The Closing of the Western Mind: The Rise of Faith and the Fall of Reason (4 page)

So began the great adventure of the Greek speculative tradition. It was not a coherent process. Martin West writes:

Early Greek philosophy was not a single vessel which a succession of pilots briefly commanded and tried to steer towards an agreed destination, one tacking one way, the next altering course in the light of its own perceptions. It was more like a flotilla of small craft whose navigators did not start from the same point or at the same time, nor all aim for the same goal; some went in groups, some were influenced by the movements of others, some travelled out of sight of each other.
¹¹

One important development was the distinguishing and segregation of the process of reasoning itself. The earliest surviving sustained piece of Greek philosophical reasoning comes from the first half of the fifth century, from one Parmenides from the Greek city of Elea in southern Italy. Parmenides attempts to grasp the nature of the cosmos through the use of rational thought alone (in other words, without any reliance on empirical observation). He realizes that no argument can begin unless some initial assumptions are made. His “It is and it is impossible for it not to be” is the assumption with which he starts. As Parmenides, through a goddess who is given the role of developing the argument, works towards his conclusion that all material is a single undifferentiated and unchanging mass, many controversies arise, not least because of the problems in using verbs such as “to be” in a completely new context, that of philosophical reasoning. But what Parmenides did achieve was to show that once basic assumptions and axioms have been agreed upon, reason can make its independent way to a conclusion. However, his conclusion, that it is rationally impossible to conceive of materials undergoing change, seems absurd, and it raises for the first time the question of what happens when observation and reason contradict each other.

A follower of Parmenides, Zeno (who also came from Elea), highlighted this issue in his famous paradoxes. An arrow which has been shot cannot move, says Zeno. How can this possibly be? Because, answers Zeno, it is always at a place equal to itself, and if so it must be at rest in that place. So, as it is
always
at a place equal to itself, it must
always
be at rest. In Zeno’s most famous paradox, Achilles, the fastest man on foot, will never catch up with a tortoise, because when he has reached the place where the tortoise was, the tortoise will have moved on, and when he has reached the place to which the tortoise has progressed, it will have moved on yet further. While reason can suggest that Achilles will never catch the tortoise, experience tells us that he will and that he will soon outstrip it. Observation and reason may be in conflict, and the result is a conundrum. The fact that the Greeks recognized such problems yet were not daunted by them is a measure of their growing intellectual confidence.

The next step, then, in this parade of intellectual innovation is to try to isolate the circumstances in which rational argument can be used to achieve certainty without being challenged by what is actually observed by our senses. Here the achievement of Aristotle was outstanding. One of Aristotle’s many contributions to the definition of certainty was the introduction of the syllogism, a means by which the validity of a logical argument can be assessed.
¹²
A syllogism is, in Aristotle’s own words, “an argument in which certain things being assumed [the premises], something different from the things assumed [the conclusion] follows from necessity by the fact that they hold.” What kinds of things can be “assumed”? The famous examples, although not used by Aristotle himself, are “All men are mortal” and “Socrates is a man.” Both premises seem fully tenable. No one has come up with an example of a man who has not died; it is part of the condition of being human. Similarly, anyone who met Socrates would have agreed that he was a man. From these two assumptions could be drawn the conclusion: “Therefore Socrates is mortal.” Aristotle went further, replacing the subjects of the assumptions with letters, so that it follows if all As are B, and C is an A, then C is B. One can substitute any suitable premises to create a valid conclusion. Aristotle goes on to explore the cases where the logic does not work. “A dog has four feet” and “A cat has four feet” are both reasonable assumptions to make from one’s experience of dogs and cats in everyday life, but it does not follow that a cat is a dog, and the student in logic has to work out why this is so. “All fish are silver; a goldfish is a fish; therefore a goldfish is silver” cannot be sustained because the example of a living goldfish would itself show that the premise that “All fish are silver” is not true.

Aristotle’s syllogisms can take us only so far; their premises have to be empirically correct and relate to each other in such a way that a conclusion can be drawn from their comparison. They provide the basis for deductive argument, an argument in which a specific piece of knowledge can be drawn from knowledge already given. The development of the use of deductive proof was perhaps the greatest of the Greeks’ intellectual achievements. Deductive argument had, in fact, already been used in mathematics by the Greeks before Aristotle systematized it. In an astonishing breach of conventional thinking, the Greeks conceived of abstract geometrical models from which theorems could be drawn. While the Babylonians knew that in any actual right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides, Pythagoras’ theorem generalizes to show that this must be true in any conceivable right-angled triangle, a major development both mathematically and philosophically. A deductive proof in geometry needs to begin with some incontrovertible statements, or postulates as the mathematician Euclid (writing c. 300 B.C.) named them. Euclid’s postulates included the assertion that it is possible to draw a straight line from any point to any other point and that all right angles are equal to each other. His famous fifth postulate stipulated the conditions under which two straight lines will meet at some indefinite point. (It was the only one recognized as unprovable even in his own day and eventually succumbed to the analysis of mathematicians in the nineteenth century.) Euclid also recognized what he termed “common notions,” truths that are applicable to all sciences, not merely mathematics, such as “If equals be added to equals, the wholes are equal.” These postulates and “common notions” might seem self-evident, but in his
Elements,
one of the outstanding textbooks in history, Euclid was able to draw no less than 467 proofs from ten of them, while a later mathematician, Apollonius of Perga, was to show 487 in his
Conic Sections.
As Robert Osserman has put it in his
Poetry of the Universe:

In a world full of irrational beliefs and shaky speculations, the statements found in
The Elements
were proven true beyond a shadow of a doubt . . . The astonishing fact is that after two thousand years, nobody has ever found an actual “mistake” in
The Elements—
that is to say a statement that did not follow logically from the given assumptions.
¹³

Later mathematicians, such as the great Archimedes (see below, p. 43), were to develop new branches and areas of mathematics from these foundations.

Dealing with the natural world is a much more complex business. It seems to be in a constant state of change—the weather changes, plants grow, wars happen, men die. As Heraclitus had observed, all is in a process of flux. Yet if an underlying order can be assumed and isolated, then some progress can be made. Such progress assumes that the gods do not disturb the workings of the world on pure whim (as they do, for instance, in prescientific thinking—if the gods can intervene to change the course of the stars or the boiling point of water at random, for instance, then nothing is predictable). The next task is to isolate cause and effect, the forces that cause things to happen in a predictable way. One finds an excellent example of this process in the
Histories
of Herodotus (probably written in the 430s B.C.). Herodotus starts his famous survey of Egypt (book 2) with speculation on the causes of the annual Nile floods. He considers three explanations which, he tells us, others have put forward. One is that the summer winds force back the natural flow of the water, and as they die down a larger volume of water is released in compensation. This cannot be true, he notes, because the floods occur even in years when the winds do not blow. Moreover, no other rivers show this phenomenon. The second explanation is that the Nile flows from an ocean that surrounds the earth. This is not a rational explanation, says Herodotus; it can only be legend. Probably Homer or some other poet (he says somewhat scornfully) introduced the idea. The third explanation is that it is melting snows that cause the floods, but surely, says Herodotus, the further south you go the hotter it gets, as the black skins of the “natives” suggest. Snow would never fall in such regions. He goes on to provide an elaborate explanation of his own, based on the sun causing the Nile to evaporate just at a time when rainfall is low, so creating an artificially low volume of water in comparison to which the normal flow is a “flood.” He misses the true cause, the heavy summer rains that run down from the mountains of Ethiopia, but even if he reaches the wrong answer, Herodotus is aware of and consciously rejects mythological explanations. He uses observation and reason to discard some explanations and formulate others. Here is the process of “scientific” thinking at work.
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One of the most famous early “scientific” texts relates to epilepsy. Epilepsy had traditionally been known as “the sacred disease,” because its sudden onset and violent nature suggested an act of the gods, yet in a text attributed to Hippocrates, probably from the early fourth century B.C., the writer states:

I do not believe that the so-called “Sacred Disease” is any more divine or sacred than any other diseases. It has its own specific nature and cause; but because it is completely different from other diseases men through their inexperience and wonder at its peculiar symptoms have believed it to be of divine origin . . . [yet] it has the same nature as other diseases and a similar cause. It is also no less curable than other diseases unless by long lapse of time it is so ingrained that it is more powerful than the drugs that are applied. Like other diseases it is hereditary . . . The brain is the cause of the condition as it is of other most serious diseases...
¹⁵

Here we have not only the specific rejection of the divine as a cause but a sophisticated attempt based on observation to say something about the real nature of epilepsy, its causes and its cures. It should be stressed, however, that the rejection of divine intervention did not mean a rejection of the gods themselves. The famous Hippocratic oath, which probably dates from the beginning of the fourth century, requires the physician to swear by the gods Apollo, Asclepius and Asclepius’ two daughters, Hygeia and Panacea. It was rather that the sphere of activity of the gods was diminished and there was greater reluctance, at least among intellectuals, to see natural events as caused by them. Alternatively, they could be seen as the forces that set in motion the regularity with which the natural world operates.

In dealing with the natural world, whether it be the universe, material objects such as earth and water, plants, animals or human beings themselves, the Greeks assumed, as a starting point, that there was an underlying order to all things. Their self-imposed task was to find out what this was for each discipline. In astronomy the Greeks made three assumptions: that the earth was at the centre of the universe, that the stars moved around it in a regular way, and that their movement was circular. In medicine the Greeks admitted that it was difficult to find a fundamental principle behind the working of so complex an organism as the human body, but they nevertheless began from the premise that the body (like the ideal city) tended towards
eunomie—
in this context, good health—and so illness suggested some aberration in the normal working of things. (The greatest physician of all, Galen, did attempt to base medical knowledge on incontrovertible, geometrical-style proofs but understandably ran into philosophical difficulties.)
¹⁶
These assumptions were only a starting point. There had then to be the gathering of empirical evidence, observations of the stars or the working of the body, so that explanations could be made. There were immense difficulties in this. Herodotus could never have reached the source of the Nile. In astronomy one had only the naked eye with which to observe the universe and rudimentary methods of preserving accurate recordings over time, although matters were helped when the findings from many centuries of observation by the Babylonians reached the Greek world in the third century B.C. Similarly in medicine, much could not be observed because a living body’s internal organs could not be seen functioning.

What is remarkable is how much the Greeks did achieve. In astronomy, for instance, of their three assumptions about the universe, one was false (that the sun revolves around the earth), but they were right in seeing a predictable pattern of behaviour in the stars, which for the planets at least was circular. Observations of the shadow of the earth on the moon convinced the Greeks that it was a sphere,
¹⁷
and their assumption that the earth was at the centre of the universe was not based on ignorance or lazy thinking but was established after serious examination of the alternatives. If the earth was moving around the sun (as Aristarchus hypothesized early in the third century B.C.), then surely its relationship with the stars would change more radically over time. (The Greeks could not conceive that the stars were as far from the earth as they really are.) If the earth spun on its axis (as Heracleides of Pontus proposed in the fourth century), why were the clouds, which could be assumed to be stationary in relationship to the moving earth, not seen to be “left behind” as it spun round? Both reason and experience seemed to confirm the Greek view of an earth-centred universe. In time, of course, science would challenge this “common sense” perception of things.