Accordingly, writers on Logic employ letters of the alphabet instead of concrete terms, (say) _X_ instead of _salt_ or instead of _iron_, and (say) _Y_ instead of _soluble_ or instead of _rusted by water_; and then a proposition may be represented by _X is Y_.

It is still more usual to represent a proposition by _S is (or is not) P, S_ being the initial of Subject and _P_ of Predicate; though this has the drawback that if we argue--_S is P_, therefore _P is S_, the symbols in the latter proposition no longer have the same significance, since the former subject is now the predicate.
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., Sec.Sec.

7-8); or the contradictory terms may be expressed by _x_ and _[x]_, _y_ and _[y]_.
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.