Zeno

Zeno

The Classical Mind
W.T. Jones
1980

Zeno's Paradoxes

1) Motion is impossible. Before you go some place you must go half-way there. These half-way theres are infinite. It is impossible to go distances infinite in number. Therefore, motion is impossible.

2) Achilles and the Tortoise - Achilles if he is chasing a tortoise will never actually overtake the tortoise in spite of seeming to be faster. No matter how fast Achilles runs he never catches where the tortoise is because of something akin to the half-way theres paradox. Achilles always ends up at a starting point of the tortoise.

Early Greek Philosophy
Jonathan Barnes
2001

Plato writes a fictional encounter between Zeno and Socrates in his dialogue Parmenides.
-Zeno was 40 when Parmenides was 65 (it was said the two were lovers)
-Zeno visited Athens for a festival when Socrates was very young
-The interaction between Zeno and Socrates has Zeno claiming that while it may seem counterintuitive to assume that only one thing exists, the opposite is actually true. By embracing monism you get less ridiculous logical outcomes than by embracing dualism or pluralism.

Zeno argues that pluralism demands that everything be infinitely divisible. If things are divided so often eventually the parts that constitute the whole will become so small they will decrease to nothing. Nothing cannot exist so there can be no division whatsoever. In this way he aims to show that the pluralists have even more crazy assertions than the monists because if everything is made up of infinitely divisible things then everything is made from things that are essentially nothing, which is a logical absurdity. This is the puzzle of dichotomy.

The whole point of Zeno's puzzles or paradoxes are not to do away with the One of Parmenides, "but rather with a plurality of things (by showing that those who hypothesize a plurality are committed to inconsistencies), thus confirming Parmenides' argument that what exists is one" (Barnes, 104).

Aristotle was not exactly kind to Zeno in his book Physics. He states that Zeno argues fallaciously and that he set up arguments simply to embarrass people. Aristotle tallies some arguments Zeno gives against motion:
1) The infinite half-way there paradoxes
2) Achilles and the tortoise
3) The traveling arrow stands still (based on the half-distances and the Achilles one)

Aristotle argues that Zeno's paradoxes are based on an erroneous presumption that time is made up of instances. But Aristotle argues that time is the limitless thing.

Zeno argues against space and places saying that if anything exists it will be in a place. But if a place exists then it will be in a place and if the place that holds the place exists it will too have to be in a place. Zeno uses the infinite regression to argue that places therefore can't exist.

Another quote from Zeno (though its veracity is doubted) about the impossibility of motion is "What is moving moves neither in the place in which it is nor in the place in which it is not" (Barnes, 108).