PREFACE. 



following work is not a republication of a former trea- 

 tise by the Author, entitled, " The Mathematical Analysis 

 of Logic." Its earlier portion is indeed devoted to the same 

 object, and it begins by establishing the same system of funda- 

 mental laws, but its methods are more general, and its range of 

 applications far wider. It exhibits the results, matured by some 

 years of study and reflection, of a principle of investigation re- 

 lating to the intellectual operations, the previous exposition of 

 which was written within a few weeks after its idea had been 

 conceived. 



That portion of this work which relates to Logic presupposes 

 in its reader a knowledge of the most important terms of the 

 science, as usually treated, and of its general object. On these 

 points there is no better guide than Archbishop Whately's 

 " Elements of Logic," or Mr. Thomson's " Outlines of the Laws 

 of Thought." To the former of these treatises, the present re- 

 vival of attention to this class of studies seems in a great measure 

 due. Some acquaintance with the principles of Algebra is also 

 requisite, but it is not necessary that this application should have 

 been carried beyond the solution of simple equations. For the 

 study of those chapters which relate to the theory of probabilities, 

 a somewhat larger knowledge of Algebra is required, and espe- 



