The Disjunctive Syllogism is one having a disjunctive proposition in its major premise. The disjunctive proposition also appears in the conclusion when the disjunction in the major premise happens to contain more than two terms. A disjunctive proposition, we have seen, is one which possesses alternative predicates for the subject in which the conjunction "_or_" (sometimes accompanied by "_either_") appears. As for instance: "Lightning is sheet _or_ forked;" or, "Arches are _either_ round or pointed;" or, "Angles are either obtuse, or right angled, or acute." The different things joined together by "or" are called Alternatives, the term indicating that we may choose between the things, and that if one will not answer our purpose we may take the other, or one of the others if there be more than one _other_. The _Rule regarding the Use of Disjunctive Syllogisms_ is that: "If one or more alternatives be denied, the rest may still be affirmed." Thus if we say that "A is B or C," or that "A is either B or C," we may _deny_ the B but still affirm the C. Some authorities also hold that "If we affirm one alternative, we must deny the remainder," but this view is vigorously disputed by other authorities. It would seem to be a valid rule in cases where the term "either" appears as: "A is _either_ B _or_ C," because there seems to be an implication that one or the other alone can be true. But in cases like: "A is B _or_ C," there may be a possibility of _both being true_. Jevons takes this latter view, giving as an example the proposition: "A Magistrate is a Justice-of-the-Peace, a Mayor, or a Stipendiary Magistrate," but it does not follow that one who is a Justice-of-the-Peace may not be at the same time a Mayor. He states: "After affirming one alternative we can only deny the others _if there be such a difference between them that they could not be true at the same time_." It would seem that both contentions are at the same time true, the example given by Jevons illustrating his contention, and the proposition "The prisoner is either guilty or innocent" illustrating the contentions of the other side. A _Dilemma_ is a conditional syllogism whose Major Premise presents some sort of alternative. Whately defines it as: "A conditional syllogism with two or more antecedents in the major, and a disjunctive minor." There being two mutually exclusive propositions in the Major Premise, the reasoner is compelled to admit one or the other, and is then caught between "the two horns of the dilemma." CHAPTER XVIII. REASONING BY ANALOGY