impossible to illustrate Logic sufficiently: the reader who is in
earnest about the cogency of arguments and the limitation of proofs, and
is scrupulous as to the degrees of assent that they require, must
constantly look for illustrations in his own knowledge and experience
and rely at last upon his own sagacity.

CHAPTER III

OF TERMS AND THEIR DENOTATION

Sec. 1. In treating of Deductive Logic it is usual to recognise three
divisions of the subject: first, the doctrine of Terms, words, or other
signs used as subjects or predicates; secondly, the doctrine of
Propositions, analysed into terms related; and, thirdly, the doctrine of
the Syllogism in which propositions appear as the grounds of a
conclusion.

The terms employed are either letters of the alphabet, or the words of
common language, or the technicalities of science; and since the words
of common language are most in use, it is necessary to give some account
of common language as subserving the purposes of Logic. It has been
urged that we cannot think or reason at all without words, or some
substitute for them, such as the signs of algebra; but this is an
exaggeration. Minds greatly differ, and some think by the aid of
definite and comprehensive picturings, especially in dealing with
problems concerning objects in space, as in playing chess blindfold,
inventing a machine, planning a tour on an imagined map. Most people
draw many simple inferences by means of perceptions, or of mental
imagery. On the other hand, some men think a good deal without any
continuum of words and without any imagery, or with none that seems
relevant to the purpose. Still the more elaborate sort of thinking, the
grouping and concatenation of inferences, which we call reasoning,
cannot be carried far without language or some equivalent system of
signs. It is not merely that we need language to express our reasonings
and communicate them to others: in solitary thought we often depend on
words--'talk to ourselves,' in fact; though the words or sentences that
then pass through our minds are not always fully formed or articulated.
In Logic, moreover, we have carefully to examine the grounds (at least
the proximate grounds) of our conclusions; and plainly this cannot be
done unless the conclusions in question are explicitly stated and
recorded.

Conceptualists say that Logic deals not with the process of thinking
(which belongs to Psychology) but with its results; not with conce