SCIENTIFIC METHOD IN PHILOSOPHY 



d, but a construction by means of data with their 

 hypothetical additions. It is obvious that any hypo- 

 thetical filling out of data is less dubious and unsatis- 

 factory when the additions are closely analogous to data 

 than when they are of a radically different sort. To 

 assume, for example, that objects which we see continue, 

 after we have turned away our eyes, to be more or less 

 analogous to what they were while we were looking, is 

 a less violent assumption than to assume that such objects 

 are composed of an infinite number of mathematical 

 points. Hence in the physical study of the geometry 

 of physical space, points must not be assumed ab initio as 

 they are in the logical treatment of geometry, but must 

 be constructed as systems composed of data and hypo- 

 thetical analogues of data. We are thus led naturally 

 to define a physical point as a certain class of those 

 objects which are the ultimate constituents of the physical 

 world. It will be the class of all those objects which, as 

 one would naturally say, contain the point. To secure a 

 definition giving this result, without previously assuming 

 that physical objects are composed of points, is an agree- 

 able problem in mathematical logic. The solution of 

 this problem and the perception of its importance are 

 due to my friend Dr. Whitehead. The oddity of regard- 

 ing a point as a class of physical entities wears off with 

 familiarity, and ought in any case not to be felt by those 

 who maintain, as practically every one does, that points 

 are mathematical fictions. The word " fiction ' is used 

 glibly in such connexions by many men who seem not 

 to feel the necessity of explaining how it can come about 

 that a fiction can be so useful in the study of the actual 

 world as the points of mathematical physics have been 

 found to be. By our definition, which regards a point 

 as a class of physical objects, it is explained both how 



