60. Conjunctive and Disjunctive Syllogisms. -- The conjunctive syllogism is that which has a conjunctive proposition for its major. This proposition alleges an incompatibility between two cases, one of which is affirmed in order to eliminate the other.

E. g.: You could not have been in Brussels and in Paris at the same time. You were in Brussels. Therefore you could not have been in Paris. -- This syllogism may be reduced to the conditional type, and follows the laws of that type.

The disjunctive syllogism has for its major a disjunctive proposition, which not merely alleges an incompatibility, but implies an alternative admitting no middle term.

Hence the disjunctive syllogism is governed by the following two rules:

(1) The disjunction laid down in the major must be complete.

(2) When the minor affirms one of the members of the disjunction, the remaining member or members must be denied in the concrusion, and vice versa.

Example: Every free act is morally good or bad. Now such or such an act (e. g., an oath) is not morally bad; therefore it is morally good. . . . Or, it is bad; therefore it is not good. . . . Or, it is good; therefore it is not bad. . . . Or, it is not good; therefore it is bad.