> The questions, "What is length?", "What is meaning?", "What is the number one?" etc., produce in us a mental cramp. We feel that we can't point to anything in reply to them and yet ought to point to something. (We are up against one of the great sources of philosophical bewilderment: we try to find a substance for a substantive.)
> The idea that in order to get clear about the meaning of a general term one had 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 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.
> Now I don't say that this is not possible. Only, putting it in this way immediately shows you that it need not happen. This, by the way, illustrates the method of philosophy.