Again, negative terms frequently occur in Logic, such as _not-water_, or
_not-iron_, and then if _water_ or _iron_ be expressed by _X_, the
corresponding negative may be expressed by _x_; or, generally, if a
capital letter stand for a positive term, the corresponding small letter
represents the negative. The same device may be adopted to express
contradictory terms: either of them being _X_, the other is _x_ (see
chap. iv., §§ 7-8); or the contradictory terms may be expressed by _x_
and _x̄_, _y_ and _ȳ_.

And as terms are often compounded, it may be convenient to express them
by a combination of letters: instead of illustrating such a case by
_boiling water_ or _water that is boiling_, we may write _XY_; or since
positive and negative terms may be compounded, instead of illustrating
this by _water that is not boiling_, we may write _Xy_.

The convenience of this is obvious; but it is more than convenient; for,
if one of the uses of Logic be to discipline the power of abstract
thought, this can be done far more effectually by symbolic than by
concrete examples; and if such discipline were the only use of Logic it
might be best to discard concrete illustrations altogether, at least in
advanced text-books, though no doubt the practice would be too severe
for elementary manuals. On the other hand, to show the practical
applicability of Logic to the arguments and proofs of actual life, or
even of the concrete sciences, merely symbolic illustration may be not
only useless but even misleading. When we speak of politics, or poetry,
or species, or the weather, the terms that must be used can rarely have
the distinctness and isolation of X and Y; so that the perfunctory use
of symbolic illustration makes argument and proof appear to be much
simpler and easier matters than they really are. Our belief in any
proposition never rests on the proposition itself, nor merely upon one