DISCOVERY 



277 



the province emerges, strongly Christianised, into the 

 history of the Church. The inscription of Diogenes gives 

 us an interesting ghmpse of the ethical ideals of a section 

 of Lycian society a century earlier. If its contribution 

 to our knowledge of Epicurean theory is slight, it forms 

 a notable landmark in the religious struggle which went 

 on in the eastern provinces during the first three centuries, 

 and has left many traces on the inscriptions of Asia 

 Minor. 



The book is the work of eleven writers. The manner 

 in which thej- have executed their task under somewhat 

 cramping conditions of space compels admiration. We 

 have onh' two complaints to make. We should have liked 

 a section on Bacchylides ; and we feel aggrieved not to be 

 told the name of the writer of the discerning essay on 

 Callimachus. 



W. M. Calder. 



The XeiD Decameron. The Tliird Volume. (Oxford, 

 Basil Blackwell, 7s. 6d.) 



Is the short story coming into its own ? There are 

 evident signs, from the number of books of short stories 

 now being published, that it is. One of the most interest- 

 ing phenomena in tliis connection is the anthology of 

 short stories by various writers. Several of them have 

 already taken the field, but The New Decameron, now in 

 its tliird volume, may be considered one of the pioneers, 

 and it has certain definite characteristics of its own. 



The title is not altogether fortunate, for the volume, 

 being the work of several hands, does not compare happily 

 with the easy, un-self-conscious tale-telling of Boccaccio. 

 The reader cannot rid himself of the feeling that the book 

 is machine-made, and the picture of the frantic though 

 clever editor, attempting to graft the very diverse subjects 

 and styles of his authors onto the main theme of the 

 experiences of Mr. Turpin's personally-conducted touring 

 party in France, persists in coming before his eyes. 



Many well-known authors have contributed to the 

 volume — amongst them Compton Mackenzie, D. H. 

 LawTence, Michael Sadleir. To our mind the two most 

 striking stories are " Chelsea Justice " by V. Sackville West 

 and " The Sceptical Poltergeist " by J. D. Beresford, wliich 

 come at the end of the book. The first narrates the 

 . revenge which a man took on a great friend, who, he 

 believed, had seduced his vdie, by shutting him up in a 

 buoy far out to sea off the Cornwall coast, and the second 

 the conversation of a psycliical researcher with "what 

 the Spiritualists and Theosophists, and so on, call an 

 ' Elemental.' " For irony and humour backed b}- a 

 suggestive thoughtfulness, this last tale would be hard 

 to beat amongst those recentlv devoted to the subject. 



E. L. 



PROBABILITY 



A Treatise on Probability. By John Mavnard Keynes. 

 ^MacmiUan & Co., Ltd., 18s.) 



The subject of Probability has a much greater import- 

 ance than it once had, and the appearance of a really 

 comprehensive treatise on the subject is to be welcomed, 

 especially when it bears the marks of careful and impartial. 



yet original, treatment shown by this volume. The day 

 when probability was regarded as a subject only for 

 theorists and philosophers has gone, and now, whether 

 we are aware of it or not, a great deal of scientific work is 

 impHcitly based upon the subject. Thus, when an experi- 

 ment is repeated and the arithmetic mean of the result 

 is taken, it is implicitly assumed that such an average is 

 the " probable " or " best " value. More often than not 

 such a procedure is justified, but one of the functions of 

 the theory of probability is to examine the logical basis 

 of such methods. Given a certain set of postulates, it is 

 possible to construct a number of theorems in probability, 

 and it is necessary that the fundamental ideas and theorems 

 of the subject should be carefully scrutinised on the 

 grounds respectively of reasonableness and logical con- 

 sistency. This the autlior has done, and his exposition 

 of the subject is clear and con\ancing ; he illustrates his 

 argument in a very interesting way, not the least interest- 

 ing illustrations being taken from arguments in legal 

 proceedings, where a judge and jurj' often have to deter- 

 mine rough measures of probability. The author gives 

 a human touch to the subject which is very refresliing. 



While n.iost people have a fairly clear notion as to what 

 is probable, the translation of a qualitative notion into 

 a quantitative one is not at all simple. Indeed, the author 

 denies that a numerical estimate of probability is always 

 possible, and therefore he avoids an explicit definition of 

 probability, though he has also other grounds for avoiding 

 such a definition. Herein he differs from the procedure of 

 previous writers who early introduced numerical methods. 

 On the philosophical side he may be correct, but there 

 is a need felt for some well-attested method whereby 

 quantitative results can be given and approximate 

 measures of probabilitj- be obtained. One of the most 

 common methods used is based upon the frequency 

 theory of probability, which, indeed, is the foundation of 

 most statistical work. Mr. Keynes' discussion of this theory 

 and of the foundations of statistical inference is a valuable 

 portion of the book, even though one's bhss may be shown 

 to be too highly correlated with ignorance. One function 

 of the theory of statistics is to provide methods by which 

 the chief characteristics of phenomena can be described, 

 while a second is to enunciate laws or generalisations. 

 Thus we may say that the arithmetic mean of a set cf 

 observed values of x is X, and that the standard deviation 

 is 5 ; these are precisely defined and simply summarise 

 the chief characteristics of the data. But when we 

 infer that X is the " probable " value of x, and that 5 is a 

 measure of probability of deviation from X, we imply a 

 set of postulates and theorems concerning probabihty. 

 As the main difficulties of the subject arise in the inter- 

 pretation of statistical results, it is vital that there should 

 be a thorough understanding of the conditions under which 

 inductions can be made ; otherwise " statistics can prove 

 anything." The author is careful to enforce the contrast 

 between statistical description and statistical induction, 

 and he deals almost entirely with the latter, whereas 

 nearly all statistical treatises are mainly concerned \\ith 

 the former. For this reason the book is a valuable supple- 

 ment to those treatises, especially as the author warns us 



