One of the chief differences between logicians and men of letters is that the latter mean many different things by one word, whereas the former do not--at least nowadays. Most mathematicians belong to the class of men of letters. I once had a manservant who told me on a certain occasion that he "never thought a word about it." I was doubtful whether to class him with such eminent mathematicians as are mentioned in the last chapter, or as a supporter of Max Müller's theory of the identity of thought and language. However, since the man was very untruthful, and he told me that he meant what he said and said what he meant,[32] the conclusion is probably correct that he really believed that the meanings of his words were not the words themselves. Thus I think it most probable that my manservant had been a mathematician but had escaped by the aid of logic. As regards his remark that he meant what he said and said what he meant, he plainly wished to pride himself on certain virtues which he did not possess, and was not indifferent to applause, which, however, was never evoked. The virtues, if so they be, and the applause were withheld for other reasons than that the above statements are either nonsensical or false. Suppose that "I say what I mean" expresses a truth. What I say (or write) is always a symbol--words (or marks); and what I mean by the symbol is the meaning of the symbol and not the symbol itself. So the remark cannot express a truth, any more than the name "Wellington" won the battle of Waterloo. FOOTNOTES: [31] _F. L._, pp. 246-7. [32] The Hatter (see Appendix H) pointed out that there is a difference between these two assertions. Thus, he clearly showed that he was a nominalist, and philosophically opposed to the March Hare who had recommended Alice to say what she meant. CHAPTER IX AMBIGUITY AND SYMBOLIC LOGIC The universal use of some system of Symbolic Logic would not only enable everybody easily to deal with exceedingly complicated arguments, but would prevent ambiguous arguments. In denying the indispensability of Symbolic Logic in the former state of things, Keynes[33] is probably alone, against the need strongly felt by Alice when speaking to the Duchess,[34] and most modern logicians. It may be noticed that the Duchess is more consistent than Keynes, for Keynes really uses the signs for logical multiplication and addition of Boole and Venn under the different shapes of the words "and" and "or." As regards ambiguity, a translation of _Hymns Ancient and Modern_ into, say, Peanesque, would prevent the puzzle of childhood as to whether the "his" in And Satan trembles when he sees The weakest saint upon his knees refers to the saint's knees or Satan's. FOOTNOTES: [33] In his _Fm. L._ [34] See Appendix I. CHAPTER X LOGICAL ADDITION AND THE UTILITY OF SYMBOLISM