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 NEW BOOKS. 269 that relations (and in particular ratios) are prior to their terms, and that, given a ratio of two distances or of two periods of time or what not, we can regard the terms of the ratio as finite or as infinite or infinitesimal of any order, the ratio remaining unchanged. The author also distinguishes various degrees of Being, by means of which it is possible to hold at the same time that a thing is in one sense and is not in another, thus solving apparent contradictions. Whatever value may belong to these views on their own account, it is certain that they do not contribute to the solution of the problem of infinity, which has been found without their aid. The motives which have led mathematicians to turn their subject first into Arithmetic, then into Logic, are very strong, but a serious attack upon this procedure would be valuable. It is to be hoped that Dr. Geissler will give us this in some future work, together with a defence of his own position against the criticisms which naturally occur to the mathematician. B. RUSSELL. Das Urteil bei Descartes. Ein Beitrag zur Vorgeschichte der Erkenntnis- theorie. Von Dr. BRODER CHRISTIANSEN. Hanau : Verlag von Olauss & Feddersen, ]902. Pp. 107. Dr. Christiansen adopts the following division of his subject : (1) Analysis of Judgment according to Descartes; (2) Judgment and Truth: the Test of Truth ; (3) Judgment and Reality : the problem of Transcendentalism. Under (1) he clearly points out the development that took place in Descartes' view of the nature of judgment from his first treatment of the subject in the Regulae where on the whole he conceives judgment as a synthesis of ideas and the negative judgment as a special case of the positive, to his later treatment in the Meditations, etc., where he conceives judgment as essentially an act of affirmation or denial, and the negative and positive as distinct kinds of judgment. In these very first pages our author's clear and scholarly manner makes itself felt. Perhaps the only uncertainty his treatment leaves in the mind is as to whether he is right in assuming that when Decartes refers to a synthesis of ideas in the Regulae he is really stating his theory of judgment (cf. pp. 12, 13 with p. 59, end of 2). Dr. Christiansen then deals with Descartes' more matured theory of judgment, and after a keen criticism of Brentano's view that judgment, according to Descartes, was an act sui generis, concludes that it is essentially an act of will. There is, of course, a theoretical element, the idea, involved in the judgment, but it only serves as object or material for the volitional factor, the act of assent in which the judgment essentially consists. Our author follows up this analysis by an extremely thorough treatment of the two elements involved in judgment, the theoretical (what did Descartes mean by an idea, and by an innate idea in particular?) and the volitional. With regard to the relation between the two in judgment it is important to notice that the intellectual insight which assures us that a certain idea is real or materially true exercises no constraint on the will. The assent of the will to the truth of the idea follows out of its own nature, the will in its purity being essentially a striving after the True and the Good. The intellectual insight is only the ' occasional ' cause of the act of assent whereby the judgment is completed. At the same time though this intellectual insight into the true (das Erkenneii) is in itself no judgment, the judgment (das Anerkennen can only guard itself from error by making an intellectual apprehension of truth the precondition of its assent. The judgment is true (formally) only when the idea assented