On such principles we can never come to any conclusion as to causes and effects. We can never predict a consequence from any of the known attributes of things. We can never say of any event that it must necessarily have followed from another; that is, that it must have had an antecedent cause. And we could never lay down a rule derived even from the greatest number of observations. Hence we must trust entirely to blind chance, abolishing all reason, and such a surrender establishes scepticism in an impregnable citadel.
Mathematics escaped Hume, because he considered that its propositions were analytical, proceeding from one determination to another, by reason of identity contained in each. But this is not really so, for, on the contrary, they are synthetical, the results depending ultimately on the assent of observers as witnesses to the universality of propositions. So Hume's empiricism leads to scepticism even in this realm.
My investigations led me to the conclusion that the objects with which we are familiar are by no means things in themselves, but are simply phenomena, connected in a certain way with experience. So that without contradiction they cannot be separated from that connexion. Only by that experience can they be recognized. I was able to prove the objective reality of the concept of cause in regard to objects of experience, and to demonstrate its origin from pure understanding, without experimental or empirical sources.
Thus, I first destroyed the source of scepticism, and then the resulting scepticism itself. And thus was subverted the thorough doubt as to whatever theoretic reason claims to perceive, as well as the claim of Hume that the concept of causality involved something absolutely unthinkable.
The World's Greatest Books (Philosophy and Economics), p. 39-40