_Of the Mixed Form of Complex Syllogism_.
§ 778. Under this head are included all syllogisms in which a
conjunctive is combined with a disjunctive premiss. The best known
§ 779. The Dilemma may be defined as--
A complex syllogism, having for its major premiss a conjunctive
proposition with more than one antecedent, or more than one
consequent, or both, which (antecedent or consequent) the minor
premiss disjunctively affirms or denies.
§ 780. It will facilitate the comprehension of the dilemma, if the
following three points are borne in mind--
(1) that the dilemma conforms to the canon of the partly conjunctive
syllogism, and therefore a valid conclusion can be obtained only by
affirming the antecedent or denying the consequent;
(2) that the minor premiss must be disjunctive;
(3) that if only the antecedent be more than one, the conclusion
will be a simple proposition; but if both antecedent and consequent
be more than one, the conclusion will itself be disjunctive.