CHAPTER VI. On the Fallacies incident to Induction. THE errors incidental to inductive reasoning and to its various subsidiary processes have already, to a great extent, been noticed in the preceding chapters. In laying down the conditions essential to the correct conduct of a process, the mistakes which result from its incorrect conduct necessarily form part of our enquiry. Though, therefore, it may be convenient to pass the inductive fallacies in review, it is assumed that the student is already acquainted with the principal errors to which his processes and methods are liable. A. To begin with the subsidiary processes, the errors incident to the process of observation, or 'the fallacies of mis-observation,' are well classified by Mr. Mill as those which arise from Non-observation and those which arise from Mal-observation. I. Non-observation may consist either (1) in neglecting some of the instances, or (2) in neglecting some of the circumstances attendant on a given instance. (1) With respect to the non-observation of instances, it was long ago pointed out by Bacon' that there is in the human mind a peculiar tendency to dwell on affirmative and to overlook negative instances. Familiar examples of this tendency will readily occur to every one. We think it a 'curious coincidence' that we should suddenly meet a man of whom we have just been talking, that some event should happen of which we dreamed the night before, or that the predictions of a fortune-teller or an almanac should be verified by the facts. The explanation of these 'curious coincidences' is that our attention is arrested by the affirmative instances, whereas 1 Intellectus humanus in iis quæ semel placuerunt (aut quia recepta sunt et credita, aut quia delectant) alia etiam omnia trahit ad suffragationem et consensum cum illis : et licet major sit instantiarum vis et copia, quæ occurrunt in contrarium; tamen eas aut non observat, aut contemnit, aut distinguendo summovet et rejicit, non sine magno et pernicioso prejudicio, quo prioribus illis syllepsibus auctoritas maneat inviolata. Itaque recte respondit ille, qui, cum suspensa tabula in templo ei monstraretur eorum qui vota solverant quod naufragii periculo elapsi sint, atque interrogando premeretur, anne tum quidem Deorum numen agnosceret, quæsivit denuo, "At ubi sunt illi depicti qui post vota nuncupata perierint?" Eadem ratio est fere omnis superstitionis, ut in astrologicis, in somniis, ominibus, nemesibus, et hujusmodi; in quibus homines delectati hujusmodi vanitatibus advertunt eventus, ubi implentur; ast ubi fallunt, licet multo frequentius, tamen negligunt et prætereunt. At longe subtilius serpit hoc malum in philosophiis et scientiis; in quibus quod semel placuit reliqua (licet multo firmiora et potiora) inficit, et in ordinem redigit. Quinetiam licet abfuerit ea, quam diximus, delectatio et vanitas, is tamen humano intellectui error est proprius et perpetuus, ut magis moveatur et excitetur affirmativis, quam negativis; cum rite et ordine æquum se utrique præbere debeat: quin contra, in omni axiomate vero constituendo, major est vis instantiæ negativa." -Novum Organum, Lib. I. Aph. xlvi. the numberless instances in which there is no correspondence between the one set of facts and the other altogether escape our notice. We probably talk scores of times during the day of persons whom we do not meet immediately afterwards; we frequently dream in the most circumstantial manner of events which never occur; and, where one prediction of a fortune-teller is verified, scores are probably falsified. The weather-prophets of the almanacs possess a considerable advantage in the fact that, whereas, at all times, there is at least a considerable chance of their predictions turning out true, there are certain periods, such as the equinoxes, at which particular kinds of weather may be anticipated with a probability amounting almost to certainty. In former generations 'coincidences' of this kind were regarded not simply as 'curious' and 'remarkable,' but as proofs of some causal connexion between the events. To talk of a person was supposed to render his presence more likely; a verified prediction was regarded as evidence of second-sight; and a comet which was observed to be followed by a war was supposed to be, if not the cause of the war, at least a messenger sent from Heaven to proclaim its approach. The tendency to take note of affirmative, and to overlook negative instances, is one of the causes of that hasty generalisation of which I shall speak in a subsequent part of this chapter2. * The following remarks of Sir John Herschel, in speaking of the verification of 'signs of the weather,' are so apposite, that I append them in a note : This tendency is considerably intensified, if the affirmative instances are regarded as illustrations of some preconceived theory, or if the evidence afforded by them be supplemented by some powerful affection of the mind. It seldom happens that men can hold themselves entirely indifferent with respect to two rival We would strongly recommend any of our readers whose occupations lead them to attend to the " signs of the weather," and who, from hearing a particular weather adage often repeated, and from noticing themselves a few remarkable instances of its verification, have "begun to put faith in it," to commence keeping a note-book, and to set down without bias all the instances which occur to them of the recognised antecedent, and the occurrence or non-occurrence of the expected consequent, not omitting also to set down the cases in which it is left undecided; and, after so collecting a considerable number of instances (not less than a hundred), proceed to form his judgment on a fair comparison of the favourable, the unfavourable, and the undecided cases; remembering always that the absence of a majority one way or the other would be in itself an improbability, and that, therefore, to have any weight, the majority should be a very decided one, and that not only in itself, but in reference to the neutral instances. We are all involuntarily much more strongly impressed by the fulfilment than by the failure of a prediction, and it is only, when thus placing ourselves face to face with fact and experience, that we can fully divest ourselves of this bias.'-Familiar Lectures on Scientific Subjects, Lecture IV. 3' Habet enim unusquisque (præter aberrationes naturæ humanæ in genere) specum sive cavernam quandam individuam, quæ lumen naturæ frangit et corrumpit; ...... vel propter differentias impressionum, prout occurrunt in animo præoccupato et prædisposito, aut in animo æquo et sedato.'-Bacon's Novum Organum, Lib. I. Aph. xlii. * ' Intellectus humanus luminis sicci non est ; sed recipit infusionem a voluntate et affectibus; id quod generat ad quod vult scientias : quod enim mavult homo verum esse, id potius credit.'—Novum Organum, Lib. I. Aph. xlix. S opinions and apply themselves to the comparatively unexciting task of collecting evidence impartially on either side. To avoid taking a side on imperfect information, even where our interests or passions are not directly concerned, is one of the last and most difficult lessons learned by the scientific intellect, and by ordinary men it is regarded as a sign of a peculiarly frigid temperament, if not of an indifference to truth. Thus, when the theory involved in the idea of witchcraft had once been conceived and accepted, and especially when it had led to the invention of a new crime, it came to be held that the burden of proof lay with those who called its reality in question. Every story which confirmed the theory would be greedily received, while instances in which the supposed powers of the witch had failed, if noticed at all, would either leave but a slight impression on the mind, or be easily accounted for by supposing the intervention of a higher power. To the numerous class engaged in the administration of the laws, a not unnatural reluctance to question the justice of the principles on which they and their predecessors had been in the habit of acting would furnish an additional inducement to pass lightly over negative instances. Fear, or dread of eccentricity, would operate in the case of others; and thus a theory of the most preposterous character, which, to a mind not preoccupied, received little or no confirmation from facts, and the truth of which could 5 When a person was convinced that he was subject to the evil |