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 or 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 attenton 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) adverecundiam, 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. 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 (N ovum 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 mains, 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.
Fallieres, Clement Armand (1841-), president of the French republic, was born at Mezin in the department of Lot-et-Garonne, where his father was clerk of the peace. He studied law and became an advocate at Nerac, beginning his public career there as municipal councillor (1868), afterwards mayor (1871), and as councillor-general of the department of Lot-et-Garonne (1871). Being an ardent Republican, he lost this position in May 1873 upon the fall of Thiers, but in February 1876 was elected deputy for Nerac. In the chamber he sat with the Republican Left, signed the protestation of the 18th of May 1877, and was re-elected in October by his constituency. In 1880 he became under-secretary of state in the department of the interior in the Jules Ferry ministry (May 1880 to November 1881). From the 7th of August 1882 to the 10th of February 1883 he was minister of the interior, and for a month (from the 29th of January 1883) was premier. His ministry had to face the question of the expulsion of the pretenders to the throne of France, owing to the proclamation by Prince Jerome Napoleon (January 1883), and M. Fallieres, who was ill at the time, was not able to face the storm of opposition, and resigned when the senate rejected his project. In the following November, however, he was chosen as minister of public instruction by Jules Ferry, and carried out various reforms in the school system. He resigned with the ministry in March 1885. Again becoming minister of the interior in the Rouvier cabinet in May 1887, he exchanged his portfolio in December for that of justice. He returned to the ministry of the interior in February 1889, and finally took the department of justice from March 1890 to February 1892. In June 1890 his department (Lot-et-Garonne) elected him to the senate by 417 votes to 23. There M. Fallieres remained somewhat apart from party struggles, although maintaining his influence among the Republicans. In March 1899 he was elected president of the senate, and retained that position until January 1906, when he was chosen by a union of the groups of the Left in both chambers as candidate for the presidency of the republic. He was elected on the first ballot by 449 votes againt 371 for his opponent, Paul Doumer.
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