Over a hundred years after Darwin, the idea that everything changes is generally accepted among educated people. It was not always so. The theory of evolution by natural selection had to fight a long and bitter struggle against those who defended the biblical view that god created all species in seven days, and that the species were fixed and immutable. For many centuries, the Church dominated science and taught that the earth was fixed at the centre of the universe. Those who disagreed were burnt at the stake.
Even today, however, the idea of change is understood in a one-sided and superficial way. Evolution is interpreted to mean slow, gradual change which precludes sudden leaps. Contradictions are not supposed to exist in nature, and where they arise in human thought are attributed to subjective error. In point of fact, contradictions abound in nature at all levels, and are the basis of all movement and change. This fact was understood by thinkers from the earliest times. It is reflected in some elements of Buddhist philosophy. It underlies the ancient Chinese idea of the principles of ying and yang. In the 4th century B.C., Hui Shih wrote the following lines:
"The sky is as low as the earth; mountains are level with marshes.
The sun is just setting at noon; each creature is just dying at birth."
(Quoted in G. Thomson, The First Philosophers, p. 69.)
Compare this to the following fragments of the founder of Greek dialectical philosophy, Heraclitus (c. 544-484 B.C.):
"Fire lives the death of air, and air lives the death of fire;
Water lives the death of earth, and earth lives the death of water." And
"It is the same thing in us that is living and dead, asleep and awake, young and old; each changes place and becomes the other."
"We step and we do not step into the same stream; we are and are not."
With Heraclitus, the contradictory assertions of the Ionian philosophers for the first time are given a dialectical expression. "Here we see land," commented Hegel, "There is no proposition of Heraclitus which I have not adopted in my Logic." (Hegel, History of Philosophy, Vol. one, p. 279.)
For all his importance, Heraclitus’ philosophy has only come down to us in about 130 fragments, written in a difficult aphoristic style. Even in his lifetime, Heraclitus was known as "the Dark" for the obscurity of his sayings. It is almost as if he deliberately chose to make his philosophy inaccessible. Socrates wryly commented that "what he understood was excellent, what not he believed to be equally so, but that the book required a tough swimmer." (Schwegler, p. 20.)
In Anti-Dühring, Engels gives the following appraisal of Heraclitus’ dialectical world outlook:
"When we reflect on nature or the history of mankind or our own intellectual activity, at first we see the picture of an endless maze of connections and interactions, in which nothing remains what, where, and as it was, but everything moves, changes, comes into being and passes away. (At first, therefore, we see the picture as a whole, with its individual parts still more or less kept in the background; we observe the movements, transitions, connections, rather than the things that move, change and are connected.) This primitive, naïve but intrinsically correct conception of the world is that of Greek philosophy, and was first clearly formulated by Heraclitus: everything is and is not, for everything is in flux, is constantly changing, constantly coming into being and passing away." (Engels, op. cit., p. 24.)
Heraclitus lived in Ephesus in the violent period of the 5th century B.C., a period of war and civil strife. Little is known of his life, except that he came from an aristocratic family. But the nature of the period in which he lived is well reflected in one of his fragments: "War is the father of all things and the king of all; and some he has made gods and some men, some bond and some free." (The fragments are here quoted throughout from the Baywater edition, reproduced in Burnet’s Early Greek Philosophers.) But Heraclitus here does not just refer to war in human society, but to the role of inner contradiction at all levels of nature as well. Indeed, it is better translated as "strife." He states that: "We must know that war is common to all and strife is justice, and that all things come into being and pass away through strife." All things contain a contradiction, which impels their development. Indeed, without contradiction, there would be no movement and no life.
Heraclitus was the first to give a clear exposition of the idea of the unity of opposites. The Pythagoreans, in fact, had worked out a table of ten antitheses:
1) The finite and the infinite
2) The odd and the even
3) The one and the many
4) The right and the left
5) The male and the female
6) The quiescent and the moving
7) The straight and the crooked
8) Light and darkness
9) Good and evil
10) The square and the parallelogram
These are important concepts, but they were not developed by the Pythagoreans, who satisfied themselves with a mere enumeration. In fact, the Pythagoreans had the position of the fusion of opposites through a "mean," eliminating contradiction by seeking the middle ground. Polemicising against this view, Heraclitus uses a most striking and beautiful image: "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." Contradiction lies at the root of everything. The desire to eliminate contradiction would actually presuppose the elimination of all movement and life, consequently, "Homer was wrong 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…"
These are profound thoughts, but are clearly at variance to everyday experience and "common sense." How can something be itself and something else at the same time? How can a thing be both alive and dead? On this kind of argument, Heraclitus poured scorn: "It is wise to hearken, not to me, but to my Word, and to confess that all things are one." "Though this Word is true evermore, yet men are unable to understand it when they hear it for the first time as before they have heard it at all. For, though all things come to pass in accordance to this Word, men seem as if they have no experience of them, when they make trial of words and deeds such as I set forth, dividing each thing according to its kind and showing how it truly is. But other men know not what they are doing when they awake, even as they forget what they do in sleep." "Fools when they do hear are like the deaf; of them does the saying bear witness that they are absent when present." "Eyes and ears are bad witnesses to men if they have souls that understand their language."
What does this mean? The Greek for Word is "Logos," from which logic is derived. Despite its mystical appearance, Heraclitus’ opening remark is an appeal to rational objectivity. Do not listen to me, he is saying, but to the objective laws of nature which I describe. That is the essential meaning. And "all things are one?" Throughout the history of philosophy, there have been two ways of interpreting reality—either as one single substance, embodied in different forms (monism, from the Greek word meaning single); or as two entirely different substances, spirit and matter (known as dualism). The early Greek philosophers were materialist monists. Latter, the Pythagorians adopted a dualist position, based upon a supposedly unbridgeable gulf between mind (spirit) and matter. This is the hallmark of all idealism. As we have seen, it has its roots in the primitive superstitions of savages who believed that the soul left the body in dreams.
The above passage is a polemic against the philosophical dualism of the Pythagoreans, against which Heraclitus defends the position of earlier Ionic monism—that there is an underlying material unity of nature. The universe has not been created, but has always existed, in a process of continuous flux and change, whereby things change into their opposites, cause becomes effect, and effect cause. Thus contradiction lies at the root of everything. In order to get at the truth, it is necessary to go beyond the appearances, and lay bear the inner conflicting tendencies of a given phenomenon, in order to understand its inner motive forces.
The ordinary intelligence, by contrast, is content to take things at face value, the reality of sense perception, the "given," the "facts," are accepted without more ado. However, such perception is at best limited, and can be the source of endless errors. To give just one example—for "sound common sense" the world is flat, and the sun goes around the earth. The true nature of things is not always evident. As Heraclitus puts it, "nature loves to hide." In order to arrive at the truth, it is necessary to know how to interpret the information of the senses. "If you do not expect the unexpected, you will not find it," he wrote, and again, "Those who seek for gold dig up much earth and find a little."
"Everything flows," was the basis of his philosophy, "You cannot step twice into the same river; for fresh waters are ever flowing in upon you." This was a dynamic view of the universe, the exact opposite of the static idealist conception of the Pythagoreans. And when Heraclitus looked for a material substance to underpin the universe, following in the footsteps of Thales and Anaximenes, he chose that most elusive and fleeting element, fire.
The idea that everything is in a constant state of flux, that there is nothing fixed and permanent, except motion and change, is an uncomfortable one for the ordinary cast of mind to accept. Human thinking is, in general, innately conservative. The desire to cling to what is solid, concrete and reliable is rooted in a profound instinct, akin to that of self-preservation. The hope for an after life, the belief in an immortal soul, flows from a rejection of the fact that all things come into existence, and also pass away—"panda rhei," everything flows. Man has stubbornly sought to attain freedom by denying the laws of nature, inventing certain imaginary privileges for himself. True freedom, however, as Hegel explained, consists in correctly understanding these laws, and acting accordingly. It was the great role of Heraclitus to provide the first more or less fully worked-out picture of the dialectical world outlook.
Heraclitus’ philosophy was greeted by incredulity and hostility even in his own lifetime. It challenged the assumptions, not only of all religion and tradition, but of the "common sense" mentality which sees no further than the end of its nose. For the next 2,500 years, attempts have been made to disprove it. As Bertrand Russell comments:
"Science, like philosophy, has sought to escape from the doctrine of perpetual flux by finding some permanent substratum amid changing phenomena. Chemistry seemed to satisfy this desire. It was found that fire, which appears to destroy, only transmutes: elements are recombined, but each atom that existed before combustion still exists when the process is completed. Accordingly it was supposed that atoms are indestructible, and that all change in the physical world consists merely in re-arrangement of persistent elements. This view prevailed until the discovery of radio-activity, when it was found that atoms could disintegrate.
"Nothing daunted, the physicists invented new and smaller units, called electrons and protons, out of which atoms were composed; and these units were supposed, for a few years, to have the indestructibility formerly attributed to atoms. Unfortunately it seemed that protons and electrons could meet and explode, forming, not new matter, but a wave of energy spreading through the universe with the velocity of light. Energy had to replace matter as what is permanent. But energy, unlike matter, is not a refinement of the common-sense notion of a ‘thing’; it is merely a characteristic of physical processes. It might be fancifully identified with the Heraclitean Fire, but it is the burning, not what burns. ‘What burns’ has disappeared from modern physics.
"Passing from the small to the large, astronomy no longer allows us to regard the heavenly bodies as everlasting. The planets came out of the sun, and the sun came out of a nebula. It has lasted some time, and will last some time longer; but sooner or later—probably in about a million million years—it will explode, destroying all the planets. So at least the astronomers say; perhaps as the fatal day draws nearer they will find some mistake in their calculations." (B. Russell, op. cit., p. 64-65.)
In the past it was thought that Heraclitus’ philosophy was a reaction against the views of Parmenides (c. 540-470 B.C.). The prevailing opinion now is that, on the contrary, the Eleatic school represented a reaction against Heraclitus. The Eleatics attempted to disprove the idea that "everything flows" by asserting the direct opposite: that nothing changes, that movement is an illusion. This is a good example of the dialectical character of the evolution of human thought in general, and the history of philosophy in particular. It does not unfold in a straight line, but develops through contradiction, where one theory is put forward, is challenged by its opposite, until this, in turn, is overturned by a new theory, which frequently appears to signify a return to the starting point. However, this apparent return to old ideas does not mean that intellectual development is merely a closed circle. On the contrary, the dialectical process never repeats itself in exactly the same way, since the very process of scientific controversy, discussion, constant re-examination of positions, backed up by observation and experiment, leads to a deepening of our understanding and a closer approximation to the truth.
Elia (or Velia) was a Greek colony in southern Italy founded about 540 B.C. by emigrants fleeing from the Persian invasion of Ionia. According to tradition, the Eleatic school was founded by Xenophones. However, his connection with the school is unclear, and his contribution was overshadowed by its most prominent representatives, Parmenides and Zeno (born 460 B.C.). Whereas the Pythagoreans abstracted from matter all determinate qualities except number, the Eleatics went one step further, taking the process to an extreme, arriving at a totally abstract conception of being, stripped of all concrete manifestations, except bare existence. "Only being is; non being (becoming) is not at all." Pure, unlimited, unchanging, featureless being—this is the essence of the Eleatic thought.
This view of the universe is designed to eliminate all contradictions, all mutability and motion. It is a very consistent philosophy, within its own frame of reference. There is only one snag. It is directly contradicted by the whole of human experience. Not that this worried Parmenides. If human understanding cannot grasp this idea, so much the worse for understanding! Zeno elaborated a famous series of paradoxes designed to prove the impossibility of movement. According to legend, Diogenes the Cynic disproved Zeno’s argument by simply walking up and down the room! However, as generations of logicians have found to their cost, Zeno’s arguments are not so easy to dispose of in theoretical terms.
Hegel points out that the real intention of Zeno was not to deny the reality of motion, but to bring out the contradiction present in movement, and the way it is reflected in thought. In this sense, the Eleatics were, paradoxically, also dialectical philosophers. Defending Zeno against Aristotle’s criticism that he denied the existence of motion, he explains:
"The point is not that there is movement and that this phenomenon exists; the fact that there is movement is as sensually certain as that there are elephants; it is not in this sense that Zeno meant to deny movement. The point in question concerns its truth. Movement, however, is held to be untrue, because the conception of it involves a contradiction; by that he meant to say that no true Being can be predicated in it." (Hegel, History of Philosophy, Vol. 1, p. 266.)
In order to disprove Zeno’s argument, it is not enough to demonstrate that movement exists, as Diogenes did, just by walking around. It is necessary to proceed from his own premises, to exhaust his own analysis of motion, and carry it to its limits, to the point where it turns into its opposite. That is the real method of dialectical argument, not merely asserting the opposite, still less resorting to ridicule. And, in fact, there is a rational basis for Zeno’s paradoxes, which cannot be resolved by the method of formal logic, but only dialectically.
"Achilles the Swift"
Zeno "disproved" motion in different ways. Thus, he argued that a body in motion, before reaching a given point, must first have travelled half the distance. But, before this, it must have travelled half of that half, and so on ad infinitum. Thus, when two bodies are moving in the same direction, and the one behind at a fixed distance from the one in front is moving faster, we assume that it will overtake the other. Not so, says Zeno. "The slower one can never be overtaken by the quicker." This is the famous paradox of Achilles the Swift. Imagine a race between Achilles and a tortoise. Suppose that Achilles can run ten times faster than the tortoise which has 1000 metres start. By the time Achilles has covered 1000 metres, the tortoise will be 100 metres ahead; when Achilles has covered that 100 metres, the tortoise will be one metre ahead; when he covers that distance, the tortoise will be one tenth of a metre ahead, and so on to infinity.
From the standpoint of everyday common sense, this seems absurd. Of course, Achilles will overtake the tortoise! Aristotle remarked that "This proof asserts the same endless divisibility, but it is untrue, for the quick will overtake the slow body if the limits to be traversed be granted to it." Hegel quotes these words, and comments: "This answer is true and contains all that can be said; that is, there are in this representation two periods of time and two distances, which are separated from one another, i.e., they are limited in relation to one another;" but then he adds, "when, on the contrary, we admit that time and space are related to one another as continuous, they are, while being two, not two, but identical." (Hegel, op. cit., p. 273.)
The paradoxes of Zeno do not prove that movement is an illusion, or that Achilles, in practice, will not overtake the tortoise, but they do reveal brilliantly the limitations of the kind of thinking now known as formal logic. The attempt to eliminate all contradiction from reality, as the Eleatics did, inevitably leads to this kind of insoluble paradox, or antimony, as Kant later called it. In order to prove that a line could not consist of an infinite number of points, Zeno claimed that, if it were really so, then Achilles would never overtake the tortoise. There really is a logical problem here. As Alfred Hooper explains:
"This paradox still perplexes even those who know that it is possible to find the sum of an infinite series of numbers forming a geometrical progression whose common ratio is less than 1, and whose terms consequently become smaller and smaller and thus ‘converge’ on some limiting value." (A. Hooper, Makers of Mathematics, p. 237.)
In fact, Zeno had uncovered a contradiction in mathematical thought which would have to wait two thousand years for a solution. The contradiction relates to the use of the infinite. From Pythagoras right up to the discovery of the differential and integral calculus in the 17th century, mathematicians went to great lengths to avoid the use of the concept of infinity. Only the great genius Archimedes approached the subject, but still avoided it by using a roundabout method.
The Pythagoreans stumbled on the fact that the square root of two cannot be expressed as a number. They invented ingenious ways of finding successive approximations for it. But, no matter how far the process is taken, you never get an exact answer. The result is always midway between two numbers. The further down the list you go, the closer you get to the value of the square root of two. But the process of successive approximation may be continued forever, without getting a precise result that can be expressed in a whole number.
The Pythagoreans thus had to abandon the idea of a line made up of a finite number of very small points, and accept that a line is made up of an infinite number of points with no dimension. Parmenides approached the issue from a different angle, arguing that a line was indivisible. In order to prove the point, Zeno tried to show the absurd consequences that would follow from the concept of infinite divisibility. For centuries after, mathematicians steered clear of the idea of infinity, until Kepler in the 17th century simply swept aside all logical objections and boldly made use of the infinite in his calculations, to achieve epoch making results.
Ultimately, all these paradoxes are derived from the problem of the continuum. All the attempts to resolve them by means of mathematical theorems, such as the theory of convergent series and the theory of sets have only given rise to new contradictions. In the end, Zeno’s arguments have not been refuted, because they are based on a real contradiction which, from the standpoint of formal logic, cannot be answered. "Even the abstruse arguments put forward by Dedekind (1831-1916), Cantor (1845-1918) and Russell (1872-1970) in their mighty efforts to straighten out the paradoxical problems of infinity into which we are led by our concept of ‘numbers,’ have resulted in the creation of still further paradoxes." (Hooper, op. cit., p. 238.) The breakthrough came in the 17th and 18th centuries, when men like Kepler, Cavalieri, Pascal, Wallis, Newton and Leibniz decided to ignore the numerous difficulties raised by formal logic, and deal with infinitesimal quantities. Without the use of infinity, the whole of modern mathematics, and with it physics, would be unable to function.
The essential problem, highlighted by Zeno’s paradoxes, is the inability of formal logic to grasp movement. Zeno’s paradox of the Arrow takes as an example of movement the parabola traced by an arrow in flight. At any given point in this trajectory, the arrow is considered to be still. But since, by definition, a line consists of a series of points, at each of which the arrow is still, movement is an illusion. The answer to this paradox was given by Hegel.
The notion of movement necessarily involves a contradiction. Consider the movement of a body, Zeno’s arrow for example, from one point to another. When it starts to move, it is no longer at point A. At the same time, it is not yet at point B. Where is it, then? To say that it is "in the middle" conveys nothing, for then it would still be at a point, and therefore at rest. "But," says Hegel, "movement means to be in this place and not to be in it, and thus to be in both alike; and this is the continuity of space and time which first makes motion possible." (Hegel, op. cit., Vol. 1, p. 273.) As Aristotle shrewdly observed, "It arises from the fact that it is taken for granted that time consists of the Now; for if this is not conceded, the conclusions will not follow." But what is this "now"? If we say the arrow is "here," "now," it has already gone.
"Motion itself is a contradiction: even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it. And the continual assertion and simultaneous solution of this contradiction is precisely what motion is." (Engels, Anti-Dühring, p. 152.)