able and suprasensible (the real nature of things, the
totality of the world, the Deity, and immortality) the special object
of philosophy, rationalism looked on the understanding as a faculty of
knowledge by which objects are given. In reality objects can never be given
through concepts; these only render it possible to think objects given
in some other way (by intuition). It is true that concepts of the
suprasensible exist, but nothing can be known through them, there is
nothing intuitively given to be subsumed under them.

With this failure to perceive the intuitive element in mathematics was
joined the mistake of overlooking its synthetic character. The syllogistic
method of presentation employed in the Euclidean geometry led to the belief
that the more special theorems had been derived from the simpler ones, and
these from the axioms, by a process of conceptual analysis; while the fact
is that in mathematics all progress is by intuition alone, the syllogism
serving merely to formulate and explain truths already attained, but not to
supply new ones. Following the example of mathematics thus misunderstood,
the mission of philosophy was made to consist in the development of
the truths slumbering in pregnant first principles by means of logical
analysis. If only there were metaphysical axioms! If we only did not
demand, and were not compelled to demand, of true science that it increase
our knowledge, and not merely give an analytical explanation of knowledge.
When once the clearness and distinctness of conceptions had been taken
in so purely formal a sense, it was inevitable that in the end, as
productivity became less, the principle should be weakened down to a mere
demand for the explanation and elucidation of the metaphysical ideas
present in popular consciousness. Thus the rationalistic current lost
itself in the shallow waters of the Illumination, which soon gave as
ready a welcome to the empirical theories--since these also were able to
legitimate themselves by clear and distinct conceptions--as it had given
to the results of the rationalistic systems.

It was thus easy to see that each of the contending parties had been guilty
of one-sidedness, and that in order to escape this a certain mean must be
assumed between the two extremes; but it was a much more difficult matter
to discover the due middle ground. Neither of the opposing standpoints is
so correct as its defenders believe, and neither so false as its oppo