SPACE AND TIME i6i 



tion is even more marked in a footnote which accompanies 

 the passage, and which runs thus : — 



" Whatever disputes there may be about mathematical 

 points, wc must allow that there are physical points — 

 that is, parts of extension, which cannot be divided or 

 lessened either by the eye or imagination. These images, 

 then, which are present to the fancy or senses, are 

 absolutely indivisible, and consequently must be allowed by 

 mathematicians to be infinitely less than any real part of 

 extension ; and yet nothing appears more certain to 

 reason than that an infinite number of them composes an 

 infinite extension. How much more an infinite number 

 of those infinitely small parts of extension, which are still 

 supposed infinitely divisible." 



Here the transition from perception to conception and 

 back again is made several times over. A point mathe- 

 matically defined is a conception and has no real existence 

 in the field of perception. It is true we base this con- 

 ception on our perceptive experience of things which are 

 not points, but the mathematical point is not a limit to 

 any process which could be carried on in the field of 

 perception ; it is the limit to a process which we imagine 

 carried on in the field of thought, in the sphere of con- 

 ceptions. If Hume means by a physical point the 

 smallest possible groups of sense-impressions which we 

 can perceive apart, then this cannot be divided or lessened 

 by the eye. But this physical point transferred from the 

 field of perception to that of conception can in the 

 imagination be divided over and over again. This 

 remark will be more clearly appreciated when we come 

 to deal with the geometrical conception of space. It 

 suffices for the present to note that Hume passes from 

 the eye to the imagination, from the mathematical to the 

 physical, from the fancy to the senses, as if the geometrical 

 theory of extension, that shorthand method of classifying 

 and describing coexisting phenomena, was itself the world 

 of phenomena. Several types of geometry can be 

 elaborated by our rational faculty, and the results, which 

 flow from them, will depend upon the statement of their 



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