[9] Cf. Appendix C, and William Robertson Smith, "Hegel and the Metaphysics of the Fluxional Calculus," _Trans. Roy. Soc., Edinb._, vol. xxv., 1869, pp. 491-511. [10] See Appendix B. [11] [This is a remarkable anticipation of the note on pp. 39-40 of Mr. Russell's book, published about three years after the death of Mr. R*ss*ll, and entitled _Our Knowledge of the External World as a Field for Scientific Method in Philosophy_, Chicago and London, 1914.--ED.] [12] Cf. _Ph. L._, pp. v.-vi. 3. [13] Cf. Pieri, _R. M. M._, March 1906, p. 199. [14] As a type of these, Humpty-Dumpty, with his inability to admit anything not empirically given and his lack of comprehension of pure mathematics, may be taken (see Appendix C). In his (correct) thesis that definitions are nominal, too, Humpty-Dumpty reminds one of J. S. Mill (see Appendix D). [15] See Frege, _Gg._, ii. p. 253. [16] See Appendix E. [17] See Frege, _Gg._, i. p. 15. [18] See the above references and also Appendix F. [19] Cf. B. Russell, _H. J._, July 1904, p. 812. CHAPTER II OBJECTIVE VALIDITY OF THE "LAWS OF THOUGHT" I once inquired of a maid-servant whether her mistress was at home. She replied, in a doubtful fashion, that she _thought_ that her mistress was in unless she was out. I concluded that the maid was uncertain as to the objective validity of the law of excluded middle, and remarked that to her mistress. But since I used the phrase "laws of thought," the mistress perhaps supposed that a "law of thought" has something to do with thinking and seemed to imagine that I wished to impute to the maid some moral defect of an unimportant nature. Thus she remonstrated with me in an amused way, since she probably imagined that I meant to find fault with the maid's capacity for thinking. CHAPTER III IDENTITY In the first chapter we have noticed the opinion that identities are fundamental to all logic. We will now consider some other views of the value of identities. Identities are frequently used in common life by people who seem to imagine that they can draw important conclusions respecting conduct or matters of fact from them. I have heard of a man who gained the double reputation of being a philosopher and a fatalist by the repeated enunciation of the identity "Whatever will be, will be"; and the Italian equivalent of this makes up an appreciable part of one of Mr. Robert Hichens' novels. Further, the identity "Life is Life" has not only been often accepted as an explanation for a particular way of living but has even been considered by an authoress who calls herself "Zack" to be an appropriate title for a novel; while "Business is Business" is frequently thought to provide an excuse for dishonesty in trading, for which purpose it is plainly inadequate.