What Does It Mean? 
245 
coveries to his father contain one truth more literal than he in¬ 
tended? He wrote of his new views " It would be damage 
eternal if they were lost. Now I cannot say more, only so much, 
that out of nothing I have created another wholly new world. ” 
These last words may perhaps remind us of the ancient adage 
"Ex nihilo nihil Jit. ” 
The arithmetics of our grandfathers contained this problem:—- 
"If a third of six be three, what will a fourth of twenty be?" 
which presented an entirely practicable excuse for certain ele¬ 
mentary mathematical gymnastics, but effected no change in 
the fact that a third of six can under no possible circumstances 
be three. 
Evidently, however, mathematical work can not be judged to 
be illegitimate merely because it rests upon a suppositious basis. 
But the question in any case may reasonably be asked whether the 
supposition is presented as a working hypothesis, a temporary 
scaffolding to be used in the erection of a real and permanent 
structure, or as being in itself a finality, although but an ex¬ 
pression in mathematical form of an apparently inconceivable 
somewhat. From a point of view implied in this we may re¬ 
spond to Prof. Smith of the University of Missouri, when having 
stated the assumptions which distinguish the Euclidian geome¬ 
try from the other systems, which he terms Hyper-Euclidian, 
he asserts the logical right of these systems to existence, and 
adds that " they lack neither interest nor importance. ” To this 
it is at least plausible to reply that such geometries, considered 
as laboriously developed systems of logical reasoning, without 
doubt have a right to existence, and possess great interest, 
especially for those whose chosen fields of work include the 
points of departure of the new thought. But it may still seem 
that their importance, which, like the importance of all truths, 
depends upon their place in the system of universal thought, 
and their relation to other parts of the system, may not be 
entirely unlike the importance of that harrowing question of 
our childhood. 
“If all the world were apple-pie, and all the sea were ink, 
And all the trees were bread and cheese, what should we have for drink?” 
