xxiv PREFACE TO THE SECOND EDITION. 



John Christian Lange, and described in a rare and un- 

 noticed work by him which I have recently found in the 

 British Museum. 1 This square involved the principle of 

 bifurcate classification, and was an improved form of the 

 Kamean and Porphyrian tree (see below, p. 702), Lange 

 seems, indeed, to have worked out his Logical Square 

 into a mechanical form, and he suggests that it might be 

 employed somewhat in the manner of Napier's Bones 

 (p. 65). There is much analogy between his Square and 

 my Abacus, but Lange had not arrived at a logical system 

 enabling him to use his invention for logical inference in 

 the manner of the Logical Abacus. Another work of 

 Lange is said to contain the first publication of the well 

 known Eulerian diagrams of proposition and syllogism. 2 



Since the first edition was published, an important 

 work by Mr. George Lewes has appeared, namely, his 

 Problems of Life and Mind, which to a great extent treats 

 of scientific method, and formulates the rules of philo- 

 sophising. I should have liked to discuss the bearing 

 of Mr. Lewes' s views upon those here propounded, but 

 I have felt it to be impossible in a book already filling 

 nearly 800 pages, to enter upon the discussion of a 

 yet more extensive book. For the same reason I have 

 not been able to compare my own treatment of the subject 

 of probability with the views expressed by Mr. Venn in 

 his logic of Chance. With Mr. J. J. Murphy's profound 

 and remarkable works on Habit, and Intelligence, and on 

 The Scientific Basis of Faith, I was unfortunately unac- 

 quainted when I wrote the following pages. They can- 

 not safely be overlooked by any one who wishes to 

 comprehend the tendency of philosophy and scientific 

 method in the present day. 



It seems desirable that I should endeavour to answer 

 some of the critics who have pointed out what they 



l Invention Novum Quadrati Logiti, Ac., Gissee Hassorum, 1714, 

 ovo. 



See Uelerweg's System of Logic, Ac., translated by Lindsay, p. 302. 



