which transcend all finite actuality of presentation and which so remain bare possibilities. Of this character of abstract thought the higher mathematical sciences are one long series of examples. Let a line be given; abstract thought can define in this line points as places where the line would be broken, mere positions without magnitude. The presented continuity of the line often seems to threaten to disappear into the endless multitude of these points. How many such points are there on a line? No possible presentation could exhaust this number. The mathematical ideal limits, of the type well known in higher mathematics, are other examples of the way in which thought can define the infinitely remote goal of a process which can never be constructively presented as a complete whole. Experience always determines the infinite universals of thought to concrete individual examples. Thought, on the other hand, even when it defines the contents of experience, always does so by viewing them as individual cases of an infinite series of possible cases.
So then, apparently, thought would transcend any possible whole of experience. There could be no experience to which was presented the concrete realisation of all that thought could and would regard as possible. For such an experience would have, for instance, to view a line as an infinite aggregate of points, adequately composing, despite their discreteness, that continuity of the line in which thought now declares that they could always possibly be found, as filling every place in it. Such an experience, exhausting all thought’s possibilities, would have to
