6 NATURE AND DESIGN OF THIS WORK. [CHAP. I. 



There is not only a close analogy between the operations of the 

 mind in general reasoning and its operations in the particular 

 science of Algebra, but there is to a considerable extent an exact 

 agreement in the laws by which the two classes of operations are 

 conducted. Of course the laws must in both cases be determined 

 independently ; any formal agreement between them can only be 

 established a posteriori by actual comparison. To borrow the 

 notation of the science of Number, and then assume that in its 

 new application the laws by which its use is governed will remain 

 unchanged, would be mere hypothesis. There exist, indeed, 

 certain general principles founded in the very nature of language, 

 by which the use of symbols, which are but the elements of 

 scientific language, is determined. To a certain extent these 

 elements are arbitrary. Their interpretation is purely conven- 

 tional : we are permitted to employ them in whatever sense we 

 please. But this permission is limited by two indispensable con- 

 ditions, first, that from the sense once conventionally established 

 we never, in the same process of reasoning, depart ; secondly, 

 that the laws by which the process is conducted be founded ex* 

 clusively upon the above fixed sense or meaning of the symbols 

 employed. In accordance with these principles, any agreement 

 which may be established between the laws of the symbols of 

 Logic and those of Algebra can but issue in an agreement of pro- 

 cesses. The two provinces of interpretation remain apart and 

 independent, each subject to its own law r s and conditions. 



Now the actual investigations of the following pages exhibit 

 Logic, in its practical aspect, as a system of processes carried on 

 by the aid of symbols having a definite interpretation, and sub- 

 ject to laws founded upon that interpretation alone. But at the 

 same time they exhibit those laws as identical in form with the 

 laws of the general symbols of algebra, with this single addition, 

 viz., that the symbols of Logic are further subject to a special 

 law (Chap, ii.), to which the symbols of quantity, as such, are 

 not subject. Upon the nature and the evidence of this law it is not 

 purposed here to dwell. These questions will be fully discussed 

 in a future page. But as constituting the essential ground of 

 difference between those forms of inference with which Logic is 



