The fallacy of accident, we have learned, occurs when one reasons from a general truth to an accidental case; whereas the fallacy of division obtains when one reasons from a collective use of a term to a distributive use; in both cases the procedure is from a larger unit to a smaller unit. Moreover, with converse accident and composition, the movement is from the smaller unit to the larger. Because of this similarity there is danger of confusing the two kinds of fallacies. As a matter of distinction between the fallacies of accident, and composition and division the attending comparative résumé may be of value:
(1) Division is similar in movement to accident, while composition resembles converse accident.
(2) A valuable cue for remembering which way division and accident move, is to recall that division in arithmetic is a procedure from the larger unit to the smaller, and therefore that division in logic would have the same signification.
(3) Division and composition pertain to mathematicalwholes; while accident and converse accident relate to logical wholes.
(4) The aggregates of division and composition may be counted or enumerated easily; while the accident and converse accident aggregates (or generals) are not easily enumerated.
(5) Division and composition relate to logical terms, whereas accident and converse accident relate to general truths.
(6) Division and composition use a term in a collective sense and then in a separate or distributive sense, or vice versa; accident and converse accident use a thought in a general and then in an accidental sense, or vice versa.
Irrelevant Conclusion (Ignoratio Elenchi).
The fallacy of irrelevant conclusion results when the argument does not squarely meet the point at issue. It is the fallacy of arguing to the wrong point either purposely or through ignorance. One in defense, who has a weak case, may be tempted to divert attention from the point in hand, realizing that a close analysis of the matter in dispute will tend to his undoing. In such instances (1) the lawyer will abuse the plaintiff, (2) the demagogue will tell humorous stories, (3) the teacher will take advantage of the ignorance of the pupil, (4) the scholar will refer to authority and (5) the magnate will fall back upon the power of position and wealth. These forms of “rhetorical thinking” are as harmful as they are popular,and furnish one of the chief reasons for giving to the common people a better understanding of “how to think” as well as “how not to think.”
Definite names have been given to the various forms of irrelevant conclusion which may be summarized as follows: