(III.) There is a third class of inferences, having reference to the existence and relations of Phenomena. These inferences determine our belief of the existence of phenomena not directly known in relation to certain other phenomena which we do know. But they have not reference merely to the present time; they extend to the occurrence of past events, in which case they depend upon historical evidence; they reach forward also to the future, constituting prevision, expectation, or probability, according to their degree of certainty. Before, however, we consider these classes of inferences, we must give more minute attention to the determining reasons upon which inference. rests. CHAP V. SECT. VIII. SECTION VIII. DETERMINING GROUND OF INFERENCE. proposed. § 183. In the preceding section we analysed certain Question particular examples of inference for the purpose of gaining a general knowledge of the process. We saw that inference is a mental assertion made, without immediate knowledge, regarding some relation between known objects; or, regarding the resistance and relation to known objects, of some object or power not directly known. We have seen that, in certain cases, the same inferences are uniformly drawn by all men, whereas, in other cases, there is room for doubt and difference; and that in all cases there is some ground upon which the inference is based. Our CHAP. V. SECT. VIII. Axioms; their nature. task, now, is to examine into the nature of this ground. It is admitted that all inferences form a part of our conscious experience; and the question is, What is it that determines this experience? In any given case of inference, why is it that we infer so-and-so, and not otherwise? When, for example, we see two lines, each equal to a third line, why do we infer that they are equal to one another? When we see the motion of any body without us taking place, why do we infer that there is some force impelling it? When we see any seed, in germinating, putting forth a pair of leaves instead of a single one, why do we infer that the future plant or tree will grow by the addition of annual layers of woody tissue upon the outside surface? In other words, what is the Sufficient Reason of inference which makes that inference necessary or legitimate? any § 184. The question of the preceding paragraph may be discussed with reference to the three classes of inferences described in the last section. We make inferences regarding the forms of the objects of knowledge, space, time, and motion; the forces which operate in nature around us; and the phenomena which present themselves, or are capable of doing so, to our senses or consciousness. In connection with the first of these classes of inference, a great deal of discussion has arisen regarding the nature of the basis upon which demonstration rests. Certain axioms —such as, "Things which are equal to the same thing are equal to one another"-are generally placed at the beginning of mathematical works, and assumed to be self-evident. And we have now to consider the CHAP. V. nature of those axioms. SECT. VIII. us that they are à priori judgments, not founded upon A priori theory. anything more simple and original than themselves. Being self-evident, and necessary, and universal, they must be original intuitions of the mind. But to this opinion, as it is generally expressed, there is a primâ facie objection. The axiom quoted above is general in its application; it applies to all things, of whatever nature they may be, which are equal to one another. And we may assume it for certain, that a proposition of this kind is not formed until after one or more particular examples of it have been known. This axiom, as well as all the others, has been generalised, and the question is, What is the nature of the particular mental acts from which it has been drawn? Now, taking the particular axiom referred to, it is manifest that the single mental act from which it is generalised must be either an intuition or an inference. A is equal to B; C is equal to B; therefore A is equal to C. This is the particular form of the general axiom, and must have preceded the general axiom in historical order. In this form the mental act appears to be an inference. A is not directly seen to be equal to C, but both A and C are seen to be equal to B; and the inference is drawn. But Empirical theory. it has been held that this apparent inference is originally an intuition; that we are not able to predicate that A is equal to C until after we have compared them directly together; and that, having seen several instances in which A and C, being each equal CHAP. V. SECT. VIII. Axiom general necessary means. to a third thing, B, are found to be equal to one another, we generalise the axiom as above. According to this view, the axiom is generalised from experience, and the particular experiences from which it is generalised are experiences, not of inference, but of intuitions, brought about by voluntary and artificial This explanation is not satisfactory. It has the appearance of being simply invented without any other reason than that it is capable of partially explaining the axiom. There is no evidence whatever that such artificial trials of equality as those postulated are ever made for the purpose indicated. And if they were actually made, the generalised axiom resulting could not have that degree of certainty which it has, unless this certainty had some other ground than the alleged experience. § 185. We must, therefore, examine the view which ised from a considers the particular act from which the general particular axiom is generalised as an act of inference. There inference. is a comparison of two things with a third thing, and the inference that the two things, being equal to the third, are equal to one another. But we must remember that the third thing, which is the medium of comparison between the two others, may not be an external object, but may be a part of our own organism. And we know, from the evidence of language, that the original medium of comparison between the lengths or other spatial relations of external objects is some part of our organism. In many languages, and perhaps in every language, the original standards of measure are particular parts of the body. A foot, a hand's breadth, a span, a cubit, a fathom, are terms of measurement, which, from being so universally used in English, and having so many analogues amongst other nations, lead to the conclusion that the parts of the body implied in them afford to men the primary standards of comparison with respect to the relative extension of objects. Now, if we analyse this primary mode of comparison into its psychological elements, we appear to get the following: The eye and the hand of a primitive man having been trained to work together, he applies the hand, outstretched to its farthest limits, to a short object; he sees that the tip of the finger and the point of the thumb coincide with the ends of the thing to be measured; he has, in other words, a certain complex act of perception, the result of which is that he pronounces the object examined a span in length. another place and time, he applies the same test to another object, with the same result; he remembers that the preceding complex act of perception was essentially similar to this one; and he infers that the length of the two objects is the same. Now, be it observed, this inference is not one which he might make or not, as he pleased. He is compelled to make it; he cannot draw any different inference; and it is this necessity of the particular inference in hand which gives the manifest universality to the axiom generalised from it. And, as we see what is the nature of the mental act which precedes the inference, we can see how the inference is necessary. A complex act of perception is compared with a At CHAP. V. SECT. VIII. |