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 ...

438 REASONING AND 1)EDUCTIVE EYIDENCE.
dence compelling our immediate assent, whIch we call mathematical or geometrical evidence. Yet such evidence is not
peculiar to mathematical science alone, for it arises from the
perception of identity, and the identity of two ideas may be
recognized, though they do not represent extension."]
Truths must be distinguished from the evidence by which they
are supported. - With respect to this passage I have only to
remark, (and the same thing is observable of every other attempt which has been made to support the opinion in question,)
that the author confounds two things essentially different; - the
nature of the truths which are the objects of a science, and the
nature of the'evidence by which these truths are established.
Granting, for the sake of argument, that all mathematical propositions may be represented by the formula a - a, it would not,
therefore, follow, that every step of the reasoning leading to these
conclusions, was a proposition of the same nature; and that, to
feel the full force of a mathematical demonstration, it is sufficient
to be convinced of this maxim, that every thing may be truly
predicated of itself; or, in plain English, that the same is the
same. A paper written in cipher, and the interpretation of that
paper by a skilful decipherer, may, in like manner, be considered
as, to all intents and purposes, one and the same thing. They
are so, in fact, just as much as one side of an algebraical equation is the same thing with the other. But does it therefore
follow, that the whole evidence upon which the art of deciphering proceeds, resolves into the perception of identity?
It may be fairly questioned, too, whether it can, with strict
correctness, be said even of the simple' arithmetical equation
2 + — 2 4, that it; may be represented by tile formula a -a.
The one is a proposition asserting the equivalence of two difrerent expressions;-to ascertain which equivalence may, in
numberless cases, be an object of the highest importance. The
other is altogether unmeaning and nugatory, and cannot, by any
possible supposition, admit of the slightest application of a practical nature. What opinion, then, shall we form of the proposition a — a, when considered as the representative of such a
formula as the binomial theorem of Sir Isaac Newton? When