HIS PHILOSOPHICAL POSITION 



with mechanical propositions, they represent no rela- 

 tions of real things. ' When thus isolated, if we regard 

 them with Kant as forms of intuition transcendentally 

 given, they constitute a form into which any empiri- 

 cal content whatever will fit, and which therefore 

 does not in any way limit or determine beforehand 

 the nature of the content. This is true, however, 

 not only of Euclid's axioms, but also of the axioms 

 of spherical and pseudo-spherical geometry. As soon 

 as certain principles of mechanics are conjoined 

 with the axioms of geometry, we find a system of 

 propositions which has real import, and which can 

 be verified or overturned by empirical observation, 

 or from experience it can be inferred. If such a 

 system were to be taken as a transcendental form 

 of intuition and thought, there must be assumed 

 a pre-established harmony between form and 

 reality.' J 



In our space of three dimensions, we can give up, 

 as it were, what we possess, and be able to imagine 

 a space of two dimensions inhabited by creatures 

 having no thickness, and living between two layers 

 infinitely close together, so that they could move 

 from side to side and backwards and forwards ; or 

 a space of one dimension, like a tunnel, in which 

 creatures having no thickness and no breadth could 

 move only backwards and forwards. We cannot, 

 however, go the other way and conceive a space of 



1 Mind, vol. i., p. 321. 

 265 



