Owing to the excellent training he had received at the Ecole Polytechnique, and by his own profound study, Renouvier was able on many technical points to meet the scientists on their own ground. His third _Essai de Critique générale_ is devoted to a study of “the Principles of Nature,” in which he criticises many of the principles and assumptions of mechanism, while many pages of his two previous _Essais_ are concerned with the discussion of questions intimately affecting the sciences.[22] [22] This is particularly noticeable in the matter printed as appendices to his chapters. (_Cf_. the _Logic_, vol 2.) An important section of his second Essay, _Psychologie rationnelle_, deals with the “Classification of the Sciences.”[23] Renouvier there points out that the attempt to classify the sciences in accordance with their degrees of certainty ends in failure. All of them, when loyal to their own principles, endeavour to display equal certainty. By loyalty Renouvier shows that he means adherence to an examination of certain classes of phenomena, the observation of facts and laws, with the proposal of hypotheses, put forward frankly as such. He draws a line between the logical and the physical sciences—a division which he claims is not only a division according to the nature of their data, but also according to method. Following another division, we may draw a line between sciences which deal with objects which are organic, living creatures, and those which are not. [23] Vol. 2, chap. xviii., _De la Certitude des Sciences et leur Classification rationnelle_, pp. 139-186, including later observations on Spencer. Renouvier’s line is not, it must be remembered in this connection, a purely imaginary one. It is a real line, an actual gap. For him there is a real discontinuity in the universe. Taine’s doctrine of a universal explanation, of a rigid unity and continuity, is, for Renouvier, anathema, _c’est la mathématisation a l’outrance_. This appears most markedly in the pages which he devotes to the consideration of _la synthèse totale_. An important section of his _Traité de Logique_ (the first _Essai de Critique générale_) deals with the problem of this Total Synthesis of all phenomena.[24] This is a conception which Renouvier affirms to be unwarrantable and, indeed, in the last analysis impossible. A general synthesis, an organisation or connected hierarchy of sciences, is a fond hope, an illusion only of a mind which can overlook the real discontinuity which exists between things and between groups of things. [24] Vol. I, pp. 107-115, and also vol. 2, pp. 202-245.