GENERAL VIEW OF NATURE AND SCOPE OF LOGIC. 25 



be true ; both cannot be false together : Between affirmation and 

 denial there is no middle course; AvTupdo-ea)? ovbev fiera^v ava 

 peo-ov (ARISTOTLE, Metaph., iii., 7 ; cf. Phys., v., 5 ; Anal. Post., 

 i, 2). 



The remarks just made about the Principle of Contradiction 

 apply equally to the Principle of Excluded Middle. The two 

 principles are closely related. The latter forbids us to think that 

 both of two contradictory attributes can be simultaneously absent 

 from a given subject ; the former forbids us to think that both can 

 be together present ; neither tells us which must be present or 

 which absent. Both principles taken together bring out the dis 

 tinction between affirmation and denial and make us realize that 

 every affirmation involves a denial and vice versa, and that we 

 cannot understand the force of either of the latter without grasping 

 the force of the other. 



Some authors have raised difficulties about the universal 

 applicability of the latter two principles. But those difficulties 

 are due, in part at least, to a confusion between contradiction and 

 contrariety (38-45). Of course between contraries which are the 

 most widely divergent attributes in a given sphere there are 

 numerous intermediate alternatives ; but there is no such alterna 

 tive between affirmation and negation. The paper on which I 

 write need not necessarily be either white or black but it must 

 evidently either be white or not be white. A thing need not 

 necessarily be either greater or less than another thing for 

 &quot; greater &quot; and &quot; less &quot; are not contradictories but it must either 

 be greater or not be greater than that other thing : and if the latter, 

 it will be either equal to or less than that thing. 1 



Another sort of difficulty is raised by asking such an admittedly absurd 

 question as this : Must honesty either be green or not be green ? For, if the 

 principle is universal, one or other alternative answer must be held to be true 

 rather than the other. This point will recur for discussion when we come to 

 deal with negative terms and certain forms of predication and of inference. 



15. REVIEW OF THE THREE PRINCIPLES. The three prin 

 ciples so far dealt with are absolutely primary and self-evident, 

 springing directly from our very notion of being or reality. 



They are necessary principles of thought in this sense that no 

 one can consciously and deliberately think in a way that would 

 violate them. Of course whenever people reason fallaciously or 



1 C/i KEYNES, Formal Logic, 4th edit., pp. 457-463. 



