Fallacy

Fallacy (Lat. fall-ax, apt to mislead), the term given generally to any mistaken statement used in argument; in Logic, technically, an argument which violates the laws of correct demonstration. An argument may be fallacious in matter (i.e. misstatement of facts), in wording (i.e. wrong use of words), or in the process of inference. Fallacies have, therefore, been classified as: I. Material, II. Verbal, III. Logical Of Formal; II. and III. are often included under the general description Logical, and in scholastic phraseology, following Aristotle, are called fallacies in dictione or in voce, as opposed to material fallacies in re or extra dictionem.

I. Material.—The classification widely adopted by modern logicians and based on that of Aristotle, Organon (Sophistici elenchi), is as follows:—(1) Fallacy of Accident, i.e. arguing erroneously from a general rule to a particular case, without proper regard to particular conditions which vitiate the application of the general rule; e.g. if manhood suffrage be the law, arguing that a criminal or a lunatic must, therefore, have a vote; (2) Converse Fallacy of Accident, i.e. arguing from a special case to a general rule; (3) Irrelevant Conclusion, or Ignoratio Elenchi, wherein, instead of proving the fact in dispute, the arguer seeks to gain his point by diverting attention to some extraneous fact (as in the legal story of “No case. Abuse the plaintiff’s attorney”). Under this head come the so-called argumentum (a) ad hominem, (b) ad populum, (c) ad baculum, (d) ad verecundiam, common in platform oratory, in which the speaker obscures the real issue by appealing to his audience on the grounds of (a) purely personal considerations, (b) popular sentiment, (c) fear, (d) conventional propriety. This fallacy has been illustrated by ethical or theological arguments wherein the fear of punishment is subtly substituted for abstract right as the sanction of moral obligation. (4) Petitio principii (begging the question) or Circulus in probando (arguing in a circle), which consists in demonstrating a conclusion by means of premises which presuppose that conclusion. Jeremy Bentham points out that this fallacy may lurk in a single word, especially in an epithet, e.g. if a measure were condemned simply on the ground that it is alleged to be “un-English”; (5) Fallacy of the Consequent, really a species of (3), wherein a conclusion is drawn from premises which do not really support it; (6) Fallacy of False Cause, or Non Sequitur (“it does not follow”), wherein one thing is incorrectly assumed as the cause of another, as when the ancients attributed a public calamity to a meteorological phenomenon; (7) Fallacy of Many Questions (Plurium Interrogationum), wherein several questions are improperly grouped in the form of one, and a direct categorical answer is demanded, e.g. if a prosecuting counsel asked the prisoner “What time was it when you met this man?” with the intention of eliciting the tacit admission that such a meeting had taken place.

II. Verbal Fallacies are those in which a false conclusion is obtained by improper or ambiguous use of words. They are generally classified as follows. (1) Equivocation consists in employing the same word in two or more senses, e.g. in a syllogism, the middle term being used in one sense in the major and another in the minor premise, so that in fact there are four not three terms (“All fair things are honourable; This woman is fair; therefore this woman is honourable,” the second “fair” being in reference to complexion). (2) Amphibology is the result of ambiguity of grammatical structure, e.g. of the position of the adverb “only” in careless writers (“He only said that,” in which sentence, as experience shows, the adverb has been intended to qualify any one of the other three words). (3) Composition, a species of (1), which results from the confused use of collective terms (“The angles of a triangle are less than two right angles” might refer to the angles separately or added together). (4) Division, the converse of the preceding, which consists in employing the middle term distributively in the minor and collectively in the major premise. (5) Accent, which occurs only in speaking and consists of emphasizing the wrong word in a sentence (“He is a fairly good pianist,” according to the emphasis on the words, may imply praise of a beginner’s progress, or an expert’s depreciation of a popular hero, or it may imply that the person in question is a deplorable violinist). (6) Figure of Speech, the confusion between the metaphorical and ordinary uses of a word or phrase.

III. The purely Logical or Formal fallacies consist in the violation of the formal rules of the Syllogism (q.v.). They are (a) fallacy of Four Terms (Quaternio terminorum); (b) of Undistributed Middle; (c) of Illicit process of the major or the minor term; (d) of Negative Premises.

Of other classifications of Fallacies in general the most famous are those of Francis Bacon and J.S. Mill. Bacon (Novum organum, Aph. i. 33, 38 sqq.) divided fallacies into four Idola (Idols, i.e. False Appearances), which summarize the various kinds of mistakes to which the human intellect is prone (see Bacon, Francis). With these should be compared the Offendicula of Roger Bacon, contained in the Opus maius, pt. i. (see Bacon, Roger). J.S. Mill discussed the subject in book v. of his Logic, and Jeremy Bentham’s Book of Fallacies (1824) contains valuable remarks.

See Rd. Whateley’s Logic, bk. v.; A. de Morgan, Formal Logic (1847); A. Sidgwick, Fallacies (1883) and other text-books. See also article Logic, and for fallacies of Induction, see Induction.

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