A MODERN GIRL AND GREEK PHILOSOPHICAL PUZZLES.
[To TUE EDITOR OF TIIE "SPECTAT0R:1 Sin,—It is often assumed that in point of subtlety and perspicacity the Greek mind is superior to that of the moderns. Having been reading Professor Gomperz's remarkable work on "Greek Thinkers," in which he incidentally discusses some of the paradoxes which puzzled the wits of the ancient philosophers, I put this assumption to the test by propounding some of these cruxes to a maiden of sixteen, one of my daughters, who has not yet been initiated into any of the mysteries of logic and metaphysics. One of these was the argument of "the Heap," which, in the words of Gomperz, "deeply impressed both contemporaries [of Eubulides, its author] and posterity, on which the subtle logician Chrysippus wrote a treatise in three books, without, as far as we can judge, ever really mastering the difficulties raised by it, and in face of which Cicero was still practically helpless" (Vol. II., p. 189). The question is: If two are a few, why not three ? if three, why not four ? and, by a gradually advancing increment of number, why not ten thousand or any other number ? Or, again, if the loss of a single hair does not make a man bald,why should the loss of two? of three P—and so on—and inferentially the loss of all ? "If, then, no addition or subtrac- tion of a unit can transform a small number of wheat grains into a heap, or a full head of hair into a bald head, how is it possible that either transition should ever be accomplished ?
We hold this piece of reasoning to be worthy of the closest attention" (Gomperz, 190). The English girl, so far from being mystified, at once detected the fallacy which underlies the argument. "The answer is that fewness is nothing absolute, but merely a comparative term. If we speak of a family, ten is not few. If we speak of the sands on the seashore, a million is few. So to speak of any number absolutely as few is absurd. It depends on what we are talking about. In the same way baldness is a relative term.. There are infinite varieties of degrees, from being very slightly bald (few hairs lost) up to total baldness (all hairs lost)." This is also virtually Gomperz's explanation after a long discussion. I then tried the modern maiden with the grain-of-millet argument devised by Zeno, one of those "subtle arguments which have puzzled the heads of generations of readers and have proved insur- mountable obstacles to more than one powerful intellect" (op. cit., I., 192). Take a grain of millet out of a bushel and let it fall on the ground, and it makes no noise. Take every grain in succession of ten thousand, let the same happen, and no sound is heard. Then collect all the grains back into the bushel and pour it out, and the result is a great noise. How, asks Zeno, can ten thousand noiseless processes make one full of noise P Again the schoolgirl was at no loss for the solution. "The falling grain is not really noiseless, but it makes a noise too slight to be noticed. Of course, the sum- total of all the small noises makes quite a big noise when they all occur together. What stupids those old philosophers must have been! "—I am, Sir, &c., A. SMYTHE PALMER.
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