Page:Mind (New Series) Volume 12.djvu/507

THE DISJUNCTIVE JUDGMENT. 493 ponens and the modus ponendo tollens in the disjunctive syllo- gism are valid. But whether the major premiss be "A is- either B or C " or " A is either not B or not C," we can by applying the same minor premisses get the same conclusion. (1) A is either B or C (2) A is either B or C A is not B A is B .-. AisC /. " A is not C (1) A is either not B or not C (2) A is either not B or not C A is not B A is B A is C /. A is not C But surely it is clear that when we say "A is either B or C " we do not mean the same thing as " A is either not B or not C " and vice versa. If some one tells us he has seen a ghost, we may declare that he is either not sane or not telling what he believes to be the truth. But it would be rather perplexing for the person who uttered this to be assured that from his assertion could be inferred the other that the ghost-seer was either sane or truthful. While admitting that sanity and truthfulness in a ghost-seer are exclusive of each other he would not desire to make any disjunction between these qualities. He means that no person who asserts that he has seen and talked with a ghost and is sane, is truthful, but not that all such who are insane are truthful. Many people may be neither sane nor truthful. (Note. Diagrams to represent the three possible cases of relation of b and c. (1) (cl?Y"""e*/ b'a& + bee both true. C (2) Q^T ~>TCN _fcy 6ec alone true. (3) vQ^tT-.^ / fc'ac alone true. The above example is illustrated by (2) if b and c are taken to represent ' truthful ' and ' sane ' respectively. The dis- junction is exhaustive between b' and c', for all not b' is c' all b is c' = no b is c.) Again, since on the exclusive interpretation of disjunction " A is either B or C " and " A is either not B or not C " are equivalent expressions, it will be impossible to commit the fallacy of denial of the antecedent or affirmation of the consequent in dilemma.