1. Parmenides and the Eleatics Using logic alone to derive startling metaphysical conclusions

2. Parmenides (ca. 515-450 BC )

3. Parmenides Lived in Elea, near Naples in southwestern Italy Reputedly influenced by Pythagoreans and Xenophanes Wrote in poetry, parts of which survive Presents his philosophy as story or vision of meeting a goddess, who tells him two Ways: 1.the Way of Truth 2.the Way of Seeming

4. The Way of Truth This way contrasts ‘is’ and ‘is not.’ The Greek ‘esti’ can mean both ▫‘… exists.’ ▫‘… is (something).’ It can often imply always is, like ‘gold is a metal.’ So ‘is not’ implies something unreal or illusory.

5. Parmenides’ “Battle-Hardened Proof” Fr. 8, line 6: Where could any change begin? It would have to come from nothing, or from something. Nothing is not and cannot do anything. But if it comes from something, it must have already been in that something. In that case, it already was: no change. To go out of existence is to become nothing, but there is no such thing as nothing.

6. ‘Is or is not’ If it is, it can’t come into being, because it is already. If it is not, it is not, and is nothing. “Nothing else either is or will be except what-is, since precisely this is what Fate bound to be whole and motionless.” Change is a word mortals invent. Is, or is not: there is no change.

7. Parmenides’ Argument 1.Nothing comes from nothing. 2.Something beginning is something coming from nothing. 3.So, there is no beginning. 4.Change is something beginning. So, there is no change.

8. The Way of Seeming? The Way of Seeming (or Opinion), is mostly lost. The end of fr. 8 seems to hint at a cosmological theory of opposed forces of fire and night, like that of the Milesians. One fragment shows Parmenides knew the Moon’s light comes from the Sun. But if thinking tells us reality, the Way of Truth shows us reality is, and our ways of seeming are not.

9. The Eleatics: Melissus and Zeno Melissus of Samos (fl. ca. 440 BC ) argued that reality must be one and infinite, as limit, plurality, and re-arrangement all imply non-being: some gap or division which is not. Zeno of Elea’s (ca. 490-430 BC ) famous paradoxes try to show that we see and describe the world in inherently self- contradictory, impossible ways.

10. The Dichotomy (fr. 6)

11. Zeno vs. Us Zeno would be critical of modern mathematical solutions: to say that an infinite series can add up to some finite number, he might say, is to be inconsistent about what “infinite” means. Or he might say that he’s not talking about a mathematical series at all, but about physical space, time, and motion.

12. Zeno vs. motion 1.To move, you must first cross half the distance moved. 2.To cross half the distance moved, you must first cross half that distance, and so on to infinity. 3.If (2), then to move, you must cross an infinite distance. 4.It is impossible to cross an infinite distance. So: it is impossible to move.

13. Achilles and the Tortoise (fr. 7)

14. The Arrow (fr. 8)

15. The Moving Rows (fr. 9) Imagine three rows (A, B, C) divided in squares of identical size. Row A doesn’t move. Row B is moving right. Row C is moving left. The moving rows each pass one square in the smallest possible unit of time.

16. The Moving Rows (fr. 9) Each square is the same size, and the moving rows each pass one square in the smallest possible unit of time. But between T1 and T2, C1 passes two squares (from B3 to B1). So, the smallest possible unit of time cannot be the smallest possible unit of time.

17. The Eleatic Legacy The Eleatics made philosophy more abstract: unlike the Milesians, who argued from observation, the Eleatics argued that the senses lead us into self-contradiction. Arguments deriving the changing world on something perfect and unchanging pass from Parmenides into theology. The principle of conservation of energy: energy cannot be created or destroyed.