characteristic of sectarians, and it illustrates the link between formal logic and sectarian politics.

The experience of the past decade or so has shown that no matter how powerful a computer is, no matter how fast it can crunch numbers, there are certain kinds of problems that humans can handle better. The difference is that humans are capable of dialectical logic.

Computers can be programmed to play a pretty good game of chess. But when someone once compared political strategy to a game of chess, Trotsky pointed out the weakness of the analogy. In chess the rules always remain the same and the pieces maintain stable identities, whereas in political struggles the strength of contending forces varies and the rules change continuously.

A computer does well in chess because its strongest virtue is its consistency. But in a rapidly changing political situation, absolute consistency can be too much of a good thing. I think that is what Emerson must have meant when he said, "A foolish consistency is the hobgoblin of little minds." (To be continued next month.)

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Mos By JOSEPH RYAN Many of them marched off to fight for their country. Others enlisted to improve their job skills. Today, hundreds of thousands of them are homeless.

A report just released by the National Coalition for the Homeless, titled "Heroes Today, Homeless Tomorrow: Homelessness Among Veterans in the United States," presents a devastating account of veterans, are Vietnam-era veterans. But increasingly, those who joined the armed forces after the Vietnam War are becoming a sizeable proportion of the homeless population ... The two largest groups of homeless veterans are those who served in Vietnam, and, increasingly, men and women who have served in peacetime since then."

In general, Vietnam-era veterans constitute roughly 40-60 percent of the homeless Abraham Menashe