Frege
ridiculed the formalist conception of mathematics by saying that
the formalists confused the unimportant thing, the sign, with the
important, the meaning. Surely, one wishes to say,
mathematics does not treat of dashes on a bit of paper.
Frege's idea could
be expressed thus: the propositions of mathematics, if
they were just complexes of dashes, would be dead and utterly
uninteresting, whereas they obviously have a kind of life.
And the same, of course, could be said of any proposition:
Without a sense, or without the thought, a proposition would
be an utterly
7.
dead and trivial
thing. And further it seems clear that no adding of
inorganic signs can make the proposition live. And the
conclusion which one draws from this is that what must be added to
the dead signs in order to make a live proposition is something
immaterial with properties different from all mere signs.