CATEGORICAL JUDGMENTS AND PROPOSITIONS. 203 



the negative proposition, e.g. &quot;No square is a triangle,&quot; &quot;No 

 bird is a quadruped,&quot; &quot; Some dogs are not collies &quot;. A moment s 

 consideration of these examples will show us that what the nega 

 tive proposition excludes from its subject is the connotation of 

 the predicate taken as a whole, collectively ; but that it does 

 not at all exclude from its subject each and every constituent 

 element or portion of the connotation of the predicate. On the 

 contrary, some portion of the connotation of the predicate agrees 

 with, or is found in, the subject, in the examples given : in all of 

 them the subject has something more or less in common with 

 the predicate. Now, it may be asked, Is this the case in all nega 

 tive predication ? In a certain sense it is, and must be, the case. 

 In order to have an intelligible comparison of two ideas at all, it 

 would appear that they must have something in common. And, 

 as a matter of fact, all objects of our thought have something in 

 common : at least the notion or concept of being, or thing, or 

 reality, in its most general sense. 



Further than this, however, it is widely contended that in order to have 

 intelligible negative predication at all, the subject and predicate must have in 

 common not merely the notion of being, but the notion of a comparatively 

 proximate genus of the subject of the judgment : that there is, for example, 

 no real predication in the proposition &quot;Virtue is not blue&quot; or &quot;Virtue is 

 not-blue &quot;. We have already discussed this question at some length (39), 

 and pointed out that the Principle of Excluded Middle cannot be held to be 

 universally applicable unless we recognize as intelligible such an alternative 

 proposition as &quot; Virtue either is or is not blue &quot;. Negative judgments of 

 the kind referred to are intelligible when made ; but they never need to be 

 made in real life : they are superfluous, because the real function of the 

 negative judgment is to ward off the error that would be contained in the 

 affit native which it denies, and people do not fall into such obvious errors 

 as the assertion that &quot; Virtue is blue &quot; would be. 1 But this function of the 

 negative judgment, and the relation of denial to affirmation generally, need to 

 be examined a little more in detail. 



98. NATURE OF SIGNIFICANT DENIAL : ITS RELATION TO 

 AFFIRMATION : ITS GROUNDS. In all judgment there is a refer 

 ence to reality (80) ; therefore, also in the negative judgment. 

 As an interpretation of reality, the negative judgment, &quot;S is 

 not P&quot; must have its ground in that reality ; and that ground 

 the logical ground or reason, we may call it must be something, 

 in our experience of the reality, whereby we are enabled to exclude 

 Pfrom S. 



1 C/. KEYNKS, Formal Logic, p. 120. 



