SECTION I. The Discipline of Pure Reason in the Sphere
of Dogmatism.
The science of mathematics presents the most brilliant example of
the extension of the sphere of pure reason without the aid of
experience. Examples are always contagious; and they exert an especial
influence on the same faculty, which naturally flatters itself that it
will have the same good fortune in other case as fell to its lot in
one fortunate instance. Hence pure reason hopes to be able to extend
its empire in the transcendental sphere with equal success and
security, especially when it applies the same method which was
attended with such brilliant results in the science of mathematics. It
is, therefore, of the highest importance for us to know whether the
method of arriving at demonstrative certainty, which is termed
mathematical, be identical with that by which we endeavour to attain
the same degree of certainty in philosophy, and which is termed in
that science dogmatical.
Philosophical cognition is the cognition of reason by means of
conceptions; mathematical cognition is cognition by means of the
construction of conceptions.
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