It is true that other kinds of sentences, optative, imperative, interrogative, exclamatory, if they express or imply an assertion, are not beyond the view of Logic; but before treating such sentences, Logic, for greater precision, reduces them to their equivalent sentences indicative. Thus, I wish it were summer may be understood to mean, The coming of summer is an object of my desire. Thou shalt not kill may be interpreted as Murderers are in danger of the judgment. Interrogatories, when used in argument, if their form is affirmative, have negative force, and affirmative force if their form is negative. Thus, Do hypocrites love virtue? anticipates the answer, No. Are 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.
§ 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.
§ 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.
The modes of compounding sentences are explained in every grammar-book. One of the commonest forms is the copulative, such as Salt is both savoury and wholesome, equivalent to two simple propositions: Salt is savoury; Salt is wholesome. Pure water is neither sapid nor odorous, equivalent to Water is not sapid; Water is not odorous. Or, again, Tobacco is injurious, but not when used in moderation, equivalent to Much tobacco is injurious; a little is not.
Another form of Exponible is the Exceptive, as Kladderadatsch is published daily, except on week-days, equivalent to Kladderadatsch is published on Sunday; it is not published any other day. Still another Exponible is the Exclusive, as Only men use fire, equivalent to Men are users of fire; No other animals are. Exceptive and exclusive sentences are, however, equivalent forms; for we may say, Kladderadatsch is published only on Sunday; and No animals use fire, except men.
There are other compound sentences that are not exponible, since, though they contain two or more verbal clauses, the construction shows that these are inseparable. Thus, If cats are scarce, mice are plentiful, contains two verbal clauses; but if cats are scarce is conditional, not indicative; and mice are plentiful is subject to the condition that cats are scarce. Hence the whole sentence is called a Conditional Proposition. For the various forms of Conditional Propositions see [chap. v. § 4].
But, in fact, to find the logical force of recognised grammatical forms is the least of a logician's difficulties in bringing the discourses of men to a plain issue. Metaphors, epigrams, innuendoes and other figures of speech present far greater obstacles to a lucid reduction whether for approval or refutation. No rules can be given for finding everybody's meaning. The poets have their own way of expressing themselves; sophists, too, have their own way. And the point often lies in what is unexpressed. Thus, "barbarous nations make, the civilised write history," means that civilised nations do not make history, which none is so brazen as openly to assert. Or, again, "Alcibiades is dead, but X is still with us"; the whole meaning of this 'exponible' is that X would be the lesser loss to society. Even an epithet or a suffix may imply a proposition: This personage may mean X is a pretentious nobody.
How shall we interpret such illusive predications except by cultivating our literary perceptions, by reading the most significant authors until we are at home with them? But, no doubt, to disentangle the compound propositions, and to expand the abbreviations of literature and conversation, is a useful logical exercise. And if it seem a laborious task thus to reduce to its logical elements a long argument in a speech or treatise, it should be observed that, as a rule, in a long discourse only a few sentences are of principal importance to the reasoning, the rest being explanatory or illustrative digression, and that a close scrutiny of these cardinal sentences will frequently dispense us from giving much attention to the rest.