PREFACE TO THE SECOND EDITION. six 



Comparing this with what is stated in Boole's Mathe- 

 matical Analysis of Logic, pp. 17-18, in his Laws of 

 Tlwught, p. 29, or in this work, pp. 32-35, we find that 

 Leibnitz had arrived two centuries ago at a clear perception 

 of the bases of logical notation. When Boole pointed out 

 that, in logic, xx = x, this seemed to mathematicians to be 

 a paradox, or in any case a wholly new discovery; but 

 here we have it plainly stated by Leibnitz. 



The reader must not assume, however, that because 

 Leibnitz correctly apprehended the fundamental principles 

 of logic, he left nothing for modern logicians to do. On 

 the contrary, Leibnitz obtained no useful results from his 

 definition of substitution. When he proceeds to explain 

 the syllogism, as in the paper on " Definitiones Logicas," 1 

 he gives up substitution altogether, and falls back upon 

 the notion of inclusion of class in class, saying, " Inclu- 

 dens includentis est includens inclusi, seu si A includit B 

 et B includit C, etiam A includet C." He proceeds to 

 make out certain rules of the syllogism involving the 

 distinction of subject and predicate, and in no important 

 respect better than the old rules of the syllogism. 

 Leibnitz' logical tracts are, in fact, little more than brief 

 memoranda of investigations which seem never to have 

 been followed out. They remain as evidence of his 

 wonderful sagacity, but it would be difficult to show that 

 they have had any influence on the progress of logical 

 science in recent times. 



I should like to explain how it happened that these 

 logical writings of Leibnitz were unknown to me, until 

 within the last twelve months. I am so slow a reader 

 of Latin books, indeed, that my overlooking a few pages 

 of Leibnitz' works would not have been in any case 

 surprising. But the fact is that the copy of Leibnitz' 

 works of which I made occasional use, was one of the 

 edition of Dutens, contained in Owens College Library. 

 The logical tracts in question were not printed in that 



1 Erdmann, p. 100. 



I 2 



