The Pythagorean Society, II The Pythagoreans regarded numbers spatially: One is the point, two is the line, three is the surface, four is the solid or body. Every material body is the expression of the number four, since it results, as a fourth term, from three constituent elements (points, lines, and surfaces). Justice is declared to be four. Five is declared to be marriage, because five is the product of three (the first masculine number) and two (the first feminine number).

The Pythagorean Society, III To the Pythagoreans the earth is not the center of the universe. The earth and the planets revolve, along with the sun, round the central fire or “hearth of the universe.”

Heraclitus I An Ephesian noble, a melancholy man who expressed his contempt for the common herd of citizens as well as for the eminent men of the past. Many of Heraclitus’s sayings are pungent in character: “Man’s character is his fate,” “Nature loves to hide,” “All things are in a state of flux.”

Heraclitus II The original contribution of Heraclitus to philosophy is his conception of unity in diversity, diversity in unity. One in many, many in one. Identity in difference, difference in identity. He use to say: “men do not know how what is at variance agrees with itself.” For him the Urstoff is fire.

The Eleatics: Parmenides, I Parmenides:A citizen of Elea (Southern Italy) and the founder of the Eleatic School He argues that Being, the One, is, and that Becoming, change, is illusion. In rejecting change and movement, Parmenides rejects sense-appearance and appeal to reason. He introduces into philosophy the distinction between Reason and Sense, Truth and Appearance, something of cardinal importance in Platonic philosophy. His philosophy is not idealism but monistic materialism (the reality that the reason apprehends is material).

The Eleatics: Parmenides, II His first great assertion is that “It is.” “It,” i.e., Reality, Being, exists and cannot not be. It was not first possible, i.e., nothing, and then existent: it was always existent. It never came into being, but simply is. What is, is uncreated, indestructible and without end. Plato uses the thesis of Parmenides concerning the unchangeability of Being and attributes it to Ideas rather that the material world.

The Eleatics: Parmenides, III Heraclitus affirmed the existence of the One or Being but argued that becoming, change and tension are essential to the One. Parmenides, on the other hand, asserted Being even to the exclusion of Becoming, affirming that change and movement are illusory. Sense tells us that there is change but truth is to be sought, not in sense, but in reason and thought.

The Eleatics: Zeno of Elea He argues for the impossibility of motion. His first argument is as follows: Let us suppose that you want to cross a stadium. In order to do so, you would have to traverse an infinite number of points (on the Pythagorean hypothesis). Moreover, you would have to travel the distance in finite time, if you wanted to get to the other side at all. But how can you traverse an infinite number of points, and so an infinite distance, in a finite time? We must conclude that you cannot cross the stadium. Indeed we must conclude that no object can traverse any distance whatsoever and that all motion is consequently impossible

Anaxagoras I A Persian citizen who came with the Persian army in the year of Salamis (480/479 BC) and settled in Athens. He was the first philosopher to settle in Athens which was later to become such a flourishing center of philosophic study. From Plato we hear that the young Pericles was a pupil of Anaxagoras

Anaxagoras II Anaxagoras accepted the theory of Parmenides that Being neither comes into being nor passes away, but is unchangeable. For him the Urstoff is Nous or mind but he described it in material terms as being “the thinnest of all things.” He made Nous purer than any material thing but never reached the idea of the immaterial or incorporeal thing.

Architecture Most important structures were temples Generic Greek architectural style was called post-beam-triangle construction. Doric Style: the earliest temple style, a 4- sided structure with a porch winding all the way around an inner room, or cella (p.47) Temple of Hera

Sculpture Kouros and Kore: freestanding statues of youths and maidens Conventional memorial sculptures intended to honor the dead, but not the individual The archaic smile Early ones seem Egyptian Ptoon Kouros Peplos Kore