Perhaps we shall reach a conclusion by the easiest way, if we subject Mill's description to a test. If we reduce it to the several propositions it contains, we get the following: (1) Every one is able to picture to himself in his imagination a reality in which events follow one another without rule, that is, so that after an event a now b appears, now c, etc., in complete irregularity. (2) The idea of such a chaos accordingly contradicts neither the nature of our mind nor our experience. (3) Neither the former nor the latter gives us sufficient reason to believe that such an irregular alternation does not actually exist somewhere in the observable world. (4) If such a chaos should be presented to us as fact, that is, if we were in a position to outlive such an alternation, then the belief in the uniformity of time relations would soon cease.
Every one would subscribe to the last of these four theses, immediately upon such a chaos being admitted to be a possibility of thought; that is, he would unless he shared the rationalistic conviction that our thought constitutes an activity absolutely independent of all experience. We must simply accept this conclusion on the ground of the previous discussion and of a point still to be brought forward.
If we grant this conclusion, however, then it follows, on the ground of our previous demonstration of the reproductive and recognitive, as well as thought elements involved in the uniform sequence, that the irregularity in the appearance of the events, assumed in such a chaos, can bring about an absolutely relationless alternation of impressions for the subject that we should presuppose to be doing the perceiving. If we still wish to call it perception, it would remain only a perception in which no component of its content could be related to the others, a perception, therefore, in which not even the synthesis of the several perception contents could be apprehended as such. That is, every combination of the different perception contents, by which they become components of one and the same perception, presupposes, as we have seen, those reproductive and recognitive acts in revival which are possible only where uniformities of succession (and of coexistence) exist. Again, every act of attention involved in identifying and discriminating, which likewise we have seen to be possible only if we presuppose uniformities in the given contents of perception, must necessarily disappear when we presuppose the chaotic content; and yet they remain essential to the very idea of such a chaos. A relationless chaos is after all nothing else than a system of relations thought of without relations! That the same contradiction obtains also in the mere mental picturing of a manifold of chaotic impressions needs no discussion; for the productive imagination as well as the reproductive is no less dependent than is our perceptive knowledge upon the reproductive recognition and upon the processes of identifying and discriminating.
Thus the mental image of a chaos could be formed only through an extended process of ideation, which itself presupposes as active in it all that must be denied through the very nature of the image. A relationless knowledge, a relationless abstraction, a relationless reproduction or recognition, a relationless identification or discrimination, in short, a relationless thought, are, as phrases, one and all mere contradictions. We cannot picture "through our relating thought," to use Helmholtz's expression, nor even in our imagination, the sense impressions that we should have if our thought were relationless, that is, were nullified in its very components and presuppositions. In the case of Helmholtz's two dimensional beings, the question at issue was not regarding the setting aside of the conditions of our thought and the substituting conditions contradictory to them, but regarding the setting aside of a part of the content of our sense intuition, meanwhile retaining the conditions and forms peculiar to our thought. In this case, therefore, we have a permissible fiction, whereas in Mill's chaos we have an unthinkable thought.
Again, the sense impressions that must be presupposed in an inherently relationless chaos have no possible relation to the world of our perception, whose components are universally related to each other through the uniformities of their coexistences and sequences. Accordingly, the remark with which Helmholtz concludes the passage above quoted holds, mutatis mutandis, here also. "If there is no sense impression known that stands in relation to an event which has never been observed (by us), as would be the case for us were there a motion toward a fourth dimension, and for those two dimensional beings were there a motion toward our third dimension; then it follows that such an 'idea' is impossible, as much so as that a man completely blind from childhood should be able to 'imagine' the colors, if we could give him too a conceptual description of them."
Hence the first of the theses in which we summed up Stuart Mill's assumptions must be rejected. With it go also the second and third. In this case we need not answer the question: In how far do these theses correspond to Mill's own statements regarding the absolute surety and universality of the causal law?
We have now found what we sought, in order to establish as a valid assertion the seeming paradox in the proof of the necessity that we ascribe to the relation between cause and effect. We have proved that the assumption of a completely irregular and therefore relationless alternation of impressions contradicts not only our experience, but even the conditions of our thought; for these presuppose the uniformities of the impressions, and consequently our ability to relate them, all which was eliminated from our hypothetical chaos. Hence we have also established that a necessary relation is implied in the thought of a constant sequence of events, which makes the uniformly following b really dependent upon the uniformly preceding a.
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From still another side, we can make clear the necessity asserted in the relation of cause and effect. We found that the connection between each definite cause and its effect is an empirically synthetic one and has as its warrant merely experience. We saw further that the necessity inherent in the causal connection contains merely the demand that there shall be something fundamental in the constantly preceding a which makes the appearance of b necessary; not, however, that it informs us what this efficacy really is, and hence also not that it informs us how this efficacy brings about its effect. Finally, we had to urge that every induction, the most general no less than the most particular, depends upon the presupposition that the same causes will be given in the reality not yet observed as in that already observed. This expectation is warranted by no necessity of thought, not even by that involved in the relation of cause and effect; for this relation begins for future experience only when the presupposition that the same causes will be found in it is assumed as fulfilled.[[22]] This expectation is then dependent solely upon previous experience, whose servants we are, whose lords we can never be. Therefore, every induction is an hypothesis requiring the verification of a broader experience, since, in its work of widening and completing our knowledge, it leads us beyond the given experience to a possible one. In this respect we can call all inductive thought empirical, that is, thought that begins with experience, is directed to experience, and in its results is referred to experience. The office of this progressing empirical thought is accordingly to form hypotheses from which the data of perception can be regressively deduced, and by means of which they can be exhibited as cases of known relations of our well-ordered experience, and thus can be explained.
The way of forming hypotheses can be divided logically into different sections which can readily be made clear by an example. The police magistrate finds a human corpse under circumstances that eliminate the possibility of accident, natural death, or suicide; in short, that indicate an act of violence on the part of another man. The general hypothesis that he has here to do with a crime against life forms the guide of his investigation. The result of the circumstantial evidence, which we presuppose as necessary, furnishes then a special hypothesis as following from the general hypothesis.