Zeno of Elea (490-430 BC): On the paradox of motion

Concerns over the inconsistencies of Ionian views on change and causation led to the articulation of a set of logical paradoxes regarding motion by a student of Parmenides called Zeno. Zeno of Elea (490-430 BC) argued that if we see things in motion and our theory does not allow motion, then our senses must lie. He postulated a Block Universe with no real change (i.e., a static form of absolute monism) which created much difficulty for later thinkers.

Take, for example, the so-called argument of Achilles. The hero of the winged foot can never overtake the turtle -- symbol of slowness -- because the hero gives the turtle the handicap of space. Let us supposed that this interval between Achilles and the turtle is twenty feet, and while the hero runs twenty feet, the turtle advances one foot. Achilles cannot reach his running mate, because while he runs twenty feet the animal moves one foot, and while he runs a foot, his rival will run one-twentieth of a foot, and successively, while Achilles runs one-twentieth of a foot, the animal will have traveled one-twentieth of a twentieth of a foot, and so on, ad infinitum.

The same is to be said of the arrow which will never reach its target. Before striking the target, the arrow must traverse half the distance, and before it reaches half this space it must traverse one-half of this half, ad infinitum. Thus the arrow remains ever at the same place, no matter how much it may seem to be displaced. Such Sophistic arguments, as Aristotle noted well, are based on a false prejudgment that space is made up of an infinite number of parts.

Posted: [May, 2003]