extraneous elements causing pathological processes; but that same philosopher, in so far as he is a complete man, and in so far as he provides for the economy of his internal life and for more easy communication with his fellows, must fashion and avail himself of the empirical. Having ideally destroyed the adjective and the adverb, the epic and the tragic kinds, the virtues of courage and of prudence, the monogamous and the polygamous family, the dog and the wolf, he must yet speak when necessary of adjectives and adverbs, of epics and tragedies, of courage and of prudence, of families formed in this or that way, of the species "dog," as though it were clearly distinguished from the species "wolf." Thus is confirmed the autonomy and the peculiar nature of the empirical or natural sciences, indestructible by philosophy as philosophy is indestructible by them. [Footnote 1: _Nov. Org._ I. §§ 81, 116; and II. in fine.] [Footnote 2: See _The Philosophy of the Practical,_ pt. i. sect. i.] [Footnote 3: Letter to d'Epinay, October 12, 1776.] VI MATHEMATICS AND THE MATHEMATICAL SCIENCE OF NATURE [Sidenote: _The idea of a mathematical science of nature._] The conception of a _mathematical science of nature_ is at variance with the thesis that recognizes the ineliminable historical foundation of the natural sciences and the consequences which follow from it. It is claimed that this mathematical science, in expressing the ideal and end of the natural sciences, would express also their true nature, which is not empirical but abstract, not synthetic but analytic, not inductive but deductive. The mathematical conception of the natural sciences would imply perfect mechanism, the reduction of all phenomena to quantity without quality, the representation of each phenomenon by means of a mathematical formula, which should be its adequate definition. [Sidenote: _Various definitions of mathematics._]