We might point to the method of abstraction generally adopted in science and to the extrapolation to ideal cases which has just been explained, and regard the assertion of the absolute determinateness of events in the world as a justified extrapolation to the ideal case. In other words, we might say that we know all the natural laws and how to apply them perfectly to the individual instances. In controversion of this it must be said that the ulterior justification of such ideal extrapolation is not yet feasible. The justification lies in the demonstration that the real cases approximate the ideal the more closely the more we actualize our presumptions. But in this case this is not feasible, since, for the greater part of our experiences, we do not even know the approximate or ideal natural laws by the help of which we can construct such ideal cases. For instance, the whole province of organic life is at present essentially like an unknown land, in which there are only a few widely separated paths ending in culs-de-sac.
16. The Freedom of the Will.
This relation explains why, on the one hand, we assume a far-reaching determinateness for many things, that is, for all those accessible to scientific treatment and regulation, and why, on the other hand, we have the consciousness of acting freely, that is, of being able to control future events according to the relations they bear to our wishes. Essentially there is no objection to be found to a fundamental determinism which explains that this feeling of freedom is only a different way of saying that a part of the causal chain lies within our consciousness, and that we feel these processes (in themselves determined) as if we ourselves determined their course. Nor can we prove this idea to be false, that, since the number of factors which influence each experience is indefinitely great and their nature indefinitely complex, each event would appear to be determined in the eyes of an all-comprehensive intellect. But to our finite minds an undetermined residue necessarily remains in each experience, and to that extent the world must always remain in part practically undetermined to human beings. Thus, both views, that the world is not completely determined, and that it really is, though we can never recognize that it is, lead practically to the same result: that we can and must assume in our practical attitude to the world that it is only partially determined.
But if two different lines of thought in the whole world of experience everywhere lead to the same result, they cannot be materially, but merely formally or superficially, different. For those things are alike which cannot be distinguished. There is no other definition of alikeness. Thus, if we see that the age-long dispute between these two views always breaks out afresh without seeming to be able to reach an end, this is readily understood, from what has been said, since the very same essential arguments which can be adduced of one view can be used as a prop for the other view, because in their essential results the two are the same. I have discussed this matter because it presents a very telling example of a method to be applied in all the sciences when dealing with the solution of old and ever recurrent moot questions. Each time we encounter such problems, we must ask ourselves: what would be the difference empirically if the one or the other view were correct? In other words, we first assume the one to be correct, and develop the consequences accordingly. Then we assume the second to be correct and develop the consequences accordingly. If in the two cases the consequences differ in a certain definite point, we at least have the possibility of ascertaining the false view by investigating in favor of which case experience decides on this point. However, we may not conclude that by this the other view has been proved to be entirely correct. It likewise may be false, only with the peculiar quality that in the case in question it leads to the correct conclusions. That such a thing is possible, every one knows who has attentively observed his own experiences. How often we act correctly in actual practice, though we have started out on false premises! The explanation of this possibility resides in the highly composite nature of each experience and each assumption. It is quite possible—and, in fact, it is the general rule—that a certain view contains true elements, but along with them false elements also. In applications of the view where the true elements are the decisive factors, true results are obtained, despite the errors present. Likewise, false results will be achieved where the false elements are decisive, despite the true results that can be had, or have been had, elsewhere, by means of the true elements. Hence, in case of the "confirmation," we can only conclude that that portion of the view essential for the instance in question is correct.
One readily perceives that these observations find application in all provinces of science and life. There are no absolutely correct assertions, and even the falsest may in some respect be true. There are only greater and lesser probabilities, and every advance made by the human intellect tends to increase the degree of probability of experiential relations, or natural laws.
17. The Classification of the Sciences.
From the preceding observations the means may be drawn for outlining a complete table of the sciences. However, we must not regard it complete in the sense that it gives every possible ramification and turn of each science, but that it sets up a frame inside of which at given points each science finds its place, so that, in the course of progressive enlargement, the frame need not be exceeded.
The basic thought upon which this classification rests is that of graded abstraction. We have seen ([p. 19]) that a concept is all the more general, that is, is applicable to all the more experiences, the fewer parts or elementary concepts it contains. So we shall begin the system of the sciences with the most general concepts, that is, the elementary concepts (or with what for the time being we shall have to consider elementary concepts), and, in grading the concept complexes according to their increasing diversity, set up a corresponding graded series of sciences. One thing more is to be noted here, that this graded series, on account of the very large number of new concepts entering, must produce a correspondingly great number of diverse sciences. For practical reasons groups of such grades have been combined temporarily. Thereby a rougher classification, though one easier to obtain a survey of, has been made. The most suitable and lasting scheme of this sort was originated by the French philosopher, Auguste Comte, since whom it has undergone a few changes.
Below is the table of the sciences, which I shall then proceed to explain: