They were advanced in obedience to a demand for the ultimate explanation of the phenomena in question, and were obtained by applying such general conceptions as were most satisfying to the reasons of their respective authors. But they contributed nothing whatsoever to a practical familiarity with the natural course of events, in this case the times and places of the planets and the tides. Hence they have not been used in the building of science. In our own day investigators have become conscious of their motive, and do not wait for historical selection to exclude powers and reasons from their province. They deliberately seek to formulate exact descriptions. To this end they employ symbols that shall serve to identify the terms of nature, and formulas that shall define their systematic relationship. These systems must be exact, or deductions cannot be made from them. Hence they tend ultimately to assume a mathematical form of expression.

Space, Time,

847. But science tends to employ for these systems only such conceptions as relate to prediction; and of these the most fundamental are and Prediction. space and time. The first science to establish its method was the science of astronomy, where measurement and computation in terms of

space and time were the most obvious means of 131 description; and the general application of the method of astronomy by Galileo and Newton, or the development of mechanics, is the most important factor in the establishment of modern science upon a permanent working basis. The persistence of the term cause, testifies to the fact that science is primarily concerned with the determination of events. Its definitions of objects are means of identification, while its laws are dynamical, i. e., have reference to the conditions under which these objects arise. Thus the chemist may know less about the properties of water than the poet; but he is preeminently skilled in its production from elements, and understands similarly the compounds into which it may enter. general conditions of all anticipation, whereby it Now the becomes exact and verifiable, are spacial and temporal. A predictable event must be assigned to what is here now, or there now; or what is here then, or there then. An experimentally verifiable system must contain space-time variables, for which can be substituted the here and now of the experimenter's immediate experience. Hence science deals primarily with calculable places and moments. The mechanical theory of nature owes its

4

success to a union of space and time through its conceptions of matter and motion. And the projected theory of energetics must satisfy the same conditions.

The Quantita

§ 48. But, furthermore, science has, as we have seen, an interest in freeing its descriptions from the peculiar angle and relativity of an tive Method. individual's experience, for the sake of affording him knowledge of that with which he must meet. Science enlightens the will by acquainting it with that which takes place in spite of it, and for which it must hold itself in readiness. To this end the individual benefits himself in so far as he eliminates himself from the objects which he investigates. His knowledge is useful in so far as it is valid for his own indefinitely varying stand-points, and those of other wills recognized by him in his practical relations. But in

4 The reader is referred to Mr. Bertrand Russell's chapters on matter and motion in his Principles of Mathematics, Vol. I. Material particles he defines as "many-one relations of all times to some places, or of all terms of a continuous one-dimensional series t to some terms of a continuous three-dimensional series s." Similarly, "when different times, throughout any period however short, are correlated with different places, there is motion; when different times, throughout some period however short, are all correlated with the same place, there is rest." Op. cit., p. 473.

attempting to describe objects in terms other than those of a specific experience, science is compelled to describe them in terms of one another. For this purpose the quantitative method is peculiarly serviceable. With its aid objects permit themselves to be described as multiples of one another, and as occupying positions in relation to one another. When all objects are described strictly in terms of one another, they are expressed in terms of arbitrary units, and located in terms of arbitrary spacial or temporal axes of reference. Thus there arises the universe of the scientific imagination, a vast complexity of material displacements and transformations, without color, music, pleasure, or any of all that rich variety of qualities that the least of human experiences contains. It does not completely rationalize or even completely describe such experiences, but formulates their succession. To this end they are reduced to terms that correspond to no specific experience, and for this very reason may be translated again into all definable hypothetical experiences. The solar system for astronomy is not a bird's-eye view of elliptical orbits, with the planets and satellites in definite phases. Nor is it this group of objects from any such point of view, or from any number

of such points of view; but a formulation of their motions that will serve as the key to an infinite number of their appearances. Or, consider the picture of the ichthysauria romping in the mesozoic sea, that commonly accompanies a text-book of geology. Any such picture, and all such pictures, with their coloring and their temporal and spacial perspective, are imaginary. No such special and exclusive manifolds can be defined as having been then and there realized. But we have a geological knowledge of this period, that fulfils the formal demands of natural science, in so far as we can construct this and countless other specific experiences with reference to it.

Development

§ 49. Science, then, is to be understood as springing from the practical necessity of anticiThe General pating the environment. This anticiof Science. pation appears first as congenital or acquired reactions on the part of the organism. Such reactions imply a fixed coördination or system in the environment whereby a given circumstance determines other circumstances; and science proper arises as the formulation of such systems. The requirement that they shall apply to the phenomena that confront the will, determines their spacial, temporal, and quantitative form. The