Blackwell Reference Online

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A ncient G reek philosophy, logic, metaphysics, philosophy of mathematics Zeno of Elea established a series of arguments against plurality and motion; these arguments are mutually related, with the aim of defending the thesis of his teacher Parmenides that what is is one and unchanging. These arguments are preserved by Aristotle in the Physics and by the Greek commentators on this book. Most of these discussions, however, are very compressed, and this has given rise to very diverse interpretations. As a result there are various versions of each argument. The two main arguments against plurality are as follows: (1) If there is a plurality of things, they are both (a) so small as to have no magnitude, and (b) so large as to be infinite. The proof of (a) is: the plurality must be composed of a number of indivisible units; but if the unit has magnitude, it must be divisible; if it is indivisible, it has no magnitude; and the composite of a number of non-magnitude units has no magnitude. The proof of (b) is: if there are many things, each must have magnitude; otherwise neither their addition nor their subtraction will make any difference to another thing, and will be nothing at all; if there is a plurality of things with magnitude, then a thing composed of them must have at least two separate magnitudes, and each of them has magnitude and can be further divisible; since this ... log in or subscribe to read full text