ARISTOTLE ON THE LAW OF CONTRADICTION. 217 let the following group of dots ||| represent all A ; then the major premiss predicates B of the entire number of dots in the group. The minor premiss tells us that All C is A, which means that all C is in the above group, say all those below the line. Then to say in the conclusion All C is B is to predicate of the dots below the line what was before predicated of these dots plus those above the line. No account was here taken of the law of con- tradiction. It is evident, therefore, that the syllogism would still remain, if the law of contradiction were banished from logic. To be sure, on the latter hypothesis the conclusion " All C is B " would not exclude "all C is not-B," but neither does it do this in our actual logic in virtue of the syllogism. It does this because the major premiss does it (the conclusion never adds to the major premiss), and the major premiss does it in virtue of the law of contradiction. The same result can be brought about without the law of contradiction by explicitly denying not-B in the major premiss ; thus, "All A is B and not not-B ". Then the conclusion, which does nothing more than repeat part of the major premiss, would here likewise state " All C is B and not not-B ". The only difference is that that which our actual logic finds it unnecessary to state explicitly because it assumes it as true a priori and universally, our hypothetical logic would have to state explicitly on the strength of experience. Moreover, since the conclusion " All C is B " excludes " All C is not-B " solely by the authority of the major premiss, it is not even in the actual logic necessary to assume the law of contradiction in the minor premiss, " All C is A," for it is evident that the conclusion would still hold, if it were true also that " All C is not-A " ; since the major premiss "All A is B " does not exclude not-A from being B. Here one may urge, granting that the syllogism would survive this hypothesis, that all its usefulness would be gone. Of what use, one would say, can a syllogism be, the conclusion of which does not exclude its opposite? Does not all our action depend upon our certainty as to the exclusion of the contrary? My answer would be that the fault is not with the syllogism but with the judgment ; for it is the latter that excludes or does not exclude the contrary ; and the judgment as an expression of the result of experience cannot be blamed for not excluding what experience shows to be compatible, any more than the judgment in actual logic can be blamed for not giving us information upon an in- definite number of attributes which we should very much like to know. Thus " All A is B " tells us nothing about C or D or E. The view here defended, that the syllogism does not presuppose the law of contradiction, is held by no less an, authority in logic than Aristotle. In a passage in the Posterior Analytics, which I shall now proceed to discuss, Aristotle states the thesis and proves it ; though, surprisingly enough, Waitz and his followers misunderstood its import. 1 1 After this paper was written I found that Maier, Die Syllogistik (Ax Aristoteles, ii., pt. 2, p. 238, note 3, understands the passage as 1 do.
