and nominal
essences of their objects coincide, while in the latter they do not; and,
further, that the real essences of substances are beyond our knowledge. The
true inner constitution of bodies, the root whence all their qualities, and
the coexistence of these, necessarily proceed, is completely unknown to us;
so that we are unable to deduce them from it. Mathematical and moral ideas,
on the other hand, and their relations, are entirely accessible, for they
are the products of our own voluntary operations. They are not copied from
things, but are archetypal for reality and need no confirmation from
experience. The connexion constituted by our understanding between the
ideas crime and punishment _(e. g_., the proposition: crime deserves
punishment) is valid, even though no crime had ever been committed, and
none ever punished. Existence is not at all involved in universal
propositions; "general knowledge lies only in our own thoughts, and
consists barely in the contemplation of our own abstract ideas" and their
relations. The truths of mathematics and ethics are both universal and
certain, while in natural science single observations and experiments are
certain, but not general, and general propositions are only more or less
probable. Both the particular experiments and the general conclusions are
of great value under certain circumstances, but they do not meet the
requirements of comprehensive and certain knowledge.

The _extent_ of our knowledge is very limited--much less, in fact, than
that of our ignorance. For our knowledge reaches no further than our ideas,
and the possibility of perceiving their agreements. Many things exist of
which we have no ideas--chiefly because of the fewness of our senses and
their lack of acuteness--and just as many of which our ideas are only
imperfect. Moreover, we are often able neither to command the ideas
which we really possess, or at least might attain, nor to perceive their
connexions. The ideas which are lacking, those which are undiscoverable,
those which are not combined, are the causes of the narrow limits of human
knowledge.

There are two ways by which knowledge may be extended: by experience, on
the one hand, and, on the other, by the elevation of our ideas to a state
of clearness and distinctness, together with the discovery and systematic
arrangement of those intermediate ideas which exhibit the relation of other
ideas, in themselves not immediately comparable. The syllo