THE CONCEPTUAL WORLD 



23 



becomes " infinitesimally " small ; and at the same 

 time we think of ourselves as becoming smaller and 

 smaller, so that we can still move about on the spot. 

 But we think of the area of the spot as becoming so 

 small that no matter how small we make ourselves 

 we are unable to move on it. 



This means that we substitute conceptual lines 

 and points and triangles for the perceptual ones of our 

 experience, and then we operate in imagination with 

 these concepts. That is to say, we carry our modes 

 of exertional activity to their limits, 1 in the way which 

 we have tried to indicate above — a process of thought 

 which is the foundation of the reasoning of the in- 

 finitesimal calculus. 



What we call space, therefore, depends on our 

 intuition of bodily exertion. This intuition includes 

 the knowledge that a certain change has occurred as 

 the consequence of the expenditure of a certain amount 

 of bodily energy, and that, as the result of this change, 

 the relation of the rest of the universe to our body 

 has become different. We think of our body as the 

 origin, or centre, of a system of co-ordinates : — 



y 



x 



o 



X 



1 See appendix, p. 346. 



y 



Fig. 4. 



