The Unity of Being
Part II Section 10
[170]
Section 10
Space and Time
Argument 1. Thesis: Space and Time are not wholes merely in the sense of parts in external relations to each other.
This thesis follows a priori1 from the previous discussion of relations. But the problem may be taken more empirically as a pragmatic or concrete test of the externalist view.
In The New Rationalism of Professor Spaulding we find this phrase: “Points, defined as unextended elements of space . . .” Such a phrase suggests that a point after all is not something which can be conceived apart from the whole of space which it is held to form a part of — that it is a part, not in the externalist’s sense, but in the opposing sense of a phase or adjective or qualitative aspect of its whole. Yet Professor Spaulding assuredly does not intend to give up his view that the part is “prior” to the whole. We must therefore suppose that the definition of point in terms of space (and an instant of time) is not essential, except perhaps on account of human limitation. If we were omniscient we could accord to the point the true measure of its independence as an inviolable self-existent entity. Still the fact remains that for us human beings a point is a meaningless nothing except as a point-in-space.
[171] Aside from space, it is, if We would face matters — a position which is nowhere, and here without a there. For if a point is anything more than a position in which no other positions are included, an ultimate “where” not reducible to a collection of “wheres” we may challenge anyone to say what the “more” here refers to. In one of the most important of all cases, therefore, the empirical evidence for independent parts of wholes is lacking.
We are told, it is true, that a point has its peculiar quale, which makes it, for instance, a point and not an instant. But this quale is either an empty word, we urge, else it denotes precisely this quality as essentially belonging to the point: namely, the quality of being a position a “here” in space (really, in the whole of sense experience, a “this” exclusive of all others, a focus of attention with two aspects that of “now” and “here,” a “point-instant” in short).
Space thus is made up of points only if it is made up of positions in itself — the circularity evidencing a principle prior to the whole taken as simply parts in relation.
The relation of instants to time is of the same order, and in this case also no definition of the instants not involving time as a whole or as a principle involved in any thought of the instants is procurable.
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Argument 2. Space and Time in reference to a Standard of Magnitude.
Thesis: Magnitude is relative to a standard which itself cannot be relative or finite but must be infinite or but must be infinite or absolute in the sense that its limitations depend, in the end, upon itself, and are measured or conceived through itself.
If the standard of degree is finite, itself a matter of degree, then we cannot employ the standard (since it will be nothing definite for us) until we are aware of its degree, and this implies a further standard. This second standard cannot be the object to be measured by the standard, for you cannot compare two degrees unless both are measured in terms of a common unit. If the object is put forward as the unit and called “one,” the reply is that to determine how many times the object goes into the standard, or vice versa, we must have the object (and the standard) determined not simply as “one” — for “one” does not measure anything. The foot rule is not 1/3 of a yardstick merely because it is “one,” but because it is 12 and the yardstick is 36. A further standard cannot be excluded if measurement is to take place.
The only alternative is to call attention to the fact of measurement by juxtaposition or coincidence. We do not, one may say, have to compare foot rule and yardstick by appealing to inches. We need only to bring the two together [173] and then move the ruler its own length along the yardstick and repeat, until the end of the latter is reached, counting the number of moves.
In his fascinating book An Enquiry Concerning the Principles of Natural Knowledge, Professor Whitehead considers the relation of congruence to coincidence. Two footrules, he says, may be made to coincide. But how do we know that when they are separated again, they are still congruent? Or rather, what do we mean by this non-coincident congruence? Surely not the possibility of coincidence. For we assume that the ruler does not alter its length while it is being transported — and the question is as to the meaning of this constancy. The judgment of possible coincidence rests upon “a direct judgment of constancy. Without such a judgment in some form or other, measurement becomes trivial. . . .
“Again, in Einstein’s own example, there is the direct judgment of the uniformity of conditions for the uniform translation of light. Thus any ordinary event among the fixed stars does not affect this uniformity for the transmission from the sun to the earth. Apart from such presuppositions, so obvious that they do not enter into consciousness, the whole theory collapses.
“These judgments of constancy are based on an immediate comparison of circumstances at different times and at different places.
“This recognition of congruity between distinct cir-[174]cumstances has no especial connection with coincidence and extends far beyond the mere judgments of tine and space. Thus judgments of the matching of colors can be made without coincidence by most people to some slight extent, and by some people with surprising accuracy . . . complete accuracy is never obtained, and the ideal of accuracy shows that the meaning is not derived from the measurement. Our recognitions are the ultimate facts of nature for science, and the whole scientific theory is nothing else than an attempt to systematize our knowledge of the circumstances in which such recognitions will occur. The theory of congruence is one branch of the more general theory of recognitions.” (Italics mine).
In other words the size of an object can not be merely the ratio of an object to an other object. For when asked what we mean by such a ratio we either resort to measurement by coincidence, which presupposes constancy or the retaining of the same size during the operation,2 or else we admit that there is involved an “immediate judgment” of size, comparable to the perception of a given shadeof yellow. We cannot perceive one object to be brighter than another except by seeing one as this brightness and another as that. A mere “brighter than” cannot be seen. Unless we give each thing a character not simply relative to other things there are no definite things to relate.
But since the character of magnitude a thing possesses must necessarily be a matter [175] of degree, or ratios between magnitudes are meaningless, and all magnitudes as such indistinguishable, the character of extension an object possesses, while not fundamentally a ratio to the magnitude of another object, but the factor which with a similar factor in the other object determines that ratio, must nevertheless stand in essential relation to some standard of degree, which is determinate without. reference to anything further. We cannot think an infinity of standards distributively, and hence if we conceive natural magnitudes and ratios as determined, we conceive a standard as determined. If we conceive a ruler to remain constant in size, if the conception has meaning for us, this must be by virtue of a final and non-finite standard which in such a conception we conceive to apply. This conception, as Professor Whitehead says, involves a reference to a fact of experience which cannot be construed save in terms of experience. This fact is that which be calls recognition. He says of it that it need not involve pure memory — i.e., recollection beyond the specious present. For it also occurs within the specious present. This recognition is just the fact that a ruler may actually be found to, or may be conceived to look the same, as to its length, during the extent of the specious present, or during a longer time; to possess a self-identical character for experience although even within the specious present there is change or passage. In what terms is this experiential character, [176] which remains identical, measured by experience? What is the standard which applies? Whitehead does not say, but the answer is in part easy. All psychological judgments of magnitude proceed in terms of just noticeable differences. A ruler involves for geometry not necessarily a greater number of points, than any part of it. But to visual experience the ruler presents a larger number of discriminable features than a section of it. The smallest object given to vision is the one that is practically one out of the thousands of bits of visual differences occupying consciousness. A pinhead involves very little visual variety. An expanse of paper, though all white, presents a multitude of distinguishable heres and theres. Remove the paper to a distance and it appears as smaller.3 Our conception of it as not smaller involves the consideration that if we had moved along with the paper, keeping it the same distance in front of us, or if we now followed it up, its original apparent size would be found to remain. Thus objects with the same apparent size at the same apparent distance (involving similar optical sensations, a complex correlation of experience factors, indescribable in purely physical terms)4 are judged to be of the same actual size.
The actuality means non-subjectivity in the sense of uniformity for all [177] observers. It may even mean more than this, indeed it must mean the ground of the possible or actual experience of subjective equality. This ground is of course independent of human observation. But the point is that the proportional relations, relations of degree, which it involves are indeterminate except by means of a standard which cannot be that of an extensional magnitude, finite or infinite. The one is no standard, but just a further demand for a standard, and the other, the extensional infinite, holds the same proportional relation to all finites. All are in reference to it, equally infinitesimal, that is, equally indeterminate.
Natural magnitudes thus require a standard which nature itself as merely objective and extensional (even if one dimension of the extent is temporal) cannot supply. Since we obviously do apply a psychical standard in experience there is no way to render our findings according to this standard objective save by assuming an analogous, indeed at bottom the same standard, to actually belong to nature as its ordering principle. In so far as we deny this identity of the subjective or actually applied standard and the objective or real standard, just in so far we deny the significance of our whole quantitative concept of nature, which as Whitehead says, is simply a concept of the relations among possible recognitions, which uses those recognitions as the unit of proportionality. Aside from that unit nature is but a possibility — but a that which allows recognitions to occur. Either you define nature, that is, in its relation [178] to human mind, or else to a super-human mind, or else to a super-human factor of recognition, of discrimination of relative richness which is the standard really operating in human experience.
If the essence of nature is its teleological relation to minds, then the values we discover objects to possess in respect to magnitude, are a revelation of the real character of objects. If the essence of nature is to be discriminated and valued, then the psychological standard we employ is not irrelevant, If the essence of nature is just to be objective, yet somehow objective in an other sense than as object to mind (what this sense is no one knows) then our quantification of nature has nothing to do with it, except as a mere something which makes the quantification possible as an occurrence, but by definition as occurrence only, and not as truth.
Our choice, then, is between nature as just the unknown cause or ground of the ratios we experience; and nature as essentially experiential, and therefore as a reality to which the ratios which are thinkable only in terms of experience can be ascribed. This latter alternative could be true only if nature is ultimately an experience entirely its own measure, and so infinite or absolute. If what things are to mind is to correspond to what they are in themselves, they must we suggest have their being in terms of what they are to a completely self-discerned mind.
In this case our human measure of relativity, the scale of just noticeable differences, may stand in some func-[179]tional relation to the real nature. For nature may be viewed not merely as that which makes experiences of a determinate structure possible, but as that which makes them possible by virtue of an inherent purpose, which orders all things in a harmony or rational interdependence. The intelligible controllable character of our experience, its continuity in change, its coordination in diversity, its harmony and beauty in variety, are simply the glimpse we catch and the share we take, in the universal purposive system. The only alternative intelligible or semi-intelligible view seems to be positivism.
Such a carefully empirical and unbiased account as that of Professor Whitehead of the theory of science thus entirely illustrates the relativity of magnitudes, not merely to other magnitudes, but to the qualitative standard foundational to magnitude to be found only in mind.
The principle of relativity itself has no essential bearing upon the issue except to enable us to realize more vividly what we might know otherwise — namely, the impossibility of a magnitude not relative to the whole system of things.
In an article by Professor DeLaguna5 the conclusion of such a relativity is reached. The implication is at the least, that the part is a function of the whole in the case of space-objects. But, furthermore, the fact remains that it is impossible for us to definitely and completely conceive the space-system as a whole. If we then conceive or experience its parts as in determinate relations of magnitude, we must be aware of a differ-[180]ent standard than that whole.
And our conception of the latter, being built out of experience depends upon the standard with reference to which alone experience recognizes determinate reterminate relations of congruence.
We proceed next to consider more closely the idea of space as a whole.
Argument 3. Space cannot be conceived as a whole except as a teleological system.
Kant’s arguments against the conceivability of space seem to us to have weight. In the first place, we point out that space is either an object of actual or imagined perception, or else of intellectual construction or conception. Now as an object of perception or imagination we cannot attain to the completeness of the spatial-whole. Any imagined expanse recognizes a beyond bounding itself. This beyond is never exhaustively pictured, and in principle we see that it could not be. On the other hand, as a conceptual object, what is space? At most it is a rule for the endless extension of images forever recognized as inadequate. But the knowledge of the inadequacy of our images does not amount to a positive conception of the spatial whole. The negation of limits is not the conception of anything. Conception can never be anything except an organizing of perceptual elements in various relations to one another. Our question then is: what combination of sense data can we conceive as forming a whole out of them, a whole not relative to a [181] beyond, but including all space within itself? Merely to suppose a series of images each larger than the other, or again, of images set out end to end, proclaiming the series to have no limit, is not to conceive the whole we are seeking. For if the series of images of ascending magnitude has no last term, the whole becomes an ideal, by hypothesis unrealizable. And in the series of images strung out end to end, we likewise reach no limit and cannot conceive the series as simultaneously existing. We have merely the negative thought that no image is the last, not the thought of all the images in a totality. The series is merely a rule of procedure for us, as Kant saw; and as a genuine simultaneous whole we cannot realize it in thought.6
The mathematical definition of an infinite series as characterized by a relation of one to one correspondence between part and whole, is not a solution of our problem. We have here merely the conception of whole and part as in the same boat, so to speak, whatever that situation nay be like. Both part and whole, as infinite, are equal in a certain sense — but we have not discovered any way of simultaneously combining in thought into one coexistent whole, the infinite series of parts. We have only uncovered a method of successive correlation by a “one-to-one” correspondence relation. Until the simultaneous whole can be conceived as such, we can not pretend to have thought a genuine content for the term space-a-whole.
[182] The instant, however, we conceive space as the content, not of a finite sense-experience like ours, but of an all-embracing and sustaining experience or life, including the whole of nature as the scope of its purposive activity, or as the expression of its creative love, we have conceived a completeness in terms of simultaneity which does not wreck itself in passing ever into a beyond. An Absolute Experience calls for no beyond over and above the content of its own awareness. It requires only that within this life of significance there should be beings standing as objects of its interest and creative preservation. But as the inclusive experience of all beings, nothing falls without its circumference. We have a genuine whole. Whether the entities included attain to an infinite number is perhaps a different problem. For, taking the wholeness or unity of the whole as more than that of number, but rather of a Life or consciousness, we can leave it undetermined what the included number may be. Their form as a real totality or collection depends upon their being possessed together simultaneously.
Considering nature as a simultaneous whole in terms of space, we find that to be in space is to be in an ever widening series of imaginal areas, or in the law of such endlessness, in either case a mere abstraction and not an all-inclusive reality. Infinite space as infinite extension is simply space as extension without limit — a quality negatively absolute, but a quality, not a totality or embracing whole, and [183] a quality infected by a negation and lacking the positive character which alone could provide the basis for that negation. The infinite is not finite, and it is more than any finite, but this negation and this transcendence supply, neither of them, what the infinite positively itself is. If we ask, how much more than any finite is the infinite we see in the answer — “infinitely more” the essential deficiency of our definition.
The idea of endlessness taken temporally is likewise an incomplete or unstable conception taken by itself. “No end can be reached,” instructs us to give up the thought of cessation, but does not tell us what positive thought to substitute for it. If We pronounce the word “forever” we get a vaguely positive sense, — of what? One can only say of freedom, or of indestructible power, or conversely of an inexorable necessity. Absolute power or self-stability is the only type of infinity that is not rendered less than that which it claims to surpass, in virtue of the negativity inhering in its definition. That the world has had no beginning may be true, but to conceive the lack of a beginning is not to conceive a positive and super-finite whole, in its wholeness or as a single and for thought completed object. Only in the idea of a Life whose contents are the events of time do we get an idea of a past before which there could be nothing, since “before” has meaning only within the life in question. Instead of the conception of all past events as in time, as their inclusive whole, i.e., in something conceivable [184] only as either a definite lapse, with a beginning and end, or as a lapse greater than any conceivable lapse and so not conceivable as such, or finally as a mere category or character of events, which, being an abstraction, cannot include the wholeness of events, — we rather conceive all events in terms of the genuine whole of an embracing Spiritual Life, preserving its past within itself and generating the future in and for itself. If future events are real now, they fall in this Experience now; if “future events” is but a class with as yet no members, then the locus and definition of the class or status to be so occupied is in terms of a whole which either includes now or is to include events. The idea of “all events” thus remains within the scope of an inclusive unity conceivable as such, as a genuinely all-concrete and embracing reality.
The question of the mode of being belonging to the future is left without further development here. There seems, perhaps, no peculiar difficulty for the Monist in this Problem. Whatever reality or unreality belongs now to the future just that mode it possesses now to the One. The problem is too great to be dealt with — in brief discussion, however.
Argument 4. Thesis: Either space includes mind or mind includes and is the foundation of space. But space cannot include mind unless it is a spiritual unity or whole.
If we cannot think mind to be in space, in a given mode of thinking of space, then over and above the entire spatial [185] and natural world we have mind, a realm of existence by itself. There must then be an inclusive realm, embracing both space and mind. Such a realm, however, as something in which mind can be conceived is at least entirely unimaginable and indescribable, unless it is an inclusive mind, or an inclusive realm of experience or spirituality of some sort.
On the other hand, in the sense in which we commonly conceive the relation of in to space, we cannot conceive mental states to be in space at all. An object in space, means for us, one which can be seen or pictured there, or in some way experienced, without depending upon that experience for its existence in space. It is moreover an object common to many observers. With psychological elements, 7 such as pain, all these conditions are reversed. Pain may be experienced as in a sense extended, but we cannot conceive the pain as actually occupying a portion of space in a sense consistent with the physical type of occupation. And the idea of space itself is, rather manifestly perhaps, innocent of competing for any territory in which to lodge itself as filling up a portion of the continuum.
Experience itself embraces a portion of space, but it fills no portion. It occupies not a cubic centimeter at the expense of anything else. To be sure it is located at a point in space in the sense that the portion it embraces and the perspective given it of this portion are relative to the position of its body.
But in the sense in which its body is at a position, as crowding out other bodies, as an object [186] potentially given to all observers in substantially the same manner, and as a reality not dependent upon human experience, the experience itself is not an element in the space-world. Conceive the experience abolished, as in sleep, and the space-system as an extended reality, is altered not by the loss of the experience, but by alterations in bodies, a very different thing.
In short the ordinary merely physical view of space runs directly counter to the idea of a whole which is capable of losing or of acquiring mental occupants.
We are content to suggest that the two types of spatial existence must have a common element or there is a contradiction in our idea of the world as a whole. And the only common element conceivable at any rate is that of the mind itself, which already and always includes both so-called psychological and physical elements. If to be in space is to be in an inclusive experience, then finite experiences8 are conceivable as in the ultimate and in one aspect spatial whole. On any other view we have a paradox.
Note. That mind operates causally at points in space intensifies without solving the problem. For in order to effect space it must be included in the same whole somehow. And the causal effects of my thought on matter do not represent the full difference between my existence and non-existence in [187] the world.
When I come into being, something has changed. I have not, for there was no previous state of me to succeed to another. And the causal change to the physical world, a set of motions in matter,9 is an analytically distinct conception from the idea of the entrance into reality of an experience, with its pleasures, pains, and ideas.
Argument 5: Professor Alexander’s Monism.
Thesis: “Space-Time” omits qualitative differences.
There seems to be no one who denies the artificiality attending Professor Alexander’s nonetheless magnificent efforts to render an account of concrete experience in terms of the single reality or principle of Space-Time, pure motion, or changing extension. There is nothing in space-time but portions or “slabs” — to use Professor Whitehead’s word — of itself. Nothing moves but motion, nothing is extended but extension, unless time is to be regarded as capable of extension. Qualities appear, therefore, by what-to an onlooker — is obviously pure magic. As J. S. MacKenzie says (“Universals and Orders,” Mind, April, 1922), “each side has simply to be assumed.” We can see, indeed, that one cannot conceive Space-Time without qualities. But we cannot nevertheless see in those qualities modifications of Space-Time itself, as the principle is given to us, or in its pure abstractness. No doubt the ultimate principle of the spatial whole is capable of self-differentiation, but “space-time,” or “pure motion” are not words which [188] throw any light upon such a capacity.
We can conceive the same portion of space-time as presenting blue, or as presenting red, but how this alternate appearance alters the portion of space-time itself, and as much, remains a mystery. Extension is no less extended, and change no less change, in either case. Difference in rate of change is a difference in terms of mathematics, and is just such a difference in the rate of change. It is quite unnecessary to pronounce it as also a difference of quality — having stated the quantitative relations, all has been stated that the premisses provide for.
Yet it is clear that space-time is something capable of registering all differences in its own terms. For it is an all-inclusive whole, so far as the world of finite entities we know is concerned. They are all in it, and this inness is one with their existence. But how all their reality can thus spring from a relation to space-time, is precisely the mystery and until we have an answer, we can say no more than that Monism is somehow true. “Space-Time” really means, for Professor Alexander, “whatever this inclusive unitary principle of the world of nature is.”10 That is the fashion in which he uses the conception! That is what he makes it do for him, but as to what it is in order to be able to do this, certainly there should be more illuminating words than the old mysteries — “space,” “time,” or even than the two compounded and analytically interconnected in some fashion. The appearance of mind out of the compound, and the appearance of value introduce irreducible [189] concepts.
If, for example, as the acutest objection of all, we consider that worth of life as a whole, on Alexander’s view, we find that to say that a certain type of pure motion, wriggling in a certain way, is good, is merely to reiterate that in that way of wriggling — it wriggles. Nothing in the world of thought is more nonsensical, when seen starkly for what it is, than the reduction of value to bare fact. On the other hand, from one point of view, nothing is closer to the truth. Value and fact, the World Life and Space-Time are one. But which side of the equation has the most content and therefore determines the nature of the other and explains it?
Conclusion. The present section is rather in the manner of suggestion and of illustration than of complete proof for our thesis. But the following properties of space and time and of space-time have been pointed out.
1. Space and Time are not definable in terms of elements conceivable apart from them — or, at any rate, describable and demonstrably conceivable.
2. Magnitude implies a non-finite and qualitative standard, which can only be conceived in any definite fashion, as the organizing and comparing function of experience or mind. Proportionality and system are best conceived in terms of purpose, or of relative wealth and harmony of values.
3. The world-whole cannot be conceived in its simultaneous completeness in terms of extension. Only the rule for the endless extension of extension can be achieved in thought.
[190] Its endless expanse as complete, an inclusive whole of co-existing parts, cannot for thought appear as complete. We think it only as something more than any thought of it — so long as thought deals with extensiona1 magnitude.
An absolute or embracing experience can be thought as a unity. For this unity or completeness is not a function of the number of items — but rather of a single living principle in which i.e., as contributing to the self-realization of which, all items are to fall. No endless beyond is in question — except as the unlimited power to create further existences falling still within the one life. The variety of entities thus falls in one containing and for thought self-completed or genuine whole.
Viewing time, the same necessity for a positive ground of the negation of finitude, for a completeness which is yet without any external other, and so the inclusive reality, thinkable together or as one, made itself apparent. Qualitative infinity or absolute power belonging to an inclusive experience, were taken as the implication forced upon us, if we wished to give the idea of “all the past” or of “all time,” a content.
4. The world whole, conceived merely as extended, seems to omit mind altogether.11
Either we have two-world-wholes on [191] our hands, one physical the other mental — in which case the same problem repeats itself — or we accept the spiritual view of unity and wholeness as alone capable of comprehending in a genuine “in” relation, the whole of experience and its contents.
5. Professor Alexander’s Monism was arraigned on the score of abstractness — of leaving us with a too meager character ascribed to Being, from which the concrete world can be derived only by assuming it. And we accused him of reducing the worth of all life to the fact that it moves in a certain manner, the worth of a certain motion to its being that motion. The entire content of the conception of value is thus emptied out, and only the idea of mere change, or motion remains.
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Endnotes
l. It is the conclusion of the previous section that no whole can exist without an underlying reality to mediate its relations.
2. And thus does not answer the question.
3. Because it tends to become but one “there.”
4. Without assuming the point at issue.
5. Phil. Rev., 1913.
6. On the inability of “relativity” to solve the paradox, see J.E. Turner, Mind, 1922.
7. Humanly owned psychological elements — we do not commit ourselves to an ultimate division of physical and psychological.
8. And all their contents or objects.
9. Conceived merely as such, or merely as objects of our “external experience.”
10. The problem of argument 3 is, of course, not met by the concept of space-time. We have the instantaneous whole of space-time but cannot conceive its wholeness in mere space-time terms.
11. It might be thought that time is the whole embracing mind and matter. No doubt it is — but what inclusion in time means would turn out a paradox also. What difference does it make to time that we are in it? As time it seems ineffected. It is more understandable that time is in mind, as a character of its life, than that time is a container transcendent of mind. We find time in change and in experience not vice versa. It is an aspect of reality not an inclusive real whole.