It follows from the resolution of disjunctive propositions into conditionals or hypotheticals given in section [193] that (questions of modality being left on one side) the force of a disjunctive as a premiss in an argument is equivalent either to that of a conditional or to that of a hypothetical proposition.
Thus,
| Either A is B or C is D, | |
| A is not B, | |
| therefore, | C is D ; |
may be resolved into the form
| If A is not B, C is D, | |
| A is not B, | |
| therefore, | C is D ; |
or into the form
| If C is not D, A is B, | |
| A is not B, | |
| therefore, | C is D. |
A corollary from the above is that those who deny the character of mediate reasoning to the mixed hypothetical syllogism must also deny it to the disjunctive syllogism, or else must refuse to recognise the resolution of the disjunctive proposition into one or more hypotheticals.
In the above example it is not quite clear from the form of the major premiss whether we have a true hypothetical or a conditional. But in the following examples, which are added to illustrate the distinction, it is evident that the alternative propositions are equivalent to a true hypothetical and to a conditional respectively:
| Either all A’s are B’s or all A’s are C’s, | |
| This A is not B, | |
| therefore, | All A’s are C’s ; |
| All A’s are either B or C, | |
| This A is not B, | |
| therefore, | This A is C.[390] |