186. This, then, is the kind of externality we are to expect from space, and our question must be: Would the existence of diverse but interrelated things be unknowable, if there were not, in sense-perception, some form of externality? This is the crucial question, on which turns the apriority of our form, and hence of the necessary axioms of Geometry.
187. The converse argument to mine, the argument from the spatio-temporal element in perception to a world of interrelated but diverse things, is developed at length in Bradley's Logic. It is put briefly in the following sentence (p. 44, note): "If space and time are continuous, and if all appearance must occupy some time or space—and it is not hard to support both these theses—we can at once proceed to the conclusion, no mere particular exists. Every phenomenon will exist in more times or spaces than one; and against that diversity will be itself an universal[187]." The importance of this fact appears, when we consider that, if any mere particular existed, all judgment and inference as to that particular would be impossible, since all judgment and inference necessarily operate by means of universal. But all reality is constructed from the This of immediate presentation, from which judgment and inference necessarily spring. Owing, however, to the continuity and relativity of space and time, no This can be regarded either as simple or as self-subsistent. Every This, on the one hand, can be analyzed into Thises, and on the other hand, is found to be necessarily related to other things, outside the limits of the given object of sense-perception. This function of space and time is presupposed in the following statement from Bosanquet's Logic (Vol. I. pp. 77–78): "Reality is given for me in present sensuous perception, and in the immediate feeling of my own sentient existence that goes with it. The real world, as a definite organized system, is for me an extension of this present sensation and self feeling by means of judgment, and it is the essence of judgment to effect and sustain such an extension.... The subject in every judgment of Perception is some given spot or point in sensuous contact with the percipient self. But, as all reality is continuous, the subject is not merely this given spot or point."
188. This doctrine of Bradley and Bosanquet is the converse of the epistemological doctrine I have to advocate. Owing to the continuity and relativity of space and time, they say, we are able to construct a systematic world, by judgment and inference, out of that fragmentary and yet necessarily complex existence which is given in sense-perception. My contention is, conversely, that since all knowledge is necessarily derived by an extension of the This of sense-perception, and since such extension is only possible if the This has that fragmentary and yet complex character conferred by a form of externality, therefore some form of externality, given with the This, is essential to all knowledge, and is thus logically à priori. Bradley's argument, if sound, already proves this contention; for while, on the one hand, he uses no properties of space and time but those which belong to every form of externality, he proves, on the other hand, that judgment and inference require the This to be neither single nor self-subsistent. But I will endeavour, since the point is of fundamental importance, to reproduce the proof, in a form more suited than Bradley's to the epistemological question.
189. The essence of my contention is that, if experience is to be possible, every sensational This must, when attended to, be found, on the one hand, resolvable into Thises, and on the other hand dependent, for some of its adjectives, on external reference. The second of these theses follows from the first, for if we take one of the Thises contained in the first This, we get a new This necessarily related to the other Thises which make up the original This. I may, therefore, confine myself to the first proposition, which affirms that the object of perception must contain a diversity, not only of conceptual content, but of existence, and that this can only be known if sense-perception contains, as an element, some form of externality.
My premiss, in this argument, is that all knowledge involves a recognition of diversity in relation, or, if we prefer it, of identity in difference. This premiss I accept from Logic, as resulting from the analysis of judgment and inference. To prove such a premiss, would require a treatise on Logic; I must refer the reader, therefore, to the works of Bradley and Bosanquet on the subject. It follows at once, from my premiss, that knowledge would be impossible, unless the object of attention could be complex, i.e. not a mere particular. Now could the mental object—i.e., in this connection, the object of a cognition—be complex, if the object of immediate perception were always simple?
190. We might be inclined, at first sight, to answer this question affirmatively. But several difficulties, I think, would prevent such an answer. In the first place, knowledge must start from perception. Hence, either we could have no knowledge except of our present perception, or else we must be able to contrast and compare it with some other perception. Now in the first case, since the present perception, by hypothesis, is a mere particular, knowledge of it is impossible, according to our premiss. But in the second case, the other perception, with which we compare our first, must have occurred at some other time, and with time, we have at once a form of externality. But what is more, our present perception is no longer a mere particular. For the power of comparing it with another perception involves a point of identity between the two, and thus renders both complex. Moreover, time must be continuous, and the present, as Bradley points out, is no mere point of time[188]. Thus our present perception contains the complexity involved in duration throughout the specious present: its mere particularity and its simplicity are lost. Its self-subsistence is also lost, for beyond the specious present, lie the past and the future, to which our present perception thus unavoidably refers us. Time at least, therefore, is essential to that identity in difference, which all knowledge postulates.
191. But we have derived, from all this, no ground for affirming a multiplicity of real things, or a form of externality of more than one dimension, which, we saw, was necessary for the truth of two out of our three axioms. This brings us to the question: Have we enough, with time alone as a form of externality, for the possibility of knowledge?
This question we must, I think, answer in the negative. With time alone, we have seen, our presented object must be complex, but its complexity must, if I may use such a phrase, be merely adjectival. Without a second form of externality, only one thing can be given at one moment[189], and this one thing, therefore, must constitute the whole of our world. The object of past perception must—since our one thing has nothing external to it, by which it could be created or destroyed—be regarded as the same thing in a different state. The complexity, therefore, will lie only in the changing states of our one thing—it will be adjectival, not substantival. Moreover we have the following dilemma: Either the one thing must be ourselves, or else self-consciousness could never arise. But the chief difficulty of such a world would lie in the changes of the thing. What could cause these changes, since we should know of nothing external to our thing? It would be like a Leibnitzian monad, without any God outside it to prearrange its changes. Causality, in such a world, could not be applied, and change would be wholly inexplicable.
Hence we require also the possibility of a diversity of simultaneously existing things, not merely of successive adjectives; and this, we have seen, cannot be given by time alone, but only by a form of externality for simultaneous parts of one presentation. We could never, in other words, infer the existence of diverse but interrelated things, unless the object of sense-perception could have substantival complexity, and for such complexity we require a form of externality other than time. Such a form, moreover, as was shown in [Chapter III., Section A (§ 135)], can only fulfil its functions if it has more than one dimension. In our actual world, this form is given by space; in any world, knowable to beings with our laws of thought, some such form, as we have now seen, must be given in sense-perception.