not traitors the vilest of mankind? anticipates the answer, Yes.  So that the logical form of these sentences is, Hypocrites are not lovers of virtue; Traitors are the vilest of mankind.  Impersonal propositions, such as It rains, are easily rendered into logical forms of equivalent meaning, thus:  Rain is falling; or (if that be tautology), The clouds are raining.  Exclamations may seem capricious, but are often part of the argument. Shade of Chatham! usually means Chatham, being aware of our present foreign policy, is much disgusted.  It is in fact, an appeal to authority, without the inconvenience of stating what exactly it is that the authority declares.

Sec. 2.  But even sentences indicative may not be expressed in the way most convenient to logicians. Salt dissolves in water is a plain enough statement; but the logician prefers to have it thus:  Salt is soluble in water.  For he says that a proposition is analysable into three elements:  (1) a Subject (as Salt) about which something is asserted or denied; (2) a Predicate (as soluble in water) which is asserted or denied of the Subject, and (3) the Copula (is or are, or is not or are not), the sign of relation between the Subject and Predicate.  The Subject and Predicate are called the Terms of the proposition:  and the Copula may be called the sign of predication, using the verb ’to predicate’ indefinitely for either ‘to affirm’ or ‘to deny.’  Thus S is P means that the term P is given as related in some way to the term S.  We may, therefore, further define a Proposition as ’a sentence in which one term is predicated of another.’

In such a proposition as Salt dissolves, the copula (is) is contained in the predicate, and, besides the subject, only one element is exhibited:  it is therefore said to be secundi adjacentis.  When all three parts are exhibited, as in Salt is soluble, the proposition is said to be tertii adjacentis.

For the ordinary purposes of Logic, in predicating attributes of a thing or class of things, the copula is, or is not, sufficiently represents the relation of subject and predicate; but when it is desirable to realise fully the nature of the relation involved, it may be better to use a more explicit form.  Instead of saying Salt—­is—­soluble, we may say Solubility—­coinheres with—­the nature of salt, or The putting of salt in water—­is a cause of—­its dissolving:  thus expanding the copula into a full expression of the relation we have in view, whether coinherence or causation.

Sec. 3.  The sentences of ordinary discourse are, indeed, for the most part, longer and more complicated than the logical form of propositions; it is in order to prove them, or to use them in the proof of other propositions, that they are in Logic reduced as nearly as possible to such simple but explicit expressions as the above (tertii adjacentis).  A Compound Proposition, reducible to two or more simple ones, is said to be exponible.