If, then, the disjunctive A is either B or C (B and C being contraries) implies that both alternatives cannot be true, it can only be adequately rendered in hypotheticals by the two forms—­(1) If A is B, it is not C, and (2)_If A is not B, it is C_.  But if the disjunctive A is either B or C (B and C not being contraries) implies that both may be true, it will be adequately translated into a hypothetical by the single form, If A is not B, it is C.  We cannot translate it into—­If A is B, it is not C, for, by our supposition, if ‘A is B’ is true, it does not follow that ‘A is C’ must be false.

Logicians are also divided in opinion as to the function of the hypothetical form.  Some think it expresses doubt; for the consequent depends on the antecedent, and the antecedent, introduced by ‘if,’ may or may not be realised, as in If the sky is clear, the night is cold:  whether the sky is, or is not, clear being supposed to be uncertain.  And we have seen that some hypothetical propositions seem designed to draw attention to such uncertainty, as—­If there is a resisting medium in space, etc.  But other Logicians lay stress upon the connection of the clauses as the important matter:  the statement is, they say, that the consequent may be inferred from the antecedent.  Some even declare that it is given as a necessary inference; and on this ground Sigwart rejects particular hypotheticals, such as Sometimes when A is B, C is D; for if it happens only sometimes the connexion cannot be necessary.  Indeed, it cannot even be probably inferred without further grounds.  But this is also true whenever the antecedent and consequent are concerned with different matter.  For example, If the soul is simple, it is indestructible.  How do you know that?  Because Every simple substance is indestructible.  Without this further ground there can be no inference.  The fact is that conditional forms often cover assertions that are not true complex propositions but a sort of euthymemes (chap. xi.  Sec. 2), arguments abbreviated and rhetorically disguised.  Thus:  If patience is a virtue there are painful virtues—­an example from Dr. Keynes.  Expanding this we have—­

      Patience is painful;
      Patience is a virtue: 
    .’.  Some virtue is painful.

And then we see the equivocation of the inference; for though patience be painful to learn, it is not painful as a virtue to the patient man.

The hypothetical, ’If Plato was not mistaken poets are dangerous citizens,’ may be considered as an argument against the laureateship, and may be expanded (informally) thus:  ’All Plato’s opinions deserve respect; one of them was that poets are bad citizens; therefore it behoves us to be chary of encouraging poetry.’  Or take this disjunctive, ’Either Bacon wrote the works ascribed to