PROFESSOR AT HEIDELBERG 265 



qualities of sensation, since space appears to us sensibly with 

 the qualities of our sensations of motion, as that through which 

 we are able to move and see. Space to him is, further, the 

 necessary form of external intuition, since it is that which we 

 perceive spatially which is for us the external world, all else 

 being the world of internal intuition or of self-consciousness, 

 and for him as for Kant space is a given form of intuition, prior 

 to all experience, since the perception of it is bound up with the 

 possibility of motor volitional impulses, the mental and bodily 

 capacity for which must be given by our organization before 

 we can have intuitions of space. Kant, however, went farther, 

 in that he assumed not only that the universal form of space- 

 intuition was given, but that it also implied a priori, and anterior 

 to all possible experience, certain more exact determinations, 

 viz. the familiar axioms of geometry so that these are also of 

 transcendental origin. 



It is here that Kant and Helmholtz part company, since to 

 the latter the question whether the axioms of geometry are 

 transcendental or laws of experience, is entirely separate from 

 that of whether space in general is a transcendental form of 

 intuition or no. 



' Kant's doctrine of the a priori forms of intuition is a very 

 happy and lucid expression of the facts, but these forms must 

 be sufficiently free and void of content to include every sort of 

 content that may turn up anywhere in the forms of perception 

 under consideration. The axioms of geometry, however, limit 

 the intuitional forms of space to such an extent, that all 

 conceivable contents are no longer admissible, if, that is to say, 

 geometry is to be applied to the real world at all.' 



If the axioms really were an innate form of spatial intuition, 

 we should not be justified in applying them to the phenomenal 

 world till it had been proved by observation and experiment 

 that the fractions of space taken as equivalent by the presup- 

 posed transcendental intuitions were physically equivalent also. 

 Helmholtz shows Kant's assumption of the a priori character of 

 the geometrical axioms to be superfluous and unjustifiable. 



On the strength of his previous investigations he is able to 

 show that it is possible to construct a geometry on the basis 

 of the single definition of physical equality, according to which, 

 under the same circumstances, in the same time, the same 



