MYSTICISM AND LOGIC 



therefore, demands that we should abstain from assum- 

 ing the existence of points and straight lines. As soon, 

 however, as we accept the view that points and straight 

 lines are complicated constructions by means of classes 

 of physical entities, the hypothesis that we have an 

 a priori intuition enabling us to know what happens to 

 straight lines when they are produced indefinitely becomes 

 extremely strained and harsh ; nor do I think that such 

 an hypothesis would ever have arisen in the mind of a 

 philosopher who had grasped the nature of physical 

 space. Kant, under the influence of Newton, adopted, 

 though with some vacillation, the hypothesis of absolute 

 space, and this hypothesis, though logically unobjection- 

 able, is removed by Occam's razor, since absolute space 

 is an unnecessary entity in the explanation of the physical 

 world. Although, therefore, we cannot refute the Kantian 

 theory of an a priori intuition, we can remove its grounds 

 one by one through an analysis of the problem. Thus, here 

 as in many other philosophical questions, the analytic 

 method, while not capable of arriving at a demonstrative 

 result, is nevertheless capable of showing that all the 

 positive grounds in favour of a certain theory are fallacious 

 and that a less unnatural theory is capable of accounting 

 for the facts. 



Another question by which the capacity of the analytic 

 method can be shown is the question of realism. Both 

 those who advocate and those who combat realism seem 

 to me to be far from clear as to the nature of the problem 

 which they are discussing. If we ask : " Are our objects 

 of perception real and are they independent of the per- 

 cipient ? ' it must be supposed that we attach some 

 meaning to the words "real " and "independent," and 

 yet, if either side in the controversy of realism is 

 asked to define these two words, their answer is pretty 



