ABSTRACT
The position reached in our last chapter has an important bearing on the principles of generalisation which we assumed at an earlier stage (Chaps. VII. and VIII.). These principles laid down, (a) that an uniformly observed parallel relation is always the ultimate basis of a general statement. Any such relation is, in the absence of counter considerations, a reason for generalising, and no other basis for generalisation exists. Hence (b) a difference in the consequents of a given fact in this case as compared with that can only be due to a difference in the surrounding facts. But conversely, any difference in the surroundings uniformly found to be followed by a change in the consequents is a basis for arguing to such a change in a fresh case. But (c) in accordance with both the above assumptions, any relation to which exception is found not being uniform ceases to be as such a basis for inference in a fresh case. And hence (d) any uniformly observed relation A—B must be generalised if no concomitant C exists, a change in which would always be followed by a change in B. But this deduc- tion may now be extended. If C does not exist, A—B must be universal. But if we have no reason to suppose C to exist, then any suggestion of C is logically worthless, and no reason can be assigned for doubting the universality of A—B. And if, further, A—B is a familiar relation, the fact that we have no reason to suppose C means that in our experience C never accompanies A, and so is a definite argument against C. For to suppose it to exist here would be to suggest without ground a difference in the order of our experience. We have to apply this argument with the limitations laid down in the last chapter. If there is no certain argument for C there may be probabilities or analogies in its favour. But as these diminish its improbability grows, and when they vanish it is disproved in accordance with the “best tests at our disposal.” We need only add that primâ facie any sort of relation may turn out to be universal, and any sort of change in the concomitants may make a difference—which points of resemblance or difference are material can only be determined by experience. Thus when we apply the principles of generalisation to the facts of experience two alternatives at once arise. A—B will be universal unless there is a C which makes a difference, and in proportion as C is probable A—B is unlikely to be universal, while in proportion as the grounds for supposing C disappear our belief in the connection of A and B is bound to increase. The relation of these alternatives is the fundamental fact of induction. This being understood, our principle may be viewed indifferently as stating that the single consideration of correspondence to an uniformly observed relation becomes the total ground of belief required, on the disappearance of any ground for supposing a disturbing element, or that it is swelled to the totality by the addition of reasons proving the impossibility of such an element. The possibility of the disturbing concomitant is the “counter-consideration,” to apply the phrase used above (Chap. X.), which must be dismissed before a suggested generalisation can be affirmed.
