" This first argument, given in Zeno's words according to Simplicius, attempts to show that there could not be many things, on pain of contradiction. Assume then that there are many things. First, he says that any collection must contain some definite number of things, neither more nor fewer. But if you have a definite number of things, he further concludes, you must have a finite — ‘limited’ — number of them; he implicitly assumes that to have infinitely many things is not to have any particular number of them. Second, imagine any collection of things arranged in space — imagine them lined up in one dimension for definiteness. Between and two of them, he claims, is a third; and in between these three elements another two; and another four between these five; and so on without end. Therefore the limited collection is also ‘unlimited’, which is a contradiction, and hence our original assumption must be false: there are not many things after all. At least, so Zeno's reasoning runs."
More on Zeno: http://plato.stanford.edu/entries/paradox-zeno/#ParPlu
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