CATEGORICAL JUDGMENTS AND PROPOSITIONS. 197 



defended the Pass at Thermopylae &quot;. This belongs to the class of indefinite 

 singulars, which we have seen to be a sub-class of particulars [92 ()]. 



Numerically definite propositions, such as &quot; Two-thirds of the 

 S s are P &quot; are ambiguous ; for they may be interpreted in the 

 stricter sense to signify that, for example, &quot; Two-thirds exactly 

 of the S s are P, and the remaining third are not P&quot; in which 

 case they are exponibles ; or to mean that &quot; Two-thirds at least, 

 and perhaps more, of the S s are P &quot;. In ordinary language, 

 sometimes the former is meant, sometimes the latter. The latter 

 form gives the judgment the lesser amount of meaning. Hence, 

 in so far as logic takes account of such propositions, it must, in 

 obedience to the Law of Parsimony, which we have applied more 

 than once already, interpret them as containing the lesser. In the 

 present case, therefore, we interpret as &quot; Some .S s are P &quot;. In 

 virtue of the law just referred to, when a form of statement, as it 

 stands in its context, is capable of two or more interpretations, 

 which ascribe to it various amounts of meaning, we are not at 

 liberty to select, in logic, any other interpretation than that 

 which ascribes to the statement the minimum amount of meaning : 

 the reason being, of course, that we have no warrant to ascribe 

 to it in the particular case any further meaning than the minimum 

 it can bear, and we might therefore err in doing so. 



Multiple Quantification. The predicate of a proposition may 

 be applied to the whole, or to an indefinite portion, of the denota 

 tion of the subject, not simply and absolutely, but with certain limi 

 tations as to time, space, or other such conditions. For example, 

 &quot; All schoolboys feel unhappy sometimes&quot;; &quot;In some schools 

 all the pupils are diligent &quot; ; &quot; In all schools all the pupils are at 

 times diligent&quot;. Such modifications of the primary quantity of 

 a proposition are instances of multiple quantification. 



Complex Propositions. Are plurative and numerically definite 

 propositions, and propositions with multiple quantification, to be 

 regarded as simple, or complex, or compound propositions (84)? 

 Can they, on account of their import, or of their implications, 

 be strictly interpreted (as exponibles}, and resolved, at least with 

 the aid of immediate inference (82), into two or more simple 

 categorical propositions? The ambiguity in classifying these and 

 certain other similar propositions as simple, complex, or compound, 

 arises from diversity of usage in regard to these latter names. 



The logical term which stands as subject or as predicate of a 

 categorical proposition, may be either a single-worded or a many- 



