RECENT ADVANCES IN SCIENCE 



MATHEMATICS. By Philip E. B. Jourdain, M.A., Cambridge. 



History. — A very useful summary of the contents of ancient 

 Indian mathematical works is given by G. R. Kaye in a little 

 book reviewed elsewhere in the present number. Prof. Florian 

 Cajori has written a very detailed and valuable paper giving 

 an account of the works of William Oughtred (Monist, 191 5, 

 25, 441). The most interesting points about Oughtred 's works 

 are the amount of symbolism used, and the fact that he was 

 the first inventor of the slide rule, though not the first to publish 

 anything about slide rules. Cajori [Open Court, 191 5, 29, 449) 

 also gives a biography and portrait of Oughtred. 



Logic and the Principles of Mathematics. — The number of 

 the Revue de Metaphysique et de Morale for September 19 14 

 only appeared in June 1915, and contains a very complete 

 account of the work of Louis Couturat followed by a biblio- 

 graphy. The account is by Andre Lalande, and we can trace 

 in it the development of Couturat 's thought from De V Infini 

 Mathematique of 1 896, through his publications on the logic of 

 Leibniz (1901, 1903) which were partly based on original re- 

 search at Hanover, through his study of the logical calculus 

 (1905), up to his exposition of modern work (chiefly by Russell) 

 of the principles of mathematics (1905 and later). Since 1901 

 Couturat became more and more occupied with the details of 

 international languages and particularly " Ido " : this was also 

 an effect of his study of Leibniz. His work on Leibniz is far 

 the most permanent part of his reputation, and mathematical 

 logicians will ever be grateful to him for it. 



Dr. Charles A. Mercier (Mind, 191 5, 24, 386) contends in 

 his usual amusing way that the syllogism is neither the only 

 nor psychologically the most natural form of argument. Cer- 

 tainly any modern logician would agree with him on this point. 

 Further, Mercier maintains that logicians merely assert that 

 there is a universal in every argument, and that in fact this is 

 not true. 



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