18 THE PRINCIPLES OF SCIENCE. [CHAP. 



i>nd B allows us indifferently to place A where B was, or 

 B where A was ; and there is no limit to the variety ot 

 special meanings which we can bestow upon the signs 

 used in this formula consistently with its truth. Thus if 

 we first specify only the meaning of the sign ?=, we may 

 say that if C is the weight of B, then G is also the weight 

 of A. Similarly 



If C is the father of B, C is the father of A ; 

 If is a fragment of B, C is a fragment of A ; 

 If C is a quality of B, C is a quality of A ; 

 If C is a species of B, C is a species of A ; 

 If C is the equal of B, C is the equal of A ; 

 and so on ad infinitum. 



We may also endow with special meanings the letter- 

 terms A, B, and C, and the process of inference will never 

 be false. Thus let the sign ooo mean " is height of," and let 

 A = Snowdon, 



B = Highest mountain in England or Wales, 

 C = 3,590 feet; 



then it obviously follows since " 3,590 feet is the height 

 of Snowdon," and " Snowdon = the highest mountain in 

 England or Wales," that, "3,590 feet is the height of the 

 highest mountain in England or Wales." 



One result of this general process of inference is that we 

 may in any aggregate or complex whole replace any part 

 by its equivalent without altering the whole. To alter is 

 to make a difference ; but if in replacing a part I make no 

 difference, there is no alteration of the whole. Many 

 inferences which have been very imperfectly included in 

 logical formulas at once follow. I remember the late Prof. 

 De Morgan remarking that all Aristotle's logic could not 

 prove that " Because a horse is an animal, the head of a 

 horse is the head of an animal." I conceive that this 

 amounts merely to replacing in the complete notion head of 

 a horse, the term " horse," by its equivalent some animal or 

 an animal. Similarly, since 



The Lord Chancellor = The Speaker of the House of 



Lords, 

 it follows that 



The death of the Lord Chancellor = The death of the 



Speaker of the House of Lords ; 

 and any event, circumstance or thing, which stands in a 



