46 DERIVATION OF THE LAWS. [CHAP. III. 



are deducible from a consideration of the operations of the mind 

 in reasoning. 



12. The remainder of this chapter will be occupied with 

 questions relating to that law of thought whose expression is 

 # 2 = x (II. 9), a law which, as has been implied (II. 15), forms 

 the characteristic distinction of the operations of the mind in its 

 ordinary discourse and reasoning, as compared with its operations 

 when occupied with the general algebra of quantity. An im- 

 portant part of the following inquiry will consist in proving that 

 the symbols and 1 occupy a place, and are susceptible of an 

 interpretation, among the symbols of Logic ; and it may first be 

 necessary to show how particular symbols, such as the above, 

 may with propriety and advantage be employed in the represen- 

 tation of distinct systems of thought. 



The ground of this propriety cannot consist in any commu- 

 nity of interpretation. For in systems of thought so truly 

 distinct as those of Logic and Arithmetic (I use the latter term 

 in its widest sense as the science of Number), there is, properly 

 speaking, no community of subject. The one of them is conver- 

 sant with the very conceptions of things, the other takes account 

 solely of their numerical relations. But inasmuch as the forms 

 and methods of any system of reasoning depend immediately upon 

 the laws to which the symbols are subject, and only mediately, 

 through the above link of connexion, upon their interpretation, 

 there may be both propriety and advantage in employing the 

 same symbols in different systems of thought, provided that such 

 interpretations can be assigned to them as shall render their for- 

 mal laws identical, and their use consistent. The ground of that 

 employment will not then be community of interpretation, but 

 the community of the formal laws to which in their respective 

 systems they are subject. Nor must that community of formal 

 laws be established upon any other ground than that of a careful 

 observation and comparison of those results which are seen to 

 flow independently from the interpretations of the systems under 

 consideration. 



These observations will explain the process of inquiry adopted 

 in the following Proposition. The literal symbols of Logic are 



i 



