In sections 29 and 30 of the Prolegomena, Kant explains how his account of synthetic
a priori truths saves causality from Hume’s skepticism by limiting its application to
the realm of experience.
In order to put to a test Hume's problematic concept (his crux metaphysicorum), the concept
of cause, we have, in the first place, given a priori by means of logic the form of a conditional
judgment in general, i.e., we have one given cognition as antecedent and another as consequent.
But it is possible that in perception we may meet with a rule of relation which runs thus:
that a certain appearance is constantly followed by another (though not conversely); and this
is a case for me to use the hypothetical judgment and, for instance, to say that if the sun
shines long enough upon a body it grows warm.
Here there is indeed as yet no necessity of connection, or concept of cause.
But I proceed and say that if this proposition, which is merely a subjective connection of
perceptions, is to be a judgment of experience, it must be regarded as necessary and universally valid.
Such a proposition would be that the sun is by its light the cause of heat.
The empirical rule is now considered as a law, and as valid not merely of appearances
but valid of them for the purposes of a possible experience which requires universal and therefore
necessarily valid rules.
I therefore easily comprehend the concept of cause as a concept necessarily belonging
to the mere form of experience, and its possibility as a synthetic unification of perceptions
in a consciousness in general; but I do not at all comprehend the possibility of a thing
in general as a cause, inasmuch as the concept of cause denotes a condition not at all belonging
to things, but to experience.
For experience can only be an objectively valid cognition of appearances and of their
succession, only so far as the antecedent appearances can be conjoined with the consequent
ones according to the rule of hypothetical judgments.
Hence if the pure concepts of the understanding try to go beyond objects of experience and
be referred to things in themselves (noumena), they have no meaning whatever.
They serve, as it were, only to spell out appearances, so that we may be able to read
them as experience.
The principles which arise from their reference to the sensible world only serve our understanding
for use in experience.
Beyond this they are arbitrary combinations without objective reality; and we can neither
cognize their possibility a priori, nor verify their reference to objects, let alone make
such reference understandable, by any example, because examples can only be borrowed from
some possible experience, and consequently the objects of these concepts can be found
nowhere but in a possible experience.
This complete (though to its originator unexpected) solution of Hume's problem rescues for the
pure concepts of the understanding their a priori origin and for the universal laws of
nature their validity as laws of the understanding, yet in such a way as to limit their use to
experience, because their possibility depends solely on the reference of the understanding
to experience, but, with a completely reversed mode of connection which never occurred to
Hume: they from are not derived from experience, but experience is derived them.
This is, therefore, the result of all our foregoing inquiries:
"All synthetic principles a priori are nothing more than principles of possible experience"
and can never be referred to things in themselves, but only to appearances as objects of experience.
And hence pure mathematics as well as pure natural science can never be referred to anything
more than mere appearances, and can only represent either that which makes experience in general
possible, or else that which, as it is derived from these principles, must always be capable
of being represented in some possible experience.