[In the following essay, Haldane considers Alexander's Space, Time and Diety in the context of Albert Einstein's general theory of relativity.]

Prof. Alexander has written a book which requires more than cursory reading. It deserves careful study. For it embodies a thoroughly modern exposition of New Realism in full detail. Moreover, these two volumes are not merely the outcome of a sustained effort at accurate investigation. They are distinguished by their admirable tone and temper. The author is throughout anxious to understand and to represent faithfully the views of those with whom he is in controversy. His reading of what has been written by the great thinkers of other schools has been closer and more intelligent than that of most New Realists, and he displays no traces of arrogance. He has done all he could to appreciate the materials furnished, not merely by mathematical and physical science, but by biology and psychology; highly important fields for his inquiry.

These very merits of Prof. Alexander's method have, however, produced their drawbacks. They have driven him beyond the current conceptions of the New Realist type into others which are not always easy to reconcile with them. In the second volume, particularly, where the author is chiefly concerned with such problems as those of the nature of the tertiary qualities of reality, of value, and of deity, the treatment leaves the impression that the subject-matter passes beyond the limits which alone are for the method legitimate. None the less, the effort made to be consistent is a notable one. But under this head I must refer the reader to the book, for the only aspect of the doctrine in it with which space allows me to concern myself is its cardinal principle as applied to physical knowledge.

To begin with, it is necessary to be clear as to what is peculiar to himself and his school in Prof. Alexander's teaching. It is not sufficiently realised that to-day the New Realists comprise a variety of groups divided by differences that are of far-reaching importance. These differences relate to the nature attributed to mind. For some of the most prominent of the American New Realists mind has no characteristic at all that distinguishes it from its objective content. Seeing means colours occurring; hearing means sounds occurring; thinking means thoughts occurring. Mind is itself just a casual selection out of the field of consciousness, and has no nature distinct from that field. When we speak of a mind, the grouping arises out of relations possessed by the objective elements themselves, relations which exist quite independently of our own action in perceiving. Minds are thus subordinate groups in a larger universe of being which includes them, and which would be unaltered if minds disappeared from it. Consciousness is thus merely a demonstrative appellation.

Now for Prof. Alexander, and, I think, for most of the English New Realists, mind has a reality independent of its object. With the latter, whatever it is, it is "compresent." The act of perceiving is one reality, the object perceived is another. Left to itself, the activity which we call mind reveals the object, with its relations (which may be universale) just as they exist independently of it. But the activity is a separate reality, which does not belong to the ordinary object world, but reveals itself in consciousness, in which it is said by Prof. Alexander to be "enjoyed." Here we have dualism, a dualism which he gets over by referring the origin of the activity of mind and the object with which it is compresent, alike, to a final reality which is the foundation of both, an ultimate space-time continuum. This, inasmuch as the flow of time enters into its very essence, is not static, but dynamic. The activity which we are conscious of (in the form, not of perception, which is of objects, but of self-enjoyment) is therefore in its turn dynamic, and its character is that of a conation.

I am not sure that the Americans, notwithstanding their boldness, are not here on safer ground. They project everything, thought, feeling, and tertiary qualities, such as goodness and beauty, into what they call a non-mental world. Prof. Alexander is more cautious. With him the native hue of resolution is, at times at least, as he progresses in his enterprise, sicklied o'er with the pale cast of thought. He seems to feel that he must retain something for a mental world. Starting with space and time as having no reality apart from one another, but as mere abstractions from aspects or attributes of the foundational reality, which is space-time or motion, the "stuff of which all existents are composed," he has to account for our actual experience. His foundationally existent activity breaks itself up into the complexes of which we are aware, and which possess, as belonging to their nature, certain fundamental and all-pervasive features which we recognise as categories. There result also qualities which appear in our experience. These form

a hierarchy, the quality of each level of existence being identical with a certain complexity or collocation of elements on the next lower level. The quality performs to its equivalent lower existence the office which mind performs to its neural basis. Mind and body do but exemplify, therefore, a relation which holds universally. Accordingly, time is the mind of space, and any quality the mind of its body; or, to speak more accurately, mind and any other quality are the different distinctive complexities of time which exist as qualities. As existents within space-time, minds enter into relations of a perfectly general character with other things and with one another. These account for the familiar features of mental life; knowing freedom, values, and the like. In the hierarchy of qualities the next higher quality to the highest attained is deity. God is the whole universe engaged in process towards the emergence of this new quality, and religion is the sentiment in us that we are drawn towards him, and caught in the movement of the world towards a higher level of existence.

I have given the general result of his inquiry as summed up in the author's own words, those used by him in concluding his final chapter. But it would be unfair to suggest that the nature of this result can be appreciated from any isolated quotation. The whole book must be read. It is admirable alike in thoroughness of method and in command of material. Still, it is obvious that the entire edifice depends for its stability on its foundation, and that the author's conception of the ultimately real as being space-time, a continuum of point-instants or pure events entirely independent of mind, is the crucial point in his reasoning. If he is right, it must be in terms of this existent that all else must be capable of expression, and it cannot itself be expressed in terms of anything beyond itself. Of course, Prof. Alexander does not dispute that when we speak of space and time as of this character we are going beyond what we learn through sense, or intuitively, and are employing constructions of reflection. He is quite entitled to do this if a non-mental world can include universals, as he insists, in common with all New Realists. Our simplest experience is, as he says, "full of our ideas." The question is whether they belong to mind or to what is not mind. We shall see presently to what path this conclusion conducts.

At this stage we have to put before us the author's analysis of the relation of space to time, an analysis that seems to me altogether admirable. Space taken in abstraction from time has no distinction of parts. Time in so far as it is purely temporal is a mere now. To find a continuum we must find distinguishable elements. Without space there would be no connection in time. Without time there would be no points to connect. There is therefore no instant of time apart from a position in space, and no point of space except in an instant of time. The point occurs at an instant, and the instant occupies a point. The ultimate stuff of the universe is thus of the character of point-instants or pure events, and it is so that we get our continuum. The correspondence is, however, not a one-to-one, but a many-one, correspondence. For one point may occur at more than one instant, and one instant may, analogously, occupy several points.

Prof. Alexander thinks that he is here in full accord with Minkowski's well-known conception of an absolute world of four dimensions, of which ordinary geometry omits the fourth, the time element. When he wrote his book Einstein's doctrine of relativity was only fully known in its first form, the "special" theory, and Prof. Alexander believes that his view of the character of the space-time continuum has left him free to accept the socalled principle of relativity in this form. For it suggests really no more than the unification of the observations of two sets of observers who may be observing an absolute world in space-time, by means of formulas of transformation in which the observations of observers with one system of co-ordinates can be rendered in terms of the coordinates of observers with a different system. It may be, he says, that the formulas are not really independent, inasmuch as they are ultimately numerical, and numbers may be wholly dependent on an absolute space and time system. Thus it would be an absolutely identical set of relations which was observed from the two systems of reference, moving rectilinearly with a relative velocity which remained uniform.

But can this be accepted in the fresh light cast by the general theory of relativity, of which the special theory is now shown by Einstein to be a mere special case? Here metaphysicians have to look over a fence into ground at present mainly occupied by the mathematician. But not exclusively so occupied. The ground is in truth a borderland where mathematics and epistemology trench on each other, and the fence is not of barbed wire. We are, indeed, compelled to try to do the best we can with unfamiliar topics if we would get at the truth about the nature of reality. The relativity doctrine now extends to accelerating motion. It has also, apparently, been demonstrated that a principle of equivalence obtains according to which any changes which an observer takes to be due to what he supposes to be attraction within a gravitational field would be perceived by him in precisely the same way if the observer's system of reference were moving with the acceleration which was characteristic of the gravitation at the observer's point of observation. The combination of these principles gives us relativity of measurement in actual experience without restriction. The gravitational principle is, in addition, here based, not on a supposed elementary law of gravitational force, whatever that means, which would leave us in metaphysical perplexities about action at a distance, but on elementary laws of the motion of bodies relatively to each other in a so-called gravitational field. There is no decision either for or against Euclidean geometry as a possible special case. But there is a decision that space, as a physical thing with unvarying geometrical properties, is to be banished, just for the same sort of reasons as the aether was banished before it. Only observable things are to be recognised as real in the new system of modern physicists.

It is therefore asserted by Einstein that, all motions and accelerations being relative to the system of reference of the observer, neither space nor time has physically independent objectivity. They are not measurable in themselves. They mean only the framework in which the minds of the observers arrange physical events, according to the conditions under which observation takes place. We may choose such frameworks as we please, but in point of fact we naturally choose so that the application of our method is the one that appears best adapted to the character of what we observe. The standard used will give their physical significances to our "geodetic lines." The apparent order in space and time has no independent existence. It manifests itself only in the events that present themselves as so ordered.

But the revolution in conception does not stop here. As so-called "gravitational fields" are everywhere present, the old special theory of relativity is nowhere an accurate account of phenomena. The velocity of light, for instance, cannot really be constant under all conditions. It is the things we observe in space and time that give to these their definite structure, and the relations in them of the things depend on the system of observation. To get at the fundamental law of the change which takes place in the space-time continuum we must look for the principle which governs the motion of a point in it as of the form of a differential law for the motion of such a point, not merely in a straight line in the Euclidean sense, but in a geodetic line which will be relative to any possible form of motion and acceleration in a gravitational field. If we can reach such a differential law under the aspect of an equation sufficiently elastic in its variables, we shall be able to fit into it mathematical expressions based on actual observation which give the "gravitational potentials" required for the application of the law. The form of the differential equation which expresses the law must therefore be such as to be applicable whatever may be the four co-ordinates of reference of the observer of motion in any conceivable gravitational field. The principle of equivalence necessitates this, and we get as the result a science of motion depending on the relativity of every kind of motion. All that is required is that the co-ordinates which are the variables in the equation of motion of a point-mass moving uniformly and rectilinearly should be so expressed as to be capable of transformation into the co-ordinates, whatever their shape, of any system of reference which moves in any path and has any accelerated motion whatsoever. This appears to have been done completely. The result is intelligible to the epistemologist who can even do no more than look across the boundary fence. The mathematical details and scaffolding he may be wholly unable to appreciate. But not the less does he feel compelled to take off his hat reverently before the shades of Gauss and Riemann, and before those who have been able to wield the mighty sword with which these great thinkers cut the knots that held physicists back from the unrestricted calculus of to-day, purified as it now is from the old assumptions.

Now the importance of this thorough-going application of the principle of the relativity of the character of the point-event continuum to the observer is obvious. It means relativity in significance for intelligence. As Prof. Eddington has recently remarked in a notable article in Mind, the intervention of mind in the laws of Nature is more far-reaching than is usually supposed by physicists. He develops this conclusion in a fashion which is impressive. Freundlich and Schick in their recent books insist on the same thesis.

But what does the word "mind" mean when used thus? Not a substance in space-time, as Prof. Alexander would have it. To start with, such an assumption would involve either the rejection of the modern doctrine of relativity as the school of Einstein has put it forward as dependent on interpretation, or something tending towards solipsism. Nor can mind mean substance in another aspect, that in which Berkeley and the Mentalists have sought to display it. Few competent students of the history of thought look on philosophy as shut up to such a view, the view which New Realism seeks to bind into the "egocentric predicament."

There is another interpretation of the meaning of mind in which it signifies neither any of these things nor yet an Absolute Mind apart from that of man, but just our own experience interpreted as being in every stage relative in its presentation, and not so merely in the relation of measurement. For Einstein's doctrine seems to be only a fragment of a yet larger and even more striking view of reality. Relativity is surely not to be confined to judgments based on the co-ordinates we employ in measurement. It may equally arise in other instances from the uncritical applications of conceptions concerned with quality as much as with quantity. From such a point of view reality, including human experience, is what it is only because we are ever unconsciously, under the influence of practical ends to be attained, limiting our systems of reference, interpreted in even a wider sense than that of Einstein. These may be limiting ends imposed on us by the mere fact that we are human beings with a particular position in Nature. The relativity of knowledge will thus assume the form of relativity of the real to general points of view, and will result in a principle of degrees extending through all knowledge and reality alike, which fall short of ideal completion. It is an old principle, as old as Greek thought. If it is true, it solves many problems and gets rid of the distinction between mental and non-mental, between idealism and realism, between mind and its object. For it accepts the "that," and confines the legitimate problem to the "what." It also gets rid of the perplexing idea of an Absolute Mind as something to be conceived as apart from us while working in us.

The idea and the method, recurring as they do in ancient and modern philosophy, are worth study by those who feel the stimulus of the new atmosphere which Einstein has provided. They may find a convenient analogue to the special principle of relativity in Kant's "Critique of Pure Reason," with its investigation of the general conditions which are required in order to render any individual experience possible. If they seek for an analogue to Einstein's general principle, they may look either in the "Metaphysics" of Aristotle or in the "Logic" of Hegel. The greatest thinkers have presented resembling conclusions in varying language.

This path is one that is not easy to tread. It is as hard to enter on as is that of the metaphysician who has to try to understand the meaning for philosophy of the absolute differential equations which Einstein employs. Prof. Alexander, however, knows the direction, if he does not now look that way. And it may be that the difficulties with which the new principle of general physical relativity seems to threaten New Realism, with its non-mental and static reality, may lead him, with his openness of mind, to consider once again whether he should not wend his steps afresh towards the wicket-gate for a further pilgrimage. But whatever the direction in which he is looking, his new book is full of stimulating material, even as it stands.