174 OF SECONDARY PROPOSITIONS. [CHAP. XI. 



DIRECT INTERPRETATION. If the proposition Y is true, then 

 either X and Z are true, or X is true and Z false, or X and Z 

 are both false. 



REVERSE INTERPRETATION. If either X and Z are true, or 

 X and Z are false, Y is true. 



The aggregate of these partial interpretations will express 

 the whole significance of the equation given. 



15. We may here call attention again to the remark, that 

 although the idea of time appears to be an essential element in 

 the theory of the interpretation of secondary propositions, it may 

 practically be neglected as soon as the laws of expression and of 

 interpretation are definitely established. The forms to which 

 those laws give rise seem, indeed, to correspond with the forms of 

 a perfect language. Let us imagine any known or existing lan- 

 guage freed from idioms and divested of superfluity, and let us 

 express in that language any given proposition in a manner the 

 most simple and literal, the most in accordance with those 

 principles of pure and universal thought upon which all languages 

 are founded, of which all bear the manifestation, but from which 

 all have more or less departed. The transition from such a lan- 

 guage to the notation of analysis would consist of no more than 

 the substitution of one set of signs for another, without essential 

 change either of form or character. For the elements, whether 

 things or propositions, among which relation is expressed, we 

 should substitute letters; for the disjunctive conjunction we 

 should write + ; for the connecting copula or sign of relation, we 

 should write =. This analogy I need not pursue. Its reality 

 and completeness will be made more apparent from the study of 

 those forms of expression which will present themselves in sub- 

 sequent applications of the present theory, viewed in more imme- 

 diate comparison with that imperfect yet noble instrument of 

 thought the English language. 



16. Upon the general analogy between the theory of Primary 

 and that of Secondary Propositions, I am desirous of adding a 

 few remarks before dismissing the subject of the present chapter. 



We might undoubtedly have established the theory of Pri- 

 mary Propositions upon the simple notion of space, in the same 



