The very same thing may be said of spatial complexes. Such factors as are always, or at any rate often, found together are taken by us as "belonging together," and out of them a concept is formed which embraces these factors. A question as to the why has here, as with the temporal complexes, no definite meaning. There are countless things that happen together once to which we pay no attention because they happen only once or but seldom. The knowledge of the fact that such a single concurrence exists amounts to nothing, since from the presence of one factor it does not lead to a conclusion as to the presence of another, and therefore does not make possible prediction. Of all the possible, and even actual combinations, only those interest us which are repeated, and this arbitrary but expedient selection produces the impression that the world consists only of combinations that can be repeated; that, in other words, the law of causality or of the type is a general one. However general or limited application those laws have, is more a question of our skill in finding the constant combinations among those that are present than a question of objective natural fact.

Thus we see the development and pursuit of all sciences going on in such a way that on the one hand more and more constant combinations are discovered, and on the other hand more inclusive relations of this kind are found out, by means of which elements are united with each other which before no one had even tried to bring together. So sciences are increasing both in the sense of an increasing complication and in an increasing unification.

If we consider from this standpoint the development and procedure of the various sciences, we find a rational division of the sum total of science in the question as to the scope and multiplicity of the combinations or groups treated of in them. These two properties are in a certain sense antithetical. The simpler a complex is, that is, the fewer elements brought together in it, the more frequently it is met with, and vice versa. One can therefore arrange all the sciences in such a way that one begins with the least multiplicity and the greatest scope, and ends with the greatest multiplicity and the least scope. The first science will be the most general, and will therefore contain the most general and therefore the most barren concepts; the last will contain the most specific and therefore the richest.

What are these limiting concepts? The most general is the concept of thing, that is, any piece of experience, seized arbitrarily from the flux of our experiences, which can be repeated. The most specific and richest is the concept of human intercourse. Between the science of things and the science of human intercourse, all the other sciences are found arranged in regular gradation. If one follows out the scheme the following outline results:

1.Theory of order.⎫
2.Theory of numbers, orarithmetic.⎬Mathematics.
3.Theory of time.⎪
4.Theory of space, orgeometry.⎭
5.Mechanics.⎫
6.Physics.⎬Energetics.
7.Chemistry.⎭
8.Physiology.⎫
9.Psychology.⎬Biology.
10.Sociology.⎭

This table is arbitrary in so far as the grades assumed can be increased or diminished according to need. For example, mechanics and physics could be taken together; or between physics and chemistry, physical chemistry could be inserted. Likewise between physiology and psychology, anthropology might find a place; or the first five sciences might be united under mathematics. How one makes these divisions is entirely a practical question, which will be answered at any time in accordance with the purposes of division; and dispute concerning the matter is almost useless.

I should like, however, to call attention to the three great groups of mathematics, energetics, and biology (in the wider sense). They represent the decisive regulative thought which humanity has evolved, contributed up to this time, toward the scientific mastery of its experiences. Arrangement is the fundamental thought of mathematics. From mechanics to chemistry the concept of energy is the most important; and for the last three sciences it is the concept of life. Mathematics, energetics, and biology, therefore, embrace the totality of the sciences.

Before we enter upon the closer consideration of these sciences, it will be well to anticipate another objection which can be raised on the basis of the following fact. Besides the sciences named (and those which lie between them) there are many others, as geology, history, medicine, philology, which we find difficulty in arranging in the above scheme, which must, however, be taken into consideration in some way or other. They are often characterized by the fact that they stand in relation with several of the sciences named, but even more by the following circumstance. Their task is not, as is true of the pure sciences above named, the discovery of general relationships, but they relate rather to existing complex objects whose origin, scope, extent, etc., in short, whose temporal and spatial relationships they have to discover or to "explain." For this purpose they make use of relations which are placed at their disposal by the first-named pure sciences. These sciences, therefore, had better be called applied sciences. However, in this connection we should not think only or even chiefly of technical applications; rather the expression is used to indicate that the reciprocal relations of the parts of an object are to be called to mind by the application of the general rules found in pure science.

While in such a task the abstraction process of pure science is not applicable (for the omission of certain parts and the concentration upon others which is characteristic of these is excluded by the nature of the task), yet in a given case usually the necessity of bringing in various pure sciences for the purpose of explanation is evident.

Astronomy is one of these applied sciences. Primarily it rests upon mechanics, and in its instrumental portion, upon optics; in its present development on the spectroscopic side, however, it borrows considerably of chemistry. In like manner history is applied sociology and psychology. Medicine makes use of all the sciences before mentioned, up to psychology, etc.