RECENT ADVANCES IN SCIENCE 191 



account of the life and work of Milhaud (cf. above) is given by 

 A. Lalande in Rev. Gen. des Set. (December 15, 191 8, 29). 

 Among deaths of mathematicians not mentioned before in this 

 quarterly may be noticed A. Benteli of Bern (November 10, 

 1917, seventieth year); E. Ott of Bern (November 17, 1917, 

 seventieth year) ; R. Jentzch of Berlin (March 21, 191 8); M. B.. 

 Weinstein of Berlin (sixty-fifth year) (Amer. Math. Monthly, 



1 91 9, 26, 179). 



An account is given (Journ. Indian Math. Soc, 1919, 11, 

 41-4) of the circumstances which led to the foundation in 1907 

 of the Indian Mathematical Society by V. Ramaswami Aiyar, 

 under the name of " The Analytic Club." 



Logic, Principles, and Theory of Aggregates. — J. Nicod 

 (Rev. de Metaphys., 191 9, 26, 37$-86) makes a critical study of 

 E. Goblot's Traite de Logique (Paris, 191 8), and gives an inter- 

 pretation of some logical points in modern symbolic logic. 



H. Eklund (ir) criticises proofs of Schoenflies, Whitehead, 

 Russell, and Broden (cf. Science Progress, 191 9, 13, 346), of 

 the non-existence of " aggregates which are members of them- 

 selves," and gives an attempt at a theory of such aggregates. 

 H. Dingier (22) continues his considerations on well-ordered 

 aggregates, and gives a reduction to the axiomatic method of 

 that part of Cantor's work which relates to ordinal numbers. 

 L. E. J. Brouwer (49) gives a set of additions and corrections 

 to his Dissertation of 1907 on the foundations of science 

 (cf. Science Progress, 191 8, 13, 3). 



In the theory of point-aggregates, Brouwer (46) considers 

 linear inner limiting sets, and F. Hausdorff (23) gives a generali- 

 sation of Caratheodory's concept of measure. 



A. Reymond (Rev. de Metaphys., 191 9, 26, 313-34), in a 

 sequel to a criticism of his which rests on a confusion between 

 cardinal numbers and ordinal numbers, attempts to explain 

 his view that, from a philosophical point of view, the defini- 

 tion given by Cantor of transfinite ordinal numbers can be 

 attacked, although technically these numbers are legitimate ; 

 and then attempts a strict definition of them. The confusion 

 mentioned seems to be still in force, and to vitiate the pro- 

 posed definition of transfinite ordinals as certain different 

 arrangements of integer numbers, in which it is not stated 

 whether the integers are cardinal or ordinal. D. Wrinch (Proc. 

 Cambridge Phil. Soc, 1919, 19, 219-33) investigates the neces- 



