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572 NEW BOOKS. a picture of the connexion or system (of the universe) in the sense in which concepts do so, but it is that system itself, as expressed and mirrored in the human spirit" (p. 95). We read accordingly of a " mathematics of the universe," in which Life plays the part that the symbol of the irrational number plays in human mathematics : it is both matter and/orce, both being and becoming, yet more than either, just as the irrational number (e.g. J2) mediates between the discrete and the continuous, between arithmetic and geometry (pp. 137 f.). Keyserling does indeed proceed to show, with much display of scientific evidence, that a common Ehythm, expressible in the same numbers, runs through such diverse things as the formation of crystals, the harmonies- of tones, the relations of colours, the arrangements of atoms, etc. (pp. 157 f., 182 f., etc.): and even through the sphere of human creative- ness and spontaneity Art. "The rhythms according to which the greatest spirits, though following their free, inward, personal disposi- tions, brought their works into existence i.e. the forms of art are the same as those which in nature have held for all time, which in end- less space direct the course of the stars, direct also the growth and decay of life on the most insignificant of planets. Hence it is that music is the highest symbol of the universe " (p. 228). Stated so, baldly, the theory appears mystical and fantastic ; in the setting of the mass of argument and illustration in the work itself, it is not so, but reasonable and almost probable. There are also many attractive suggestions made on which it has been impossible to touch here. , J. L. M. Kritik der Freiheitstheorien. Eine Abhandlung iiber das Problem der Willensfreiheit von JOSEPH MACK. Leipzig: Johann Ambrosius Earth, 1906. Pp. 283. Price 4 '50 mks. At one time philosophers seemed to have wearied of disputing about the freedom of the will. But with the reaction against the exclusive pre- dominance of scientific categories, interest in the problem of freedom is- fast reviving. Infallible symptom of this is the flood of pamphlets on the subject which is being poured forth in Germany. Mr. Mack's book is a fair sample of its class. It contains a defence of freedom which is not without ingenuity, though I suspect that it will be read with mis- givings even by friends of his cause. His main line of argument appears to be this : Free, in the widest sense, is whatever follows its own nature, obeys the laws of its own being. In this sense all nature, the falling stone, the growing tree, so far as they fall or grow without interference (artificial? human?), are free. Man, too, is free if he obeys the laws of his nature. But this purely verbal reconciliation of freedom and necessity does not carry us. far. The question is not, whether a thing which follows the laws of its nature deserves to be called free, but whether the laws of nature and of man are the same, whether the categories (especially causality) which we apply to nature, are also adequate for the explanation of human con- duct. A natural object, just because it obeys the laws of its being, can in no case behave otherwise than it does. Man is normally conscious that he can act and will otherwise than he does. Hence the problem : If man is merely a piece of nature, subject like nature to causality, this possibility of alternatives is mere illusion, as the determinist maintains. The defender of freedom, therefore, has to show that man has specific qualities which lift him above nature. Mr. Mack finds two such char- acteristics which, in the end, are seen to be closely connected : (1) Man