Nevertheless, mathematical science, so highly vaunted for its apodeictic certainty, must at last fall under this empiricism for the same reason for which Hume put custom in the place of objective necessity in the notion of cause and, in spite of all its pride, must consent to lower its bold pretension of claiming assent a priori and depend for assent to the universality of its propositions on the kindness of observers, who, when called as witnesses, would surely not hesitate to admit that what the geometer propounds as a theorem they have always perceived to be the fact, and, consequently, although it be not necessarily true, yet they would permit us to expect it to be true in the future.In this manner Hume's empiricism leads inevitably to scepticism, even with regard to mathematics, and consequently in every scientific theoretical use of reason (for this belongs either to philosophy or mathematics).Whether with such a terrible overthrow of the chief branches of knowledge, common reason will escape better, and will not rather become irrecoverably involved in this destruction of all knowledge, so that from the same principles a universal scepticism should follow (affecting, indeed, only the learned), this I will leave everyone to judge for himself.
As regards my own labours in the critical examination of pure reason, which were occasioned by Hume's sceptical teaching, but went much further and embraced the whole field of pure theoretical reason in its synthetic use and, consequently, the field of what is called metaphysics in general; I proceeded in the following manner with respect to the doubts raised by the Scottish philosopher touching the notion of causality.If Hume took the objects of experience for things in themselves (as is almost always done), he was quite right in declaring the notion of cause to be a deception and false illusion;for as to things in themselves, and their attributes as such, it is impossible to see why because A is given, B, which is different, must necessarily be also given, and therefore he could by no means admit such an a priori knowledge of things in themselves.Still less could this acute writer allow an empirical origin of this concept, since this is directly contradictory to the necessity of connection which constitutes the essence of the notion of causality, hence the notion was proscribed, and in its place was put custom in the observation of the course of perceptions.
It resulted, however, from my inquiries, that the objects with which we have to do in experience are by no means things in themselves, but merely phenomena; and that although in the case of things in themselves it is impossible to see how, if A is supposed, it should be contradictory that B, which is quite different from A, should not also be supposed (i.e., to see the necessity of the connection between A as cause and B as effect); yet it can very well be conceived that, as phenomena, they may be necessarily connected in one experience in a certain way (e.g., with regard to time-relations); so that they could not be separated without contradicting that connection, by means of which this experience is possible in which they are objects and in which alone they are cognisable by us.And so it was found to be in fact; so that I was able not only to prove the objective reality of the concept of cause in regard to objects of experience, but also to deduce it as an a priori concept by reason of the necessity of the connection it implied; that is, to show the possibility of its origin from pure understanding without any empirical sources; and thus, after removing the source of empiricism, I was able also to overthrow the inevitable consequence of this, namely, scepticism, first with regard to physical science, and then with regard to mathematics (in which empiricism has just the same grounds), both being sciences which have reference to objects of possible experience;herewith overthrowing the thorough doubt of whatever theoretic reason professes to discern.