184 METHODS IN SECONDARY PROPOSITIONS. [CHAP. XII. 



t = 0, y = 0, x (1 - z) = 0, * = 0, x = ; 



yielding the following interpretations : 



God is not changed to a worse state. 



He is not changed by Himself. 



If He suffers change, He is changed by another. 



He is not changed by another. 



He is not changed. 



We thus reach by a different route the same conclusion. 



Though as an exhibition of the power of the method, the 

 above examples are of slight value, they serve as well as more 

 complicated instances would do, to illustrate its nature and cha- 

 racter. 



7. It may be remarked, as a final instance of analogy between 

 the system of primary and that of secondary propositions, that 

 in the latter system also the fundamental equation, 



x (1 - x) = 0, 



admits of interpretation. It expresses the axiom, A proposition 

 cannot at the same time be true and false. Let this be compared 

 with the corresponding interpretation (III. 15). Solved under 



the form 







by development, it furnishes the respective axioms : "A thing is 

 what it is:" " If a proposition is true, it is true:" forms of what has 

 been termed " The principle of identity." Upon the nature and 

 the value of these axioms the most opposite opinions have been 

 entertained. Some have regarded them as the very pith and mar- 

 row of philosophy. Locke devoted to them a chapter, headed, 

 " On Trifling Propositions."* In both these views there seems 

 to have been a mixture of truth and error. Regarded as sup- 

 planting experience, or as furnishing materials for the vain and 

 wordy j anglings of the schools, such propositions are worse than 

 trifling. Viewed, on the other hand, as intimately allied with 

 the very laws and conditions of thought, they rise into at least a 

 speculative importance. 



* Essay on the Human Understanding, Book IV. Chap. viii. 



