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 ...

REASONING AND DEDUCTIVE EVIDENCE. 461
easiest applications of mathematical theory occurs in those
branches of optics which are distinguished by the name of
catoptrics and dioptrics. In these, the physical principles from
which we reason are few and precisely definite, and the rest
of the process is as purely geometrical as the Elements of
Euclid.
In that part of astronomy, too, which relates solely to the
phenomena, without any consideration of physical causes, our
reasonings are purely geometrical. The data, indeed, on which
we proceed, must have been previously ascertained by observation; but the inferences we draw from these are connected with
them by mathematical demonstration, and are accessible to all
who are acquainted with the theory of spherics.
In physical astronomy, the law of gravitation becomes also a
principle or datum in our reasonings; but, as in the celestial
phenomena it is disengaged from the effects of the various
other causes which are combined with it near the surface of our
planet, this branch of physics, as it is of all the most sublime
and comprehensive in its objects, so it seems, in a greater
degree than any other, to open a fair and advantageous field for
mathematical ingenuity.
On the fundamental law of belief involved in all our reasonings about contingent trutbs. - In the instances which have
been last mentioned, the evidence of our conclusions resolves
ultimately not only into that of sense, but into another law of
belief formerly mentioned; that which leads us to expect the
continuance, in future, of the established order of physical pheIlomena. A very striking illustration of this presents itself in
the computations of the astronomer; on the faith of which he
predicts, with the most perfect assurance, many centuries before
they happen, the appearances which the heavenly bodies are to
exhibit. The same fact is assumed in all our conclusions in
natural philosophy; and something extremely analogous to it
in all our conclusions concerning human affairs. They relate,
in both cases, not to necessary connections, but to probable or
contingent events; of which, how confidently soever we may
expect them to take place, the failure is by no means perceived
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