Finally, let us recall our real subject and, so far as the infinite is concerned, draw the balance of all our reflections.  The final result then is:  nowhere is the infinite realized;  it is neither present in nature nor admissible as a foundation in our rational thinking — a remarkable harmony between being and thought.  We gain a conviction that runs counter to the earlier endeavors of Frege and Dedekind, the conviction that, if scientific knowledge is to be possible, certain intuitive conceptions [Vorstellungen] and insights are indispensable;  logic alone does not suffice.  The right to operate with the infinite can be secured only by means of the finite.

The role that remains to the infinite is, rather, merely that of an idea — if, in accordance with Kant’s words, we understand by an idea a concept of reason that transcends all experience and through which the concrete is completed so as to form a totality — an idea, moreover, in which we may have unhesitating confidence within the framework furnished by the theory that I have sketched and advocated here.  (p. 392).