REVIEWS 533 



previously examined may vitiate the conclusion. The above is a very brief and 

 crude summary of Mr. Sidgwick's argument, but it expresses the gist of it. Avery 

 important part of ordinary thinking is, therefore, the examination of the premises 

 in the light of the particular conclusion which it is sought to deduce. 



The natural inference from this line of argument seems to be that logic should 

 be regarded as a strictly formal science, like mathematics, and that no logical 

 process can guarantee the material truth of the conclusions. Many logicians have 

 adopted this attitude more or less consistently. We should naturally expect that 

 it would appeal to Mr. Sidgwick and that he would be classed as a consistently 

 formal logician. It is, however, not accurate so to describe him, natural as is the 

 mistake of attributing to him such an attitude. 1 Why it is not his attitude is not 

 quite clear. He does not, like Dr. Mercier, object to the syllogism as a logical 

 form. The reason appears to be that he regards the process of the formal deduc- 

 tion of conclusions from premises as so negligible a portion of the process of actual 

 thinking that no science dealing with it is required. But then he has written a 

 text-book on elementary logic. The truth is that Mr. Sidgwick has not clearly 

 and explicitly stated his position on this matter. Were Mr. Sidgwick merely 

 writing an elementary text-book, indeterminateness on this or any other philo- 

 sophical question would not be of great moment. But to one who, like Mr. Sidg- 

 wick, is attacking old-fashioned logic, the lack of a clear and definite attitude on 

 fundamentals is a serious omission. 



Having said so much by way of criticism, it only remains to express the 

 highest appreciation of the general tone and substance of Mr. Sidgwick's work. 

 The works reviewed, especially the Application of Logic, are an admirable resume 

 of the puzzles and difficulties that naturally arise in everyday disputes. Purely 

 formal fallacies are rarely of importance. The material problems— definition, 

 ambiguity, the degree of applicability of general rules — are of greater moment. 

 These Mr. Sidgwick examines thoroughly and well. Such an examination we 

 can read and appreciate entirely apart from philosophical differences. Any one 

 interested in the tricks and devices of the skilled disputant, in the kinds of 

 fallacies which are commonly accepted as truth and in the best methods of com- 

 bating them, can be referred with confidence to Mr. Sidgwick's work. 



H. S. Shelton. 



MATHEMATICS 



Theory of Functions of a Complex Variable. By Dr. Burkhardt. Trans- 

 lated by Professor Rasor. Published by Messrs. D. C. Heath & Co. 

 [Pp. xiii + 432.] (Price lis. 6d. net.) 



THIS important translation of one portion of Dr. Burkhardt's Funktionen theo- 

 retischer Vorlesutigen will be cordially received by all who are interested in the 

 teaching of mathematics. The German book, since its publication in 1897, has 

 passed through four editions, the translation by Professor Rasor being based 

 upon the 1912 edition. The book is a masterly introduction to the Theory of 

 Functions ; the subject is developed with exceptional power, and the style has 

 the ease and subtle charm of simplicity. In the course of successive editions 

 Dr. Burkhardt has carefully revised his matter, and a comparison between the 

 present translation and the first edition has proved how unremittingly the author 



1 I myself so described him in a recent number of the Quarterly Review, but I am given 

 to understand that the description, though not inaccurate in the sense in which I use it, is 

 misleading. 



