NOTE IN REPLY TO MR. A. W. BENN. 511 (5) Mr. Berm has in his ' Reply ' done me the service to call attention to another example of his methods of interpretation, of which I took no notice in my article for a very simple reason. In that article (p. 39) he said that Plato confessed to never having met a mathematician who could reason. I made no comment on this for the adequate reason that I remembered nothing in Plato quite like Mr. Benn's statement, and had no notion to what passage he might be alluding. He now alters "never" into 'hardly ever,' and supplies the reference to Eep. 53 b. But on referring to the Greek I find that what is actually said there is simply that the education of the philosophic ruler must not stop short at mathe- matics, because very few mere mathematical specialists (ot ravra SfLvol) are dialecticians. The exaggeration which transforms the reasonable proposition that few mathematicians are finished meta- physicians into the sweeping charge that hardly any of them ' can reason ' is Mr. Benn's. (6) I shall not take up much space in replying to Mr. Benn's concluding strictures on my own articles. I trust Mr. Benn will allow me to say that he is quite mistaken in supposing that I was
- displeased ' at his silence about my former articles on the Par-
'inenides. I mentioned his silence and the inference I had drawn from it simply to show that controversy between us as to the meaning of the second part of the dialogue would probably be fruit- less. As it appears from what he now says about my earlier articles that my interpretation of his silence was quite correct, I do not see why he should object to my remark about it. Next as to my present paper. May I suggest that Mr. Benn has no right to dismiss my interpretation with the comment that ' equations to curves ' are ' entirely outside Plato's ken,' unless he is prepared also to maintain that the fundamental conception of a curve as a locus, i.e., as an assemblage of points fulfilling a specified condition, is also entirely out of Plato's ken? The equational form is simply a convenient way of expressing this conception of a locus, and if we once admit that the concept of locus was within the ken of Plato and his contemporaries the anachronism involved in speaking by way of illustration of the * equation to a circle ' is not greater than that which we commit when in translating an arithmetical passage from Greek we substitute Arabic numerals for letters of the alphabet. As for my " marvellous commentary on Zeno's argument about the ofjLOLa Kal dvd/Aoia," I must point out, even at the expense of spoiling Mr. Benn's borrowed jests, that my interpretation was not " got out of two words," but was put forward as a conjecture based on what we know of the general character of Zeno's anti- Pythagorean polemic and of the views against which it was directed. We know that the problem of continuity was one which occupied Zeno in the very work from which Plato is quoting, and we have every reason, as Prof. Gaston Milhaud has shown, to believe that it was ~the discovery of incommensurables which forced the problem of continuity upon the attention of Greek thinkers. I believe therefore
