66 THE SCIENCE OF LOGIC: 



contradictories is always more or less limited, that exhausted by a pair of 

 formal contradictories is supposed to be coextensive with all being : &quot; non- 

 man 3 is supposed to denote all things other than men. Whether we ever 

 de facto use such purely negative terms and concepts in our actual thought 

 and speech may be seriously doubted. It has even beer, contended by some 

 logicians that they cannot figure as genuine terms in our thought : that they 

 stand for no reality but only for a mere creation of formal logic, an ens 

 rationis : that they are a perverted way of expressing the logical relation estab 

 lished by the mind between subject and predicate in the negative judgment. 

 We certainly cannot deny that it is only in connexion with judgment, with 

 predication, with affirmation and denial, that the division of terms into posi 

 tive and negative can become intelligible at all : contradiction is primarily 

 between judgments, not between terms. 1 The very use of the word &quot; nega 

 tive &quot; reminds us of negation, and negation is judgment. Taken in itself, 

 apart from judgment, what can the idea or the term &quot;not-white&quot; imply or 

 denote ? Not certainly the absence from the mind of the idea &quot;white &quot; : on 

 the contrary it involves the presence of the latter in the mind. &quot; Not-white &quot; 

 is not, therefore, the pure negation of the idea &quot;white &quot;. Nor again can its 

 object be everything that is absent from the mind thinking of white ; for cer 

 tainly an idea cannot stand for what is merely absent from the mind. But 

 perhaps it has for object &quot; everything that is not white&quot; whether present to 

 the mind in any more explicit way or not ? That is to say, when the mind 

 thinks of &quot;white things &quot; or of &quot;things possessing the attribute of whiteness,&quot; 

 perhaps it can do so only by mentally distinguishing them from &quot;things that 

 are not white &quot; : so that every positive mental concept would divide the realm 

 of its denotation into two mutually exclusive departments or classes, a class of 

 which the concept can, and a class of which it cannot, be predicated ? And 

 would not the term &quot;not-white &quot; come in this indirect way to denote all the 

 members of the latter class to stand for &quot; whatever is not white &quot; ? 2 It this 

 be so, the mind has reached the concept &quot;not-white &quot; only through a pro 

 cess of implicit judgment : a process of conceiving objects which have a cer 

 tain attribute, denying it of all other objects, and holding these latter together 

 only by this purely negative bond of denial. But to arrive at such an inde 

 finite denotation for &quot;not-white,&quot; it is not necessary, as Sigwart seems to 

 imply, 3 to have gone through an indefinite series of judgments. From the 

 perception of even one single &quot;not-white &quot; thing, we can abstract the general 

 concept : &quot; whatever is not white &quot;. 



Purely negative terms, thus understood to include in their denotation 

 everything thinkable except the things denoted by the corresponding positive 

 term, have been described as infinite or limiting terms, and the propositions 

 in which they are predicates, infinite or limiting propositions. 



It is not true to say that such terms are utterly meaningless and incon 

 ceivable, expressive of no real concept, on the ground that it is impossible to 



1 Two contradictory terms looked at in themselves, apart from their relation to 

 judgment, have been called by Dr. Keynes complementary terms, as exhausting the 

 sphere of denotation between them (op, cit., p. 162). 



2 &quot; While it may be said that A and not-A involve intensively only one concept, 

 they are extensively mutually exclusive,&quot; KEYNES, op. cit., p. 58. 



3 Logic, p. 135, quoted by KEYNES, loc. cit. 



