164 OF SECONDARY PROPOSITIONS. [CHAP. XI. 



true, and those contingent or phenomenal relations of things 

 which are sometimes true and sometimes false. But the forms of 

 language in which both kinds of propositions are expressed ma- 

 nifest a common dependence upon the idea of time ; in the one 

 case as limited to some finite duration, in the other as stretched 

 out to eternity. 



6. It may indeed be said, that in ordinary reasoning we are 

 often quite unconscious of this notion of time involved in the very 

 language we are using. But the remark, however just, only 

 serves to show that we commonly reason by the aid of words 

 and the forms of a well-constructed language, without attending 

 to the ulterior grounds upon which those very forms have been 

 established. The course of the present investigation will afford an 

 illustration of the very same principle. I shall avail myself of 

 the notion of time in order to determine the laws of the expression 

 of secondary propositions, as well as the laws of combination of 

 the symbols by which they are expressed. But when those 

 laws and those forms are once determined, this notion of time 

 (essential, as I believe it to be, to the above end) may practically 

 be dispensed with. We may then pass from the forms of com- 

 mon language to the closely analogous forms of the symbolical 

 instrument of thought here developed, and use its processes, and 

 interpret its results, without any conscious recognition of the idea 

 of time whatever. 



PROPOSITION II. 



7. To establish a system of notation for the expression of 

 Secondary Propositions, and to show that the symbols which it 

 involves are subject to the same laws of combination as the corres- 

 ponding symbols employed in the expression of Primary Propo- 

 sitions. 



Let us employ the capital letters X, Y, Z, to denote the ele- 

 mentary propositions concerning which we desire to make some 

 assertion touching their truth or falsehood, or among which we 

 seek to express some relation in the form of a secondary propo- 

 sition. And let us employ the corresponding small letters x, y, z, 

 considered as expressive of mental operations, in the following 



