REVIEWS 6;i 



biassed by teachers. I should put down their answers as to what 6 times o 

 amounts to, I should work out the average of their answers to six places of 

 decimals, and should then decide that, at the present stage of human development 

 this average is the value of 6 times 9." 



There are arrows of wit to pierce all armours. A book for all who can stand a 

 joke, and who love critical acumen better than personal dignity. 



A. E. Heath. 



De Wijsbegeerte der Wiskunde van Theistisch Standpunt. By D. H. Th. 

 Vollenhoven. [Pp. xvi + 447-] (Amsterdam : Wed. G. van Soest 

 1918.) 



It is nowadays often recognised by philosophers that their work, if it is not to 



be mere mythology, must be based on scientific results, and proceed according 



to scientific method. The present Thesis for the degree of Doctor of Philosophy 



at the University of Amsterdam has the merit of realising this truth. For the 



purposes of a notice in a scientific journal, it is only necessary to draw attention 



to what may be called the substructure of Dr. Vollenhoven's essay. There is 



some likeness to the old-fashioned philosophies in the fact that the first part deals 



with a priori constructions of the possible solutions of the problems of the book; 



but the other parts will be found to contain much of interest to those who work 



at the problems of the universe by a scientific method. The second part is 



historical, and deals with empiricism, formalism, and intuitionism ; in the last 



division there is an account of the work of, among others, Galileo, Descartes, 



Leibniz, Newton, and Kant, which, however, does not go into detail, and is not 



free from small inaccuracies of quotation (cf. pp. 106, 108). The third part treats 



non-Euclidean geometries, "the logic of relations" (in which the modern aspect 



of this subject is not touched), "the theory of objects" of Meinong and others, 



Cantor's introduction of the actually infinite, and the arithmetisation of geometry. 



The fourth part deals with critical attitudes — modern empiricism, modern 



formalism, and modern intuitionism. Modern formalists are represented by 



Mannoury and Bertrand Russell, and modern intuitionalists by Poincare and 



L. E. J. Brouwer : Brouwer's work should be better known in Britain. There is a 



long and fairly satisfactory account of Mr. Russell's work and play, though the 



account is somewhat marred by failure to see jokes : thus, one part (only) of a 



skit on Mr. Russell's philosophy by the present writer is mentioned with apparent 



seriousness on p. 241 ; the character of the whole skit may be judged from the 



review which appears elsewhere in the present number of Science Progress. 



The notices of the work of Frege (pp. 195, 224-9) and Peano (pp. 229, 278, 289) 



are much too slight to be of service. 



Philip E. B. Jourdain. 



The Theory of Measurements. By Lucius Tuttle, B.A., M.D., Associate in 

 Physics at Jefferson Medical College, Philadelphia. [Pp. xiv + 303.] 

 (Philadelphia : Jefferson Laboratory of Physics, 1916. Price 31.25.) 



" FOR the student of mathematics," says the author (p. v), " this book is intended 

 to furnish an introduction to some of the applications of the exact sciences and 

 their relation to the 'practical' sciences and useful arts, and is primarily intended 

 to give him a knowledge of facts and methods, but without neglecting the accurate 

 exercise of his reasoning powers. For the student of physical science it is intended 

 especially to emphasise general considerations of measurement, theory of errors, 



