4 SCIENCE PROGRESS 



{Rev. de. Metaphys. 191 9, 26, 149-51) of Gaston Milhaud (cf. 

 Science Progress, 1919, 13, 522), it is stated that he had 

 finished a book, Descartes Savant. 



Logic and Principles of Mathematics. — C. D. Broad (Mind, 

 191 8, 27, 389-404) shows that the degree of belief which we 

 actually attach to the conclusions of well-established induc- 

 tions cannot be justified by any known principle of probability, 

 unless some further premiss about the physical world be 

 assumed. Broad does not attempt to state this principle, 

 but Jourdain (ibid. 191 9, 28, 162-79), who arrived independently 

 at the need indicated, does. This " principle of causality," 

 which is shown to be more fundamental than B. Russell's " prin- 

 ciple of induction," is the necessarily a priori assumption that 

 there is a one-one (not many-one, as with Mach) relation be- 

 tween the " universe " of mathematical physics and any part 

 of it. In a continuation of this paper, Jourdain will maintain, 

 against Broad, that probability is not a purely logical attribute 

 of propositions which is independent of the nature of the 

 particular world we happen to inhabit. 



It is of interest that, according to B. Russell (ibid. 124), 

 all the modifications in the Principia Mathematica made to the 

 notations of Russell's (1902) logic of relations are due to A. N. 

 Whitehead. 



Jourdain (Nature, 191 9, 103, 45) gives in detail a very 

 particular case of his theorem (cf. Science Progress, 191 8, 

 13, 178) for which critics asked and in which chains of type 

 to are constructed out of chains of respectively all the finite 

 ordinal types. The most notable point is the emphasis laid 

 on the fact that, in the arrangement of the " chains " of M 

 in classes of " direct continuations," there are here none of 

 these classes left over in each of which are not members of all 

 finite types. The class (k n ) of all those chains which are of 

 ordinal type n (which exists, by hypothesis, for all finite w's) 

 assigns, without any arbitrary choice, one chain to each of the 

 classes of direct continuations already formed — k n forming, by 

 the rule given, classes exactly like those formed already, but 

 with additions. 



D. M. Wrinch (Monist, 1919, 29, 141— 5) practically repeats 

 much of B. Russell's theories about " existence." R. A. 

 Arms (ibid. 146-52) considers the relation of logic to mathe- 

 matics, and V. F. Lenzen (ibid. 152-60) maintains that White- 



