[385] This is Kant’s argument. A more plausible argument would be that there is no minor term. It will be found, however, that, in the reduction of the mixed hypothetical syllogism to the form of a pure hypothetical syllogism, something corresponding to a minor term has to be introduced. Compare [note 2] on page 352.
(2) “In the so-called hypothetical syllogism, the minor and the conclusion indifferently change places”.[386] This statement is erroneous. Taking the valid syllogism given at the commencement of this section and transposing the so-called minor and the conclusion, we have a fallacy.
[386] This argument is Hamilton’s. He remarks that, in hypothetical syllogisms, “the same proposition is reciprocally medium or conclusion” (Logic, ii. p. 379). Dr Ray (Deductive Logic, Note C) holds that Hamilton is here wrongly interpreted; and that he meant no more than that with a hypothetical premiss If A is B, C is D, a relation between A and B may be either the other premiss (as in the modus ponens) or the conclusion (as in the modus tollens). Dr Ray is possibly right. But if so, Hamilton does not express himself clearly. For A is B (the premiss of the modus ponens) is certainly not the same proposition as A is not B (the conclusion of the modus tollens). It may be added that the argument in its new form is irrelevant. In the categorical syllogism we have something precisely analogous. For given a major premiss All M is P, a relation between M and S may be the minor premiss (in which case M will be the middle term), or it may be the conclusion (in which case M will be the major term). Compare the syllogisms: All M is P, All S is M, therefore, All S is P ; All M is P, No S is P, therefore, No S is M.
(3) “The major in a so-called hypothetical syllogism consists of two propositions, the categorical major of two terms.” This merely tells us that a hypothetical syllogism is not the same in form as a categorical syllogism, but seems to have no bearing on the question whether the so-called hypothetical syllogism is a case of mediate or of immediate inference.
Turning now to the other side of the question no satisfactory answers seem possible to the following arguments in favour of regarding the mixed hypothetical syllogism as a case of mediate inference. In any such syllogism, the two premisses are quite distinct, neither can be inferred from the other, but both are necessary in order that the conclusion may be obtained. Again if we compare with it the inferences which are on all sides admitted to be immediate inferences from the hypothetical proposition, the difference between the two cases is apparent. From If P is true then Q is true, I can infer immediately If Q is not true then P is not true ; but I require also to know that Q is not true in order to be able to infer that P is not true.
357 And whether the mixed hypothetical syllogism can or can not be actually reduced to pure categorical form, it can at least be shewn to be analogous to the ordinary categorical syllogism, which is admitted to be a case of mediate reasoning. Moreover there are distinct forms—the modus ponens and the modus tollens—which are analogous to distinct forms of the categorical syllogism; and fallacies in the mixed hypothetical syllogism correspond to certain fallacies in the categorical syllogism.
The argument in favour of regarding the modus tollens—If P is true then Q is true, but Q is not true, therefore, P is not true—as mediate inference is still more forcible; but of course the modus ponens and the modus tollens stand or fall together.[387]
[387] In section [316] it will be shewn further that the hypothetical syllogism and the disjunctive syllogism also stand or fall together.
Professor Croom Robertson (Mind, 1877, p. 264) has suggested an explanation as to the manner in which this controversy may have arisen. He distinguishes the hypothetical “if” from the inferential “if,” the latter being equivalent to since, seeing that, because. No doubt by the aid of a certain accentuation the word “if” may be made to carry with it this force. Professor Robertson quotes a passage from Clarissa Harlowe in which the remark, “If you have the value for my cousin that you say you have, you must needs think her worthy to be your wife,” is explained by the speaker to mean, “Since you have &c.” Using the word in this sense, the conclusion C is D certainly follows immediately from the bare statement If A is B, C is is D; or rather this statement itself affirms the conclusion. When, however, the word “if” carries with it this inferential implication, we cannot regard the proposition in which it occurs as merely hypothetical. We have rather a condensed mode of expression including two statements in one; it may indeed be argued that in the single statement thus interpreted we have a hypothetical syllogism expressed elliptically.[388]
[388] Compare Mansel’s Aldrich, p. 103.