CATEGORICAL JUDGMENTS AND PROPOSITIONS 231 



This inference is always legitimate, provided we change the 

 quality of the proposition in the process. Hence the Law of 

 Obversion : Negative the predicate and change the quality of the 

 proposition, leaving its quantity unaltered. 



Hence A obverts to E ; E to A ; I to O ; O to I. 



We can pass backward from the obverse to the obvertend : 

 they are equivalent propositions. 



In applying the process of obversion to concrete examples, 

 care must be taken not to use the material negative, or privative 

 term (39, 41), instead of the formal contradictory, unless in cases 

 when the former is equivalent to the latter. Thus, instead of 

 non-mortal, non-equal, non-material, we may use the terms im 

 mortal, unequal, immaterial. But instead of the terms non-happy, 

 non-rich, non-holy, non-kind, we may not use the terms unhappy, 

 poor, unholy, unkind. 



It may be asked whether obversion is really an inference at all, and not 

 merely a verbal change (82, 106). We are commonly understood to have 

 drawn an inference when we have made some distinct step or advance in 

 thought, from our first judgment ; when we have made explicit something 

 that was not explicit, something that was not part of the meaning of our first 

 proposition ; when our second proposition can be said to express a new trutJi, 

 or a new judgment, and not merely the original judgment in different words. 

 This test is usually accepted in theory, but the application of it is often diffi 

 cult : owing to the fact that the same judgment may be formulated in different 

 terms ; and often, conversely, different judgments may be expressed in one 

 and the same (ambiguous) prepositional form. 1 Judged by the principle in 

 question, obversion can scarcely be said to be a real inference, at least if 

 the negative term be understood as purely negative (39). It is rather a verbal 

 change. There is, in the process, no distinct, conscious advance of thought. 

 Mere denial and affirmation are too closely allied to each other, too intimately 

 involved in each other, to leave room for any real progress of thought in pass 

 ing frorn the one to the other. If P and not-P are formal contradictories, 

 then, by the Principle of Contradiction, we can pass from &quot; S is P &quot; to &quot; S is 

 not P&quot; from &quot;Twice two and the half of eight are equal &quot; to &quot;Twice two 

 and the half of eight are not unequal &quot; : where the latter proposition denies no 

 positive alternative to the former, but merely denies the denial of the former ; 

 and, by the Principle of Excluded Middle, we can pass from &quot; 5 is not P &quot; 

 to &quot; S is P,&quot; from &quot; Steam is not visible &quot; to &quot; Steam is invisible &quot; : where the 

 latter predicate gives no positive alternative to the former. 



But if, in any judgment, we give not-P ^positive connotation, by limiting 

 P and not-P to a restricted universe, if, e.g., we take P and not-P to mean 

 blue and some colour other than blue, then we cannot pass from the proposi 

 tion &quot; Noble blood is not blue &quot; to &quot; Noble blood is not-blue &quot; (meaning 



1 Cf. JOSEPH, op. cit., p. 218. 



