When people write down any statement such as “The curfew tolls the knell of parting day,”[26] which we will call “C” for shortness, what they mean is not “C” but the meaning of “C”; and not “the meaning of ‘C’” but the meaning of “the meaning of ‘C’.” And so on, ad infinitum. Thus, in writing or in speech, we always fail to state the meaning of any proposition whatever. Sometimes, indeed, we succeed in conveying it; but there is danger in too great a disregard of statement and preoccupation with conveyance of meaning. Thus many mathematicians have been so anxious to convey to us a perfectly distinct and unmetaphysical concept of number that they have stripped away from it everything that they considered unessential (like its logical nature) and have finally delivered it to us as a mere sign. By the labours of Helmholtz, Kronecker, Heine, Stolz, Thomae, Pringsheim, and Schubert, many people were persuaded that, when they said “‘2’ is a number” they were speaking the truth, and hold that “Paris” is a town containing the letter “P.” When Frege pointed out[27] this difficulty he was almost universally denounced in Germany as “spitzfindig.” In fact, Germans seem to have been influenced perhaps by that great contemner of “Spitzfindigkeit,” Kant, to reject the White Knight’s[28] distinctions between words and their denotations and to regard subtlety with disfavour to such a degree that their only mathematical logician except Frege, namely SchrÖder—the least subtle of mortals, by the way—seems to have been filled with such fear of being thought subtle, that he made his books so prolix that nobody has read them.

Another term which, as we shall see when discussing the paradoxes of logic, mathematicians are accustomed to apply to thought which is more exact than any to which they are accustomed is “scholastic.”[29] By this, I suppose, they mean that the pursuits of certain acute people of the Middle Ages are unimportant in contrast with the great achievements of modern thought, as exemplified by a method of making plausible guesses known as induction,[30] the bicycle, and the gramophone—all of them instruments of doubtful merit.

CHAPTER VIII