n8 MYSTICISM AND LOGIC 



the use of points can lead to important physical results, 

 and how we can nevertheless avoid the assumption that 

 points are themselves entities in the physical world. 



Many of the mathematically convenient properties of 

 abstract logical spaces cannot be either known to belong 

 or known not to belong to the space of physics. Such 

 are all the properties connected with continuity. For 

 to know that actual space has these properties would 

 require an infinite exactness of sense-perception. If 

 actual space is continuous, there are nevertheless many 

 possible non-continuous spaces which will be empirically 

 indistinguishable from it ; and, conversely, actual space 

 may be non-continuous and yet empirically indistinguish- 

 able from a possible continuous space. Continuity, 

 therefore, though obtainable in the a priori region of 

 arithmetic, is not with certainty obtainable in the space 

 or time of the physical world : whether these are con- 

 tinuous or not would seem to be a question not only 

 unanswered but for ever unanswerable. From the point 

 of view of philosophy, however, the discovery that 

 a question is unanswerable is as complete an answer as 

 any that could possibly be obtained. And from the 

 point of view of physics, where no empirical means of 

 distinction can be found, there can be no empirical 

 objection to the mathematically simplest assumption, 

 which is that of continuity. 



The subject of the physical theory of space is a very 

 large one, hitherto little explored. It is associated with 

 a similar theory of time, and both have been forced upon 

 the attention of philosophically minded physicists by the 

 discussions which have raged concerning the theory of 

 relativity. 



(3) The problem with which Kant is concerned in the 

 Transcendental Esthetic is primarily the epistemological 



