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function and purpose they discharge in the cosmic process." He maintained that the world is will, and will means for him force or impulse; "but," says Professor Caldwell, he still conceives of will in primarily a negative way. He comes in the end to tell us what the world is not, and what the end of life is not." We may detect here the germ of his Buddhistic and pessimistic predilections.

The result is a sort of illusionism, which Schopenhauer essays to escape from by his peculiar treatment of the religious problem. "In its highest reaches," says Professor Caldwell, "Schopenhauer's philosophy becomes virtually a metaphysic "of the redemption of the individual from his own misery and from that of the "world. . . . His treatment of religion is important. It is essentially different from ́ ́that of Kant and from rationalism generally, laying far more stress on the pecu"liarly religious feelings as elements in the solution of the religious problem."

It is no adequate characterisation of Schopenhauer's philosophy, Professor Caldwell thinks, to call it pessimism. "Schopenhauer himself attached quite as much importance to the positive aspects of his system as to the negative." His success among the degenerates is owing to the circumstance that "it is naturally com"forting at times to be able to put one's self in the hands of a man who had the **strength to assault all intellectual presuppositions and theories about life whatso"ever, and, in particular, to help to overturn a philosophy whose proudest boast "it was to exhibit the intellect or the idea as actually victorious over both nature "and history." His success generally is due to the fact that his philosophy chronilces "the effort a century has had to make to reconcile its ideal theories about life with the facts that science has disclosed or thinks it has discovered."

Lastly, Professor Caldwell emphasises Schopenhauer's contempt for dogma and history, which incapacitated him from understanding and justly appreciating even his own mission, which was to " correlate idealism and realism, Platonism and life." Therein, according to Professor Caldwell, lay his real work, of which, however, strange to say, he was absolutely unconscious. As to his influence, "he "appealed to those who were without any gospel, to those who felt that the will "was at the bottom of everything, but who yet could not feel that they had been “'wrong in believing something else to be at the bottom of everything. The re"deeming thing about him and those who began to listen to his teaching was that "both he and they had got hold of a fact greater, perhaps, than they could reckon "with, but still a fact."

From the preceding statements we may, perhaps, also gather some inkling of Professor Caldwell's own views. T. J. MCC.

GRUNDRISS Der Geschichte der Philosophie, zum Selbststudium und für VorLESUNGEN. Von Dr. Johannes Rehmke, o. ö. Professor der Philosophie zu Greifswald. Berlin: Carl Duncker. 1896. Pages, 308.

The literature of Germany is extraordinarily rich in histories of philosophy, and their number seems to be steadily on the increase. The last to enter the field is

Dr. Johannes Rehmke, Professor of Philosophy in Greifswald, who has now enriched the growing cycle of his works by the present business-like and concise Rudiments, designed for autodidactic purposes or for collateral use with lectures. Its succinct form, utterly eschewing comments and discussions, its banishment of all biographical details, the omission of unnecessary prefaces and introductions, are all qualities which unite in making it unique and valuable and deserving of recommendation for students whose interest is not in need of being aroused. So far as we have been able to examine it, it is a faithful miniature reproduction of its material, devoting to each thinker adequate space, measured by his relative importance in the development of philosophy.

Professor Rehmke characterises the object of philosophy to be the defining of reality, full and entire, in terms of its general controlling factors; hence its designation of universal or fundamental science. Its expressed function is the answering of all general questions touching the world or reality in its largest sense.

Excluding India and all tentative and groping speculation (we cannot infer from the author's statements whether he places the philosophy of India on the same level with primitive and unsystematic attempts at solving the problems of existence), he makes philosophy begin with the Greeks. The development of philosophy is divided into two main parts—the history of ancient, and the history of modern philosophy: the first comprising the time from 600 B. C. to 1600 A. D.; the latter embracing the period from 1600 A. D. to the present. To the ancient period 101 pages are devoted, and to the modern 203. The entire era of the rise of Grecian philosophy, extending from the Ionic physiologers through the Pythagoreans, Heracliteans, Eleatics, Empedocles, Anaxagoras, and the Atomicians to the Sophists, receives but 23 pages. The commanding figures of ancient philosophy, Socrates, Plato, and Aristotle, receive 38. The decline of ancient philosophy, which is made to extend from the Peripatetics, Epicureans, Stoics, etc. to Scholasticism, Western Mysticism, and the philosophical Humanists of the sixteenth century, receives 39 pages. Modern philosophy is divided into three periods, the Pre-Kantian, the Kantian, and the Post-Kantian. In the first, Bacon (3 pages), Hobbes (8 pages), Descartes (14 pages), Geulinx, Malebranche, Spinoza (18 pages), Locke (11 pages), Berkeley (7 pages), Hume (16 pages), the Scottish School, the philosophers of the French Illumination, Leibnitz (17 pages), Wolff, and the philosophers of the German Aufklärung, receive consideration. To Kant, forty-six pages are devoted. After Kant are treated Fichte (11 pages), Schelling (3 pages), Hegel (5 pages), Schleiermacher, Schopenhauer (8 pages), Herbart (6 pages), and Lotze (3 pages). Lotze concludes the work. A glance at the preceding list and the figures showing the space devoted to the respective philosophers, will indicate the scope and predilections of Professor Rehmke's treatment. Its economic qualities alone might justify its translation into English, provided this could be fluently and not woodenly done.

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DE PLATONICIS MYTHIS. Thesim Facultati Litterarum Parisiensi. Proponebat Ludovicus Couturat. Paris Felix Alcan. 1896. Pages, 119.

SUR UNE NOUVELLE MÉTHODE POUR DÉTERMINER LA CHRONOLOgie des dialogues DE PLATON. Mémoire lu le 16 Mai, 1896, à l'Institut de France, devant L'Académie des Sciences Morales et Politiques. By W. Lutoslawski. Paris: H. Welter. 1896. Pages, 34. Price, 2 Fr.

The work of M. Louis Couturat forms a thesis presented to the Faculty of Letters at Paris. In examining the contradictions of the traditional conception of the Platonic doctrines, which students of the subject have left unexplained, the author has noted that the majority of the difficulties spring from the comparison of texts embodying mythical views with purely didactic passages of the Dialogues, and that consequently a criticism of the Platonic myths should precede every expressed interpretation of Plato's doctrines. Thus he has remarked that many passages which interpreters have taken as the dogmatic expression of Plato's thought, are obviously expressions of irony or allegory on the philosopher's part. To distinguish between the two species of expression, therefore, he has first subjected to scrutiny the actual myths of Plato, and with the criteria thus gathered has proceeded to the investigation of all anomalous passages, hoping to prove by his tests that the same are allegorical utterances. He has thus constructed from the actual myths a working allegorical vocabulary for the interpretation of Plato's veiled myths, and has found that God, the idea of divinity, the idea of reminiscence, the pre-existence and survival of the soul, all belong to this category. The circulation and perusal of M. Couturat's thesis will not be enhanced by its being written in

Latin.

While upon this subject attention should be called to a little brochure by W. Lutoslawski, Professor at the University of Kazan, on a new method of determining the chronology of the Dialogues of Plato, being a memoir read in May last before the Institute of France. Professor Lutoslawski gives here a brief outline of his comprehensive labors in this field, which to the special student will be of undoubted interest. As Professor Lutoslawski is at work upon an English volume, to be published by Longmans, and containing the full elaboration of his views, it is unnecessary for us to say anything more than that his researches are based upon the stylistic differences of the Platonic Dialogues as corroborated by the method of "logical comparisons" treated in this memoir.

A MACHINE FOR SOLVING NUMERICAL EQUATIONS.

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A curious machine for the mechanical solution of equations, invented by Mr. George B. Grant of Boston, Mass., is described in the American Machinist for Sept. 3, 1896 (New York: 256 Broadway), which is of considerable theoretical interest, and if the delicacy of its construction bears out its author's claims, is not without practical importance. Five scale-beams, pivoted on parallel sliding car

riages vertically arranged and carrying negative and positive pans, have their right (positive) arms, AN, so jointed at variable points B as to act successively on one another. The ratio of the distances AN/B N=x is kept uniform by means of a gearing, from the wheels of which through the carriage and guiding them run screws. This ratio is indicated on a graduated scale, having values from 1 to ∞, by a pointer attached to the fulcrum of the lower beam. Compounding the ratios of the jointed (positive) lever-arms we obtain the condition of equilibrium, and as the corresponding expression therefor, from the multiplication of four binomial factors, the typical equation of the fourth degree ±a x1+ bx3 + cx2+dx±e=0, the coefficients of which represent the weights to be placed in the respective positive and negative pans. The ratio of distances, or the root of the equation, is then readily determined by turning a crank, being reached and indicated when the machine assumes equilibrium.

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Since for x to be zero the distance BN would have to be infinitely great (AN/BN=x), the machine will not find roots approximating to zero; but this difficulty may be obviated by transformation. Also large roots cannot be determined with precision, for BN will have long passed below the limits of mechanical manipulation before x has attained very large values; in fact the distance between the values 1 and 2 on the scale is eight or nine times that between 16 and ∞. This also may be partly remedied by transformation. On the other hand, the machine does not require the multiple roots to be thrown out, nor that the co-efficient of the highest term should be either positive or unity. Also, since any beam may be left unweighted and hence the coefficient of the corresponding term reduced to zero, the machine will solve partial equations and consequently extract the roots of numbers representable in the common binomial form. The inventor claims it to be practicable to construct a machine delicate enough to find roots to two or three decimal places, so that the instrument might be used as a partial practical substitute for Sturm's theorem.

The free end of any beam, furnished with a pencil point, would trace a curve representing the equation. But the true equational curve must be indirectly produced. It is possible that with the appropriate mechanism, conquering the limitations of the machine, this curve might be directly traced; and it would then, at least for purposes of instruction, furnish a more powerful and certainly more graphic means of elucidating the equation than the scale. At the points of equi

librium the curve would cross the line of the abscissas and so indicate the roots measured on that line, we could see at a glance the character of the roots, etc. This geometrical method of investigating equations has a wide practical application and was beautifully presented a century ago by Lagrange, who even suggested an instrument for resolving upon this basis numerical equations of all degrees, without limitation of the positive or negative character, or magnitude, of the roots. It would be interesting to know if Lagrange's idea has ever been developed. (See the Séances des Ecoles Normales for 1794-1795.) T. J. McC.

PERIODICALS.

REVUE DE MÉTAPHYSIQUE ET DE MORALE. Vol. IV. No. 4.

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LA GÉOMÉTrie" de DescARTES AU POINT DE VUE DE SA MÉTHODE. By B.
Gibson.-LA Méthode de Descartes AVANT LE DISCOURS. By J. Berthet.
-LE DÉVELOPPEMENT DE La pensée de Descartes depuis les
JUSQU'AUX "' MÉDITATIONS." By P. Natorp.- LA PREUVE ONTOLOGIQUE
CARTÉSIENNE DÉFENDUE CONTRE LEIBNITZ. By A. Hannequin.-LES Re-
CHERCHES DE DESCARTES SUR LA CONNAISSANCE DU MONDE EXTÉRIEUR. By
H. Schwarz.- DESCARTES PHYSICIEN. By P. Tannery.- DESCARTES ET
SNELLIUS, D'APRÈS QUELQUES DOCUMENTS NOUVEAUX. By D. J. Korteweg.-
DU RAPPORT DE LA MORALE À LA SCIENCE DANS LA PHILOSophie de Descartes.
By E. Boutroux.-LE TRAITÉ DES PASSIONS de Descartes et l'Ethique de
SPINOZA. By V. Brochard.-L'INFLUENCE DE LA PHILOSophie cartésiENNE
SUR LA LITTÉRATURE FRANÇAISE. By G. Lanson.-LE CHRISTIANISME DE
DESCARTES. By M. Blondel.-Descartes jugé par VICO.
By F. Tocco-
CorrespondanCE DE DESCARTES (Autographes et copies manuscrites). By
Ch. Adam.-(Paris: Armand Colin & Cie.)

The editors of the Revue de Métaphysique et de Morale have paid a fitting tribute to the memory of Descartes in this stately number of their journal. Descartes was born in 1596, and in commemoration of the third centenary of his birth, they have devoted a whole special number to the consideration of his life, work, and influence. The number has been made international in character, and all the principal countries of Europe have been represented. Descartes is treated under five aspects: (1) of his method; (2) of his metaphysics; (3) of his physics; (4) of his ethics; and (5) of his influence and personality. The wealth of matter offered by the Revue will be apparent from a glance at the contents, which are given above.

It may not be inopportune to mention on this occasion the project of a complete edition of the works of Descartes which the editors of the Revue have in hand, the cost of which is to be defrayed by international subscription. The edition will take up ten volumes of from seven hundred to seven hundred and fifty pages each, two of which are to be published yearly. Each volume will cost twenty-five francs, but may be had by subscribers to the Revue for fifteen francs. (Editor, M. Xavier Léon, 39 rue des Mathurins, Paris, France; Publishers, Armand Colin & Cie, 5 rue de Mézières. Yearly subscription, 15 francs.)

PROCEEDINGS OF THE ARISTOTELIAN SOCIETY FOR THE SYSTE-
MATIC STUDY OF PHILOSOPHY. Vol. III.
No. 2.
PRESIDENTIAL ADDRESS.-Time and the Absolute. By B. Bosanquet, M. A.,
LL. D. WHAT IS MEANT BY THE A Priori ELEMENt in KnowleDGE? By

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