CATEGORICAL JUDGMENTS AND PROPOSITIONS. 199 



The mere grammatical combination of two or more categorical 

 propositions in one and the same sentence does not give rise to a 

 compound proposition, in the sense in which we have used this 

 term (ibid.} : to have a strictly &quot; compound&quot; proposition, the com 

 bination of the simple ones must give rise to a new judgment , 

 distinct from each and all of the simple components. However, 

 the grammatical statement which merely combines two or more 

 simple categorical propositions, without thereby expressing any 

 further judgment as arising from their combination, has been 

 usually called a &quot;compound categorical proposition &quot;; particu 

 larly when, as is usually the case, the grammatical combination 

 of them leads to a more condensed form of expression than they 

 could receive if expressed separately. 



Bearing in mind this wider acceptation of the term &quot; compound 

 proposition,&quot; we are in a position to deal with a form of proposi 

 tion of which we have already had a few examples, the Exponible 

 Proposition. This may be defined as a categorical proposition 

 which, though apparently simple, is really capable of being resolved 

 into two or more simple propositions. Hence the name &quot; ex- 

 ponible &quot;. As we have seen already, plurative and numerically 

 definite propositions are, when strictly interpreted, exponibles. 

 The two most important classes, however, of exponibles are (a) the 

 exclusive proposition, and (b) the exceptive proposition ; to which 

 we may also add (c) inceptive and desitive propositions. 



(a) The Exclusive Proposition is introduced by &quot;alone,&quot; 

 &quot;only,&quot; &quot; none but,&quot; u none except,&quot; &quot;none (no) . . . who are 

 (is) not &quot;. For example, &quot; The virtuous alone are happy,&quot; &quot; Only 

 graduates are eligible (or, Graduates are the only eligible people),&quot; 

 &quot; None but the brave deserve the fair &quot;. Logicians are not agreed 

 as to whether such propositions are &quot;compound&quot; or &quot;simple&quot;. 1 

 The question turns on the distinction between import and im 

 plications (82). There can be no doubt about what is at all 

 events the principal meaning of such propositions. What is 

 primarily meant (i) is : &quot;No non-virtuous are happy,&quot; &quot;No non- 

 graduates are eligible,&quot; etc. : in general &quot; No non-S is P&quot;. They 

 are, therefore, universal negatives. The further propositions, (2) 

 &quot; Some S s (if there be any) are P [&quot; Some graduates (if there be 

 any) are eligible &quot;], and (3) &quot; All Fs (if there be any) are S &quot; 

 [&quot; All eligible people (if there be any such) are graduates&quot;], will 



1 Cf. WELTON, Logic, i., p. 179. KEYNES, Formal Logic, pp. 104 n., 205. 

 MELLONE, Introd. Text-book of Logic, p. 61. 



