74 TWO THEORIES OF KNOWLEDGE 



by observation and measurement from sensible 

 data, are empirical and approximate. A geometrical 

 proposition such, for example, as the assertion that 

 the three angles of a triangle are equal to two right 

 angles is not merely approximate. It has no 

 dependence on measurement. It is absolutely 

 true. It is ascertained deductively, and therefore 

 measurement is not involved, and is never employed. 

 Its truth is not ascertained by measurement. It 

 is not verified by measurement. It in no degree 

 depends upon the sensible figure. It is equally 

 true for every human being whatever be the degree 

 of accuracy of the figure by the aid of which he 

 studies it, or indeed whether he studies it by figure 

 v or otherwise, as must necessarily be the case with 

 the born blind. 



There may be many different forms of energetic 

 transmutation which may determine many other 

 forms of space besides that form of tridimensional 

 space in which our Activity is involved. For such, 

 a different geometry may and will be applicable ; but 

 for the tridimensional conditions of our activity the 

 proposition is necessary and absolute. No measure- 

 ment of any stellar parallax, however minute and 

 whatever the result might be, could have any bear- 

 ing on its truth. Geometry is the science of the pure 

 forms of our motor activity amidst corporeal bodies. 



