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It's all about the deep questions.

October 1, 2011

Posted by on In this paradox Zeno argues that all motion is impossible, which is a pretty substantial conclusion. What kind of reasoning could possibly lead someone to this completely counterintuitive conclusion? Well here is the gist of the story that Zeno spells out:

Imagine Achilles wanted to complete a race, lets say it was one mile long for convenience. It’s clear that if he wants to complete the race, he will eventually have to make it to the half way point. After he finishes the task of traversing the first half mile, he must then reach the half way point between 1/2 a mile and 1 mile. So, he must now finish the task of getting to the 3/4 mile point. However, continuing along this line of thought, Achilles has infinitely many tasks to complete! He has to traverse 1/2 a mile, 3/4 a mile, 7/8 a mile, 15/16 a mile, etc. Each task will also take a finite number of time! Since it is logically impossible to **complete** a series of infinitely many tasks (each requiring a finite amount of time), Zeno tells us that Achilles can never finish the race. Furthermore, this argument can easily be generalized to anything moving from point A to point B where A and B are distinct.

**The Racetrack Argument**

1. If something is to move from A to B, where A and B are distinct, then it would have to complete an infinite number of tasks.

2. It is impossible for anything to complete an infinite number of tasks.

3. Therefore, nothing can move from A to B, where A and B are distinct.

So, now we should take a hard look at the premises. Read more of this post

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