Other examples where the terms of the disjunctive may not be mutually exclusive:
(1) “Lord Bacon was either exceedingly studious or phenomenally bright.” (Undoubtedly he was both.)
(2) “This teacher is a graduate either of Harvard or of Yale.” (Perhaps both.)
(3) “The defendant is either a liar or a thief.” (The one often leads to the other.)
(4) “To succeed one must either seize the opportunity as it passes or make his own.” (The best success results from doing both.)
Incomplete enumeration:
The cause of the disease was either the water or the milk,
It was not the milk,
∴ It was the water.
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.”