progress of science is marked by the growth of these conceptions in the direction of comprehen siveness on the one hand, and of refinement and delicacy on the other. Man lives in an environment that is growing at the same time richer and more extended, but with a compensatory simplification in the ever closer systematization of scientific conceptions under the form of the order of

nature.

The Determi

nation of the

ural Science.

§ 50. At the opening of this chapter it was maintained that it is a function of philosophy to criticise science through its generating Limits of Nat- problem, or its self-imposed task viewed as determining its province and selecting its categories. The above account of the origin and method of science must suffice as a definition of its generating problem, and afford the basis of our answer to the question of its limits. Enough has been said to make it clear that philosophy is not in the field of science, and is therefore not entitled to contest its result in detail or even to take sides within the province of its special problems. Furthermore, philosophy should not aim to restrain science by the imposition of external barriers. Whatever may be said of the sufficiency of its categories in any region of the world, that body

of truth of which mathematics, mechanics, and physics are the foundations, must be regarded as a whole that tends to be all-comprehensive in its own terms. There remains for philosophy, then, the critical examination of these terms, and the appraisal as a whole of the truth that they may

express.

Natural

Science is

51. The impossibility of embracing the whole of knowledge within natural science is due to the fact that the latter is abstract. This Abstract. follows from the fact that natural science is governed by a selective interest. The formulation of definitions and laws in exclusively mechanical terms is not due to the exhaustive or even preeminent reality of these properties, but to their peculiar serviceableness in a verifiable description of events. Natural science does not affirm that reality is essentially constituted of matter, or essentially characterized by motion; but is interested in the mechanical aspect of reality, and describes it quite regardless of other evident aspects and without meaning to prejudice them. It is unfortunately true that the scientist has rarely been clear in his own mind on this point. It is only recently that he has partially freed himself from the habit of construing his terms as final and

1

5

exhaustive. This he was able to do even to his own satisfaction, only by allowing loose rein to the imagination. Consider the example of the atomic theory. In order to describe such occurrences as chemical combination, or changes in volume and density, the scientist has employed as a unit the least particle, physically indivisible and qualitatively homogeneous. Look for the atom in the body of science, and you will find it in physical laws governing expansion and contraction, and in chemical formulas. There the real responsibility of science ends. But whether through the need of popular exposition, or the undisciplined imagination of the investigator himself, atoms have figured in the history of thought as round corpuscles of a grayish hue scurrying hither and thither, and armed with special appliances wherewith to lock in molecular embrace. Although this is nonsense, we need not on that account conclude that there

'That the scientist still permits himself to teach the people a loose exoteric theory of reality, is proven by Professor Ward's citation of instances in his Naturalism and Agnosticism. So eminent a physicist as Lord Kelvin is quoted as follows: "You can imagine particles of something, the thing whose motion constitutes light. This thing we call the luminiferous ether. That is the only substance we are confident of in dynamics. One thing we are sure of, and that is the reality and substantiality of the luminiferous ether." Vol. I, p. 113.

are no atoms.

There are atoms in precisely the sense intended by scientific law, in that the formulas computed with the aid of this concept are true of certain natural processes. The conception of ether furnishes a similar case. Science is not responsible for the notion of a quivering gelatinous substance pervading space, but only for certain laws that, e. g., describe the velocity of light in terms of the vibration. It is true that there is such a thing as ether, not as gratuitously rounded out by the imagination, with various attributes of immediate experience, but just in so far as this concept is employed in verified descriptions of radiation, magnetism, or electricity. Strictly speaking science asserts nothing about the existence of ether, but only about the behavior, e. g., of light. If true descriptions of this and other phenomena are reached by employing units of wave propagation in an elastic medium, then ether is proved to exist in precisely the same sense that linear feet are proved to exist, if it be admitted that there are 90,000,000 x 5,280 of them between the earth and the sun. And to imagine in the one case a jelly with all the qualities of texture, color, and the like, that an individual object of sense would possess, is much the same as in the other to imag

ine the heavens filled with foot-rules and tapemeasures. There is but one safe procedure in dealing with scientific concepts: to regard them as true so far as they describe, and no whit further. To supplement the strict meaning which has been verified and is contained in the formularies of science, with such vague predicates as will suffice to make entities of them, is mere ineptness and confusion of thought. And it is only such a supplementation that obscures their abstractness. For a mechanical description of things, true as it doubtless is, is even more indubitably incomplete.

§ 52. But though the abstractness involved in scientific description is open and deliberate, we The Meaning must come to a more precise under

of Abstract

ness in Truth. standing of it, if we are to draw any conclusion as to what it involves. In his "Principles of Human Knowledge," the English philosopher Bishop Berkeley raises the question as to the universal validity of mathematical demonstrations. If we prove from the image or figure of an isosceles right triangle that the sum of its angles is equal to two right angles, how can we know that this proposition holds of all triangles?

"6 To which I answer, that, though the idea I have in view whilst I make the demonstration be, for instance,