The idea that in order to get clear about the meaning of a general term one ha[s|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.