requiring proof, or all proof would be impossible, as there would be no starting point for the process. The fallacy in this form is, then, not committed whenever a proposition is assumed without proof, but when the proposition thus assumed is one which needs just the same kind of proof, bearing on just the same point, as the proposition which is to be deduced from it. "Sound probation," says Dr. Davis, "must depart from such principles as are either immediately given as ultimate, or mediately admit of proof from other sources than the proposition itself in question.' As examples of this form of the fallacy we may give : His cowardice may be inferred from his cruelty, for all cruel men are cowards'; 'A table of logarithms must be entertaining, for all books are so.' A striking example is found in the First Chapter of Mr. Spencer's Education. After stating that " acquirement of every kind has two valuesvalue as knowledge and value as discipline," Mr. Spencer goes on to discuss the value of different subjects from the point of view of knowledge. He then turns to the disciplinary value of studies, and commences his disquisition with the following flagrant petitio:-" Having found what is best for the one end, we have by implication found what is best for the other. We may be quite sure that the acquirement of those classes of facts which are most useful for regulating conduct, involves a mental exercise best fitted for strengthening the faculties. would be utterly contrary to the beautiful economy of Nature, if one kind of culture were needed for the gaining of information and another kind were needed as a mental gymnastic." It It is this mode of the fallacy which is referred to when it is said that the syllogism is a petitio principii. The other modes of petitio principii are not of much importance. The third mode-of assuming the particular to prove the universal which involves it-is of the nature of a generalisation from simple enumeration." Aristotle himself seems to be guilty of this when he maintains that slavery is in accord with natural law, on the ground that 1 Op. cit., 2 See pp. 271-275, the neighbouring barbarians, being inferior in intellect, are the born bondsmen of the Greeks."1 The fourth mode is only a variety of the first. Thus, to take Aristotle's example, when, in trying to show that the healing art is knowledge of what is wholesome and unwholesome, it is successively assumed to be the knowledge of each. The fifth mode is when a proposition which is in reciprocal relation to another proposition is assumed as a means of proving the latter. Aristotle's example is the assumption that the side of a square is incommensurable with the diagonal when the proposition to be proved is that the diagonal is incommensurable with the side. Other examples are: London is north of Brighton, therefore, Brighton is south of London; Philip was the father of Alexander, therefore, Alexander was the son of Philip; 'Everywhere the light of life and truth was lacking, for darkness covered the earth, and gross darkness the people.' In all these cases we have obviously no passage of thought; it is the same judgment which is expressed in different words; nor does the new expression unfold any meaning which was previously implicit. 2. Ignoratio Elenchi.-By an elenchus-i.e. a refutation-Aristotle meant a syllogism with a conclusion contradictory of the thesis to be refuted. The ignoratio elenchi was then applicable only to disputation, and consisted in arguing beside the mark, in answering to the wrong point, in establishing a proposition which did not overthrow the original thesis. But the scope of the fallacy may well be extended-as it usually is by modern logicians -to include all cases in which instead of the required conclusion, a proposition which may be mistaken for it is established. This might appropriately be called ignoratio or mutatio conclusionis. In every case the error consists in proving the wrong point. It is thus a violation of the most general rule of method-to be clear as to the purpose. As an example of ignoratio elenchi we may take 1 Davis, op. cit., p. 289. See Aristotle, Politics, i. 2. the common argument against a classical education that "throughout his after career, a boy, in nine cases out of ten, applies his Latin and Greek to no practical purposes. This is to ignore the fact that the advocates of a classical education do not claim that Latin and Greek are of direct use in practical life. What they do urge is that the study of the classics furnishes an unrivalled mental training; and it is to the disproof of this proposition that a true elenchus must be addressed. No fallacy is more common or more easily committed than ignoratio. Anyone who has had experience of disputations and debates knows how constantly recurrent is the tendency to wander from the real point at issue, especially when the subject under discussion is a wide one, and how necessary it is for a speaker occasionally to begin his remarks by reminding the disputants what the question under discussion really is. This tendency must be guarded against especially when any practically important results flow from the conclusion reached. Thus, as De Morgan tells us : "The pleadings in our courts of law, previous to trial, are intended to produce, out of the varieties of statement made by parties, the real points at issue, so that the defence may not be ignoratio elenchi, nor the case the counter fallacy ignoratio conclusionis. If a man were to sue another for debt, for goods sold and delivered, and if the defendant were to reply that he had paid for the goods furnished, and plaintiff were to rejoin that he could find no record of that payment in his books, the fallacy would be palpably committed. The rejoinder, supposed true, shows that either defendant has not paid, or plaintiff keeps negligent accounts; and is a dilemma, one horn of which only contradicts the defence. It is plaintiff's business to prove the sale from what is in his books, not the absence of payment from what is not, and it is then defendant's business to prove the payment by his vouchers."2 This leads on to that form of the fallacy which consists in throwing the burden of proof on the wrong side. Proof of an assertion should generally be given by the person 2 Op. cit., p. 260. 1 Spencer, Education, Ch. I. who makes that assertion, and to endeavour to transfer to an opponent the task of proving the negative of that assertion is an ignoratio elenchi. It is often said that it is difficult, if not impossible, to prove a negative. And this is true so long as the negative is a bare denial. But the establishment of every positive proposition proves a number of negatives. If, then, the number of possible alternatives are few, the proof of any one of them negates all the others. This principle is adopted in law. "For instance, a homicide, as such, is considered by the law as a murderer unless, failing justification, he can prove he had no malice. . . The case stands thus:—the alternatives are few, so that proving the negative of one, which the accused is called on to do, can be done by proving the affirmative one out of a small number. There is but malice, heat of blood, misadventure, insanity, etc., to which the action can be referred. Of these few things it is easier for the accused to establish some one out of several, above all when motive is in question (of which only himself can be in possession of the most perfect knowledge), than it is for the prosecutor to establish a particular one. Another principle on which he is called on to establish a negative (or rather another positive) is that the burden of proof fairly lies on the one to whom it will be by much the easiest."1 One form of the fallacy is to confuse objections against the thesis proposed with its disproof. Especially is this likely to be committed when the question at issue is some proposed change, say in the law. Against most reforms some objections can be urged, but to treat these as necessarily fatal is an ignoratio elenchi; the point to be established is that those objections outweigh the reasons for the proposed change, and simply to point out their existence is entirely beside the mark. One common specimen of this form of the fallacy is to object to a certain conclusion as tending to establish a position deemed undesirable. Here we have what De Morgan calls "the great fallacy of all, the determination to have a particular conclusion, and to find 1 De Morgan, ibid., p. 261. arguments for it,"1 coming into play. The conclusion being fore-ordained, all arguments which make against it are refused a hearing. Another form of the fallacy is to prove, or disprove, part of what is required, and to dwell on that to the exclusion of the remainder. Thus, if one disputant supports a conclusion by weak arguments, his opponent may confine himself to showing the weakness of his arguments, and leave his readers or hearers to infer that, consequently, the conclusion drawn from those arguments is false. The handle thus given to the enemy should be a warning against the practice of urging bad arguments in support of a good cause. A more extreme case of the same mode of committing the fallacy is the taking exception to a mere illustration or part of an illustration, which has no essential connexion with the point in dispute. The very use of illustration at all is liable to be an ignoratio elenchi. For an illustration is intended to make some point of difficulty clearer and easier of comprehension to the hearer or reader. But the user of the illustration may mistake the point which will need elucidation, and may illustrate the wrong point. And there may equally be an ignoratio on the part of the pupil. As De Morgan says: "The greatest difficulty in the way of learners is not knowing exactly in what their difficulty consists; and they are apt to think that when something is made clear, it must be the something." And he rightly goes on to point out the danger incident to the use of concrete examples in the study of the rules of formal inference. "If the student receives help from an example stated both in matter and form, the odds are that the help is derived from the plainness of the matter, and from his conviction of the matter of the conclusion. The right perception may, no doubt, be acquired by reflection on instances; but the minds which are best satisfied by material instances are also those which give themselves no further trouble." 993 The use of illustrations is also liable to the fallacy in another way—the person 2 Ibid., p. 266. 3 Ibid., pp. 266-267. 1 Ibid., p. 264. |