Ancient Greek Philosophy. Part 1. Pre-Socratic Greek philosophers. The pre-Socratic philosophers rejected traditional mythological explanations for the phenomena they saw around them in favor of more rational explanations. Many of them asked: From where does everything come? From what is everything created? How do we explain the plurality of things found in nature? How might we describe nature mathematically? The Milesian school was a school of thought founded in the 6th Century BC. The ideas associated with it are exemplified by three philosophers from the Ionian town of Miletus, on the Aegean coast of Anatolia: Thales, Anaximander, and Anaximenes. They introduced new opinions contrary to the prevailing viewpoint on how the world was organized. Philosophy of nature These philosophers defined all things by their quintessential substance (which Aristotle calls the arche) of which the world was formed and which was the source of everything. Thales thought it to be water. But as it was impossible to explain some things (such as fire) as being composed of this element, Anaximander chose an unobservable, undefined element, which he called apeiron. He reasoned that if each of the four traditional elements (water, air, fire, and earth) are opposed to the other three, and if they cancel each other out on contact, none of them could constitute a stable, truly elementary form of matter. Consequently, there must be another entity from which the others originate, and which must truly be the most basic element of all. The unspecified nature of the apeiron upset critics, which caused Anaximenes to define it as being air, a more concrete, yet still subtle, element. Anaximenes held that by its evaporation and condensation, air can change into other elements or substances such as fire, wind, clouds, water, and earth. Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were much influenced by mathematics. Like Thales, Pythagoras is rather known for mathematics than for philosophy. His immediate followers were strongly influenced by him, and even until today Pythagoras shines through the mist of ages as one of the brightest figures of early Greek antiquity. Pythagoras founded a society of disciples which has been very influential for some time. Men and women in the society were treated equally -an unusual thing at the time- and all property was held in common. Members of the society practised the master’s teachings, a religion the tenets of which included the transmigration of souls and the sinfulness of eating beans. Pythagoras’ followers had to obey strict religious orders where it was forbidden to eat beans, to touch white cocks, or to look into a mirror beside a light. Pythagoras, like no other, embodied the contradistinctions of the mystical and rational world, which is woven into his personality and philosophy. In his mind, numbers, spirits, souls, gods and the mystic connections between them formed one big picture. After Pythagoras introduced the idea of eternal recurrence into Greek thought, which was apparently motivated by his studies of earlier Egyptian scriptures, the idea soon became popular in Greece. It was Pythagoras’ ambition to reveal in his philosophy the validity and structure of a higher order, the basis of the divine order, for which souls return in a constant cycle. This is how Pythagoras came to mathematics. It could be said that Pythagoras saw the study of mathematics as a purifier of the soul, just like he considered music as purifying. 1 Pythagoras and his disciples connected music with mathematics and found that intervals between notes can be expressed in numerical terms. They discovered that the length of strings of a musical instrument correspond to these intervals and that they can be expressed in numbers. The ratio of the length of two strings with which two tones of an octave step are produced is 2:1. Music was not the only field that Pythagoras considered worthy of study, in fact he saw numbers in everything. He was convinced that the divine principles of the universe, though imperceptible to the senses, can be expressed in terms of relationships of numbers. He therefore reasoned that the secrets of the cosmos are revealed by pure thought, through deduction and analytic reflection on the perceptible world. This eventually led to the famous saying that “all things are numbers.” He associated numbers with form, relating arithmetic to geometry. Heraclitus of Ephesus (ca. 535–475 BC) was a pre-Socratic Greek philosopher, a native of Ephesus, Ionia, on the coast of Asia Minor. Heraclitus is known for his doctrine of change being central to the universe, and that the Logos is the fundamental order of all. He became famous as the "flux and fire" philosopher for his proverbial utterance: "All things are flowing." In spite of the difficulties, Heraclitus was admired by his contemporaries for the theory of flux, which influenced many generations of philosophers after him. Let us look at the idea of flux and fire. Before Heraclitus, the world of the ancient Greeks had been fairly static. The Greeks before Heraclitus focused on the essence of things, its nature and being, which they deemed unchangeable. In contrast, Heraclitus said: "You cannot step into the same river twice, for fresh waters are ever flowing in upon you." This simple sentence expresses the gist of his philosophy, meaning that the river isn't actually the same at two different points in time. - He told people that nothing is the same now as it was before, and thus nothing what is now will be the same tomorrow. With this he planted the idea of impermanence into Greek thought, and indeed, after Heraclitus Greek philosophy was not the same anymore. Heraclitus held that fire is the primordial element out of which everything else arises. Fire is the origin of all matter; through it things come into being and pass away. Fire itself is the symbol of perpetual change because it transforms a substance into another substance without being a substance itself: "This world, which is the same for all, no one of gods or men has made; but it was ever, is now, and ever shall be eternal fire." When Heraclitus speaks of God, he doesn't mean the Greek gods, neither a personal entity. Instead he thinks that God is living in every soul and even in every material thing on earth. The fiery element is the expression of God in everything, thus he is in every sense a pantheist. Another of Heraclitus' main teachings can be called the "unity of opposites". The unity of opposites means that opposites cannot exist without each other - there is no day without night, no summer without winter, no warm without cold, no good without bad. The Eleatics were a school of pre-Socratic philosophers at Elea, a Greek colony in Campania, Italy. The group was founded in the early fifth century BCE by Parmenides. Other members of the school included Zeno of Elea and Melissus of Samos. Parmenides of Elea. His only known work is a poem which has survived only in fragmentary form. In it, Parmenides describes two views of reality. In the Way of Truth, he explained how reality is 2 one; change is impossible; and existence is timeless, uniform, and unchanging. In the Way of Opinion, he explained the world of appearances, which is false and deceitful. The Way of Truth discusses that which is real, which contrasts in some way with the argument of the Way of Opinion, which discusses that which is illusory. Under the Way of Truth, Parmenides stated that there are two ways of inquiry: that it is, that it is not. He said that the latter argument is never feasible because nothing can not be: For never shall this prevail, that things that are not are. Thinking and the thought that it is are the same; for you will not find thought apart from what is, in relation to which it is uttered. For thought and being are the same. It is necessary to speak and to think what is; for being is, but nothing is not. Thus, he concluded that "Is" could not have "come into being" because "nothing comes from nothing". Existence is necessarily eternal. He was struggling with the metaphysics of change, which is still a relevant philosophical topic today. Zeno of Elea was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic, and Bertrand Russell credited him with having laid the foundations of modern logic. He is best known for his paradoxes. Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. Several of Zeno's eight surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another; and most of them were regarded, even in ancient times, as very easy to refute. Three of the strongest and most famous—that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight—are presented in more detail below. Zeno's arguments are perhaps the first examples of a method of proof called also known as proof by contradiction. The Paradoxes of Motion Achilles and the tortoise “In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.” In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise.