_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
form is


_The Dilemma_.

§ 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.