This real vagueness of class terms is equally true whether we consider those terms used extensively or intensively, that is to say whether in relation to all the members of the species or in relation to an imaginary typical specimen.  The logician begins by declaring that S is either P or not P. In the world of fact it is the rarest thing to encounter this absolute alternative; S1 is pink, but S2 is pinker, S3 is scarcely pink at all, and one is in doubt whether S4 is not properly to be called scarlet.  The finest type specimen you can find simply has the characteristic quality a little more rather than a little less.  The neat little circles the logician uses to convey his idea of P or not P to the student are just pictures of boundaries in his mind, exaggerations of a natural mental tendency.  They are required for the purposes of his science, but they are departures from the nature of fact.

1.6.  Empty terms.

Classes in logic are not only represented by circles with a hard firm outline, whereas in fact they have no such definite limits, but also there is a constant disposition to think of all names as if they represented positive classes.  With words just as with numbers and abstract forms there have been definite phases of human development.  There was with regard to number, the phase when man could barely count at all, or counted in perfect good faith and sanity upon his fingers.  Then there was the phase when he struggled with the development of number, when he began to elaborate all sorts of ideas about numbers, until at last he developed complex superstitions about perfect numbers and imperfect numbers, about threes and sevens and the like.  The same was the case with abstract forms; and even to-day we are scarcely more than heads out of the vast subtle muddle of thinking about spheres and ideally perfect forms and so on, that was the price of this little necessary step to clear thinking.  How large a part numerical and geometrical magic, numerical and geometrical philosophy have played in the history of the mind!  And the whole apparatus of language and mental communication is beset with like dangers.  The language of the savage is I suppose purely positive; the thing has a name, the name has a thing.  This indeed is the tradition of language, and even to-day, we, when we hear a name are predisposed—­and sometimes it is a very vicious disposition—­to imagine forthwith something answering to the name.  We are disposed, as an incurable mental vice, to accumulate intension in terms. If I say to you Wodget or Crump, you find yourself passing over the fact that these are nothings, these are, so to speak mere blankety blanks, and trying to think what sort of thing a Wodget or a Crump may be.  You find yourself led insensibly by subtle associations of sound and ideas to giving these blank terms attributes.