VII 



The Non-Mathematical Sciences 



1HAVE devoted six of my eight chapters to 

 sciences which are either wholly mathemati- 

 cal or which need mathematics for their under- 

 standing and their expression. And yet if I seem 

 to have given them the greater weight, it is 

 merely because they require only a few concepts 

 and these of the most highly refined nature, as 

 compared with the great sciences which derive 

 but little assistance from mathematics, and rest 

 upon independent foundations; certainly not 

 because the attainments in these latter sciences 

 are less worthy of our admiration. These non- 

 mathematical sciences involve a very much 

 larger number of separate concepts which, for 

 the most part, show a little more of the raw 

 material of experience from which they have 

 been derived, with less refinement in the proc- 

 esses of abstraction and idealization. As an ex- 

 ample of these let us consider the concept of 

 material substance. 



Matter has not been fully defined as a scien- 

 tific concept. If we should say it is that which 

 has mass, then light would be classed as matter. 



