656 PSYCHOLOGY. 



Mill is himself compelled to say, to find the number four 

 in it, and so on. 



The relation of numbers to experience is just like that 

 of ' kinds' in logic. So long as an experience will keep its 

 kind we can handle it by logic. So long as it will keep its 

 number we can deal with it by arithmetic. Sensibly, how- 

 ever, things are constantly changing their numbers, just as 

 they are changing their kinds. They are forever breaking 

 apart and fusing. Compounds and their elements are never 

 numerically identical, for the elements are sensibly many 

 and the compounds sensibly one. Unless our arithmetic 

 is to remain without application to life, we must somehow 

 make more numerical continuity than we spontaneously find. 

 Accordingly Lavoisier discovers his weight-units which re- 

 main the same in compounds and elements, though volume- 

 units and quality-units all have changed. A great discovery ! 

 And modern science outdoes it by denying that compounds 

 exist at all. There is no such thing as ' water ' for 

 'science ;' that is only a handy name for H^ and O when 

 they have got into the position H-O-H, and then affect 

 our senses in a novel way. The modern theories of atoms, 

 of heat, and of gases are, in fact, only intensely artificial 

 devices for gaining that constancy in the numbers of 

 things which sensible experience will not show. " Sensible 

 things are not the things for me," says Science, "because 

 in their changes they will not keep their numbers the same. 

 Sensible qualities are not the qualities for me, because they 

 can with diflSiculty be numbered at all. These hypothetic 

 atoms, however, are the things, these hypothetic masses 

 and velocities are the qualities for me ; they will stay num- 

 bered all the time." 



By such elaborate inventions, and at such a cost to the 

 imagination, do men succeed in making for themselves a 

 world in which real things shall be coerced per fas aut 

 nefas under arithmetical law. 



The other branch of mathematics is geometry. Its ob- 

 jects are also ideal creations. Whether nature contain 

 circles or not, I can know what I mean by a circle and 

 can stick to my meaning ; and when I mean two circles I 



