more than two—and in this case may properly be Trilemma, Tetralemma, Polylemma. § 662. Its forms are as follow, and they are regulated by the combined laws of Hypothetical and Disjunctive Reasoning: : I. SIMPLE CONSTRUCTIVE. If A is B, C is D, and if X is Y, C is D; Therefore C is D. Here the common consequent is inferred. II. COMPLEX CONSTRUCTIVE. If A is B, C is D, and if X is Y, E is F; Therefore either C is D, or E is F. The point of these two forms is, that whatever alternative be chosen, the same conclusion is inevitable. III. DESTRUCTIVE. If A is B, C is D, and if X is Y, E is F; 512 CHAPTER XXXVIII. FALLACIES—FORMAL AND MATERIAL. (1.) FORMAL FALLACIES, § 663. Fallacy, in the widest sense of the term, includes every form of reasoning, or apparent reasoning, which leads to a conclusion either invalid, or such as ought not to be accepted, because of a fault in one or both of the premisses. A reasoning may be bad (1.) because the conclusion does not follow from the premisses; (2.) because the premiss or premisses are false in point of fact, or unduly assumed; (3.) because the conclusion is not the proof of the point which it is adduced to prove, or which the reasoner professes to prove. § 664. A fallacy is regarded either as a Paralogism or a Sophism, the former when the person reasoning is in error, either as to premiss or conclusion, and is at the same time unaware of it; the latter, when a reasoning, bad either in matter or form, or in both, is employed with a full consciousness of it on the part of the writer or speaker, and thus with the purpose of deceiving. This, of course, is of no logical importance. What the science of Logic professes to do is to deal with the essential character of the reasoning itself, -so far as its rules can reach it. § 665. Aristotle divides fallacies into two classes-viz., those παρὰ τὴν λέξιν and ἔξω τῆς λέξεως, or, as it was afterwards put, in dictione et extra dictionem—in the expression and beyond it. Under the first head-in Dictione-he classes six fallacies-viz. (1.) óμovvμía (equivocation); (2.) àμpißoλía (ambiguity); (3.) ovvbeσis (fallacia a sensu diviso ad sensum com positum); (4.) diaípeois (fallacia a sensu composito ad sensum divisum) ; (5.) προσωδία (accent); (6.) σχῆμα τῆς λέξεως (figura dictionis). § 666. Under the second head-extra Dictionem-he has seven classes: (1.) tapà тò ovμßeßŋkós (fallacia ratiocinationis ex accidente); (2.) tò átλŵs ʼn μǹ åñλôs (a dicto simpliciter ad dictum secundum quid); (3.) Tоù èλéyxov ayvola (ignoratio elenchi); (4.) парà тò éжÓμеνоv (fallacia ratiocinationis ex consequente ad antecedens); (5.) τὸ ἐν ἀρχῇ λαμβάνειν αἰτεῖσθαι (petitio principii); (6.) Tò un aitiov is actiov Tibévai (fallacia de non causa ut causa); (7.) τὸ τὰ πλείω ἐρωτήματα ἕν ποιεῖν (fallacia plurium interrogationum).1 § 667. Aristotle has thus really anticipated all the forms of fallacy which have been dealt with by subsequent logicians. But the division into in Dictione et extra Dictionem is not satisfactory or well founded. The class, in Dictione, may properly be referred to fallacies in the inference,-to cases, in fact, in which the conclusion does not follow from the premisses, that is, Formal Fallacies. § 668. Those under the second head, extra Dictionem, may as a rule be referred either to the class of formal fallacies, or to that of Material Fallacies, in which the conclusion, while following from the premisses, is based on false or irrelevant premisses. This will appear as we proceed. § 669. There is, properly speaking, no specific class of the fallacies of language (in Dictione). Language may doubtless. give rise to incorrect or invalid inference, but it does so because it leads to a violation of formal or logical law,— chiefly, in fact, to the making use of four instead of three terms in a reasoning. This is known as quaternio terminorum, or the logical quadruped. This is most commonly manifested in what is known as Ambiguous Middle; in other words, in the use of a term which indicates more than one notion, and which is taken in a double sense in the reasoning. For the ambiguity of a word does not necessarily lead to invalidity of inference, unless in so far as the ambiguity is made use of in the reasoning process. § 670. The only sound division of Fallacies accordingly is into (1.) those in which the fault is in the reasoning process itself,-in other words, those in which the conclusion 1 Top. viii. 11; De Soph. Elench., § i., c. iv. v. does not follow from the premisses; and (2.) those in which, while the conclusion is justly drawn, one or more of the premisses is incorrect, in point of fact, unduly assumed, or such as, while professedly meeting the point at issue, really do not, and only yield a conclusion irrelevant to the question proposed. Thus there emerge only two grand kinds of Fallacies -those in the Form and those in the Matter of the reasoning. § 671. It should be noted generally regarding fallacies, that several of them have a tendency to run into each other, and that a so-called reasoning may be fallacious in more than one way. It is enough, however, if a bad reasoning can be fairly referred to one class or species of fallacy. All that can be aimed at in the classification of fallacies is to make the classes as exact as possible,-to specify their discriminating feature, and to show generally how the particular fallacy is to be avoided. And this classification at present must be based on the logical point of view. The sources of fallacy and of sophism, lying in natural tendencies and in surrounding circumstances in the intelligence, and in the moral and imaginative nature of man, in impulses and preconceptions -form quite an independent sphere of inquiry. This was sketched in general, and, at the same time, grand outline by Bacon in his well-known Idola : 1 "A complete history of sophism," says a French writer, "would be the political history of mankind." § 672. Under the first head-the class of Formal Fallacy -we have the following: (1.) Those which violate the essential principle of the constitution of syllogism, as involving more than three terms. (2.) Those which proceed on the non-distribution of the middle term—that is, on its particular distribution in each premiss. (3.) Those that proceed on the universal distribution or quantification of major or minor term in the conclusion, while it was not taken universally in the premisses. (4.) Those which proceed to an affirmative conclusion, while one premiss is negative. (5.) Those which proceed on a so-called reasoning, in which neither premiss is affirmative. (6.) (In Hypothetical Reasonings.) Those which proceed 1 See Novum Organum, Book I. aph. xxxviii. et seq. from the denial of the antecedent to the denial of the consequent. (7.) Those which proceed from the affirmation of the consequent to the affirmation of the antecedent. These exhaust the possibilities of formal error in Mediate Inference. There are other possibilities of error in Immediate Inference, as in Conversion, Opposition, Integration, Restriction; but these have already been provided for in the rules. laid down regarding them.1 § 673. (1.) To the first of those heads-the quaternio terminorum-may be referred all the cases of what is known as Ambiguous Middle. Here we have really two middle terms whose difference is cloaked under some accident of expression; and thus, as we have a different concept in each of the premisses, the extremes of the conclusion have not been compared with the same third. Whately regards Ambiguous Middle as a semilogical fallacy—that is, partly in the matter (or expression), and partly in the form. It is essentially the latter a formal fallacy, for it misleads only through its informality. § 674. Fallacies whose invalidity arises from ambiguity in terms, and the formal vice of which is a quaternio terminorum, may be classed as follows: (1.) Homonymia, or Equivocation. (2.) Prosodia, or Accent. (3.) Amphiboly. (4.) Figura Dictionis, including Paronymous Words, Etymology, Figurative and Direct Sense. (5) Composition and Division, including the fallacy of Interrogation. (6.) Fallacia a dicto secundum quid ad dictum simpliciter ; and the converse, A dicto simpliciter ad dictum secundum quid. § 675. Those kinds of fallacies may be found in any term of a reasoning; but as a rule they are cases of what is known as Ambiguous Middle, the middle term being that upon which the conclusion essentially depends. In the case where a premiss is not false, or unduly assumed, and where the conclusion is not invalidly drawn from the premisses, the fault will usually be found in the double sense of the Middle Term. There we ought to look for it. 1 See above, chapters xxvii. and xxviii. |