A COMPENDIOUS CLASSIFICATION OF THE SCIENCES. 27 the thinkers themselves. Were " the given " a chaos, no sub- jective forms, call them " necessary" or not, could set it in order. Nor does it seem reasonable on the other hand that, if there are no intelligible laws to which it is really conform- able, the modes of formulating it suggested from time to time by some of its casual conjunctions should agree so well with the rest. To maintain that there is now an approach to unanimity on these points may seem paradoxical. But, in the end, what historical reason is there for expecting that the opposition between a priori and a posteriori methods, or between Eationalism and Experientialism, will be the one permanent line of cleavage between philosophic schools? After the logic of the sciences come the positive sciences as such. The first question that arises with respect to these concerns the position of Mechanics. Shall we, with Comte, place at the end of the mathematical sciences Rational Mechanics? Or shall we separate Mechanics as a whole from Mathematics, and make it the fundamental department of Physics ? It seems to me that the incontestable portion of Kant's mathematical doctrine necessitates the second position. With Mechanics comes in the conception of "mass," which cannot be educed from space as a pure form of intuition, but has direct reference to data of sense supplied by the feelings of pressure and touch. Yet Comte's view was not altogether ungrounded. The higher branches of mathematics, such as those that deal with infinitesimals and with imaginary quantities, have been elaborated, as Prof. Bain has pointed out, in close connexion with physical investigations, and often for the sake of solving definite physical problems. Everything except their primary assumptions may have been evolved by pure mathematical construction and formal reasoning; but, if the assumptions themselves are not congruous with the physical order of nature, the theories as a whole remain mere curiosities, and can scarcely be regarded as in any proper sense "true". The reason for including them in Mathematics while excluding Rational Mechanics seems, however, to be this. In Rational Me- chanics the idea of a moving mass is fundamental. In Mathematics, whatever may be the manner in which any of its peculiar assumptions are finally selected as worthy to form the ground of a special theory, they can be treated actually as determinations of space .and number without direct reference to mass. This is of course the normal relation of a simpler to a more complex science. The fact that the more complex science furnishes it with some of its problems does not destroy its logical priority.
