If so and so is the case, such and such follows.

So and so is the case.

... Such and such follows.

To which the Respondent would reply: Accipio antecedentem, nego consequentiam, and argue accordingly. Petrus Hispanus does not give the Hypothetical Syllogism as a Syllogism: he merely explains the true law of Reason and Consequent in connexion with the Fallacia Consequentis in the section on Fallacies. (Summulæ. Tractatus Sextus.)

II.—Disjunctive Syllogisms.

A Disjunctive Syllogism is a syllogism in which the Major Premiss is a Disjunctive Proposition, i.e., one in which two propositions are declared to be mutually incompatible. It is of the form Either A is B, or C is D.[3]

If the disjunction between the alternatives is really complete, the form implies four hypothetical propositions:—

(1) If A is B, C is not D.

(2) If A is not B, C is D.