When such an argument as this is advanced, it must be with the knowledge that every other alternative has received satisfactory investigation. Without this assurance one could justly claim that the disease might have been caused by the _meat_ or _fish_ supply. Complete enumeration means that the investigation has narrowed the facts to the boundary of the field covered by the alternatives. The fallacy of incomplete enumeration is also one of “begging the question.” 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, ∴ He does not live in either Boston or Albany. or He does not live in New York, ∴ He lives in either Boston or Albany. (2) The season must have been either summer, or autumn, or winter, or spring; It was neither autumn, nor winter, nor spring, ∴ It must have been summer. or It was either autumn, or winter, or spring, ∴ It could not have been summer. =12. REDUCTION OF THE DISJUNCTIVE ARGUMENT TO THE HYPOTHETICAL AND THEN TO THE CATEGORICAL.= It would seem that the laws of the disjunctive contradict those of the categorical syllogism; for we apparently derive from two affirmatives a negative conclusion, and we also derive an affirmative conclusion when one premise is negative. This objection is seen to be nugatory when the disjunctive is reduced to the categorical form. The reduction involves the two steps of first changing the disjunctive to the hypothetical form and then to the categorical form. The following illustrations will suffice to make the matter clear: (1) _Disjunctive._ A is either B or C A is B ∴ A is not C _Hypothetical._ If A is B, then A is not C A is B ∴ A is not C _Categorical._ The case of A being B is the case of A not being C In this case A is B ∴ A is not C