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 ...

- 141r t REASONING AND DEDUCTIVE EVIDENCE.
tenmatize its conclusions, as far as possible, agreeably to rules
suggested by mathematical method.
Arbitrary selection of the prenmises in mathematical reasoning.
In pure mathematics, where the truths which we investigate
are all coexistent in point of' time, it is universally allowed,
that one proposition is said to be a consequence of another, only
with a reference to our established arrangements. Thus, all the
properties of the circle might be as rigorously deduced from any
one general property of the curve, as from the equality of the
radii. But it does not therefore follow, that all these arrangements would be equally convenient; on the contrary, it is evidently useful, and indeed necessary, to lead the mind, as far as
the thing is practicable, from what is simple to what is more
complex. The misfortune is, that it seems impossible to carry
this rule universally into execution; and accordingly, in the
most elegant geometrical treatises which have yet appeared,
instances occur, in which consequences are deduced from principles more complicated than themselves.
Such inversions, however, of what may justly be regarded as
the natural order, must always be felt by the author as a sulbject
of regret; and, in proportion to their frequency, they detract
both from the beauty and from the didactic simplicity of his
general design.
Abstract conclusions in mechanics should be verified by experiment. — The same thing often happens irn the elementary
doctrines of natural philosophy. A very obvious example
occurs, in the different demonstrations given by writers on
mechanics, from the resolution of forces, of the fundamental
proposition concerning the lever; demonstrations in which the
proposition, even in the simple case when the directions of the
forces are supposed to be parallel, is inferred from a process of
reasoning involving one of the most refined principles employed
in the mechanical philosophy. I do not object to this arrangement as illogical; nor do I presume to say that it is injudicious.
I would only suggest the propriety, in such instances, of confirming and illustrating the conclusion by an appeal to experiment; an appeal which, in natural philosophy, possesses an