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 ...

450 REASONING AND DEDUCTIVE EVIDENCE.
It must indeed be owned, with respect to the conclusions
hitherto mentioned on the subject of space, that they are rather
of a metaphysical, than of a mathematical nature; but they
are net, on that account, the less applicable to our purpose; for
if the theory of Beddoes had any foundation, it would lead us
to identify with physics the former of these sciences as well as
the latter; at least, all that part of the former which is employed about space or extension, —a favorite object of metaphysical as well as of mathematical speculation. The truth,
however, is, that some of our metaphysical conclusions concernof the truth of this axiom, but that our assent is given merely by thinking
of it, or as soon as we understand the meaning of the words, he answers,
" one of the characteristic properties of geometrical forms is their capacity
of being painted in the imagination with a distinctness equal to reality."
These mental pictures are "just as fit subjects of geometrical experimentation as the realities themselves." " The foundations of geometry would
therefore be laid in diiect experience, even if the experiments, (which in
this case consist merely in attentive contemplation) were practised solely
upon what we call our ideas, — that is, upon the diagrams in our minds,
and not upon outward objects."
But we declare that the lines could not meet even if they were prolonged
to infinity,- a fact which cannot be proved by actual observation, because we cannot follow them to infinity. Mr. Mill replies, that, without
so following them, "we may know that, if they ever do meet, or indeed
if, after diverging from one another, they begin again to approach, this
must take place, not at an infinite,. but at a finite distance. Supposing,
therefore, such to be the case, we can transport ourselves thither in imagination, and can firame a mental image of the appearance which one or
both of the lines must present at that point, which we may rely upon as
being precisely similar to the reality. Now, whether we fix our contemplation upon this imaginary picture, or call to mind the generalizations we
have had occasion to make from former ocular observation, we shall either
way be equally satisfied, that a line which, after diverging from another
straight line, begins to approach to it, produces the impression on our
senses which we describe by the expression'a bent line,' not by the expression,'a straight line.'"
The first argument being thus disposed of, we proceed to the second.
"Axioms (it is asserted) are conceived by us not only as true, but as universally and necessarily true. Now experience cannot possibly give to
any proposition this character. I may have seen snow a hundred times,
and may have seen that it was white; but this cannot give me entire