TY - JOUR
AU - Abraham, William E.
AB -  40 The Nature of Zeno's Argument Against Plurality in DK 29 B I WILLIAM E. ABRAHAM Simplicius has preserved (Phys. 140, 34) a Zenonian argument pur- porting to show that if an object of positive magnitude has parts from which it derives its size, then any such object must be at once of infinite magnitude and zero magnitude. This surprising consequence is based upon a construction which Zeno makes, but his argument is widely thought to be grossly fallacious. Most often he is supposed to have misunderstood the arithmetic of his own construction. Evidently, any such charge must be premised on some view of the particular nature of the sequence to which Zeno's construction gives rise. I seek to develop a view that Zeno's argument is in fact free from fallacy, and offer reason to fear that his real argument has usually been missed. For ease of reference, I reproduce a translation of Simplicius in DK 29 B 1. (He showed the infinity of) size earlier by means of the same reasoning, for having first established that if a being did not have a size, it would not even be, he proceeds: if then it is, each must 
TI - The Nature of Zeno's Argument Against Plurality in DK 29 B I
JF - Phronesis
DO - 10.1163/156852872X00213
DA - 1972-01-01
UR - https://www.deepdyve.com/lp/brill/the-nature-of-zeno-s-argument-against-plurality-in-dk-29-b-i-sAUzWNymv4
SP - 40
EP - 52
VL - 17
IS - 1
DP - DeepDyve
ER -