CATEGORICAL JUDGMENTS AND PROPOSITIONS 225 



other : it asserts the entire falsity of the latter in all its parts, by 

 setting up a counter-assertion as far removed as possible from 

 the latter (i 12). But, evidently, in doing this it may go too far. 

 It may pass the mean in which the truth may lie, and fall itself 

 into the falsity of the other extreme. 



Comparing contradictory with contrary opposition, we see that 

 the latter is less perfect than the former, inasmuch as contraries 

 are incompatible only as regards their truth, not as regards their 

 falsity, and are not mutually inferable as contradictories are. 



We can disprove, or deny, or break down the truth of, a universal proposi 

 tion by establishing the truth either of its contradictory or of its contrary. The 

 former is obviously the easier and the safer way. It is the easier way, because 

 any one single exceptional instance, expressed by a particular proposition, 

 suffices to break down the truth of a universal rule ; whereas complete knowledge 

 is necessary in order to establish the contrary, which is a universal. It is the 

 safer way, because while one single exception might overthrow the contrary 

 that has been set up in disproof of a given universal, it would take a uni 

 versal proposition to overthrow the contradiction set up in disproof of that 

 universal. &quot; One would deny that all men are liars with much greater 

 strength of conviction than one would assert that * no men are liars &quot;. 1 



Evidently, it is only between propositions farthest removed from 

 each other on some scale as the universal affirmative and negative 

 are that contrary opposition in the strict sense can exist. And 

 between the strict contradictory and the strict contrary of a given 

 extreme, or universal proposition, we may conceive an indefinite 

 number of propositions all incompatible with the latter, and in 

 creasing in their divergence from it, towards the contrary. Any 

 one of these will form, with the original proposition, a pair of 

 contraries in the wider sense : propositions which, although not 

 farthest removed from each other, are incompatible as regards 

 their truth, but may both be false, admitting a mean of truth 

 between them. 



In giving the laws of the various kinds of opposition so far explained, we 

 have confined our attention to the formal opposition which arises from an 

 examination of quality and quantity. If we take into account a knowledge of 

 the matter (85) whether, namely, the propositions are in materia necessaria 

 or in materia contingent! we can make further inferences. If, for instance, 

 the propositions in question be in materia necessaria, we can infer equally 

 from subalternant to subalternate, or vice versa, both as to truth and as to 

 falsity ; and also that two contraries in materia necessaria cannot be false 

 together. 



1 WELTON, Logic, i., p. 236. 

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