ON THE INTERPRETATION OF PLATO'S PAEMENIDES. 29 are no real units there to be numbered. Again we shall seem to have carried our subdivision to its utmost limit, and to have found a " least part " (e.g. an " atom "), which we can if we will treat as the unit ; while yet again this unitary " least part " will itself contain an indefinite number of parts, in comparison with which it will itself seem many and large. From which it follows that, if we take each from the suitable point of view, the " whole " and the " part " will appear equal to one another (165 A, ica-l i'cro? fj.i]i> TO?? TroXXot? Kal oyu/epot<?, sc., its own parts, e/cacrro? OJKOS 8o^aadt)(7erai elvai ov 'yap av pertftuivev etc /netbz'os 19 arrov (f>aiv6fji,vo<t Trplv et? TO yLterafi) So^eiv eeiv, i.e., since you can by judicious arrangement make an object A which normally appears several times as great as B look less than B, it is clear that by the proper arrangement you can also make them seem equal). So again, one " heap " will seem, but will only seem, to be itself an ordered system (Trepa? e;;aji' 7rpo<? eavTov) or a part of such a system (Trepas e-^wv ?rpo? aov O'JKOV}, while on a closer inspection we shall find that the appearance was an illusion. We can find a " beginning" before every " beginning," a " middle " which is in the midst of every " middle," an " end " after every " end," and so on in indefinitum. For without units there can be no such thing as system. So altogether, whatever object one tries to think, it vanishes away, for lack of its interpretation as an organic unity, that is as an idea, into an infinite multiplicity of infinitesimals. And we may say of every such object that while it seems when seen from a distance and by a short-sighted spectator to be one, the keener insight which studies it at close quarters (eyyvQev Be Kal b%v VOOVVTI) detects its indefinite multiplicity. So, recapitulating our conclusions, we find once more, on our present hypothesis, that we can both assert and deny the seeming unity and systematic character of any and every object. Similarly we can predicate both likeness and unlike- ness of our "heaps ". Viewed from a distance they all look to be alike and to be very much the same thing, but when you examine them more minutely you find they are full of diversity and unlikeness. And so, concludes Parmenides, we can easily show that the " heaps " touch and do not touch each other, are all in motion and all at rest, come into and pass out of being, and yet again neither become nor pass away. And with this declaration the eighth hypothesis comes to an end. The hypothesis we have gone through has clearly a double function. (1) It serves to confirm us in our prefer-
