Epistemology of appearance

All of the post-Parmenidean philosophers, like Parmenides himself, presupposed that the real world is different from the one that human beings perceive. Thus arose the problems of epistemology, or theory of knowledge. According to Anaxagoras, everything is contained in everything. But this is not what people perceive. He solved this problem by postulating that, if there is a much greater amount of one kind of particle in a thing than of all other kinds, the latter are not perceived at all. The observation was then made that sometimes different persons or kinds of animals have different perceptions of the same things. He explained this phenomenon by assuming that like is perceived by like. If, therefore, in the sense organ of one person there is less of one kind of stuff than of another, that person will perceive the former less keenly than the latter. This reasoning was also used to explain why some animals see better at night and others during the day. According to Democritus, atoms have no sensible qualities, such as taste, smell, or colour, at all. Thus, he tried to reduce all of them to tactile qualities (explaining a bright white colour, for instance, as sharp atoms hitting the eye like needles), and he made a most elaborate attempt to reconstruct the atomic structure of things on the basis of their apparent sensible qualities.

Also of very great importance in the history of epistemology was Zeno of Elea (c. 495–c. 430 bce), a younger friend of Parmenides. Parmenides had, of course, been severely criticized because of the strange consequences of his doctrine: that in reality there is no motion and no plurality because there is just one solid being. To support him, however, Zeno tried to show that the assumption that there is motion and plurality leads to consequences that are no less strange. This he did by means of his famous paradoxes, saying that the flying arrow rests since it can neither move in the place in which it is nor in a place in which it is not, and that Achilles cannot outrun a turtle because, when he has reached its starting point, the turtle will have moved to a further point, and so on ad infinitum—that, in fact, he cannot even start running, for, before traversing the stretch to the starting point of the turtle, he will have to traverse half of it, and again half of that, and so on ad infinitum. All of these paradoxes are derived from the problem of the continuum. Although they have often been dismissed as logical nonsense, many attempts have also been made to dispose of them by means of mathematical theorems, such as the theory of convergent series or the theory of sets. In the end, however, the logical difficulties raised in Zeno’s arguments have always come back with a vengeance, for the human mind is so constructed that it can look at a continuum in two ways that are not quite reconcilable.

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Metaphysics of number

All of the philosophies mentioned so far are in various ways historically akin to one another. Toward the end of the 6th century bce, however, there arose, quite independently, another kind of philosophy, which only later entered into interrelation with the developments just mentioned: the philosophy of Pythagoras of Samos (c. 580–c. 500 bce; see also Pythagoreanism). Pythagoras traveled extensively in the Middle East and in Egypt and, after his return to Samos, emigrated to southern Italy because of his dislike of the tyranny of Polycrates (c. 535–522 bce). At Croton and Metapontum he founded a philosophical society with strict rules and soon gained considerable political influence. He appears to have brought his doctrine of the transmigration of souls from the Middle East. Much more important for the history of philosophy and science, however, was his doctrine that “all things are numbers,” which means that the essence and structure of all things can be determined by finding the numerical relations they express. Originally, this, too, was a very broad generalization made on the basis of comparatively few observations: for instance, that the same harmonies can be produced with different instruments—strings, pipes, disks, etc.—by means of the same numerical ratios—1:2, 2:3, 3:4—in one-dimensional extensions; the observation that certain regularities exist in the movements of the celestial bodies; and the discovery that the form of a triangle is determined by the ratio of the lengths of its sides. But because the followers of Pythagoras tried to apply their principle everywhere with the greatest of accuracy, one of them—Hippasus of Metapontum (flourished 5th century bce)—made one of the most fundamental discoveries in the entire history of science: that the side and diagonal of simple figures such as the square and the regular pentagon are incommensurable (i.e., their quantitative relation cannot be expressed as a ratio of integers). At first sight this discovery seemed to destroy the very basis of the Pythagorean philosophy, and the school thus split into two sects, one of which engaged in rather abstruse numerical speculations, while the other succeeded in overcoming the difficulty by ingenious mathematical inventions. Pythagorean philosophy also exerted a great influence on the later development of Plato’s thought.

The speculations described so far constitute, in many ways, the most important part of the history of Greek philosophy because all of the most fundamental problems of Western philosophy turned up here for the first time. One also finds here the formation of a great many concepts that have continued to dominate Western philosophy and science to the present day.

Anthropology and relativism

In the middle of the 5th century bce, Greek thinking took a somewhat different turn through the advent of the Sophists. The name is derived from the verb sophizesthai, “making a profession of being inventive and clever,” and aptly described the Sophists, who, in contrast to the philosophers mentioned so far, charged fees for their instruction. Philosophically they were, in a way, the leaders of a rebellion against the preceding development, which increasingly had resulted in the belief that the real world is quite different from the phenomenal world. “What is the sense of such speculations?” they asked, since no one lives in these so-called real worlds. This is the meaning of the pronouncement of Protagoras of Abdera (c. 490–c. 420 bce) that “man is the measure of all things, of those which are that they are and of those which are not that they are not.” For human beings the world is what it appears to them to be, not something else; Protagoras illustrated his point by saying that it makes no sense to tell a person that it is really warm when he is shivering with cold because for him it is cold—for him, the cold exists, is there.

His younger contemporary Gorgias of Leontini (flourished 5th century bce), famous for his treatise on the art of oratory, made fun of the philosophers in his book Peri tou mē ontos ē peri physeōs (“On That Which Is Not; or, On Nature”), in which—referring to the “truly existing world,” also called “the nature of things”—he tried to prove (1) that nothing exists, (2) that if something existed, one could have no knowledge of it, and (3) that if nevertheless somebody knew something existed, he could not communicate his knowledge to others.

The Sophists were not only skeptical of what had by then become a philosophical tradition but also of other traditions. On the basis of the observation that different nations have different rules of conduct even in regard to things considered most sacred—such as the relations between the sexes, marriage, and burial—they concluded that most rules of conduct are conventions. What is really important is to be successful in life and to gain influence over others. This they promised to teach. Gorgias was proud of the fact that, having no knowledge of medicine, he was more successful in persuading a patient to undergo a necessary operation than his brother, a physician, who knew when an operation was necessary. The older Sophists, however, were far from openly preaching immoralism. They, nevertheless, gradually came under suspicion because of their sly ways of arguing. One of the later Sophists, Thrasymachus of Chalcedon (flourished 5th century bce), was bold enough to declare openly that “right is what is beneficial for the stronger or better one”—that is, for the one able to win the power to bend others to his will.