De Morgan[31] said that, “if all mankind had spoken one language, we cannot doubt that there would have been a powerful, perhaps universal, school of philosophers who would have believed in the inherent connexion between names and things; who would have taken the sound man to be the mode of agitating the air which is essentially communicative of the ideas of reason, cookery, bipedality, etc.... ‘The French,’ said the sailor, ‘call a cabbage a shoe; the fools! Why can’t they call it a cabbage, when they must know it is one?’”

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.

CHAPTER IX