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 ...

ABSTRA&CTIONo 135
the former are expressed in an appropriated language, with
which we are not accustomed to associate particular notions.
Hence they exhibit the efficacy of signs as an instrument of
thought in a more distinct and palpable manner, than the
speculations we carry. on by words, which are continually
awakening the power of conception.
When the celebrated Vieta showed algebraists, that, by substituting in their investigations letters of the alphabet, instead
of known quantities, they might render the solution of every
problem subservient to the discovery of a general truth, he did
not increase the difficulty of algebraical reasonings: he only
enlarged the signification of the terms of which they were expressed. And if, in teaching that science, it is found expedient
to accustom students to solve problems by means of the particular numbers which are given, before they are made acquainted with literal or specious arithmetic, it is not because
the former processes are less intricate than the latter, but because their scope and utility are more obvious, and because it
is more easy to illustrate, by example than by words, the diff-erence between a particular conclusion and a general theorem.
The difference between the intellectual processes of the
vulgar and of the philosopher, is perfectly analogous to that between the two states of the algebraical art before and after the
time of Vieta; the general terms which are used in the various
sciences, giving to those who can employ them with correctness
and dexterity, the same sort of advantage over the uncultivated
sagacity of the bulk of mankind, which the expert algebraist
possesses over the arithmetical accountant.
The utility of langutae. - If the foregoing doctrine be admitted as just, it exhibits a view of the utility of language,
which appears to me to be peculiarly striking and beautiful; as
it shows that the same faculties which, without the use of signs,
must necessarily have been limited to the consideration of individual objects and particular events, are, by means of signs,
fitted to embrace, without effort, those comprehensive theorems,
to the discovery of which, in detail, the united efforts of the
whole human race would have been unequal. The advantage