192 THE LIMITATIONS OF SCIENCE 



tulates which are given to him by others, or assumed 

 by himself. Thus he may derive the laws of mechanics 

 from a postulate that bodies have three spatial dimen- 

 sions, which is verified by observation; but he is also 

 interested in the mechanics of bodies which would 

 prevail if there were four dimensions to space, a pos- 

 tulate not verifiable. He develops a geometry which 

 requires the axiom that parallel lines do not inter- 

 sect ; and at the same time he studies another geometry 

 based on the axiom that parallel lines do intersect. He 

 finds it no more important as an exercise in analysis 

 to study a solar system which is subservient to forces 

 of attraction, than one which obeys a law of repulsion. 

 That is, he is not limited at all to what we call the 

 reality of an objective and material world, and mathe- 

 matical deductions regarding an imaginative world will 

 have very little influence on society. So, also, the 

 purely hypothetical parts of such abstract subjects as 

 physics, chemistry, and astronomy are not very influ- 

 ential in a direct manner, but indirectly they have had 

 an enormous influence since they have been taken 

 as an example for the development of biology and that 

 class of sciences known as political and social. Specu- 

 lations in these subjects have a direct and intimate 

 bearing on the character of the individual and on so- 

 ciety. Thus a ready proneness to accept hypothesis 

 and speculation as well as observation has resulted 

 in the crude laws and dogmas of eugenics, and has put 



