Round of applause for Zeno the marvelous mental magician for creating the paradoxes of motion. Most people will have heard of the race of Achilles and the Tortoise where if Achilles gives the tortoise a head start it can be argued that, even though Achilles runs at twice the speed of the tortoise he can never catch the tortoise. This is because by the time he reaches the tortoise’s original position the tortoise will have reached ahead to a new position and so it continues on and the race becomes unending.
This left me thinking what is going on here? Of course Achilles catches the Tortoise. How many times when playing sport have you not caught up to someone who was ahead of yourself. And so it begins that Philosophy tries to destroy the idea that motion exists or doesn’t exist. Hahaha. The logic involved in making this paradox of motion is of the most basic form; that even though we agree with the premises we have talked ourselves into agreeing with a totally false conclusion. So to truly refute the paradox we must refute the claim about the positions of Achilles and the Tortoise at exactly the same time and their relationship of their distance to each other.
Why I said that Zeno was a mental magician is because what he is doing is a mental sleight of hand. He ultimately has us caught up in an unending chase. We mentally move Achilles to where the tortoise was and then we envisage the tortoise moving ahead although by a small distance. And again we repeat this scenario, the tortoise is still ahead of Achilles and eventually we think what am I doing wrong this is not true. The problem I believe is that Zeno has us focusing on distances, and not on what governs motion and that is speed. And speed is distance covered at a certain rate.
The runner is moving his legs very fast, the tortoise very slowly. With every stride of the runner the gap is shortened until a position is reached where Achilles and the tortoise are equal and then Achilles overtakes the tortoise. This is the truth of reality. Zeno has very cleverly left out of his argument that the distance between Achilles and the Tortoise has diminished over the time it takes Achilles to reach the original position of the Tortoise. This gap is shortened to Nil and then Achilles is in the lead.
It is the differences in the rates of motion of Achilles and the tortoise that absolve you from this paradox but it is not mentioned in anyway shape or form. It is sometimes not, what is seen, but what is not seen that is important and hence why I said in this paradox the ‘sleight of hand’ is really a ‘Sleight of the Mind’. So from a logical perspective Zeno has left out a premise about the nature of motion because to add it in would make nonsense of his paradox.