Q2 THE FOURTH DIMENSION. 



angular velocity of the apparent motions of the fixed stars is expli- 

 cable from the assumption of an axial motion of the firmament, that 

 the fixed stars are really rigidly placed in a celestial sphere rotating 

 about its axis. It must not be forgotten that our comprehension of 

 the phenomena of the real world consists of two elements : first, of 

 that which the things really are; and, second, of that by which we 

 rationally apprehend the things. This latter element is partly de- 

 pendent on the sum of the experiences which we have before ac- 

 quired, and partly on the necessity, due to the imperfection of rea- 

 son, of our classifying the multitudinous isolated phenomena of the 

 world into categories which we ourselves have formed, and which, 

 therefore", are not wholly derived from the phenomena themselves, 

 but to a great extent are dependent on us. 



Besides geometrical reasons, Zallner has also adduced cosmo- 

 logical reasons to prove the existence of a four- dimensional space. 

 To these reasons belong especially the questions, whether the num- 

 ber of the fixed stars is infinitely great, whether the world is finite 

 or infinite in extension, whether the world had a beginning or will 

 have an end, whether the world is not hastening towards a condition 

 of equilibrium or dead level by the universal distribution of its matter 

 and energy ; the problems, also, of gravitation and action at a dis- 

 tance ; and finally, the questions concerning the relations between 

 the phenomena in the world of sense-perception to the unknown 

 things-in-themselves. All these questions which can be decided in 

 no definite sense, led Zollner and his followers to the assumption 

 that a four-dimensioned space inclusive of the space of experience 

 must really exist. But more careful reflection will show that this 

 assumption does not dispose of the difficulties but simply displaces 

 them into another realm. Furthermore, even if four-dimensioned 

 space did unravel and make clear all the cosmological problems 

 which have bothered the human mind, still, its existence would not 

 be proved thereby; it would yet remain a mere hypothesis, designed 

 to render more intelligible to a being who can only make experiences 

 in a three-dimensional space, the phenomena therein which are full 

 of mystery to it. A four-dimensioned space would in such case pos- 

 sess for the metaphysician a value similar to that which the eth^r 



