We are now in a position to say something, though of a purely formal character, about the general nature of the true and real. If the intellect rejects as self-contradictory any 'simple' union of differents, and if the only way in which it can avoid self-contradiction in bringing differents together is to connect the differents as mutually implicatory elements of an encompassing unity, then, it appears, no content can be accepted by the intellect as expressing 'reality' unless it be got into the form of a unity which exhibits a perfect mutual implication. Only thus can the intellect's inherent demand be satisfied. Our next task, however, is to see that although such a unity is the inherent demand of the intellect, and thus needful for the assurance of apprehending ultimate reality, it is a unity that is not attainable by intellect. And this failure, it will appear, is a failure not merely in degree. It is a failure in principle. For - and this is the central paradox of human experience - the route which the intellect takes, and must take, in its efforts to realise its ideal, is one which never can, by reason of its intrinsic character, lead to the desired goal of mutually implicatory system, or 'unity in difference' - which never can, therefore, yield us apprehension of the real.
The whole issue may be said to turn upon the nature of a 'ground.' We have seen that thought demands a ground for its connections of differences, and that only by positing such a ground does it escape the contradiction of uniting bare A with not-A. But we shall also have to see that what a 'ground' concretely means in actual thinking is always something which remains partially external to the differences it connects. To secure a 'ground,' accordingly, is still to be left with a further question which demands an answer - 'How is the ground itself connected with the elements it connects?' Hence is provoked the inquiry after a deeper ground. But since this deeper ground must also be partially a 'third thing' relatively to the elements it connects, a like problem recurs. And this process, it would seem, must continue ad infinitum. The further back we push the 'ground' or the 'why,' the more unified and coherent doubtless becomes the system of differences we affirm. But the true manifold-in-unity wherein mutual implication is perfect, the self-explanatory identity in difference which thinking craves and will alone accept as expressing the ultimate real, must forever elude its grasp.
The point may be perhaps best elucidated by means of a concrete illustration, which we shall draw from a familiar sphere. Suppose we are reflecting upon the rational justification of the simple statement that if the carburretor-jet of a motor-car is partially choked there is a tendency in the engine to misfire. We want to understand the 'why' of this situation, to find a 'ground' or intelligible nexus for the connection affirmed. Our first suggestion will be, no doubt, that the ground lies in the ignition system of the engine as dynamically conceived, the special core of the connection being the thinning of the petrol supply to the cylinder. And with this insight the intellect does achieve a partial satisfaction. But, it is plain, only partial satisfaction. However adequate the explanation may be for practical needs, from the speculative point of view it at once gives rise to a further problem. For it is certainly not self-evident how the 'ground' here laid bare stands to the 'differences' it connects. It is necessary to 'ask, Why should a thinning of the petrol supply result from a partially choked jet, and why should a thinning of the petrol supply result in the occasional failure of combustion? To suppose that these questions answer themselves is sheer speculative blindness.
Since there is nothing in this particular illustration which is not paralleled in every other endeavour of thought to rationalise its world,1 let us express the situation which has here arisen in the generalised form of symbolic representation. When we say that a choked jet is the occasion of misfiring, we are uniting differences which we may call A and B. But we are aware of the necessity of establishing a 'ground' for the union of A and B. Our initial ground we take to be 'the ignition system of the engine as dynamically conceived.' Here we have the X, or systematic identity, which was alluded to in our early abstract statement of intellectual process. Again, every connection has a special core within the system X. Here, it is the thinning of the petrol supply to the cylinder. We may call this core C. And we may say that what the explanation is doing is to justify the union of A with B on the ground that A is bound up with C which is bound up with B within the system X. But we saw, once more, that the connection of the thinning of the petrol supply neither with a choked jet nor with misfiring is self-evident. That is (continuing our generalised statement) how C is connected with A, and again with B, requires further elucidation, sets for us a fresh problem. Or, expressed in terms of the whole system as apprehended, the systematic identity C is observed not to issue in the union of A and B by the internal necessity of its own nature. We have a unity which is still partially external to its differences, and which therefore points beyond itself to a higher unity for final intellectual satisfaction.
1 Certain qualifications of this statement will have to be made later.
But let us follow the course of rationalisation a little further in our selected instance. It will elicit no new point of principle, but may assist in making clearer the fundamental defect (metaphysically speaking) which I wish to expose in the process under examination.