24 THE SCIENCE OF LOGIC. 



object of thought, A, does not get us beyond the unity expressed 

 by the first reference to A. But identity is more than unity. We 

 cannot conceive identity unless we conceive diversity : and what 

 the principle really expresses is identity amid diversity. It finds 

 its real application in the proposition A is B, no less than in the 

 tautology A is A in the statement that &quot; Snow is white,&quot; no less 

 than in the formula &quot;Snow is snow&quot;. What it really demands, 

 therefore, is this : that an object of thought, when subjected to 

 mental analysis and regarded from different points of view and 

 under different aspects, be considered and understood to remain 

 objectively identical with itself throughout. Everything is its own 

 nature : Everything is what it is : Whatever is, is : Once true 

 always true : Truth is at all times true : Truth must be ever in 

 conformity with itself Aelyap trav TO d\r)0&amp;lt;$ dvToeavTcpo/jLoXoyovfjL- 

 evov elvai TrdvTrj (ARISTOTLE, Anal. Pr., i., 321). 



13. THE PRINCIPLE OF CONTRADICTION may be stated 

 thus : The same thing cannot be and not be at the same time and 

 under the same respect: Idem non potest simul esse et non esse 

 secundum idem : A cannot both be B and not be B : The same at 

 tribute cannot be at the same time affirmed and denied of the same 

 subject: ASvvarov ovnvovv ravrov vnro\a^jBdvLv elvau KOI /JLTJ 

 elvai (ARISTOTLE, Metaph., iv., 3 ; cf. idem., iii., 4). Contradic 

 tory Judgments cannot both be true ; of two such one must be false. 



This principle is likewise involved in every judgment we make 

 more directly in every negative judgment. With the Principle 

 of Identity of which it is the correlative it expresses the nature 

 of affirmation and denial ; and both principles underlie all imme 

 diate inferences from our judgments. It must obviously be 

 understood to refer to one and the same object of thought in ex 

 actly the same circumstances, not to different parts or aspects of 

 the same thing nor to the same thing at different times. It would 

 indeed be more accurate to say that the principle abstracts alto 

 gether from time, and simply states that contradictory attributes 

 cannot be asserted of any single object of thought ; when, how 

 ever, reference is made to time, the principle must be understood 

 as referring to the impossibility of contradictory attributes inhering 

 in the same subject at one and the same time. 



14. THE PRINCIPLE OF EXCLUDED MIDDLE is variously ex 

 pressed by saying that Everything must either be or not be : A 

 either is or is not B : Any attribute must be either affirmed or 

 denied of any given subject : One of any pair of contradictories must 



