We may conclude that no single function can be assigned to all
hypothetical propositions: each must be treated according to its own
meaning in its own context.

§ 5. As to Modality, propositions are divided into Pure and Modal. A
Modal proposition is one in which the predicate is affirmed or denied,
not simply but _cum modo_, with a qualification. And some Logicians have
considered any adverb occurring in the predicate, or any sign of past or
future tense, enough to constitute a modal: as 'Petroleum is
_dangerously_ inflammable'; 'English _will be_ the universal language.'
But far the most important kind of modality, and the only one we need
consider, is that which is signified by some qualification of the
predicate as to the degree of certainty with which it is affirmed or
denied. Thus, 'The bite of the cobra is _probably_ mortal,' is called a
Contingent or Problematic Modal: 'Water is _certainly_ composed of
oxygen and hydrogen' is an Assertory or Certain Modal: 'Two straight
lines _cannot_ enclose a space' is a Necessary or Apodeictic Modal (the
opposite being inconceivable). Propositions not thus qualified are
called Pure.

Modal propositions have had a long and eventful history, but they have
not been found tractable by the resources of ordinary 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