But the utility of symbolic logic should not be estimated by the brevity with which propositions may sometimes be expressed by its means. Logical simplicity, in fact, can very often only be obtained by apparently complicated statements. For example, the logical interpretation of "The father of Charles II was executed" is, "It is not always false of _x_ that _x_ begat Charles II, and that _x_ was executed and that 'if _y_ begat Charles II, _y_ is identical with _x_' is always true of _y_."[37] From the point of view of logic, we may say that the apparently simple is most often very complicated, and, even if it is not so, symbolism will make it seem so,[38] and thus draw attention to what might otherwise easily be overlooked. FOOTNOTES: [35] Cf. Chapter XXIV below. [36] C. S. Peirce's notation for the relation "converse of P." [37] Russell, _Md._, N. S., vol. xiv., October 1905, p. 482. [38] Russell, _International Monthly_, vol. iv., 1901, pp. 85-6; cf. _M._, vol. xxii., 1912, p. 153. [This essay is reprinted in _Mysticism and Logic_, London and New York, 1918, pp. 74-96.--ED.] CHAPTER XI CRITICISM Those people who think that it is more godlike to seem to turn water into wine than to seem to turn wine into water surprise me. I cannot imagine an intolerable critic. It seems to me that, if A resents B's criticism in trying to put his (A's) discovery in the right or wrong place, A acts as if he thought he had some private property in truth. The White Queen seems to have shared the popular misconception as to the nature of criticism.[39] FOOTNOTES: [39] See Appendix J. CHAPTER XII HISTORICAL CRITICISM From a problem in Diophantus's _Arithmetic_ about the price of some wine it would seem that the wine was of poor quality, and Paul Tannery has suggested that the prices mentioned for such a wine are higher than were usual until after the end of the second century. He therefore rejected the view which was formerly held that Diophantus lived in that century.[40] The same method applied to a problem given by the ancient Hindu algebraist Brahmagupta, who lived in the seventh century after Christ, might result in placing Brahmagupta in prehistoric times. This is the problem:[41] "Two apes lived at the top of a cliff of height _h_, whose base was distant _mh_ from a neighbouring village. One descended the cliff and walked to the village, the other flew up a height _x_ and then flew in a straight line to the village. The distance traversed by each was the same. Find _x_." FOOTNOTES: [40] W. W. Rouse Ball, _A Short Account of the History of Mathematics_, 4th edition, London, 1908, p. 109. [41] _Ibid._, pp. 148-9. CHAPTER XIII IS THE MIND IN THE HEAD?