Development Of The Human Soul

Appendix 7. (1212).

Zeno's celebrated four arguments against the existence of motion are given by Aristotle in Physics, 6: 9. The first three arguments are against continuous motion, not properly speaking against motion. Two of them tend to demonstrate the impossibility of a movable thing's arriving at a term if it has to pass through infinite parts of space, and suppose space to be actually divisible into infinite small spaces. The third argument however supposes, as Aristotle himself observes, that time is actually divided into an infinite number of instants. He says that a moving body would be stationary at every instant, and would not move. Reduced to a better form, this argument could be put in the following way: 'A body must be in some place. But if it is in some place, it must be there for some time, however small this time may be. If it were not in a place for some time, it would not be in a place. It is essential to the existence of body that it remain stationary in some place. Therefore, it cannot be in continuous movement.' The fourth argument is not only against continuous movement, but against movement itself, whatever concept may be formed of it, and is used to show that motion would involve the following absurdity: 'Half a time is equal to a whole time.' This, however, is sophistry. The absurdity would arise from the fact that a body, in order to move on a stationary table, would have to use double the time to cross the table that another body of equal rapidity would use to cross another body as long as the table, if the table moves in the opposite direction and with a speed equal to the body which crosses it.