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112 CRITICAL NOTICES : objections as this against M. Eibot's account of emotion ; since they merely form a direct contradiction of what he must regard as the fundamental proposition of a theory of feeling. Yet I have thought it necessary to point out this difficulty, in order to suggest that the view that emotion is merely sensation of expression is an artificially simple explanation, and fails to account for emotion as a concrete reality. Even those, however, who differ most widely from M. Eibot can hardly fail to recognise the skill and simplicity with which he presents his thesis, and the learning and acuteness that characterise his investigation of a subject with which few psycho- logists have come to such close quarters. His book is certainly a solid contribution to the discussion. It is, perhaps, to be regretted that M. Eibot has not furnished fuller references to the authors whom he consults and criticises. A bibliography of the subject, such as he could furnish, would be of the utmost value to many readers. Among slight inaccuracies, it may be mentioned that the English ethnologist " Taylor " to whom frequent references are made is Mr. Tylor. CHAELES DOUGLAS. De rinfini f Mathematique. Par Louis COUTURAT, Ancien Eleve de 1 ' Ecole normale superieure, Agrege de Philosophie, Licien- cie es Sciences Mathematiques, Docteur es Lettres. Paris : Felix Alcan, 1896. Pp. xxiv., 659. THE relation of number to quantity forms perhaps the most diffi- cult, as well as the most fundamental, of the problems of mathe- matical philosophy. On this problem at least three radically different views may be taken. We may, with Mill and most thorough-going empiricists, regard number as empirically derived from quantity, and quantity itself as a datum in experience. Or we may regard number as wholly a priori, and quantity as the result of applying to experienced data the a priori category of number. This view has been much advocated in France of late years, especially in M. Hannequin's important work on Atomism. 1 Lastly, we may hold that number and quantity are wholly inde- pendent categories, and that the application of number to quantity, as it occurs in measurement, has no deeper motive than one of convenience. The last of these three is the view of M. Couturat, who is forced, in the course of an able apology for mathematical infinity, to devote most of his space to the relations of quantity and 1 Essai Critique sur I 'Hypothec dts Atomes. Paris, 1894. M. Hanne- quin's book and M. Couturat' s should be compared, as they deal ably with almost the same theme from different standpoints.