90 



NATURE 



[January 19, 1922 



Congress of Philosophy in Paris. 



T^HIS congress, which was held 'n Paris on Decern- 

 ■■■ ber 27-31 last, was organised by the Soci^td 

 frangaise de Philosophie. It was not international 

 in the same sense as the series of conferences inter- 

 rupted by the war, but consisted of a special session 

 of the French society, in which British, American, 

 Italian, and Belgian societies were invited to take 

 part by sending delegates. The British delegates 

 were members of the Aristotelian Society, and in- 

 cluded Prof. Wildon Carr, Miss H. D. Oakeley and 

 Dr. Dorothy Wrinch, of the University of London, 

 Prof. J. A. Smith, Mr. W. D. Ross, and Dr. F. C. S. 

 Schiller, of the University of Oxford, Prof. W. R. 

 Sorley, of the University of Cambridge, and Prof. 

 Hoernl^, of the University of Durham. 



The session was admirably organised under four 

 sections. The first, devoted to logic and methodology, 

 was presided over by M. Paul Painlev6 ; the second, 

 devoted to metaphysics and psychology, by M. Henri 

 Bergson ; the third, which dealt with the history of 

 philosophy, was under the presidency of Prof. Levy 

 Bruhl ; and the fourth section, dealing with social 

 and moral philosophy, was organised by Prof. Bougie. 

 The mornings were occupied with sectional meetings ; 

 in addition, each section arranged one general after- 

 noon meeting. Receptions in honour of the delegates 

 were given by the president of the Soci^t^ frangaise 

 and by the Rector of the Sorbonne, and the Soci^t^ 

 frangaise de Philosophie also entertained all the 

 members of the congress to dinner at the Club de la 

 Renaissance. 



Recent Developments of Relativity Theory. 

 _ In Section I. two subjects of scientific interest were 

 discussed, viz. the theory of relativity and the theory 

 of probability. The discussion of relativity, under 

 the chairmanship of the president of the Soci^t6 

 frangaise de Philosophie, was opened by Dr. Dorothy 

 Wrinch, who gave an account of the developments of 

 the theory of relativity due to Weyl and Eddington. 

 She explained how the electromagnetic-force tensor 

 has been identified with a quite specific function of 

 definite significance, in virtue of the fact that the 

 electromagnetic force satisfies the usual Maxwellian 

 equations, by means of an extension of the geo- 

 metrical system dealt with by Einstein. Dr. Wrinch 

 pointed out that the method of achieving this result 

 was logically similar to the method used by Einstein 

 in his identification of the energy tensor, covering 

 energy, momentum, and stress in a field, with a 

 certain function in his generalised geometry, and, 

 indeed, the function used by Eddington in his further 

 generalisations (Proc. Roy. Soc, 192 1). Dr. Wrinch 

 then referred to the existence of the new tensor dis- 

 covered by Eddington (ibid.), and also to the fact that, 

 although it is a development of the ordinary *G^„ 

 tensor (in the sense that the *G^v tensor is an ab- 

 breviated summary of it), its physical significance is 

 very uncertain at present. The Important logical 

 procedure^ adopted by Eddington in the introduction 

 of the axiom of the comparabilitv of proximate rela- 

 tions was then made clear. 



Prof. Langevin, who followed, gave an account of 

 the develooment of the theorv of relativity from its 

 origin in the experiment of Michelson and Morley to 

 its ramifications at the present day. He laid par- 

 ticular stress on the parallelism which has occurred 

 in the development of geometry and phvslcs, and he 

 contrasted at some length the very different charac- 

 NO. 2725, VOL. 109] 



teristics of these two parts or the theory of relativity. 

 Prof. Langevin then gave an account of the curious 

 manner in which non-Euclidean geometry has been 

 developed from the Euclidean geometry of the last 

 century, and he described the successive generalisa- 

 tions due to Weyl and Eddington. In the course of 

 his exposition of Eddington 's results Prof. Langevin 

 then pointed out the manner in which geometry 

 seems now to have gone ahead of physics, in that the 

 geometrical function referred to atove has not as yet 

 been identified with any physical idea. 



M. Paul Painlev^, who was the next speaker, 

 brought forward certain objections to the theory of 

 relativity which he had alreadv indicated In two com- 

 munications to the Paris Academy of Sciences In 

 October and November last. He discussed in par- 

 ticular the admissible forms of the Interval length ds, 

 and pointed out the fact that various generalised 

 functions /(r) might be substituted for r In the co- 

 efficients of the squared differentials in the usual 

 formula for the square of this Interval length. All 

 these forms indifferently satisfy the conditions, giving 

 (e.^.) the same resulting motion of the perihelion of 

 Mercury, but differing, on the other hand, in regard 

 to the effect of solar gravitation on light traversing 

 the sun's field. M. Palnlev^ laid great stress on this 

 multiplicity of possible forms, and criticised the theory 

 of Einstein on the ground of the multiplicity of pos- 

 sible forms In this particular formula and in other 

 formulae introduced at later stages. 



A further objection was brought against the theory 

 on the ground that no dynamical system can be con- 

 structed unless a privileged set of axes exists. Prof. 

 Langevin, afterwards dealing with this point and with 

 some of the paradoxes arising from It, and also from 

 certain other postulates, pointed out that all theories 

 allow the existence of a privileged set of axes in the 

 neighbourhood of each point, but that no one set is 

 necessarily applicable to the whole universe. A spirited 

 discussion between the above-mentioned speakers fol- 

 lowed, which dealt chiefly with certain of the more 

 striking paradoxes to which the theory appears inevit- 

 ably to lead. 



The Theory of ProhabiUty. 



Another meeting of Section I. of the congress — 

 on this .occasion a purely sectional meeting — discussed 

 the modern developments of the theory of probability. 

 The chair was taken by M. Hadamard, in the regretted 

 absence of M. Emil Borel on account of illness. In 

 his paper on " Les Axiomes du Calcul des Probabilit^s, " 

 M. Paul L^vy made public some important results 

 which he has recently obtained by the application of 

 the analytical Ideas used by Lebesgue in his work 

 on the theory of functions to F(x), the function repre- 

 senting the probability of an event x. The starting 

 point of his theory is the fact that this function F(x) 

 is necessarily a monotonic Increasing bounded function 

 of X. M. L^vy Introduces <p(z). a fonction carac- 

 tiristique of the probability, by refining it In terms of 

 a Stleltje's integral, 



(f,(z) = j e^^'-dF(x). 



This function he finds to be suflficlent to determine 

 F(x), and to be of fundamental importance In the later 

 development of the leading ideas In a strict mathe- 

 matical form. The paper raised many new points of 



