II. 



MATHEMATICAL DEFINITIONS AND 

 EDUCATION. 



I. I have to speak here of general definitions in 

 mathematics. At least that is what the title of the 

 chapter says, but it will be impossible for me to 

 confine myself to the subject as strictly as the rule 

 of unity of action demands. I shall not be able to 

 treat it without speaking to some extent of other 

 allied questions, and I must ask your kind forgiveness 

 if I am thus obliged from time to time to walk among 

 the flower-beds to right or left. 



What is a good definition ? For the philosopher 

 or the scientist, it is a definition which applies to 

 all the objects to be defined, and applies only to 

 them ; it is that which satisfies the rules of logic. 

 But in education it is not that ; it is one that can be 

 understood b)- the pupils. 



How is it that there are so many minds that are 

 incapable of understanding matiiematics ? Is there 

 not something paradoxical in this ? Here is a 

 science which appeals only to the fundamental 

 principles of logic, to the principle of contradiction, 

 for instance, to what forms, so to speak, the skeleton 

 of our understanding, to what we could not be de- 

 prived of without ceasing to think, and yet there are 



