CONCEPTIONS OF SPACE AND TIME. 91 



forms, must mean that they can bo thought of without any concrete 

 embodiment whatsoever; that one can think of Time, as a pure 

 abstraction, without having in one s mind any concrete succession. 

 Now, this doctrine is in the last degree questionable.&quot; 



I quite agree with. Prof. Bain that &quot;this doctrine is in 

 the last degree questionable ; &quot; but I do not admit that this 

 doctrine is implied by the definition of Abstract Science 

 which I have given. I speak of Space and Time as they 

 are dealt with by mathematicians, and as it is alone possible 

 for pure Mathematics to deal with them. While Mathe 

 matics habitually uses in its points, lines, and surfaces, 

 certain existences, it habitually deals with, these as repre 

 senting points, lines, and surfaces that are ideal ; and its 

 conclusions are true only on condition that it does this. Points 

 having dimensions, lines having breadths, planes having 

 thicknesses, are negatived by its definitions. Using, though 

 it does, material representatives of extension, linear, super 

 ficial, or solid, Geometry deliberately ignores their material 

 ity ; and attends only to the truths of relation they present. 

 Holding with Prof. Bain, as I do, that our consciousness 

 of Space is disclosed by our experiences of Matter argu 

 ing, as I have done in The Principles of Psychology, that it 

 is a consolidated aggregate of all relations of co-existence 

 that have been severally presented by Matter ; I never 

 theless contend that it is possible to dissociate these re 

 lations from Matter to the extent required for formulating 

 them as abstract truths. I contend, too, that this separa 

 tion is of the kind habitually made in other cases ; as, for 

 instance, when the general laws of motion are formulated 

 (as M. Comte s system, among others, formulates them) in 

 such way as to ignore all properties of the bodies dealt with 

 save their powers of taking up, and retaining, and giving 

 out, quantities of motion; though these powers are incon 

 ceivable apart from the attribute of extension, which is 

 intentionally disregarded. 



