ct 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.

Now this is true not only of quite empty terms but of terms that carry
a meaning. It is a mental necessity that we should make classes and use
general terms, and as soon as we do that we fall into immediate danger
of unjustifiably increasing the intension of these terms. You will find
a large proportion of human prejudice and misunderstanding arises from
this universal proclivity.

1.7. NEGATIVE TERMS.

There is a particular sort of empty terms that has been and is
conspicuously dangerous to the thinker, the class of negative terms. The
negative term is in plain fact just nothing; "Not-A" is the absence
of any trace of the quality that constitutes A, it is the rest of
everything for ever. But there seems to be a real bias in the mind
towards regarding "Not-A" as a thing mysteriously in the nature of A, as
though "Not-A" and A were species of the same genus. When one speaks of
Not-pink one is apt to think of green things and yellow things and to
ignore anger or abstract nouns or the sound of thunder. And logicians,
following the normal bias of the mind, do actually present A and not-A
in this sort of diagram:--

(the letter A inside a circular boundary, together with the words Not A,