If the harbour is frozen, the ships cannot come in. The harbour is frozen. [.'.] The ships cannot come in. This is a Hypothetical Syllogism, _Modus Ponens_. Express the Hypothetical Major in the form of the general proposition which it implies, and you reach a conclusion (in _Barbara_) which is only grammatically different from the original. All frozen harbours exclude ships. The harbour is frozen. [.'.] It excludes ships. Again, take an example of the _Modus Tollens_-- If rain has fallen, the streets are wet. The streets are not wet. [.'.] Rain has not fallen. This is reducible, by formulating the underlying proposition, to _Camestres_ or _Baroko_ of the Second Figure. All streets rained upon are wet. The streets are not wet. [.'.] They are not streets rained upon. Hypothetical Syllogisms are thus reducible, by merely grammatical change[2], or by the statement of self-evident implications, to the Categorical form. And, similarly, any Categorical Syllogism may be reduced to the Hypothetical form. Thus:-- All men are mortal. Socrates is a man. [.'.] Socrates is mortal. This argument is not different, except in the expression of the Major and the Conclusion, from the following:-- If Socrates is a man, death will overtake him. Socrates is a man. [.'.] Death will overtake him. The advantage of the Hypothetical form in argument is that it is simpler. It was much used in Mediaeval Disputation, and is still more popular than the Categorical Syllogism. Perhaps the prominence given to Hypothetical Syllogisms as syllogisms in Post-Renaissance text-books is due to the use of them in the formal disputations of graduands in the Universities. It was the custom for the Disputant to expound his argument in this form:-- 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. (_Summulae. 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. (3) If C is D, A is not B. (4) If C is not D, A is B.