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. 409
their author, appears from the following passage, which occurs
afterwards: "The principal act of ratiocination is the finding
the agreement or disagreement of two ideas, one with another,
by the intervention of a third. As a man, by a yard, finds two
houses to be of the same length, which could not be brought
together to measure their equality by juxtaposition."
This use of the words intuition and reasoning, is surely somewhat arbitrary. The truth of mathematical axioms has always
been supposed to be intuitively obvious; and the first of these,
according to Euclid's enumeration, affirms, that if A be equal to
B, and B to C, A and C are equal. Admitting, however,
Locke's definition to be just, it only tends to confirm what has
been already stated with respect to the near affinity, or rather
the radical identity, of intuition and of reasoning. When the
relation of equality between A and B has once been perceived,
A and B are completely identified as the same mathematical
quantity; and the two letters may be regarded as synonymous,
wherever they occur. The faculty, therefore, which perceives
the relation between A and C, is the same with the faculty
which perceives the relation between A and B, and between
B and C.*
* [Stewart's doctrine, that reasorning is nothing more than a series of intuitive judgments, seems to be true according to one signification of the word
reasoninq, and false according to another. The word reasoning is sometimes
used to denote a series of propositions, or syllogisms, properly arranged,
which constitute the proof of a particular doctrine; but it more firequently
denotes, that act or process of the mind, by which the proper syllogisms, or intermediate propositions, are discovered and rightly put together, so as to constitute such a proof. This effort of mind may be a
very laborious and difficult one, and would be improperly designated by
such a word as intuitionl, which implies ease and instantaneousness of
operation. Take the geometrical theorem, that the square described on
the hypothenuse of a right-angled triangle is equal to the sum of the
squares on the two other sides; it is proved by a series of propositions,
the connection of each one of which with its predecessor, is seen intuitively. But if the old story is true, Pythagoras was so overjoyed when,
after long study, he had succeeded in discovering these propositions, and
putting them together so as to constitute a proof of the theorem, that he
sacrificed a hecatomb of oxen to show his gratitude to the gods.]
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