TERMS. 39 



Certain Special Conditions of Logical Symbols. 



In order that we may argue and infer truly we must 

 treat our logical symbols according to the fundamental 

 laws of Identity and Difference. But in thus using our 

 symbols we shall frequently meet with combinations of 

 which the meaning will not at first be apparent. In some 

 cases, for instance, we may learn that an object is * yellow 

 and round/ in other cases that it is * round and yellow ' : 

 there arises the question whether these two descriptions 

 are identical in meaning or not. Or again, if we proved 

 that an object was ' round round' the meaning of such an 

 expression would be open to doubt. Accordingly we must 

 take notice, before proceeding further of certain special 

 laws which govern the combination of logical terms. 



In the first place the combination of a logical term 

 with itself is without effect, just as the repetition of a 

 statement does not alter the meaning of the statement : 

 'a round round object' is simply 'a round object/ What 

 is yellow yellow is merely yellow ; metallic metals cannot 

 differ from metals, nor elementary elements from elements. 

 In our symbolic language we may similarly hold that AA 

 is identical with A, or 



A = AA = AAA = &c. 



The late Professor Boole is the only logician in modern 

 times who has drawn attention to this remarkable property 

 of logical terms b ; but in place of the name which he gave 

 to the law, I have proposed to call it The Law of Sim- 

 plicity 6 . Its high importance will only become apparent 

 when we attempt to determine the relations of logical and 

 mathematical science. Two symbols of quantity, and only 



b 'Mathematical Analysis of Logic,' Cambridge, 1847, P- X 7- 'An 

 Investigation of the Laws of Thought/ London, 1854, p. 29. 

 c ' Pure Logic/ p. 1 5. 



