nary Logic, and are now
generally neglected by the authors of text-books. No doubt such
propositions are the commonest in ordinary discourse, and in some rough
way we combine them and draw inferences from them. It is understood
that a combination of assertory or of apodeictic premises may warrant an
assertory or an apodeictic conclusion; but that if we combine either of
these with a problematic premise our conclusion becomes problematic;
whilst the combination of two problematic premises gives a conclusion
less certain than either. But if we ask 'How much less certain?' there
is no answer. That the modality of a conclusion follows the less certain
of the premises combined, is inadequate for scientific guidance; so
that, as Deductive Logic can get no farther than this, it has abandoned
the discussion of Modals. To endeavour to determine the degree of
certainty attaching to a problematic judgment is not, however, beyond
the reach of Induction, by analysing circumstantial evidence, or by
collecting statistics with regard to it. Thus, instead of 'The cobra's
bite is _probably_ fatal,' we might find that it is fatal 80 times in
100. Then, if we know that of those who go to India 3 in 1000 are
bitten, we can calculate what the chances are that any one going to
India will die of a cobra's bite (chap. xx.).

Sec. 6. Verbal and Real Propositions.--Another important division of
propositions turns upon the relation of the predicate to the subject in
respect of their connotations. We saw, when discussing Relative Terms,
that the connotation of one term often implies that of another;
sometimes reciprocally, like 'master' and 'slave'; or by inclusion, like
species and genus; or by exclusion, like contraries and contradictories.
When terms so related appear as subject and predicate of the same
proposition, the result is often tautology--e.g., _The master has
authority over his slave; A horse is an animal; Red is not blue; British
is not foreign_. Whoever knows the meaning of 'master,' 'horse,' 'red,'
'British,' learns nothing from these propositions. Hence they are called
Verbal propositions, as only expounding the sense of words, or as if
they were propositions only by satisfying the forms of language, not by
fulfilling the function of propositions in conveying a knowledge of
facts. They are also called 'Analytic' and 'Explicative,' when they
separate and disengage the elements of the connotation of the subject.
Doubtless, such propo