and this is the modus ponens.[382]
[382] A categorical syllogism in Camestres may similarly be reduced to Celarent without transposing the premisses. Thus, All P is M, No S is M, therefore, No S is P, becomes, by contraposition of the major and obversion of the minor premiss, No not-M is P, All S is not-M, therefore, No S is P.
308. Is the reasoning contained in the mixed hypothetical syllogism mediate or immediate?[383]—Kant, Hamilton,[384] Bain, and others argue that inferences of the kind that we have just been considering are properly to be regarded not as mediate, but as immediate, inferences.
[383] Similar arguments on both sides may be used in the case where a conditional premiss and a categorical premiss are combined.
[384] Logic, ii. p. 383. On page 378, however, Hamilton seems to take the other view.
Now, taking the syllogism—
| If P is true then Q is true, | |
| but P is true, | |
| therefore, | Q is true, |
355 the conclusion is at any rate apparently obtained by a combination of two premisses, and the process is moreover one of elimination, namely, of the proposition P is true. Hence the burden of proof certainly lies with those who deny the claims of such an inference as this to be called mediate.
Bain (Logic, Deduction, p. 117) seems to argue that the so-called hypothetical syllogism is not really mediate inference, because it is “a pure instance of the law of consistency”; in other words, because “the conclusion is implied in what has already been stated.” But is not this the case in all formal mediate inference? It cannot be maintained that the categorical syllogism is more than a pure instance of the law of consistency; or that the conclusion in such a syllogism is not implied in what has been already stated. But possibly Bain may mean that the conclusion is implied in the hypothetical premiss alone. Indeed he goes on to say, “’If the weather continues fine, we shall go into the country’ is transformable into the equivalent form ‘The weather continues fine, and so we shall go into the country.’ Any person affirming the one, does not, in affirming the other, declare a new fact, but the same fact.” Surely this is not intended to be understood literally. Take the following:—If war is declared, I must return home; If the sun moves round the earth, modern astronomy is a delusion. Are these respectively equivalent to the statements, War has been declared, and so I must return home; The sun moves round the earth, and so modern astronomy is a delusion? Besides, if the proposition If P is true then Q is true implies the truth of P, what becomes of the possible reasoning, “But Q is not true, therefore, P is not true”?
Further arguments that have been adduced on the same side are as follows:—
(1) “There is no middle term in the so-called hypothetical syllogism”.[385] The answer is that there is an element 356 in the premisses which does not appear in the conclusion, and that this corresponds to the middle term of the categorical syllogism.