It is a common and convenient practice to illustrate logical doctrines by examples: to show what is meant by a Proposition we may give _salt is soluble_, or _water rusts iron:_ the copulative exponible is exemplified by _salt is savoury and wholesome_; and so on. But this procedure has some disadvantages: it is often cumbrous; and it may distract the reader's attention from the point to be explained by exciting his interest in the special fact of the illustration. Clearly, too, so far as Logic is formal, no particular matter of fact can adequately illustrate any of its doctrines. 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., §§ 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_.