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 ...

NSOMINALISM AN'D REALIS3M. 109
thing, that every process of reasoning is perfectly analogouls to
an algebraical operation. TYhat I mean by "the other intellectual processes distinct from reasoning, which it is necessary
for us sometimes to employ in the investigation of truth," will, I
hope, appear clearly from the following remarks.
iental operations subsidiary to reasoning. - In algebraical
investigations, it is well known, that the practical application of
a general expression is frequently limited by the conditions
which the hypothesis involves; and that, in consequence of a
want of attention to this circumstance, some mathematicians of
the first eminence have been led to adopt the most paradoxical
and absurd conclusions. Without this cautious exercise of the
judgment in the interpretation of the algebraical language, no
dexterity in the use of the calculus will be sufficient to preserve
us firom error. Even in algebra, therefore, there is an application of the intellectual powers perfectly distinct from any process of reasoning, and which is absolutely necessary for conducting us to the truth.
In Geometry, we are not liable to adopt the same paradoxical
conclusions, as in algebra; because the diagrams, to which our
attention is directed, serve as a continual check on our reasoning powers. These diagrams exhibit, to our very senses, a variety of relations among the quantities under consideration,
which the language of algebra is too general to express; in consequence of which, we are not conscious of any effort of the
judgment distinct from a process of reasoning. As every geometrical investigation, however, may be expressed algebraically,
it is manifest, that in geometry, as well as in algebra, there is an
exercise of the intellectual powers, distinct from the logical process; although, in the former science, it is rendered so easy, by
the use of diagrams, as to escape our attention.
The same source of error and of absurdity, which exists in
algebra, is to be found, in a much greater degree, in the other
branches of knowledge. Abstracting entirely from the ambiguity of language, and supposing also our reasonings to be logically accurate, it would still be necessary for us, from time to
time, in all our speculations, to lay aside the use of words, and to
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