∴ He is guilty.
10. THE FIRST RULE OF DISJUNCTIVE ARGUMENTS.
It may be said that disjunctive arguments depend on two rules. This is the first: The major premise must assert a logical disjunction. A logical disjunction involves two requisites; first, the alternatives must be mutually exclusive; second, the enumeration must be complete.
Illustrations of illogical major premise.
Terms not mutually exclusive:
This boy is either inattentive or indolent,
He is not inattentive,
∴ He is indolent.
It is obvious that the boy might be both inattentive and indolent. Experience teaches that the qualities are usually concurrent, and to assume that the boy must be either one or the other is a clear case of “begging the question.”
Some logicians maintain that “either—or” signify that both alternatives cannot be false, but that both may be true. If this viewpoint were adopted, the major premise of the illustration would not be a case of begging the question. It is unnecessary to argue the point, if it is made perfectly clear which view is to obtain in this discussion. Briefly stated the two points are these. First opinion: “Either—or” when used logically, mean that if the first alternative is false the second must be true, or if the first alternative is true the second must be false. Second opinion: “Either—or” when used logically mean that if the first alternative is false, the second must be true; but if the first alternative is true, the other may or may not be true. This treatise adopts the first opinion. With us all alternative arguments to be logical must be mutually contradictory; i. e., when one is false, the other must be true and when one is true the other must be false; both cannot be false, neither can both be true. When it is intended that this implication should not obtain, then the expressed alternative will take this form, “The boy is either inattentive or indolent or both.”