66 PRINCIPLES OF SYMBOLICAL REASONING. [CHAP. V. 



CHAPTER V. 



OF THE FUNDAMENTAL PRINCIPLES OF SYMBOLICAL REASONING, AND 

 OF THE EXPANSION OR DEVELOPMENT OF EXPRESSIONS INVOLV- 

 ING LOGICAL SYMBOLS. 



1 . r |TEIE previous chapters of this work have been devoted to 

 -*- the investigation of the fundamental laws of the opera- 

 tions of the mind in reasoning; of their development in the 

 laws of the symbols of Logic; and of the principles of expression, 

 by which that species of propositions called primary may be repre- 

 sented in the language of symbols. These inquiries have been 

 in the strictest sense preliminary. They form an indispensable 

 introduction to one of the chief objects of this treatise the con- 

 struction of a system or method of Logic upon the basis of an 

 exact summary of the fundamental laws of thought. There are 

 certain considerations touching the nature of this end, and the 

 means of its attainment, to which I deem it necessary here to 

 direct attention. 



2. I would remark in the first place that the generality of a 

 method in Logic must very much depend upon the generality of 

 its elementary processes and laws. We have, for instance, in the 

 previous sections of this work investigated, among other things, 

 the laws of that logical process of addition which is symbolized 

 by the sign + . Now those laws have been determined from the 

 study of instances, in all of which it has been a necessary condi- 

 tion, that the classes or things added together in thought should 

 be mutually exclusive. The expression x + y seems indeed un- 

 interpretable, unless it be assumed that the things represented 

 by x and the things represented by y are entirely separate ; 

 that they embrace no individuals in common. And conditions 

 analogous to this have been involved in those acts of conception 

 from the study of which the laws of the other symbolical opera- 

 tions have been ascertained. The question then arises, whether 



