326 THE SCIENCE OF LOGIC. 



114. SUBCONTRARY OPPOSITION is the opposition which exists 

 between two particular propositions of opposite quality : between I 

 and O. The laws of subcontrary opposition are: 



(1) Subcontraries cannot be false together ; 



(2) Subcontraries may be true together. 



(1) They cannot be false together, for if they were, their respec 

 tive subalternants also, A and E, would each be false (by laws of 

 subalternation), and hence contradictories would be false together, 

 which is impossible. Or thus : if either subcontrary be false its 

 contradictory must be true, and hence the subaltern of that con 

 tradictory must be true ; but this latter is the other subcontrary. 

 Hence subcontraries cannot be false together. This proof is an 

 appeal to the Principle of Excluded Middle^ and may also be stated 

 in this way: since &quot;some&quot; is entirely indefinite, and has the 

 same sense of &quot; some, possibly all &quot; in each subcontrary, we can 

 see at once that there can be no mean between the statement 

 &quot;some are ... &quot; and &quot;some are not . . . Either must be 

 true. 



It has been argued, against this law, that I and O may be false together : 

 &quot; A and E may both be false. Therefore I and O being possibly equivalent 

 to them, may both be false also.&quot; J This is a fallacious argument, an instance 

 of the fallacy a sensu diviso ad sensum compositum. It argues that because 

 I is sometimes equivalent to A, and O sometimes to E, therefore the two equi 

 valences can exist at the same time ; but it is precisely when A and E are 

 both false that I and O cannot be simultaneously equivalent to A and E respec 

 tively. 



(2) Subcontraries may, however, be true together ; so that, 

 given the truth of one, we cannot infer the falsity of the other ; 

 (unless in the case of judgments in materia necessaria, for the ex 

 pression of which subcontraries are inappropriate). 



This law may be verified by assuming I as true, for example : 

 A then remains doubtful ; E is false ; but from this we cannot infer 

 that I is false : it may be true or false. This proof simply shows 

 that the Principle of Contradiction does not apply to subcontraries, 

 and that therefore they may be true together, since either does 

 not go sufficiently far to give even a bare denial of the other. 



Of course, whenever both are true together, the actual &quot; some &quot; 

 referred to in each proposition is different, though there is nothing 

 in the form to tell us this. In such a case, the &quot;some&quot; actually 

 means &quot; some, not all &quot; ; but we are not supposed to know this 



1 STOCK, Deductive Logic, p. 139, 



