Shakespeare, or there were two men of the highest genius in the same age and country.’  This means that it is not likely there should be two such men, that we are sure of Bacon, and therefore ought to give him all the glory.  Now, if it is the part of Logic ’to make explicit in language all that is implicit in thought,’ or to put arguments into the form in which they can best be examined, such propositions as the above ought to be analysed in the way suggested, and confirmed or refuted according to their real intention.

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.

Sec. 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 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.).