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Zeno's Plurality Paradoxes

Zeno also argued against the notion that there is a plurality of objects, for the common sense world of spatially extended objects is supposedly an illusion. Two of the better-known plurality paradoxes are:

(1) If something is divisible, then it is infinitely divisible. Now if each part has zero size, then the total has zero size, for an infinite number of zero lenghts add up to zero. If on the other hand each part has some finite size, then the total is infinite, for an infinite number of finite lenghts, however minuscule, must add up to an infinite total. So something divisible is either infinite or else has no size at all. Thus something finite is not divisible.

(2) The total number of things is both finite and infinite. It is finite because, if there are many things, then there must be as many as there are "neither more nor less". And in that case their number is limited, hence finite. But on the other hand if there are many things, they must be infinite in number, for between any two there must always be others, and between those others still, and so on. (This paradox apparently is meant to apply to spatial points, rather than to physical objects.)

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