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 VIII. CORRESPONDENCE. Mr. Monck, in his review of my Elements of Logic (Mixo XXXII., 603), has touched on one or two points in which I have ventured to deviate from the beaten track. As the questions raised may perhaps be of interest to logicians gent- rally, may I ask permission to make some observations in explanation and defence of my views ? The first point relates to Reductio per (or ad) Impossibik. Logicians have sometimes objected to this process as " awkward, roundabout, and operose " (Bowenl The way in which it is usually stated is indeed needlessly awk- ward. But my objection is more fundamental. I maintain that it is a delusive process, inasmuch as it is not really Keduction at all. My argu- ment, which was published at length in Hermathena for 1881, is as follows : The true use of Reduction is to show that all mediate reasoning is capable of being brought under one type, that to which Aristotle's Dictum applies. Hence in the case of any given syllogism the problem of Reduction is : From the given premisses to deduce the required conclusion by reasoning which (so far as it is not immediate) is wholly in the first figure. This is what is actually done in the case of all the moods except Baroko and Bokardo. Let us confine ourselves to Baroko. ' Every P is M ; Some S is not M ; therefore Some S is not P.' This is ' reduced ' to Barbara thus : ' Every P is M ; Every S is P ; therefore Every S is M '. So far, well ; but how do we elicit from this the required conclusion, ' Some S is not P ' ? Thus : ' Since the conclusion is false and Some S is not M, one of the premisses must have been false ; and, as the major was given true, the minor was false, and therefore Some S is not P '. Now what I say is, that since this latter piece of reasoning is clearly an essential step in the argument, we are bound to put it into the first figure, and hitherto it has not been shown that this is possible. All that the syllo- gism in Barbara has done for us is to show that, granting that ' Every P is M, ! we have a right to say that. ' If every S is P, then every S is M :. We then reason from the denial of the consequent and say, ' But Some S is not M, therefore Some S is not P '. Mr. Monck has taken precisely the same view of the function of this syllogism in Barbara. He says : " Vhen this new conclusion is reached, we have established that, if the original con- clusion is false (that is, if its contradictory is true), either the Retained Premiss or the Suppressed Premiss, or both of them, are false ; whence it follows, again, that if both premisses are true, the original conclusion is true also" (Introduction to Logic, p. 179). I think the reasoning is less awkward if we state once for all that the premiss ' Every P is M ' is granted ; we have then a conditional argument founded on Barbara which is natural enough. It is also easy enough to reduce it to a categorical form, thus : For the conditional : ' If every S is P, even- S is M ' ; we substi- tute the categorical equivalent : ' Every P is M '. But as the denial of the consequent gave us ' Some S is not M,' for our minor, we have simply got back our original friend Baroko. Mr. Monck's criticism is as follows : " In every syllogism the truth of the conclusion depends on the hypothesis that the premisses are true, and if this hypothesis is sufficient to render the reasoning hypothetical, every syllo- gism is a hypothetical syllogism. But if the distinct existence of the cate- gorical syllogism is conceded, where is the material difference between showing that the conclusion is true on the hypothesis that the premisses are true, and showing that one (at least) of the premisses is false, on the