CHAPTER XXIII.
Of the Disjunctive Syllogism.
§ 760. Roughly speaking, a Disjunctive Syllogism results from the combination of a disjunctive with a simple premiss. As in the preceding form, the complex proposition is regarded as the major premiss, since it lays down a hypothesis, which is applied to fact in the minor.
§ 761. The Disjunctive Syllogism may be exactly defined as follows—
A complex syllogism, which has for its major premiss a disjunctive proposition, either the antecedent or consequent of which is in the minor premiss simply affirmed or denied.
§ 762. Thus there are four types of disjunctive syllogism possible.
Constructive Moods.
(1) Either A is B or C is D. (2) Either A is B or C is D.
A is not B. C is not D.
.'. C is D. .'. A is B.
Either death is annihilation or we are immortal.
Death is not annihilation.
.'. We are immortal.
Either the water is shallow or the boys will be drowned.
The boys are not drowned.
.'. The water is shallow.