CHAP. XII.] METHODS IN SECONDARY PROPOSITIONS. 177 



CHAPTER XII. 



OF THE METHODS AND PROCESSES TO BE ADOPTED IN THE TREAT- 

 MENT OF SECONDARY PROPOSITIONS. 



1. TT has appeared from previous researches (XI. 7) that the 

 -- laws of combination of the literal symbols of Logic are the 

 same, whether those symbols are employed in the expression of 

 primary or in that of secondary propositions, the sole existing 

 difference between the two cases being a difference of interpre- 

 tation. It has also been established (V. 6), that whenever dis- 

 tinct systems of thought and interpretation are connected with 

 the same system of for*nal laws, i. e., of laws relating to the com- 

 bination and use of symbols, the attendant processes, intermediate 

 between the expression of the primary conditions of a problem 

 and the interpretation of its symbolical solution, are the same in 

 both. Hence, as between the systems of thought manifested in 

 the two forms of primary and of secondary propositions, this com- 

 munity of formal law exists, the processes which have been es- 

 tablished and illustrated in our discussion of the former class of 

 propositions will, without any modification, be applicable to the 

 latter. 



2. Thus the laws of the two fundamental processes of elimi- 

 nation and development are the same in the system of secondary 

 as in the system of primary propositions. Again, it has been 

 seen (Chap. vi. Prop. 2) how, in primary propositions, the inter- 

 pretation of any proposed equation devoid of fractional forms 

 may be effected by developing it into a series of constituents, and 

 equating to every constituent whose coefficient does not vanish. 

 To the equations of secondary propositions the same method is 

 applicable, and the interpreted result to which it finally conducts 

 us is, as in the former case (VI. 6), a system of co-existent denials. 

 But while in the former case the force of those denials is ex- 

 pended upon the existence of certain classes of things, in the 

 latter it relates to the truth of certain combinations of the ele- 



