534 CHAPTER XXXIX. FALLACIES (2.) MATERIAL FALLACIES. $709. Before proceeding to consider the Material Fallacies, or those in which, while the conclusion actually follows from the premisses, it is yet incorrect in point of fact, or irrelevant to the point at issue, it is necessary to observe the relations of true and false premisses to the character of the conclusion, as itself true or false. On this subject the following rules may be laid down :— (1.) If both premisses be true, that is, correct representations of reality, and if the conclusion be validly drawn therefrom, we have the certainty of a true conclusion, or judgment in harmony with fact. This is grounded, as Aristotle has pointed out, on the law of Non-contradiction. If A being, B necessarily is; and B not being, A necessarily is not; then if A is true, B is necessarily true: otherwise, the same thing (A) would at one and the same time be and not be.1 (2.) If one premiss be true, and the other false, or even if both premisses be false, and the conclusion be correctly drawn from them, the conclusion may yet be true in point of fact. In this case we have not a sufficient reason for our belief in the truth of the conclusion, so far as this argument goes; but we may still correctly hold the conclusion as true in point of fact. (a) One premiss false. Thus : No white is animate; All snow is white; Therefore no snow is animate. 1 An. Pr., ii. 2. Here the conclusion is true in point of fact, but not because of the reason given. (b) Both premisses false. Thus : No man is animate; Every stone is a man; Therefore no stone is animate. Here, also, the conclusion is true in point of fact, but not because of the reason given. In these cases the true emerges by chance, as Aristotle remarks—not from the necessity of things. To suppose this rule otherwise would be to fall into one form of the hypothetical fallacy already noticed-viz., the antecedent is not, therefore the consequent is not : If man is, animal is; But man is not; This is really equivalent to the fallacy of supposing that because the reason is false, the conclusion alleged to be founded on it is false; or because a reason adduced has been disproved, the conclusion has necessarily and absolutely been disproved. Suppose a person argues for the existence of Deity from the alleged fact of its being universally believed, or believed by all nationalities, an opponent might conceivably overthrow the proof by adducing an instance of a nation in which no such belief exists. In this case the proof would go for nothing; but it would be a fallacy to suppose that the conclusion was absolutely disproved. § 710. (3.) If the conclusion be false, and there be no flaw in the reasoning, one or other of the premisses must be false. If the conclusion be true, the truth of the premisses is not thereby guaranteed; but if the conclusion, formally valid, is false, the falsity of a premiss, one or both, is established.1 This principle is of the utmost importance in examining a hypothesis. From a false hypothesis you may deduce a true proposition, as Ptolemy did, when, from an incorrect description of the celestial movements, he deduced the nature 1 See An. Pr., ii. 4. and periods of the eclipse of the moon, and the duration of the month and year. In these cases, conclusions true in point of fact were drawn from erroneous premisses. It comes to this, that the antecedent may, and therefore commonly does, extend more widely than the antecedent as predicate to the subject; for what springs from this cause may also issue from another. For example, if you cut a right cone so by the plane, that the section is parallel to the base, there will be a circle; but if there be a circle, this is rarely the cause of it.1 § 711. Material Fallacies depend either (1.) on the falsity of the premiss or premisses, or (2.) on the undue assumption of a premiss, or (3.) on the irrelevancy of the conclusion in respect of the question proposed or point at issue. § 712. (1.) With regard to false premisses, the conclusion correctly drawn from them may be either true or false. But this of course is by accident; and there is no reason or necessity which, in the argument, can be held as guaranteeing it. This is known as the fallacia falsi medii, as it is on the connection of the middle term with the extremes, in this case unreal, that the conclusion is supposed to turn. § 713. The fallacy of Imperfect Disjunction may be taken as an instance of a false premiss. In Indirect Proof, which depends mainly on disjunction, and a disjunctive major premiss, fallacy frequently arises from an incompleteness in the disjunctive statement. The principle of disjunction is, as we have seen, the full statement or exhaustion of the possibilities of the case, and a consequent reasoning from affirmation to negation, or negation to affirmation. Clearly, then, if we omit a possible case to start with, our conclusion will be materially false. § 714. In Mathematics, complete disjunction is easily accomplished—as when we say, rectilineal triangle is either rectanoular, or obtuse angular, or acute angular. If this figure is not the first, it is either the second or third. But in the Observational and Moral Sciences this is not so easily carried out. In Theology our disjunction is often purely nominal, as turning on a subject which is incapable, from its nature, as transcending experience, of strict definition and exhaustive possibilities. 1 Cf. An. Pr., ii. 4; and Trendelenburg in loco, El Log., § 32. Thus, it has been argued that we cannot live happily in this world, since in life we must either abandon ourselves to our passions, or combat them.1 If we do the former, we have no happiness, but a feeling of shame and dissatisfaction. If we do the latter, we live in a constant state of internal warfare, and, therefore, of pain. This disjunction is incomplete, inasmuch as we omit the alternative of reasonable control and temperance in life, which may lead to happiness, perhaps alone to what people call happiness. We have an illustration of imperfect disjunction in the case of the reasoning of the Islanders of Otaheite, when Captain Cook arrived on their shores, bringing a sheep in his vessel. They were puzzled at first, not having seen quite such an animal before. How was it to be classed? All the creatures known to them were pigs, dogs, rats, and birds. The new object appeared to be neither a pig, nor a dog, nor a rat, therefore they concluded it was a bird of some new sort, for birds were to them of varied kinds. § 715. In a reasoning, whether simple or complex, there are two essential rules. (1.) "That no proposition [which is provable] be employed as a principle of probation, which stands itself in need of proof. (2.) "That nothing else be proved than the proposition for whose proof the probation was instituted." 2 The first of these rules should be qualified by the terms in square brackets. There are propositions of immediate certainty, which may be employed legitimately in probation. These two rules embrace the various forms of formal fallacy, known as (1.) Petitio principii, or Fallacia quæsiti medii, τὸ ἐν ἀρχῇ αἰτεῖσθαι. (2.) Ύστερον πρότερον. (3.) Circulus in demonstrando,-diallelus,—ó d' åλλýλwv τρόπος. (4.) Saltus vel Hiatus in demonstrando, Leap in Probation. (5.) Heterozetesis, Ignoratio vel Mutatio Elenchi, and Transitus in aliud genus, vel a genere ad genus,-petáßaois eis ἄλλο γένος. § 716. Petitio Principii, taken first in its wider sense, de 1 Cf. Reiffenberg, Logique, p. 101. For some excellent illustrations of incomplete disjunction in Apagogical Demonstration, see Ueberweg, Logic, p. 532. 2 Hamilton, Logic, iv., L. xxvi. p. 52. notes any reasoning in which a premiss is assumed, the certainty of which is not greater than that of the conclusion it is adduced to prove, and which may be doubted on the same grounds as the conclusion itself. This is the undue assumption of a premiss in the widest sense,-a premiss open to doubt, uncertain, not conceded by the opponent, or not properly to be conceded by him, unless it can be established on grounds similar to those which would establish the conclusion. By the older logicians this was expressed by the assumption, "Id quod æque ignotum est ac ipsa quæstio."1 Hamilton gives as an illustration of Petitio Principii in this its wider sense, Aristotle's argument for slavery. The barbarians, as of inferior intellect, are the bondsmen of the Greeks, and the Greeks, as of superior intellect, are the born masters of the barbarians. Here, of course, the assumption in the premisses of relative inferiority would be questioned by an opponent as much as the conclusion itself. An opponent of slave-holding might be met by the proposition or argument that slavery is to be upheld because it brings cheap labour, and this is an advantage to the general social wellbeing. The opponent might very fairly reply that this advantageeven if admitted-is not proved to counterbalance the disadvantages of slave-holding, in its bearings on the moral and social character of the people among whom it subsists. He might urge, besides, that the conclusion is irrelevant to the true and higher point at issue as to whether slavery is permissible at all on moral grounds. This runs into a case of the fallacy to be noticed below-known as Ignoratio Elenchi. § 717. What is known as the saltus or leap in a probation may, as Hamilton points out, be reduced to the first form of the Petitio Principii. We may, for the sake of brevity, omit propositions in a proof; this is not the saltus proper. We do so in the Sorites, which is quite valid. But when, in a series of reasonings, we pass from one proposition to another, which is not logically connected with the former, except through another intermediate proposition, which we have not proved, then we commit a saltus. This, in fact, is simply an instance of an unduly assumed premiss,-generally, as if it did not need proof, while it does require it. 1 Cf. Duncan, Inst. Log., v. p. 321. Thus: 2 Logic, iv. L. xxvi. |