The idea that in order to get clear about the meaning of a
general term one ha
d to find the common element
in all its applications, has shackled philosophical
investigation; for it has not only led to no result, but also made
the philosopher dismiss as irrelevant the concrete cases, which
alone could have helped him to understand the usage of the general
term. When Socrates
asks the question, “what is knowledge?” he
does not even regard it as a
preliminary answer to
enumerate cases of knowledge. If I wished to find out
what sort of thing arithmetic is, I should be very content indeed
to have investigated the case of a finite cardinal
31.
arithmetic.
For
(a) this would lead me on to all the more
complicated cases,
(b) a finite cardinal
arithmetic is not incomplete, it has no gaps which are then filled
in by the rest of arithmetic.