E. B. Hunt on Physical and Metaphysical Infinity. 5 
| dto which our entire sphere of visible stars makes but a sen- 
ar le mass of matter. Throughout the entire range of organic 
existence there mill be in fact fur each species a specific infinity, 
and we cannot say but in the treasure house of the actual uni- 
verse, there may be an infinite series of organic perceptive powers 
which bear to each other the relation of the successive orders of 
differences in differential calculus. Whatever may be the fact 
as to actual nature, such an infinite series of successive infinities 
is metaphysically conceivable. The clear apprehension of the 
idea of infinity which may be gleaned from physical grounds 
gives a basis for indefinite metaphysical fabrications without 
| i the least departing from the true inductive idea of intinity. 
But science has not to deal with the supposable except as it is 
ty 
involved in the actual, and it belongs not to _ piss or to a 
| cussed are en aye Metusted all specitic intelligences are in it 
. ignored, and even the Divine Intelligence may ‘be supposed in 
some way concrete in conditions too specific to be truly stated in 
respect to limits, by the abstract infinity of pure analysis. The 
very possibility. of positive definition as applied to any being 
however exalted, excludes the abstract: symbo ee infinity from 
entering a correct exegesis of its nature. For what then does the 
abstract symbol of infinity stand? It at least ee as a formula 
for all specific infinities which by the interpolation of the proper 
constants expresses the quantitive relations in any actual case of 
infinity. The abstract symbol is a grouping of specific cases: 
whether it is more than this may not be for man to say. 
One inference from these views of infinity is that the ordinary 
. definition of the asymptotic curve needs correction. The math- 
ematical formula of incessant and incessantly diminishing ap- 
roach between a straight line and a curve or between two curved. 
ines, or the same relative to plane and curved surfaces is not 
uppose an intellect of the proper or differential grade to be dul 
cognizant. of asymptotic lines at an infinite distance; it would 
find no actual contact, but the same law of approach | expresse 
in the analytical formula would still go on until an intellect of 
ential “esa. and so on to infinity. The order of perceptions 
Raion would be progressively higher than that dem 
suet entials of the variable, Here then there is no true i 
use with the other idea of tangency at an infinite distance. _ 
a 
the second differential order would have to be called inas the 
cognizant power: this in turn must give place to a third differ- 
required to ap ppreciate the second, third, &c. differentials of the - : 
anded for 
