A COMPENDIOUS CLASSIFICATION OF THE SCIENCES. 25 restored, though it cannot be said that definitive conclusions have yet been reached. It is henceforth clear, however, that the character of the special logic which belongs to mathe- matics can only be determined by an investigation like that of Kant's Transcendental ^Esthetic. Such an investigation is necessarily metaphysical. Psychological theories of the origin of space as a mental form can at most furnish hints towards fixing the problem. Whatever the final result may be, Kant has determined the method of the inquiry. For the classification of the sciences, it is sufficient to note that mathematical truth, though "material" and no longer purely "formal," does not yet suffice to determine anything whatever about the order of nature. This was fully recog- nised by Kant, who saw that before even "synthetic" propositions regarding space and number can be applied to phenomena, certain other general maxims, beyond both these and the laws of thought, are needed. The case may be illustrated as when we were discussing the applicability of the Law of Contradiction. Let us suppose ourselves to have the power of counting, and of drawing figures in an imaginary space. Then, if we can provide bur constructions with names, and can somehow communicate with similar intelli- gences, we may work out a system of pure arithmetical and geometrical truth. But suppose that, so far as external nature is concerned, we are confronted with an absolute and lawless flux. Then we can do nothing whatever with our mathematical system. It is of no use to us that the results of counting and of drawing follow with necessity, if numer- able things alter their number from moment to moment and figured things change their shapes at random. For abstract geometrical truth indeed it is not required that perfect triangles and perfect circles should exist in nature ; but, for applicability of deductions about those geometrical figures, things marked out with figures that approximate to them must retain their shapes long enough for the deductions to be also approximately applicable during a time that is not merely infinitesimal. To give us the least rudiment of physical or natural science, we evidently require some recognisable perdurability or con- stancy in things. This requirement is now expressed as the Uniformity of Nature. In antiquity it found expression partly in very slight outlines of a logic of Induction, but most expressly in axioms of which the general form was that nothing is produced from nothing and that nothing can return to nothing. This conception goes back to the beginnings of the Ionian physics. For the history of modern science, its
