Page:Philosophical Review Volume 9.djvu/556

540 analysis. "With the development of arithmetic, algebra, and modern analysis a new sphere of experience was unrolled, and its conquest has marked the establishment of the concepts of law, of causality, and of determinism in science, until finally the whole development culminated with Leibnitz and John Bernoulli in the notion of a function." It remained for the successors of Descartes to extend to nature in its entirety his conception of the union between geometry and algebra.

The problem for science is equivalent to what in mathematics might be called "the search for the form of the function," by which through mere mechanical manipulation dependent variables may be determined from independent variables. There is or there is not a discoverable connection between certain given events of nature. It is the business of the scientific inquirer to discover the form of that connection. The law of falling bodies and the law of refraction, two simple instances of actual scientific laws, involve special features of the economy of thought, prophesy of the future, and reconstruction of the facts of the past. "The element of comparison is at the basis of all scientific explanation. Bare description does not necessarily constitute the essence of science, and scientific description understood in its highest and in its lowest sense, always proceeds by comparison." The conception of scientific explanation, which makes of it a description of nature, involves an elimination of the metaphysical elements from science, economy and simplicity of the notions of science, and the power of reconstructing nature. All scientific systems, all so-called natural laws, are intellectual devices for reproducing the course of nature in the imagination. According to the view of the writer of this article, scientific explanation is itself a natural phenomenon. "Thus dualism is eliminated, and the conformity of the mind to the world appears as the natural conformity of two coordinate parts of the same consistent and orderly whole. Science takes its rise as the forms of life have taken their rise, by the adaptation of the mind to its environment."

Heretofore the science of geometry, says M. Calinon, has been based entirely upon the principle of geometrical equality, that is, two figures have been called equal to one another if they coincide when one is superimposed upon the other. Two equal figures have been considered as two different positions of the same figure. This, however, gives no absolute standard of measurement. Therefore the new or numerical geometry rejects the principle of geometric equality, and replaces it by the principle of numerical or relative equality. It takes as its base a numerical definition of distance which then becomes, for all practical purposes, an absolute standard and from this it deduces all its propositions. For all measurements are purely relative. They depend upon the choice of some one