§ 784. It must be noticed that the simple destructive dilemma would not admit of a disjunctive consequent. If we said,
If A is B, either C is D or E is F,
Either C is not D or E is not F,
we should not be denying the consequent. For 'E is not F' would make it true that C is D, and 'C is not D' would make it true that E is F; so that in either case we should have one of the alternatives true, which is just what the disjunctive form 'Either C is D or E is F' insists upon.
§ 785. In the case of the complex constructive dilemma the several members, instead of being distributively assigned to one another, may be connected together as a whole—thus—
If either A is B or E is F, either C is D or G is H.
Either A is B or E is F.
.'. Either C is D or G is H.
In this shape the likeness of the dilemma to the partly conjunctive syllogism is more immediately recognisable. The major premiss in this shape is vaguer than in the former. For each antecedent has now a disjunctive choice of consequents, instead of being limited to one. This vagueness, however, does not affect the conclusion. For, so long as the conclusion is established, it does not matter from which members of the major its own members flow.
§ 786. It must be carefully noticed that we cannot treat the complex destructive dilemma in the same way.
If either A is B or E is F, either C is D or G is H.
Either C is not D or G is not H.
Since the consequents are no longer connected individually with the antecedents, a disjunctive denial of them leaves it still possible for the antecedent as a whole to be true. For 'C is not D' makes it true that G is H, and 'G is not H' makes it true that C is D. In either case then one is true, which is all that was demanded by the consequent of the major. Hence the consequent has not really been denied.
§ 787. For the sake of simplicity we have limited the examples to the case of two antecedents or consequents. But we may have as many of either as we please, so as to have a Trilemma, a Tetralemma, and so on.