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.  Sec. 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.