Page:Mind (New Series) Volume 12.djvu/509

 THE DISJUNCTIVE JUDGMENT. 495 The simplest and normal type of complex constructive dilemma is : If A is B it is D = all b is d = bad If A is C it is F = all c is / = caf A is either B or C = if A is not b it is C = b'ac ( + if A is b it is not c = bee} .'. A is either D or F = if A is not d it is / = d'af It will be shown that from the given premisses the con- clusion cannot be made to yield if A is d it is not / = def. From the various premisses shown above we have to elicit a conclusion showing a relation between d and /. Take the minor b'ac; this gives by immediate inference c'ab, which combined with the first limb of the major, bad, gives as con- clusion c'ad : bad b'ac = c'ab c'ad Similarly b'ac and caf give b'af. Again c'ad = d'ac + caf give d'af, i.e., all not d is/ = if A is not d it is/; which is the same as ' A is either D or F,' interpreted only exhaustively. And it can be easily seen that, however we interpret the minor, it is impossible to reach the conclusion def = no d is /; for bee with bad will yield no universal conclusion, nor will it do any better when taken along with caf. Hence, as there is no other available premiss, there is no way of reach- ing the conclusion def, which we should have to do if ' A is either D or F ' were exclusive. A man at the top of a burning house may reason thus, ' If I jump from the window I shall break my leg and if I do not I shall be burned to death'. Between jumping and not jumping there is no middle course. These two alternatives exclude one another and exhaust all the possibilities (it is a case of a priori disjunction), but though the minor premiss is, in this case, both exhaustive and exclusive, the conclusion cannot be held to be so. It is "I must either get my leg broken or be burned to death ". But this can only be held to mean "If I do not face the certainty of getting my leg broken I shall be burned to death " and its equivalent " If I escape death by burning it will be only at the cost of a broken leg ". But the unfortunate man cannot be sure that the accident to his limb will procure him safety from burn- ing (he might be scorched fatally even though he took the leap) ; nor can he promise himself that he will not break his leg before the flames consume him. It is obvious then that