Chapter VII.
CONDITIONAL ARGUMENTS.—HYPOTHETICAL SYLLOGISM, DISJUNCTIVE SYLLOGISM, AND DILEMMA.
The justification of including these forms of argument in Logic is simply that they are sometimes used in debate, and that confusion may arise unless the precise meaning of the premisses employed is understood. Aristotle did not include them as now given in his exposition of the Syllogism, probably because they have no connexion with the mode of reasoning together to which he appropriated the title. The fallacies connected with them are of such a simple kind that to discuss as a question of method the precise place they should occupy in a logical treatise is a waste of ingenuity.[1]
I.—Hypothetical Syllogisms.
| If A is B, C is D A is B ... C is D | Modus Ponens. | |
| If A is B, C is D C is not D ... A is not B | Modus Tollens. |
A so-called Hypothetical Syllogism is thus seen to be a Syllogism in which the major premiss is a Hypothetical Proposition, that is to say, a complex proposition in which two propositions are given as so related that the truth of one follows necessarily from the truth of the other.
Two propositions so related are technically called the Antecedent or Reason, and the Consequent.
The meaning and implication of the form, If A is B, C is D, is expressed in what is known as the Law of Reason and Consequent:—