NATURE OF THE JUDGMENT AND PROPOSITION. 165 



The reduction of an ordinary statement to some one or other 

 of the prepositional forms explicitly recognized in logic, is called 

 formulation. Some of the common forms of statement fall more 

 naturally into one logical scheme, some more naturally into 

 another. But in all attempts at formulation we must have 

 clear notions as to the exact meaning of the judgment to be 

 &quot; formulated,&quot; and the meaning of the prepositional form to 

 which we wish to reduce it. To interpret a proposition is to 

 attach a meaning or import to it ; and this will, of course, depend 

 partly on the meaning (intensive and extensive) of the terms that 

 enter into the proposition, and partly on the signification we attach 

 to the synthesis or connexion of the terms, i.e. to the copula. Fixing 

 the exact meaning of more or less ambiguous terms is, in a certain 

 degree, a conventional or selective process ; interpreting the mean 

 ing of a given prepositional form is, likewise, in some measure 

 optional : and the question whether a judgment expressed in a 

 given prepositional forrn is true or false, will depend not only 

 on its matter, but on what is recognized by common agreement 

 to be the import of its prepositional form. 



It was said above that what is practically the same judgment 

 may be expressed in different prepositional forms. The limita 

 tion is a necessary one, for a judgment often loses some of its 

 import when its mode of verbal expression is altered. Hence 

 arises the very important distinction between the meaning or im 

 port of a given prepositional form, and what are called its implica 

 tions, i.e. all the truths that are necessarily involved in it, and 

 which may be extracted from it by careful and prolonged mental 

 scrutiny. These mental processes and their products immediate 

 inferences as they are called will be dealt with below (chaps, v., 

 vi.). Here we wish to point out that, owing to neglect of this 

 distinction between import and implication^- there has been much 

 misunderstanding about the supposed conflicting claims of the 

 various interpretations of prepositional forms put forward, at 

 one time or another, by logicians. 2 



1 These technical terms have been used as synonyms in reference to the meaning 

 of concepts and terms. Cf. Bk. i., chap, i., 30-34. 



2 &quot; The assignment of meaning is within certain limits arbitrary and selective. 

 But if element a necessarily involves element b, then a having been assigned as 

 part of the meaning of a given prepositional form, it is no question of meaning as to 

 whether the form in question does or does not imply b, and there is nothing arbitrary 

 or selective in the solution of this question.&quot; 



&quot; Sometimes the elements a and b mutually involve one another. It may then 



