ii 4 SCIENTIFIC METHOD IN PHILOSOPHY 



sensible space, they must be an inference. It is not easy 

 to see any way in which, as independent entities, they 

 could be validly inferred from the data ; thus here again, 

 we shall have, if possible, to find some logical con- 

 struction, some complex assemblage of immediately given 

 objects, which will have the geometrical properties 

 required of points. It is customary to think of points 

 as simple and infinitely small, but geometry in no way 

 demands that we should think of them in this way. All 

 that is necessary for geometry is that they should have 

 mutual relations possessing certain enumerated abstract 

 properties, and it may be that an assemblage of data of 

 sensation will serve this purpose. Exactly how this is to 

 be done, I do not yet know, but it seems fairly certain 

 that it can be done. 



The following illustrative method, simplified so as to 

 be easily manipulated, has been invented by Dr Whitehead 

 for the purpose of showing how points might be manu- 

 factured from sense-data. We have first of all to observe 

 that there are no infinitesimal sense-data : any surface we 

 can see, for example, must be of some finite extent. 

 But what at first appears as one undivided whole is often 

 found, under the influence of attention, to split up into 

 parts contained within the whole. Thus one spatial 

 object may be contained within another, and entirely 

 enclosed by the other. This relation of enclosure, by 

 the help of some very natural hypotheses, will enable us 

 to define a " point " as a certain class of spatial objects, 

 namely all those (as it will turn out in the end) which 

 would naturally be said to contain the point. In order 

 to obtain a definition of a " point " in this way, we 

 proceed as follows : 



Given any set of volumes or surfaces, they will not in 

 general converge into one point. But if they get smaller 



