56 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
but now named Euclidean by certain analysts whose so-called 
geometry is symbolic. Geometry is therefore able*to deal with all 
aspects of extension, without regard to limit, in spite of some in- 
firmity in the Greek method, for scale cannot affect the generality 
of extension relations, and abstract unconditioned space is not an 
entity but a mere negation, concerning which relative propositions 
are unintelligible. A false philosophy regarding space is at the 
root of all modern heresies concerning geometry and mensuration, 
founded in misapprehension of the Euclidean inductions or gene- 
ralizations.* 
The first law of motion is but the formulated recognition of in- 
ertia, which is only manifest in conjunction with motion, actively 
or passively. It was known to Galileo, and laid down by Descartes 
as a law in his Principia. It is a cosmical truth, bound up with 
the absolute nature of mass and the true relations of extension, 
which correlates the whole fabric of dynamical knowledge with 
rectilinear geometry, curvilinear motion being demonstrably not a 
simple state of conservation under inertia, but a resultant of mul- 
tiple forces. The simple action of mass under the first law of 
motion, if undisturbed, furnishes the absolute unreturning recti- 
lineal path which overthrows all speculation about possible ideal 
spaces. I here recall a book written by a learned American of 
Philadelphia—learned, that is, according to the mediaeval stand- 
ard of the colleges—and published only during the past year, en- 
* There are two opposite though similar forms of error in the assumptions 
regarding space. The first is that space is a specific or perhaps generic en- 
tity or objectivity per se, possessed of conditions and attributes, like sub- 
stance, such as dimension (in several), differentia in locality, figure, as cur- 
vature, etc. (hence necessarily finite), and only uncognizable by us simply 
for lack of perceptive faculties to correspond. This is the fundamental 
error, as it seems to me, of Riemann and Lobatschewsky. The second is 
that of the older Cartesians, who viewed space as but the mere attribute or 
synonym of substance, and inconceivable apart from it, so that bodies sep- 
arated by void space would be absolutely in contact without regard to dis- 
tance. Both of these speculations are purely metaphysical, and non-exper- 
iential, the latter resulting from the old scholastic method of syllogistic de- 
duction from primary postulates of verbal definition, and the former from 
similar inferences from the forms of the analytical logic of symbols, the use 
of which is still in the scholastic stage. Like Zeno’s paradox, these merely 
intellectual difficulties should be removable by intellectual processes. 
