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First, one could read him as first dividing the object into 1/2s, thenone of the 1/2s—say the second—into two 1/4s, then one ofthe 1/4s—say the second again—into two 1/8s and so on. Inthis case the result of the infinite division results in an endlesssequence of pieces of size 1/2 the total length, 1/4 the length, 1/8the length … . And then so the total length is (1/2 + 1/4+ 1/8 + …) of the length, which Zeno concludes is an infinitedistance, so that the pluralist is committed to the absurdity thatfinite bodies are ‘so large as to be unlimited’.

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Since the Bs and Cs move at same speeds, they willbe aligned with the As simultaneously.

Library of Congress Catalog Data: ISSN 1095-5054

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Almost everything that we know about Zeno of Elea is to be found inthe opening pages of Plato’s Parmenides. There we learnthat Zeno was nearly 40 years old when Socrates was a young man, say20. Since Socrates was born in 469 BC we can estimate a birth date forZeno around 490 BC. Beyond this, really all we know is that he wasclose to Parmenides (Plato reports the gossip that they were loverswhen Zeno was young), and that he wrote a book of paradoxes defendingParmenides’ philosophy. Sadly this book has not survived, andwhat we know of his arguments is second-hand, principally throughAristotle and his commentators (here we draw particularly onSimplicius, who, though writing a thousand years after Zeno,apparently possessed at least some of his book). There were apparently40 ‘paradoxes of plurality’, attempting to show thatontological pluralism—a belief in the existence of many thingsrather than only one—leads to absurd conclusions; of theseparadoxes only two definitely survive, though a third argument canprobably be attributed to Zeno. Aristotle speaks of a further fourarguments against motion (and by extension change generally), all ofwhich he gives and attempts to refute. In addition Aristotleattributes two other paradoxes to Zeno. Sadly again, almost none ofthese paradoxes are quoted in Zeno’s original words by theirvarious commentators, but in paraphrase.

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In this final section we should consider briefly the impact that Zenohas had on various philosophers; a search of the literature willreveal that these debates continue.

Here we should note that there are two ways he may be envisioning theresult of the infinite division.

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But what could justify this final step? It doesn’t seem thatbecause an object has two parts it must be infinitely big! And neitherdoes it follow from any other of the divisions that Zeno describeshere; four, eight, sixteen, or whatever finite parts make a finitewhole. Again, surely Zeno is aware of these facts, and so must havesomething else in mind, presumably the following: he assumes that ifthe infinite series of divisions he describes were repeated infinitelymany times then a definite collection of parts would result. Andnotice that he doesn’t have to assume that anyone could actuallycarry out the divisions—there’s not enough time and knivesaren’t sharp enough—just that an object can begeometrically decomposed into such parts (neither does he assume thatthese parts are what we would naturally categorize as distinctphysical objects like apples, cells, molecules, electrons or so on,but only that they are geometric parts of these objects). Now,if—as a pluralist might well accept—such parts exist, itfollows from the second part of his argument that they are extended,and, he apparently assumes, an infinite sum of finite parts isinfinite.

The Poetry of Emily Dickinson. Complete Poems of 1924. Comprises 597 poems

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The Atomists: Aristotle (On Generation and Corruption316b34) claims that our third argument—the one concerningcomplete divisibility—was what convinced the atomists that theremust be smallest, indivisible parts of matter. See Abraham (1972) fora further discussion of Zeno’s connection to the atomists.