Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

RHEASON. 3t93
either to Locke, to Reid, or to Campbell,) that furnishllts, if I
mistake not, the true explanation of the peculiarity already
remarked in mathematical evidence.
But the truth of the axioms is presupposed or implied in all our
reasonings. —After what has been just stated, it is scarcely
necessary for me again to repeat, with regard to mathematical
axioms, that although they are not the principles of our reasoning, either in arithmetic or in geometry, their truth is supposed
or implied in all our reasonings in both; and, if it were called
in question, our further progress would be impossible. In both
of these respects, we shall find them analogous to the other
classes of primary or elemental truths, which remain to be considered.
Nor let it be imagined, from this conces'on, that the dispute
turns merely on the meaning annexed to the word principle.
It turns upon an important question of fact; whether the
theorems of geometry rest on the axioms, il the same sense in
which they rest on the definitions? or (to rtate the question in'i manner still more obvious) whether:ioms hold a place;n geometry at all analogous to what is occupied in natural
Philosophy, by those sensible phenome1lo ~ hich form the basis
Qf that science? Dr. Reid compares I'em sometimes to the
ne set of propositions, and sormef'* ~s to the other. If the
%oregoing observations be just O jv oear no analogy to either.
What are' first przi',c'l>r,' inscience. - The difference
F opinion between L(YAke,,l?' Reid, of which I took notice in.le foregoing par' o#' tkLi, scr tion, appears greater than it really
s, in consequAvnc.e f,1' ambiguity in the word principle, as
~,mployed by tale var;e-. In its proper acceptation, it seems to,.e to denc'e an a'sumption, (whether resting on fact or on
rypothesis,) urJn which, as a datum, a train of reasoning proeeeds; and for the falsity or incorrectness of which, no logical
"figor in the subsequent process can compensate. Thus the.gravity and the elasticity of the air, are principles of reasoning,n our speculations about the barometer. The equality of the
angles of incidence and reflection; the proportionality of the
sines of incidence and refraction; are principles of reasoning in
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