469 CHAPTER XXXV. THE METHODS OF INDUCTION. $608. It has been said-(1.) "That in the complexity of things or sequences, observation and experiment are needed to analyse the accidental from the essential or permanent, and to determine regarding a given phænomenon that upon which its real existence depends-that is, its cause or conditionfor all the finite is conditioned. (2.) "That we must seek not only the conditions which determine the existence of a phænomenon, but the properties which exclude it or which are indifferent to it." 1 We thus need certain rules and methods of Observation and Induction, in virtue of which we may find what is invariably connected in experience; mainly, in a word, distinguish the casual from the causal,-what is connected simply by arbitrary or contingent association from what is linked together objectively, or in the order of nature. § 609. The aim of Inductive Method with Bacon is the search after "Form." Concrete substances are made up of "simple natures" or qualities-they are "formæ copulata"; if we can reach the form of the simple nature, we can see how it is produced, and thus proceed to the composition of substances. The forms of substances are, at least, ultimately discoverable. A substance with him means a congeries of qualities. Qualities are "simple natures"; but form is ambiguous. It is taken to mean essence, definition, &c., of a thing, and the cause, hence law, of a thing. Form thus applies to the essential 1 Franck, Dict. Phil. Ind. qualities of a class, to the attributes of a concrete substance, or to a quality itself.1 § 610. As in an object the essential qualities are those upon which certain other or derivative qualities depend-may depend —even as their cause; and as the form of a quality is really the cause of that quality, the two meanings of form come to coincide. The essential qualities, for example, of a triangle or square are given in the definition, and on these all the demonstrated properties depend. The form or cause of heat, to use Bacon's illustration, is motion-a kind of motion. Thus the search after form resolves itself practically into the search after causes. If by cause we understand, as we ought to do, not only what as a determination precedes the effect or consequent in time, but that also which is concomitant with the effect in time, the expression "form" may well take in the whole scope of causal relation as sought for by induction. § 611. The essential point of Bacon's inductive Method lies in Exclusion (Exclusiva): "Inductio mala est quæ per enumerationem simplicem principia concludit scientiarum, non adhibitis exclusionibus et solutionibus, sive separationibus naturæ debitis." 2 Again: "Naturam separare debet, per rejectiones et exclusiones debitas; ac deinde, post negativas tot quot sufficiunt, super affirmativas concludere."3 Again, more particularly, he says: "Est itaque Inductionis veræ opus primum (quatenus ad inveniendas formas) rejectio sive exclusiva naturarum singularum, quæ non inveniuntur in aliqua instantia, ubi natura data adest; aut inveniuntur in aliqua instantia, ubi natura data abest; aut inveniuntur in aliqua instantia crescere, cum natura data decrescat; aut decrescere, cum natura data crescat. Tum vero post rejectionem et exclusivam debitis modis factam, secundo loco (tanquam in fundo) manebit (abeuntibus in fumum opinionibus volatilibus), forma affirmativa, solida, et vera, et bene terminata." 4 § 612. As aids to the Method of Exclusion, Bacon gives the three tables-viz. : (1.) The table of Presence or the appearance (comparentia) to the intellect of all known instances, which agree in the 1 Cf. Fowler, Nov. Org., Int. 2 Nov. Org., i. 69. same nature, although the matter or circumstances are most unlike. (2.) The table of Absence, or the appearance to the intellect of instances which want the given nature; because the form, as has been said, ought to be not less absent when the given nature is absent, than to be present when it is present. (3.) The table of Comparison, or the appearance to the intellect of instances in which the nature, regarding which there is inquiry, is present according to greater and less; whether the appearance made be of increment or decrement in the same subject or by turns in diverse subjects. Any nature may not be received for the time as form, unless it uniformly decrease when the nature itself decreases; and, in like manner, is constantly increased when the nature itself is increased.1 § 613. After the tables, Bacon proceeds to state certain remaining auxiliaries of the intellect in seeking a true and perfect interpretation of nature and induction. Under this head he gives the first place to "the Prerogatives of Instances (Prærogativis Instantiarum). These are "characteristic phanomena selected from the great miscellaneous mass of facts which occur in nature, and which, by their number, indistinctness, and complication, tend rather to confuse than to direct the mind in its search for causes and general heads of induction." 2 § 614. First among the Prerogative Instances, Bacon places the Solitary Instances (Instantias Solitarias). Those are solitary instances, he says, which exhibit the nature concerning which there is inquiry in such subjects as have nothing in common with other subjects, except that nature itself; or again, which do not exhibit the nature regarding which there is inquiry in such subjects as are similar through all with other subjects, except in that very nature itself. It is manifest that instances of this sort remove doubts, and accelerate and strengthen the exclusion; so that a few of these are equivalent to many. This and other examples which follow in illustration, leave but little to make explicit Mill's 1 Nov. Org., ii. 11, 12, 13. 2 Herschel, Discourse on Study of Natural Philosophy, § 190. Nov. Org., ii. 21. Cf. Fowler, methods of agreement and difference.1 Bacon even speaks of the instances solitary, "quatenus ad similitudinem"; and those solitary, "quatenus ad discrepantiam." 2 The Instantia Migrantes, under the Prerogative, readily suggest the method of Concomitant Variations.3 § 615. Among the Prerogative Instances, Bacon has the Crucial Instance (Instantia Crucis). This means an observation or experiment which by its nature definitely settles one or other of two or more hypotheses, or possible antecedents, as the true one. We suppose nothing changed, except a particular antecedent as present or absent; and with this we find the effect in question, present or absent. This readily suggests the method of Difference.* § 616. The Tables given by Bacon, and other statements, seem to indicate that he supposed science was to be built up, first, by observation of facts arranged as the same or different; secondly, by induction therefrom, giving us laws of more or less generality, the axiomata media; and thirdly, from these intermediate laws rising to the highest generalisations. This cannot be taken as the sole mode in which science has progressed since his time; for the element of Deduction, making use of the imperfect or limited generalisation in new spheres, and where the antecedent or cause was not observable, has done most to build up our knowledge of the physical universe. But the method of Bacon did forecast the mode of certain discoveries, and in its reverse form it is that in which the ascertained laws of science are best stated. And its influence as a protest against arbitrary anticipation of the order of nature cannot be overestimated. § 617. As has been pointed out by Herschel, Mill, and frequently illustrated by Professor Fowler, Bacon's Method of Exclusions "proceeds on the assumption that every phænomenon has only one cause, that is to say, is due to only one set of conditions. Of the 'simple natures' there is some one, and one only, which, if it could be found, is the 'form' of the natura data. But the same event may be due to one set of conditions at one time, and to a different set at another. 1 Novum Organum, ii. 22. 2 Cf. Professor Fowler's admirable edition of the Novum Organum, p. 409. 3 Nov. Org., ii. 23. 4 Nov. Org., ii. 36. Hence, though it is invariably true that the same cause is always followed by the same effect, the converse proposition that the same effect is always due to the same cause would frequently be misleading." 1 § 618. Mill has well analysed the methods of Induction, and gives certain Rules or Canons, which, though open to criticism in expression and details, are in substance those generally received. Mill, in fact, has made explicit what Bacon foreshadowed, and what Herschel had already in the main put more clearly. The First Method-called the Method of Agreement-is thus stated: "If two or more instances of the phænomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phænomenon ;" or, as it has been put," the sole invariable antecedent of a phænomenon is probably its cause." 2 § 619. In order to make this canon available, the first requisite is ample observation of the circumstances or actual antecedents of the phænomenon in question. When we find among those antecedent circumstances that there are some whose presence or absence does not affect the actual occurence of the phænomenon or event, we infer that these are not essential to it; in a word, that they are casual not causal. If, however, we be able to find an antecedent, either one circumstance or sum of circumstances, which alone invariably precedes or accompanies the phænomenon, we are entitled to infer with probability that that is the cause, or that the phænomenon depends on it as effect. But we ought to observe in regard to this method, that all which it tells us is simply that the antecedent is the cause in the given circumstances; in other words, it is a cause of the effect, but not necessarily the only cause, or the cause at all times and in all circumstances. § 620. As has been pointed out by numerous logicians, and in these days emphasised by Mill and others, the same (similar) phænomenon, or event, or effect, may follow from several different causes. This was the very commonplace of logic and of usual practice ere modern ignorance invested it with the dignity of a 1 Fowler, Nov. Org., Int., p. 62. 2 Jevons, Logic, 241. |