THE METAPHYSICAL ANSWER TO ZENO'S PARADOXES
THE METAPHYSICAL ANSWER TO ZENO’S PARADOXES
D. R. Khashaba
Ever since Zeno of Elea proposed his famous paradoxes scholars have been trying to find logical or (lately) mathematical solutions or resolutions for these paradoxes. All attempts in this direction are futile since they ignore Zeno’s purpose, which was to defend Parmenides’s doctrine of the One against the common pluralist or ‘realist’ view of things.
The pluralists thought Parmenides’ denial of multiplicity was contradicted by the actual existence of things in space and time. Zeno’s paradoxes were intended to show the inherent contradictoriness of the notions of space and time. Unfortunayely, this is a lesson lost even on the erudite of our own day who find it hard to acknowledge that space and time are conceptual fictions, useful fictions, necessary for dealing with our fragmented world, but fictions nevertheless.
In nature there is no space, there is no time, there are no things. Plato said that you cannot say of any ‘thing’ in the actual world ‘it is this’ or ‘it is such’, for before you say it, it has ceased to be what ii was. Again Plato said the real is no other thing than activity (dunamis) ( Sophist, 247e).Nature is a total flux as Heraclitus saw, a perpetually ongoing single process as Whitehead would say. Absolutely, no ‘thing’ is separate or separable from the Whole; relatively, a thing has as much actuality as it is a transient whole within the perpetual Whole, in other words, in as much as it is an ‘event’ (to resort again to Whitehead).
Watch a cat preparing to jump to a high spot, say the top of a wall. For a while, a second or two, she fixes her sight on the spot to be reached. Certainly in that second or two the intelligence inherent in her whole being determines the correct thrust needed. If it is more than is correct she would fly over the wall and fall on the other side; if it is less than is correct she would knock against the wall and fall down. The sighting, the thrust, the jump, the target are inseparable aspects of one act, one whole. The whole is the real and only what is whole has a share in reality. In conceptual thinking (a thing apparently peculiar to human beings) we break up the whole into distinct elements, dimensions, stages, etc. We create abstractions. We err when we take our abstractions for final, independent, actual things, and then we fall into endless quandaries.
The logical and mathematical resolutions of Zeno’s paradoxes, to rescue the fictions of space and time create other fictions, which in turn may prove useful for certain theoretical and practical purposes, but which cannot remedy the intrinsic contradictoriness of the notions of space and time. The only cogent answer to Zeno’s paradoxes is the metaphysical answer, and our metaphysical answer amounts to conceding the validity of Zeno’s refutation of pluralism as a philosophical standpoint.
D. R. Khashaba
December 3, 2016