1 878.] On Space of Four Dimensions. 229 
space has been developed by means of the law of causality, 
which has been implanted in us a priori , and we have come 
to the idea of the third dimension in order to overcome the 
apparent inconsistency of faCts, the existence of which 
experience daily convinces us. 
The moment we observe in three-dimensioned space con- 
tradictory fadts, — i.e., faCts which would force us to ascribe 
to a body two attributes or qualities which hitherto we 
thought could not exist together, — the moment, I say, in 
which we should observe such contradictory faCts in a three- 
dimensioned body, our reason would at once be forced to 
reconcile these contradictions. 
There would be such a contradiction, for example, if we were 
to ascribe to one and the same objeCt at once mutability and 
immutability, the most universal attribute of a body being 
the quantity of its ponderable matter. In conformity with 
our present experience we consider this attribute as unalter- 
able. As soon, however, as phenomena occur which prove 
it to be alterable, we shall be obliged to generalise our 
representation of the ideality of a body so as to bring the 
observed change in the quantity of its matter in accordance 
with its hitherto-imagined unchangeableness. 
On page 235 of his book the author quotes the celebrated 
mathematician Riemann, who says in his work “ Concerning 
the Hypotheses upon which Geometry is Founded:” — 
“ The explanation of these faCts can only be found by 
starting from the aCtual theories of the appearance 
of all phenomena which are confirmed by experience, 
and of which, as they now are, Newton has laid the 
foundation. Urged forward by faCts, which we can- 
not explain through our hitherto-conceived theories, 
we slowly remodel our conceptions. If phenomena 
occur which, according to our conception, were to be 
expeCted with probability, our theories are confirmed, 
and our confidence in them is founded upon this 
confirmation by experience. If, however, something 
occurs which we do not expeCt, which according to 
our theory was improbable or impossible, the task is 
imposed on us to remodel our theory, in order to 
make the observed faCts cease to be in contradiction 
with our improved theory. The completion of our 
system of ideas forms the explanation of the unex- 
pected observation. Our conception of nature by 
this process grows slowly to be more complete and 
more just, at the same time it retreats more and 
more beneath the surface of appearances.” 
