process, in our third lecture. You want from a realist the facts, and all the facts, which are essential to his scheme. He names you the facts. You point out that since he inevitably names you a variety of facts, he must also admit that the connections or relations of these facts are real. And then you rightly add that the system in question must be self-representative and endless. But hereupon first appears the contradiction of Realism, viz., when you see that none of these endlessly numerous connections actually connect, because they are to be connections amongst beings that, by definition, are independent of knowledge, and therefore, as we saw, of one another, in such wise that their ties and links, if ever these ties seem to exist at all, must, upon examination, be found to be other real beings, as independent of the facts that they were to link as these, in their first essence, were of one another. The endlessly many elements of this world turn out, then, to be endlessly sundered. The Kette of the realist is a chain of hopelessly parted links. It is this aspect of the matter which gives their true cogency to the arguments of Mr. Bradley’s first book. We do not see, then, how the real that is in any final sense independent of knowledge can be either One or Many or both One and Many. And we do not see this because we can see and define nothing but what is linked with knowledge. But within knowledge itself we do, indeed, still find the self-representative system.
So much for the realistic conception of Being. But if we turn to another conception of the nature of reality, namely, to our Third Conception of Being, then we once more find that this conception, too, involves a self-representative system of the type here in question. For this result has been already illustrated by the number-system, by the Gedankenwelt of Dedekind, and by the other mathematical instances cited; since all of these objects, when mathematically defined, appear primarily as beings of the third type of our list. Whether they possess any deeper form of Being, we have yet to see. In general, however, it is interesting to note that, in the proof of the mathematical possibility or validity of infinite systems given
