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.
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