Page:Mind (New Series) Volume 12.djvu/508

 494 G. R. T. ROSS : The formula for a simple dilemma is : If A is B it is D and if A is C it is D But A is either B or C 7T~ AisD But as alternatives are exclusive, A is either not B or not C will be eqivalent to A is either B or C. If we take as an example of a minor premiss in a dilemma the statement which we find in Jevons (Elementary Lessons, p. 168) as conclusion of a destructive dilemma, that a person who speaks irreverently of Scripture is either not wise or not good and add as a major that we should cherish the company of one who is either wise or good, then on the theory of the equivalence of positive and negative disjunctions we should have to conclude that we should cherish the company of one who speaks irreverently of Scripture ! To avoid this result, those who hold to the position that a disjunctive judgment should express complete exclusion would have to maintain that the above negative disjunctions are carelessly worded ; but, as has been pointed out before, no amendment would be satisfactory that stopped short of the very far-fetched formula : ' He is either merely not wise or merely not good or neither wise nor good '. But it is quite unnecessary to adopt a form of words so remote from ordinary expression, for it can be shown that the disjunction serves all logical purposes (except indeed the establishment of a conclusion by the disputed modus ponendo tollens which will be discussed later on) if we interpret it as merely exhaustive without necessarily being exclusive, i.e., 1 If A is not b it is c ' is the only hypothetical necessarily implied in disjunction. The minor premiss of a dilemma is always a disjunction, but this disjunction enters the argument only so far as it is exhaustive; furthermore, however we interpret the minor premiss, whether as exhaustive only or both exclusive and exhaustive, the conclusion of the argument, when disjunc- tive, is proved only in so far as it is exhaustive, never as exclusive. Since hypothetical and disjunctive reasoning is true only in so far as it obeys the canons which were formulated first of all for the categorical syllogism, and since reasoning is perhaps clearest when reduced to that type, I propose to prove my last assertions by an analysis of a dilemma which reduces it to its categorical elements.