CATEGORICAL JUDGMENTS AND PROPOSITIONS. 195 



an universal not fully determined &quot; j 1 judgments which, therefore, 

 approximate either to the collective or to the abstract universal. 



Examples of each would be &quot; Some women have ruled 

 kingdoms,&quot; and &quot;Some pigments fade&quot;. The former is a state 

 ment &quot; about unnamed individuals &quot; ; 2 the extension of the subject 

 is thought of; the judgment is assertoric ; and it has been de 

 scribed as an historical judgment. The latter asserts the com 

 patibility or separability of attributes ; the intension of the 

 subject is thought of; the judgment is really a contingent or 

 problematic modal ; and it has been described as a scientific 

 judgment. 



When the particular proposition results from observation of instances of a 

 class, it serves to suggest the corresponding universal as a proposition that 

 may possibly be true, i.e. as a scientific hypothesis ; * and it thus marks a 

 stage in our progress towards some universal or scientific truth : 4 either 

 towards the proposition &quot; S as such is P &quot; ; or towards the proposition that &quot; All 

 the S*s of a certain kind, with a certain limitation, are P &quot; ; that e.g. &quot;All S s 

 that are M are P,&quot; or &quot; SM as such is P&quot; ; and if this latter sub-class of 

 S s be scientifically important a special name will soon be found for it. It 

 is universal, necessary truths the expression of laws, metaphysical, physical, 

 and moral that are of importance as embodying scientific knowledge. 



Then, as we shall see later, the particular proposition is a more appropri 

 ate form than the universal for asserting the existence of certain things. &quot; If, 

 for example, we say that * some engines can drag a train at a mile a minute for a 

 long distance, our object is primarily to affirm that there are such engines ; 

 and this would not be so clearly expressed in the universal proposition of which 

 the particular is said to be the incomplete and imperfect expression &quot;. 5 It is, 

 perhaps, this implication of the existence of S s in the universe of discourse, 

 that mainly marks the distinction between the denotative or assertoric par 

 ticular &quot;Some S s are (not) /&quot;s,&quot; and the corresponding modal form, the 

 problematic modal, &quot; S may be (need not be) P &quot; (130). Anyhow, the incom 

 pleteness of the knowledge expressed by &quot; Some S s are P &quot; does not lie in 

 doubt as to whether the enumeration of S s is complete, but rather in un 

 certainty about the nature of S about its connotation rather than its denota 

 tion, uncertainty as to whether it necessarily involves -P : which uncertainty 

 is more clearly expressed by the modal &quot; S may be P &quot; (90). 



Finally, perhaps the most important function of the particular proposi 

 tion is to contradict the universal of opposite Quality, thus furnishing us 

 with an exceedingly useful check upon false or hasty generalizations. 



94. PLURATIVE AND NUMERICAL PROPOSITIONS. MULTIPLE 

 QUANTIFICATION : COMPLEX PROPOSITIONS. A plurative pro 

 position is one to whose subject are prefixed the quantitative signs 



1 JOSEPH, op. cit., p. 158. 2 ibid., p. 218. 3 Cf. book iv., chap, v., infra. 

 4 Cf. VENN, op. cit., p. 168. 5 KEYNES, Formal Logic, p. 102. 



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