RECENT ADVANCES IN SCIENCE 541 



central differences, the developments being traced in their 

 chronological order beginning with Newton. 



A useful set of notes on recent publications by A. Favaro, 

 J. Ginsburg, W. H. Bussey, B. Petronievics, F. Cajori, E. Mil- 

 losevich, L. Viriglio, D. E. Smith, O. Zanotti-Bianco, G. Mil- 

 haud, H. Suter, C. Tweedie, G. Bigourdan, G. Vacca, and L. A. 

 Perriere de Silva are given by G. Loria {Boll, di bibl. e st. delle 

 set. mat. 191 7, 19, 88-94). 



Some further letters that passed between Cremona and 

 Schlafli from 1872 to 1887 are given by J. H. Graf {ibid. 65-73 ; 

 cf. Science Progress, 191 8, 12, 363). 



Logic and Principles of Mathematics. — C. E. Van Horn 

 {Proc. Camb. Phil. Soc. 191 7, 19, 22-31) makes use of the new 

 function of propositions introduced into logic by Sheffer in 

 191 3, and b}r which the other functions (negation, disjunction, 

 implication, and conjunction) may be defined, to reduce the 

 number of primitive propositions in symbolic logic. However, 

 some steps in his work are unsatisfactory, as was pointed out 

 by J. G. P. Nicod at the end of his paper next mentioned. 

 Nicod {ibid. 32-41) is concerned independently with exactly 

 the same problem as Van Horn, but the subject is dealt with 

 much more completely and in a way that seems free from 

 objection. The eight primitive proportions of the theory of 

 implication given in Whitehead and Russell's Principia Mathe- 

 matica are reduced, by the help of Sheffer 's new primitive idea, 

 to three — two non-formal and one formal. The formal pro- 

 position is very complicated in statement. 



J. B. Shaw {Monist, 191 6, 26, 397-414), in an attack upon 

 mathematical logic, gives yet another illustration of what seems 

 to be the common feature of all such attacks, viz. the inability 

 to distinguish between the collection of truths discovered in 

 logic or mathematics — and which of course is not created by 

 our " intuition " — and the process by which we discover these 

 truths — in which of course " intuition " is used. Some of the 

 errors and irrelevances in Shaw's article are pointed out by 

 Philip E. B. Jourdain {ibid. 191 7, 27, 460-67). 



L. S. Hill {Amer. Math. Monthly, 191 7, 24, 345-8) gives an 

 example of a continuous series widely different from those 

 discussed by Huntington in his book on the Continuum (re- 

 viewed in Science Progress, 191 8, 12, 516). 



T. Levi-Ci vita's five papers of 191 7 from the Rendiconti of 



