i62 THE GRAMMAR OF SCIENCE 



fundamental axioms. From these types we select that 

 one which will enable us to describe the widest range of 

 phenomena in the briefest possible formula, or which will 

 enable us with the greatest accuracy to classify the 

 differences between groups of sense-impressions. We 

 have no more right to quarrel with the geometrician's con- 

 ception of the infinite divisibility of space than with his 

 conception of the circle, or with the physicist's conception 

 of the atom. One and all are pure ideals beyond the 

 range of perceptual experience. What we must ask is : 

 How far are these conceptions of service in enabling us to 

 briefly describe and classify our perceptions ; how far do 

 they aid us in mentally storing up past experience as a 

 guide for future action ? A point and an ellipse may be 

 absolutely absurd in the world of perceptions, but they 

 are none the less valid and useful conceptions if they 

 help us to describe and predict the motion of the earth 

 about the sun. The paradoxes which Hume finds in the 

 conclusions of geometry only exist so long as we assert 

 that every conception has a precise counterpart in per- 

 ception, and forget that science is only a shorthand de- 

 scription of nature and not nature itself. 



8 4. — The Space of Memo jy and Thought 



Before we pass from the subject of real or perceptual 

 space, we ought to note that this mode of perceiving 

 phenomena appears not only in association with immediate 

 sense-impressions, but also with the stored impresses of 

 past experience. To be accurate, we ought perhaps to 

 say that the mode of remembrance is akin to the mode 

 of perception — unless, indeed, we are using the word 

 perception to refer to the consciousness alike of an 

 " external " sense-impression and of an " internal " sense- 

 impress. In all probability these processes of what Locke 

 would term external and internal perception are much 

 the same, only the sources from which they draw their 

 material are different. In this case it is sufficient to say 

 that space as a mode of perception applies as much to 



