Page images
PDF
EPUB

general laws of Universal Causation and the Uniformity of Nature. The validity of the induction in question is thus artificially connected with the validity of these universally accepted inductions, and we are enabled to argue from the truth of the latter to that of the former.

Uncontradicted experience, of course, implies a great variety of instances, and, from this point of view, every well-grounded Inductio per Enumerationem Simplicem might be represented as an application of the Method of Agreement. But to represent it in this form would often weaken its force. For, while our experience may be so wide as to justify us in affirming the constant union of two or more circumstances, the number of other common circumstances, known or suspected, with which these are found in invariable combination, may be so large as to render it impossible for us to satisfy even approximately the conditions of the Method of Agreement. Here, as elsewhere, an argument often admits of being stated in two ways, and it is the office of the logician to state it in that form in which it carries the largest amount of conviction, or rather offers the most satisfactory kind of proof.

It is, as we have already pointed out in the First Chapter 2, by means of an Inductio per Enumerationem Simplicem that we establish what have been called 'Inductions of Co-existence.' This is the case, when, as the result of a wide experience, two phenomena

2 Pp. 7-9.

are found to be invariably co-existent, but we have no. evidence to connect them as cause and effect, or even as effects of the same cause. Such are the attributes which are found to be invariably united in the same Natural Kinds, that is to say, in the same species of plants, animals, and minerals; such are the two properties of Inertia and Gravity which are found united in all matter. In all these cases, there is probably some causal connection, hitherto undetected, between the coexisting phenomena; but while we are unable to apply with any success the more refined inductive methods, we must content ourselves with regarding the uniformity as simply one of co-existence. If we made any progress towards the discovery of a causal connection, the uniformity would be transferred to another category, and would rank amongst the inductions discussed in the last chapter. Meanwhile, these inductions, depending simply on uncontradicted experience, and being at present inaccessible to the Methods of Elimination, must be regarded as generalisations awaiting further investigation 3.

The term 'Empirical Generalisation' or 'Empirical Law' might be conveniently appropriated to express the

3 For a further discussion of the Uniformities of Co-existence, the reader is referred to Mr. Bain's Logic, Bk. iii. ch. 3. I am disposed to estimate more highly than Mr. Bain the probability that these uniformities might, if our knowledge were extended, be ultimately resolved into Uniformities of Causation, and hence they do not appear to me to require any separate or detailed treatment in a work on Logic.

result of an Inductio per Simplicem Enumerationem. Though these expressions are employed with great latitude, it is usually regarded as characteristic of an Empirical Law or Generalisation that it can only be received as true within the limits of the data from which it is derived, that at another time, at another place, or under different circumstances from those under which the observations were made, it might be found to break down. It is true that, owing to the conflict of causes, this description applies to many of the conclusions arrived at by means of the Inductive Methods, but it is peculiarly applicable to the results of the Inductio per Simplicem Enumerationem, and it would be extremely convenient to possess an expression by which the results of this method might be at once distinguished from those of scientific induction on the one hand, and those of analogy (to be discussed presently) on the other. Instances of Empirical Laws in this restricted sense are such generalisations as that certain animals or flowers are of a certain colour, that certain tribes of men are less capable of civilisation than others, and, perhaps, that certain appearances of sky are indicative of certain changes of weather. There are, of course, some cases in which it is difficult to determine whether a given conclusion has been arrived at by the Inductio per Simplicem Enumerationem or by an imperfect application of the Method of Agreement, that is to say,

4 See Herschel's Discourse on the Study of Natural Philosophy, § 187, and Mill's Logic, Bk. III. ch. xvi. § 4.

whether it is based on instances taken indifferently, or on selected instances 5.

Another form of imperfect induction is the Argument from Analogy. Here we do not argue from a number

5 I have avoided any special discussion of what are called 'Empirical Laws,' both on account of the extremely indeterminate use of the expression, and because such a discussion is calculated, in my opinion, needlessly to perplex the student by the complicated questions to which it leads. The advanced student can refer to Mr. Mill's Logic, Bk. III. ch. XV., and Bk. V. ch. v. § 4, but he will be introduced, I venture to suggest, to more difficulties than he will find solved.

6 It will be observed that the word 'Analogy' is here employed in the sense of resemblance.' In the stricter and more ancient meaning of the term, it signifies an equality of relations (iσórηs λóywv). See Aristotle's Ethics, Bk. v. 3 (8). The reader will find the two significations of the word 'Analogy' discriminated in the Elements of Deductive Logic, Part III. ch. i. note 2.

Archbishop Whately defines Analogy as a Resemblance of Relations. This definition, if intended to represent the ancient signification of the word, is incorrect. The Aristotelian Analogy is an equality, not a resemblance of relations. The instance given in Eth. Nic. i. 6 (12) is that, in man, the reason (voûs) bears to the living principle (4vxý) the same relation that the faculty of vision (os) bears to the body (o@μa): ὡς γὰρ ἐν σώματι ὄψις, ἐν ψυχῇ νοῦς. The assertion, in this instance, it will be noticed, is that the relation to each other of the two former members of the analogy is, not similar to, but the same as, that of the two latter. The Aristotelian term åvaλoyía, in fact, exactly corresponds with the term Proportion as employed by mathematicians, and it was by the word Proportio, when not availing themselves of the Greek word Analogia itself, that the Romans expressed this form of argument. See Quinctilian, Inst. Orat. i. 6 : ' Analogiæ quam proxime ex Græco transferentes in Latinum proportionem vocaverunt, hæc vis est: Ut id, quod dubium est, ad aliquid simile, de quo non quæritur, referat; ut incerta

of instances, as in the case of Inductio per Simplicem Enumerationem, but from a number of points of resemblance. The argument is not, that because S, T, U, V, W, &c. exhibit the union of m with a, b, c, we may therefore expect to find m in Z, or wherever else a, b, c may occur; but that, because X and Y (any two or more instances) agree in the possession of certain qualities a, b, c, we may expect to find the quality m which is presented by X exhibited also in Y. The argument is based, not on the number of instances in which the two sets of qualities are found united, but on the number of qualities which are found to be common to two or more instances: the argument is not that I have so often observed a, b, c in conjunction with m that I believe these qualities to be conjoined invariably, but that I know X and Y to resemble each other in so many points that I believe them to resemble each other in all.

Thus, because the moon resembles the earth in being a large spheroid revolving round another body, as well as in various other particulars, it may be argued that it probably resembles the earth also in sustaining animal and vegetable life on its surface. But, if every ground of resemblance furnishes a probable reason for assigning to the one body any property known to belong to the other, it is evident that every ground of dissimilarity will also furnish a probable reason for denying of the first

certis probet.' I am indebted for this quotation to Mr. Austin's Lectures on Jurisprudence, vol. iii. p. 255.

« PreviousContinue »