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 ...

428;REASONING AND DEDUCTIVE EVIDENCEo
use of definitions, that any parallel can be drawn between
mathematics and those branches of knowledge which relate to
facts; and, therefore, it is not a fair argument in proof of their
general utility, to appeal to the unrivalled certainty of mathematical science, —a preeminence which that science derives
from a source altogether different, though comprehended under
the same name, and which she will forever claim as her own
exclusive prerogative.
tive sciences relate exclusively to nmatters of fct. The relations of ideas,that is, of abstractions, or pure ideas, are made known to us by intuition
or reflection. They are pure creations of the intellect; in their uncompounded or abstract character, they are not derived from observation, and
are therefore not perverted by that great source of error, the imperfection
of the senses, or the limitations of our power of perception. When we
entertain these ideas, or reason about them, the mind is closed to all outward impressions, and fr'eed even from tile memory of their former occurrence. The ideas that are contemplated then, are contemplated in their
entireness; for, being uncompounded, if they are apprehended at all, they
must be perfectly apprehended, and, consequently, the relations between
them are discerned at once, or by intuition. The office of the definition
is to shut out the consideration of those qualities which are not included
in the definition, because they are imperfectly known. Our attention
being thus confined to wthat we kcnow perfectly, the reasoning proceeds
without any possibility of error. All the conclusions of pure mathematics, pure logic, and pure reason, are metaphysical truths, and we can no
more doubt them than we can question the accuracy of the multiplication
table.
When we come to investigate matters ofJfct, or to reason about them,
we enter upon totally different ground. Instead of abstractions, we have
realities; instead of shutting out sensible evidence altogether, we are
obliged to rely upon it exclusively; instead of intuitions, we have observations and experiments; instead of demonstration, we have induction;
instead of the objects of inquiry being perfectly simple and uncompounded, they are made up of an unknown and unknowable number of
elements and qualities. The imperfections of the senses come in here, to
their full extent, as causes of possible error. The objects of physical science must always be impefectly knowznv; we never can be sure that our
analysis of them is perfect, or that our observation has taken in all their
outward qualities. The attractive power of the loadstone was known for
centuries before its polarity was discovered. Down to the times of Watt
and Cavendish, water was supposed to be a simple element, and it figures