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. 457
CONTINGENT TRIJTHS. 1. VNarrow field of demonstrative evidence. - If the account which has been given of the nature of
demonstrative evidence be admitted, the province over which it
extends must be limited almost entirely to the objects of pure
mathematics. A science perfectly analogous to this, in point
of evidence, may, indeed, be conceived, as I have already remarked, to consist of a series of propositions relating to moral,
to political, or to physical subjects; but as it could answer no
other purpose than to display the ingenuity of the inventor,
haidly any thing of the kind has been hitherto attempted.
The only exception which I can think of, occurs in the speculations formerly mentioned under the title of theoretical mechanrcs.
On the application of mat/hematics in practical geometry and
physics. - But if the field of mathematical demonstration be
limited entirely to hypothetical or conditional truths, whence, it
may be asked, arises the extensive and the various utility of
mathematical knowledge in our physical researches, and in the
arts of life? The answer, I apprehend, is to be found in certain peculiarities of those objects to which the suppositions of
the mathematician are confined; in consequence of which peculiarities, real combbinations of circuzmstances may fall under the
examination of our senses, approximating far more nearly to
what his definitions describe, than is to be expected in any other
theoretical process of the human mind. Hence a corresponding coincidence between his abstract conclnsions, and those facts
in practical geometry and in physics which they help him to
ascertain.
For the more complete illustration of this subject, it may be
observed in the first place, that although the peculiar force of
that reasoning which is properly called mathematical, depends
on the circumstance of its principles being hypothetical, yet if,
in any instance, the supposition could be ascertained as actually
existing, the conclusion might, with the very same certainty, be
applied. If I were satisfied, for example, that in a particular
circle drawn on paper, all the radii were exactly equal, every
property which Euclid has demonstrated of that curve, might
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