SYMBOLISM AND MEANING
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 Schroeder--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.
FOOTNOTES:
[26] Cf. _Md_, N. S., vol. xiv., October 1905, p. 486.
[27] In _Z. S._, for example.
[28] See Appendix G.
[29] Cf. Chapter XXXVII below.
[30] Cf. _P. M._, p. 11, note.