Zeno's first paradox
The first paradox
1. The first paradox concerns the absolute motion of a single object, assuming that space is continuous. The argument is often referred to as the ‘dichotomy’.
2. Zeno starts by assuming what his opponent says is possible: motion. In particular, the motion of a single body across a finite distance in a finite time.
3. To make things vivid, let’s specify the moving object, and where it is supposed to be moving: Imagine a sprinter, who starts running at one end of a 100 metre straight track, and runs to the other end. Zeno’s opponents (probably including yourself) think that it really is possible that runners can do this. (i.e. They think that it is not just an illusion.) Zeno begins by assuming that his opponents are correct, and then the fun starts.
4. Zeno points out, given that we are assuming that space is continuous, that before the runner can cover the whole 100 metres she has to cover half the distance, i.e. run 50 metres.
5. Zeno then repeats the move just made (point 4) and points out that the move can be repeated an infinite number of times: before the runner can cover 50 metres, she has to run 25, before that she must run 12.5, before that 6.25, etc. Recall that we are assuming that space is continuous, which means that any finite piece of it, such as a sprint track, can be divided into infinitely many parts, which are infinitely small.
6. Zeno then argues that to cover each of these infinitely small parts will take a certain amount of time.
7. But to take a certain amount of time an infinite number of times adds up to an infinite amount of time. So it would take the runner forever to cover 100 metres.
P.S. this is just a c&p from my philosophy course.
I know this is ridiculous but i just find it so amusing. Just thought i would share. If anyone really wants to make it less amusing feel free to point out where he went wrong.
Whatever goes upon two legs is an enemy.
Whatever goes upon four legs, or has wings, is a friend.
No animal shall wear clothes.
No animal shall sleep in a bed.
No animal shall drink alcohol.
No animal shall kill any other animal.
All animals are equal.