a hyacinth, it would be a blue one. This form of induction (Inductio per Simplicem Enumerationem) may have no value whatever. In most cases, the condemnation passed on it by Bacon' is perfectly just: 'Inductio quæ procedit per enumerationem simplicem, res puerilis est, et precario concludit, et periculo exponitur ab instantia contradictoria, et plerumque secundum pauciora quam par est, et ex his tantummodo quæ præsto sunt, pronunciat.' But when we have reason to think that any instances to the contrary, if there were such, would be known to us, the argument may possess considerable value, and when, as in the case of the Laws of Causation and of the Uniformity of Nature, we feel certain, from a wide and various experience, that there are no cases to the contrary, no stronger argument (to us individually) can be adduced. It is rarely, however, that an Inductio per Simplicem Enumerationem can afford us this certainty. Our trustworthy inductions are, in the great majority of cases, the result of our detecting some fact of causation among the observed phenomena. We find, for instance, that, amongst the observed phenomena, a, b, c, d of X, a is the cause of c, and, consequently, if we observe the phenomenon a in Y, we infer that, if there are no counteracting circumstances, Y will possess the quality c as well; or, if we 1 Novum Organum, Lib. I. aph. cv. 2 It must be remembered that a complete enumeration of instances, when we know the enumeration to be complete, inasmuch as it leaves no room for an inference from the known to the unknown, does not furnish an inductive but a deductive argument. See Elements of Deductive Logic, Part III. ch. i. appended Note 2. 3 observe the phenomenon c in Y, we infer that it is not unlikely that a may be present as well. The problem of Induction, therefore, resolves itself (except in the rare cases in which we may legitimately employ Inductio per Enumerationem Simplicem, or in which we have no other resource) into the problem of detecting facts of Causation. Certain rules for this purpose have been laid down by Mr. Mill, called by him the Experimental Methods, but which we shall distinguish as the Inductive Methods. These Methods, it will be noticed as we proceed, are all methods of elimination, or devices by which we are enabled to argue from a comparatively small number of instances. with the same certainty as if they were ever so numerous. Before proceeding to state and explain these Rules or Methods, it may be useful to make some preliminary remarks on the nature of the causal relations which subsist among phenomena. (1) The same cause, unless there are counteracting circumstances, that is, other causes which prevent it from acting or which modify its action, is invariably followed by the same effect. (2) As already shown (Chapter I. pp. 13-15), several causes may have co-operated in producing any given effect. In this case, it is not unusual to speak of the 'combination of causes or the sum of the causes.' 3 We say 'not unlikely,' for c might be due to some other cause as well as a, and, therefore, the presence of c does not enable us to infer with certainty the presence of a, as does that of a the presence of c. (3) The same effect may be due to several distinct causes, or combinations of causes, being due sometimes to one and sometimes to another, and, hence, though we may always argue from a particular cause to its effect, we cannot always argue from an effect to any particular cause. Thus, ignition may be due, not only to the concentration of the rays of solar heat, but also to friction, electricity, &c. This fact has given occasion to the expression Plurality of Causes.' (4) It frequently happens that between the original! cause and the ultimate effect there intervene a number of intermediate causes. Thus, suppose we make an experiment by which motion is converted into heat, heat into electricity, and electricity into chemical affinity; we may, roughly speaking, say that motion has been the cause of the chemical affinity, or chemical affinity the effect of the motion, but, speaking strictly, we ought to enumerate the intervening causes. (5) Sometimes a number of effects appear to be produced simultaneously by the same cause. Thus, it would appear that there are many cases in which, if one of the agents, motion, heat, light, electricity, magnetism, and chemical action, is excited, the rest are developed simultaneously *. These simultaneous effects, whether we conceive that they are really or only apparently simultaneous, would be called joint or common effects of the cause. Similarly the expression 'joint effects' would be employed for the effects produced by the same cause on * See Grove's Correlation of Physical Forces, Concluding Remarks. different bodies, or different portions of the same body. Thus, if a blow bruises my forehead, and at the same time gives me a headache, the bruise and the headache may be called joint effects of the blow. These joint effects may be, as it were, in different degrees of descent from the same cause. Thus, if the headache incapacitates me for work, my incapacity for work and the bruise on my forehead will be joint effects, but in different degrees of descent from the original cause. Any phenomena which are connected, either as cause and effect, and that either immediately or remotely, or as joint effects, and that either in the same or in different degrees of descent from the same cause, may be spoken of as being causally connected, or as causal relations, or as being related to one another through some fact of causation. We now proceed to the statement of the Inductive Methods. METHOD OF AGREEMENT. If two or more instances of the phenomenon under investigation have only one other circumstance in common, that circumstance may be regarded, with more or less of proba 5 The statement of the Canons is taken, with some modifications, from Mr. Mill's Logic. The authorities for the various examples, when these are not of a familiar character, are cited at the foot of the page. bility, as the cause (or effect) of the given phenomenon, or, at least, as connected with it through some fact of causation. Wherever the phenomenon a is found, we observe that b is found, either invariably or frequently, in conjunction with it. This fact leads us to suspect that there is some causal connection between them. On what grounds, and under what circumstances, are we justified in drawing such an inference? And what is the particular character of the inference which we are justified in drawing? The answer to these questions involves many difficulties, of which we shall now attempt to offer a solution. When antecedents and consequents are discriminated in this discussion, antecedents will be represented by Roman capitals, A, B, C, &c., and consequents by Greek characters, a, B, y, &c. When circumstances are not distinguished as antecedents and consequents, we shall employ the small Roman letters, a, b, c, &c. Now, suppose that we have A B followed by a ẞ, and A C by a y; it might, at first sight, appear that A must be the cause of a, or, if we were attempting to ascertain the effect of a given cause (which, however, is a much rarer application of this method), that a must be the effect of A. And there is much plausibility in this supposition, for whatever can, in any given instance, be excluded, or, to use the technical term, eliminated without We add or frequently,' as it is not necessary that the conjunction shall be invariable. The student need not, however, at present trouble himself with this distinction, which will be fully explained below. See PP. 134, 141-143. |