CATEGORICAL JUDGMENTS AND PROPOSITIONS 223 



Since contradiction is the relation between affirmation and 

 denial, to deny the truth of a proposition is the same as to assert 

 the truth of its contradictory, and to assert the truth of a proposi 

 tion is to deny the truth of its contradictory. Every affirmative 

 judgment, therefore, asserted as true, implies the falsity of a 

 negative judgment suggested by it ; and similarly, every negative 

 judgment asserted as true, implies the falsity of a suggested 

 affirmative judgment (98). 



Every judgment, therefore, has a contradictory. Have any 

 judgments more than one contradictory ? Simple judgments 

 have not. But it has been stated sometimes by logicians that 

 compound judgments may be contradicted in various ways, or, 

 have more than one contradictory. This is not true, if we take the 

 terms &quot; contradict? &quot; contradictory&quot; in the strict sense. What is 

 true rather is this, that a compound judgment yields two or more 

 simple judgments, each of which may have a (simple) contradic 

 tory, whose truth is incompatible with the truth of the (compound) 

 original, though its falsity may not be incompatible with the 

 falsity of the original. But these are not real contradictories 

 of that original. The compound judgment has really only one 

 contradictory , which will be also a compound judgment. For in 

 stance, the compound &quot; All S is P and all P is S &quot; is contra 

 dicted by the compound &quot; Either some S is not P or some P is 

 not S&quot;. The simple judgment &quot;Some S is not P&quot; is incom 

 patible with the original ; but it is not the contradictory of the 

 original : for even were it false we could not thence infer the 

 truth of the compound original. 



A little reflection on this example will show that in order to 

 contradict^ a proposition we must assert only the minimum which is 

 necessary and sufficient to break down the truth of that proposition. 

 Therefore it is that there is no mean between a proposition and 

 its contradictory. But if we pass beyond this minimum, necessary 

 to break down the truth of the former, we leave place for a mean 

 of truth between the original and our new proposition. Hence, 

 from the falsity of this latter we cannot infer the truth of the 

 original : both may be false together. Our new form is some 

 thing more than the mere contradictory of the original : it has 



1 We may of course refute, or show the falsity of, a proposition, by going 

 further than merely contradicting it, e.g, by establishing the truth of its contrary 

 (see 113). 



