Page:Mind (New Series) Volume 12.djvu/506

 492 G. E. T. BOSS: until the alternative terms both stand for positive concepts, until we know what we mean by b' (in our illustration acute and obtuse angled), in which case our judgment is better symbolised by "A is either B or C" than by "A is either B or B' ". We have then to interpret what we mean by a real dis- junction, one in which C is not by definition not-B. It is still apparent in those disjunctions that a categorical basis is assumed. When we say such and such a kind of flower blooms either in spring or in autumn, "blooms" is the predicate categorically asserted, and when we declare that some one is either a fool or a rogue, objectionable person is probably the basal quality common to both. Now there are three possible suppositions as to the rela- tion between b and a in real disjunctions. (1) That both propositions hold, both "If A is not b it is c " and "If A is b it is not c" (b'ac + bee). This is the exclusivist theory and its supporters point to such judgments as "lines are either straight or curved," "organ pipes are either closed or open " in seeking evidences for their plea. The special type of such judgments as those last quoted, where it is apparent that both the independent assertions S'aP and SeP are true, will be investigated later on. (2) Then there is the possibility that b and c may be exclusive but need not between them exhaust the whole of the proximate genus, e.g., dog and wolf do not exhaust the Canidae. Such a statement, however, is not a disjunction. Logicians are quite clear that the disjunctive judgment is at least exhaustive, that all not-6 is c. If I say " this species of fish is found either in lakes or rivers," when I know that it is found also in the ocean, I make a misleading statement. (3) There is lastly the possibility that b and c may be merely alternatives not mutually exclusive, as, e.g., fool and rogue. Now if the first possibility is true and both the hypotheticals "If A is not b it is c " and "If A is b it is not c " are to be found in the disjunction, it will follow that " A is either B or C " and "A is either not B or not C " mean exactly the same thing; for the former is equivalent to " If A is not b it is c " and " If A is b it is not c " (all not b is c + no b is c) and the second becomes "If A is not not-6 it is not c " and " If A is uot-b it is not not-c " ; these simplified come to " If A is b it is not C " and " If A is not b it is c " exactly the same pair of propositions as the other disjunction yielded. This result can be shown in another way. According to the theory of complete exclusion both the modus tollendo