you clearly and
distinctly conceive, exists, if the idea of it involve existence."

In these four rules we have the essential part of one half of Des
Cartes's system, the other, which is equally important, is the attempt
to solve metaphysical problems by mathematical aid. To mathematics he
had devoted much of his time. He it was who, at the age of twenty three,
made the grand discovery of the applicability of algebra to geometry.
While deeply engaged in mathematical studies and investigations, he
came to the conclusion that mathematics were capable of a still further
simplification, and of much more extended application. Impressed with
the certainty of the conclusions arrived at by the aid of mathematical
reasoning, he began to apply mathematics to metaphysics.

His ambition was to found a system which should be solid and
convincing. Having searched for certitude, he had found _its basis_ in
consciousness; he next wanted a _method_, and hoped he had found it in
mathematics.

He tells us that "those long chains of reasoning, all simple and
easy, by which geometers used to arrive at their most difficult
demonstrations, suggested to him that all things which came within human
knowledge, must follow each other in a similar chain; and that provided
we abstain from admitting anything as true which is not so, and that
we always preserve in them the order necessary to deduce one from the
other, there can be none so remote to which we cannot finally attain,
nor so obscure but that we may discover them."

Acting out this, he dealt with metaphysics as we should with a problem
from Euclid, and expected by rigorous reasoning to discover the truth.
He, like Archimedes, had wished for a standing place from which to use
the lever, that should overturn the world; but, having a sure standing
place in the indubitable fact of his own existence, he did not possess
sufficient courage to put forth the mighty power--it was left for one
who came after him to fairly attempt the over-throw of the world of error
so long existent.

Cartesianism was sufficiently obnoxious to the divines to provoke
their wrath; and yet, from some of its peculiarities, it has found many
opponents amongst the philosophical party. The Cartesian philosophy
is founded on two great principles, the one metaphysical, the other
physical. The metaphysical is Des Cartes's foundation-stone--the "I
think, therefore I am." This has been warmly attacked as not being
logical.