Our own human experience clearly falls far short of such an ideal, and that for two reasons. To begin with, our experience is incomplete in respect of its data: there is much in reality which never directly enters into the structure of our experience at all. Of much of what falls within the scope of our knowledge we can only say, in a general way, how it would appear to ourselves supposing certain conditions of its perceptibility to be realised, and even these conditions are usually only most imperfectly known. What the actual matters of psychical fact corresponding to these conditions and to the appearance which they would determine for us are, we are totally unable to say. Again, there may well be much in the real world which never, even in this indirect way, enters into the structure of human knowledge at all. Hence our human experience and the intellectual constructions by which we seek to interpret it have always the character of being piecemeal and fragmentary. Perfect apprehension of systematic reality as a whole would be able to deduce from any one fact in the universe the nature of every other fact. Or rather, as the whole would be presented at once in its entirety, there would be no need for the deduction; every fact would be directly seen as linked with every other by the directly intuited nature of the system to which all facts belong. But in our imperfect human apprehension of the world our facts appear to be largely given us in isolation and independence of one another as bare “casual conjunctions” or “collocations,” and the hypotheses by which we seek to weld them into a system, however largely determined by the character of our data, never quite get rid of an element of arbitrary “free” construction. They are never fully necessitated as to their entirety by the nature of the facts they serve to connect. Hence we can never be certain that our hypothetical constructions themselves are true in the sense of consisting of statements of what for a completed experience would be matters of fact. Our ideal is to connect our presented facts by constructions in which each link is itself matter of fact, or experience, in the sense that it would under known conditions form the content of a direct apprehension. But it is an ideal which, owing to the fragmentary character of our own experience, we are never able adequately to realise. In all our sciences we are constantly compelled to use hypothetical constructions, which often are, and for all we know always may be, merely “symbolic,” in the sense that, though useful in the co-ordination of experienced data, they could never themselves become objects of direct experience, because they conflict either with the general nature of experience as such, or with the special nature of the particular experiences in which they would have to be presented. Our scientific hypotheses thus present a close analogy with the uninterpretable stages in the application of an algebraical calculus to