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 } MODUS [.'.]C is D | PONENS. If A is B, C is D | C is not D } MODUS [.'.]A is not B | 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:-- "_When two propositions are related as Reason and Consequent, the truth of the Consequent follows from the truth of the Antecedent, and the falsehood of the Antecedent, from the falsehood of the Consequent_". If A is B, C is D, implies that If C is not D, A is not B. If this subject is educative, it quickens the wits; if it does not quicken the wits, it is not educative. Admitted, then, that the law of Reason and Consequent holds between two propositions--that If A is B, C is D: admitted also the Antecedent, the truth of the Consequent follows. This is the MODUS PONENS or Positive Mode, where you reach a conclusion by obtaining the admission of the Antecedent. Admit the Antecedent and the truth of the Consequent follows. With the same Major Premiss, you may also, under the Law of Reason and Consequent reach a conclusion by obtaining the denial of the Consequent. This is the MODUS TOLLENS or Negative Mode. Deny the Consequent and one is bound to deny the Antecedent. But to guard against the fallacy technically known as FALLACIA CONSEQUENTIS, we must observe what the relation of Reason and Consequent does not imply. The truth of the Consequent does not involve the truth of the Antecedent, and the falsehood of the Antecedent does not involve the falsehood of the Consequent. "If the harbour is frozen, the ships cannot come in." If the harbour is not frozen, it does not follow that the ships can come in: they may be excluded by other causes. And so, though they cannot come in, it does not follow that the harbour is frozen. QUESTIONS CONNECTED WITH HYPOTHETICAL SYLLOGISMS.