PREFACE 



TO THE SECOND EDITION. 



FEW alterations of importance have been made in pre- 

 paring this second edition. Nevertheless, advantage has 

 been taken of the opportunity to revise very carefully 

 both the language and the matter of the book. Cor- 

 respondents and critics having pointed out inaccuracies 

 of more or less importance in the first edition, suitable 

 corrections and emendations have been made. I am under 

 obligations to Mr. C. J. Monro, M.A., of Barnet, and o 

 Mr. W. H. Brewer, M.A., one of Her Majesty's Inspectors 

 of Schools, for numerous corrections. 



Among several additions which have been made to the 

 text, I may mention the abstract (p. 143) of Professor 

 Clifford's remarkable investigation into the number of 

 types of compound statement involving four classes of 

 objects. This inquiry carries forward the inverse logical 

 problem described in the preceding sections. Again, the 

 need of some better logical method than the old Barbara 

 Celarent, &c., is strikingly shown by Mr. Venn's logical 

 problem, described at p. 90. A great number of candidates 

 in logic and philosophy were tested by Mr. Venn with this 

 problem, which, though simple in reality, was solved by 

 very few of those who were ignorant of Boole's Logic. 

 Other evidence could be adduced by Mr. Venn of the need 

 for some better means of logical training. To enable the 



