150 THE LIMITATIONS OF SCIENCE 



As for the third postulate, which is called matter, it 

 may be taken in the most general sense as the some- 

 thing which makes space and time concrete or sensible. 

 The necessity in science for such a postulate is clear, 

 for science deals with the phenomena of an objective 

 world. Even those men of science most opposed to 

 the idea that mass is the measure of matter still 

 postulate an entity identical with matter, as just de- 

 fined, although they may call it by a different name, 

 such as energy or electricity. And the distinction be- 

 tween mathematics and science lies in the conception of 

 this third postulate. In pure mathematics, matter be- 

 comes the abstract postulate, quantity. When discuss- 

 ing velocity abstractly there is then no need to con- 

 sider the properties of the thing moving, but in physics 

 there is such a need. Or again, when dealing with 

 space relations the mathematician is in no way limited 

 to the restricted number of three dimensions which our 

 sense perception of the material universe imposes on 

 science. 



The supreme value of mathematics to science is due 

 to the fact that scientific laws and theories have their 

 best, if not their only complete, expression in mathe- 

 matical formulae; and the degree of accuracy with 

 which we can express scientific theory in mathematical 

 terms is a measure of the state of a science. Thus 

 it is possible to classify sciences according to their 

 development, from the accumulation of statistics of 



