RECENT ADVANCES IN SCIENCE 115 



this modern research into the logical foundations of mathe- 

 matics is simply a natural continuation of the work of three 

 men who must be ranked among the greatest pure mathe- 

 maticians of the nineteenth century — Weierstrass, Dedekind, 

 and Cantor. It is interesting to remember that Weierstrass 

 once said that the final object of mathematical research was a 

 knowledge of the principles of science. 



Some of Couturat's last — but by no means his best — work on 

 exposition of mathematical logic is an article in Windelband 

 and Ruge's Encyclopaedia of the Philosophical Sciences (English 

 edition, vol. i., Macmillan & Co., Ltd., 191 3, 7s. 6d. net). 



If we glance at the works of modern German writers on the 

 principles of logic and science in general, such as Driesch and 

 Natorp, we cannot fail to be struck by the absence of in- 

 telligent criticism of modern work on principles. In this they 

 are not very greatly surpassed by Brunschvicg's recent French 

 work on mathematical philosophy, in which the author seems 

 to have tried unsuccessfully to imitate the scholarly learnedness 

 of some of Couturat's works. The best recent works on 

 questions concerning the foundation of mathematics and mathe- 

 matical physics have all been produced in Great Britain. Of 

 course, the first place must be given to Dr. Whitehead and 



B. Russell's Principia Mathcmatica, of which the first volume 

 appeared in 1910, the second in 1912, and the third in 1913 

 (Cambridge University Press). A fourth volume is to be 

 concerned with the principles of geometry. Other questions 

 closely connected with the principles of mathematics, and which 

 used to be considered as " philosophical," are treated in 



C. D. Broad's Perception, Physics, and Reality : an Enquiry into 

 the Information that Physical Science can Supply about the Real 

 (Cambridge University Press, 1914, 10s. net), A. A. Robb's 

 Theory of Time and Space (Cambridge University Press, 1914, 

 10s. 6d. net), and Russell's "Lowell Lectures" of 1914 on Our 

 Knowledge of the External World as a Field for Scientific Method 

 in Philosophy (Chicago and London, Open Court Publishing 

 Co., 75. 6d. net). It is only to be expected that, in the work 

 just mentioned, we should have topics discussed which are 

 so interesting to the logician and mathematician as infinity, 

 continuity, and Zeno's puzzles about motion. In November 

 1914, Russell's " Herbert Spencer Lecture " on Scientific Method 

 in Philosophy (Oxford, Clarendon Press, 1914, is. 6d. net) was 



