V 



vi PREFACE. 



powers, because they furnish us with a great body of 

 precise and successful investigations. In these sciences 

 we meet with happy instances of unquestionable deductive 

 reasoning, of extensive generalization, of happy prediction, 

 of satisfactory verification, of nice calculation of proba 

 bilities. We can note how the slightest analogical clue 

 has been followed up to a glorious discovery, how a rash 

 generalization has at length been exposed, or a conclusive 

 experimentum crucis has decided the long-continued strife 

 between two rival theories. 



In following out my design of detecting the general 

 methods of inductive ^investigation, I have found that the 

 more elaborate and interesting processes of quantitative 

 induction have their necessary foundation in the simpler 

 science of Formal Logic. The earlier, and probably by 

 far the least attractive part of this work, consists, there 

 fore, in a statement of the so-called Fundamental Laws of 

 Thought, and of the all-important Principle of Substi 

 tution, of which, as I think, all reasoning is a develop 

 ment. The whole procedure of inductive inquiry, in its 

 most complex cases, is foreshadowed in the combinational 

 view of Logic, which arises directly from these fundamental 

 principles. Incidentally I have described the mechanical 

 arrangements by which the use of the important form 

 called the Logical Abecedarium, and the whole working 

 of the combinational system of Formal Logic, may be ren 

 dered evident to the eye, and easy to the mind and 

 hand. 



The study both of Formal Logic and of the Theory of 

 Probabilities, has led me to adopt the opinion that there 

 is no such thing as a distinct method of induction as con 

 trasted with deduction, but that induction is simply an 

 inverse employment of deduction. Within the last cen 

 tury a reaction has been setting in against the purely 

 empirical procedure of Francis Bacon, and physicists have 



