Now, what is the cause of this difference in the fortune of the
philosopher and the mathematician, the former of whom follows the path
of conceptions, while the latter pursues that of intuitions, which
he represents, a priori, in correspondence with his conceptions? The
cause is evident from what has been already demonstrated in the
introduction to this Critique. We do not, in the present case, want to
discover analytical propositions, which may be produced merely by
analysing our conceptions- for in this the philosopher would have
the advantage over his rival; we aim at the discovery of synthetical
propositions- such synthetical propositions, moreover, as can be
cognized a priori. I must not confine myself to that which I
actually cogitate in my conception of a triangle, for this is
nothing more than the mere definition; I must try to go beyond that,
and to arrive at properties which are not contained in, although
they belong to, the conception. Now, this is impossible, unless I
determine the object present to my mind according to the conditions,
either of empirical, or of pure, intuition. In the former case, I
should have an empirical proposition (arrived at by actual measurement
of the angles of the triangle), which would possess neither
universality nor necessity; but that would be of no value.
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