Other examples of a possible incomplete enumeration:
(1) “Jones lives either in Boston or New York.”
(2) “Mary is studying either algebra or geometry.”
(3) “He either committed suicide or was lynched.”
(4) “Either the Giants or the Boston Americans will win the pennant.”
11. SECOND RULE OF DISJUNCTIVE ARGUMENTS.
The second rule is made so self evident by the first that there is little need of a detailed discussion concerning it. The rule is this: When the minor premise affirms or denies one of the alternatives of a logical disjunction, the conclusion must, in order, deny or affirm all of the others. To put it differently: When the “minor” affirms, the conclusion must deny every other alternative, and vice versa. When there are but two alternatives reference to any of the foregoing disjunctive arguments will make the rule clear. There may be, however, more than two alternatives. In such a case, if the first rule is observed then the second becomes applicable.
ILLUSTRATIONS:
(1) John Doe lives either in Boston, Albany, or New York;
He lives in New York,