34 SCIENCE AND METHOD. 



One example has just shown us the importance 

 of terms in mathematics ; but I could quote many- 

 others. It is hardly possible to believe what economy 

 of thought, as Mach used to say, can be effected by 

 a well-chosen term. I think I have already said 

 somewhere that mathematics is the art of giving the 

 same name to different things. It is enough that 

 these things, though differing in matter, should be 

 similar in form, to permit of their being, so to speak, 

 run in the same mould. When language has been 

 well chosen, one is astonished to find that all demon- 

 strations made for a known object apply immediately 

 to many new objects : nothing requires to be changed, 

 not even the terms, since the names have become the 

 same. 



A well-chosen term is very often sufficient to remove 

 the exceptions permitted by the rules as stated in the 

 old phraseology. This accounts for the invention of 

 negative quantities, imaginary quantities, decimals to 

 infinity, and I know not what else. And we must 

 never forget that exceptions are pernicious, because 

 they conceal laws. 



This is one of the characteristics by which we re- 

 cognize facts which give a great return : they are the 

 facts which permit of these happy innovations of 

 language. The bare fact, then, has sometimes no great 

 interest: it may have been noted many times without 

 rendering any great service to science ; it only acquires 

 a value when some more careful thinker perceives the 

 connexion it brings out, and symbolizes it by a term. 



The physicists also proceed in exactly the same 

 way. They have invented the term " energy," and the 

 term has been enormously fruitful, because it also 



