68 PRINCIPLES OF SYMBOLICAL REASONING. [CHAP. V. 



by any symbolical process of reasoning, does not depend upon 

 our ability to interpret the formal results which have presented 

 themselves in the different stages of the investigation. There 

 exist, in fact, certain general principles relating to the use of 

 symbolical methods, which, as pertaining to the particular sub- 

 ject of Logic, I shall first state, and I shall then offer some re- 

 marks upon the nature and upon the grounds of their claim to 

 acceptance. 



4. The conditions of valid reasoning, by the aid of symbols, 

 are 



1st, That a fixed interpretation be assigned to the symbols 

 employed in the expression of the data; and that the laws of the 

 combination of those symbols be correctly determined from that 

 interpretation. 



2nd, That the formal processes of solution or demonstration 

 be conducted throughout in obedience to all the laws deter- 

 mined as above, without regard to the question of the interpreta- 

 bility of the particular results obtained. 



3rd, That the final result be interpretable in form, and that 

 it be actually interpreted in accordance with that system of in- 

 terpretation which has been employed in the expression of the 

 data. Concerning these principles, the following observations 

 may be made. 



5. The necessity of a fixed interpretation of the symbols has 

 already been sufficiently dwelt upon (II. 3). The necessity that 

 the fixed result should be in such a form as to admit of that in- 

 terpretation being applied, is founded on the obvious principle, 

 that the use of symbols is a means towards an end, that end 

 being the knowledge of some intelligible fact or truth. And 

 that this end may be attained, the final result which expresses 

 the symbolical conclusion must be in an interpretable form. It 

 is, however, in connexion with the second of the above general 

 principles or conditions (V. 4), that the greatest difficulty is 

 likely to be felt, and upon this point a few additional words are 

 necessary. 



I would then remark, that the principle in question may be 

 considered as resting upon a general law of the mind, the know- 

 ledge of which is not given to us a priori, i. e. antecedently to 



