RUSSELL-SPACE AND THE ELUSIVE SELF
American University March 21 2000
Introduction: It has been more than two and a half centuries since Hume reported that “when I enter most intimately into what I call myself...I can never catch myself without a perception, and never can observe any thing but the perception” [TH p. 252]. The self, it might be said, is introspectively “elusive.” If I am right, the elusiveness of the self can be placed on the same footing with another fact of introspection, namely, that I cannot introspect the experiences of another. The primary objective of this paper is to show that relating these two facts is made possible by speaking of privacy in spatial terms, rather than terms such as “belonging” to a mind in some special way. Russell’s theory of perspective space, or what in the title I have called “Russell-space,” provides the animus for such an undertaking, although my conclusions and Russell’s do not always coincide.
Imagine that you can see in every direction and that you can see where every part of every thing is. Suppose your neighbor can do the same and that at every place there is an observer much like yourself. In such a world, you would be quite like what Leibniz called a “monad” or perhaps what Wittgenstein meant by “the geometrical eye” (NL p.299). Your perspective and all other perspectives would collectively constitute something very much like what Russell called “perspective space” or “public space.” Russell was not alone in his recognition of the need for a geometry of perspectives. Henri Poincare, the French mathematician, had already observed that the geometry of our visual experiences is tied to that of perspective. At one point, he remarksPerceptual space is only an image of geometric space, an image altered in shape by a sort of perspective, and we can represent to ourselves objects only by bringing them under the laws of this perspective. (FS p. 71).It is sometimes maintained that our idea of three dimensional space is itself constructed from two dimensional representations. Faced with the question whether ordinary physical space itself is constructed from mere representations, Russell found himself in a perplexing situation. A possible way out was suggested by T. P. Nunn’s somewhat indelicate but powerful arguments in favor of epistemological realism. Nunn had argued persuasively, if not successfully, that secondary qualities as well as primary qualities exist in the things said to have them. However, his realism with respect to secondary qualities carried him to extremes. At one point ([SQ] p.209), he goes so far as to say that when a stick placed in water is made to appear bent it is not just apparently bent it actually is bent. Russell was basically sympathetic to the idea that spatial relations obtain independently of experiencers, but he was unsure where to locate seemingly conflicting spatial properties. Conflict arises, for example, when a penny you see as round is seen by me as oval. Unless we are prepared to deny that we see the same objects, and thereby move away from naive realism by embracing sense-data as mental representations, nothing prevents us from the conclusion that both ovalness and roundness are located at the same place, a seeming impossibility. Adding to the complexity of this circumstance, Russell held an act-object view of what are sometimes called “mental actions,” one so radical that even pains are to be construed as intentional objects (ML p.99). Russell, then, needed to accomplish three things as economically as possible: First, he needed to resolve the relationship between the space of experience and public space; second, his realism required that he reject not that space is a construct, which he believed, but that it is mental which he did not believe; finally, and perhaps most significantly, he needed to overcome the appearance of conflict we have just described in the attribution of geometrical properties. Russell would attempt to accomplish all three things by making a bold philosophical move.
What he would say is that the space of nature has six dimensions, possessing what we might describe as subspaces consisting of perspectives (ML p.103). Not only could he retain his belief that the ultimate constituents of matter are physical but he could also hold that they are objects of immediate acquaintance (ML p.96). By adding three dimensions to the original Euclidean three he would account not only for the relations between public and perceived space, but he would guarantee that the realist found places of occupancy for seemingly conflicting spatial properties.
Each perspective is unique; things seen from one perspective are never exactly like those seen from another perspective. Each perspective is a world of its own (EW p.92). Not all such worlds, however, are perceived. The ones that are Russell calls “private worlds” (EW p.93). A private world contains its own space and it is in this space that a person lives his life, insofar as his experiences are concerned (ML p.117). But if such a world is private, such privacy doesn’t mean estrangement, since although worlds may be private there are certain similarities between them that allow for correlation. Such similarities are sometimes sufficient to make communication possible (ML p.117). It is, therefore, similarity between private worlds that makes public language possible, just as the system of perspectives constitutes the possibility of moving through a public space. When there is a close resemblance between worlds they are said to be “near” one another. But no matter how “near” they get they remain private. Each perspective contains its own space (EW 94) but places in different perspectives never exist in the same space (ML 117,118). A particular belongs to that perspective consisting of all particulars simultaneous with that particular (ML p.105). Although the details of Russell’s all too briefly stated theory are subject to controversy, there is some basis in Russell’s later work for regarding the space of a private world as a fragment of an entire, but single, perspective (AM p. 200).
There are numerous things present in a private world, and yet a private world occupies but a single perspective in public space. There is no change of place within a private world, for any change of place in such a world would result in a change of perspective and a change in perspective is movement through public space. Thus, the self is immovable within a private world.
The Properties of Perspective Space: Two properties of perspective space which are quite useful in probing the nature of the self and the absence of direct awareness of the experiences of others are separability and connectedness. The idea of connectedness will be crucial to our understanding of privacy s patially conceived. Mathematicians have identified three ways in which a space can be said to be connected (Mendelson [TP] p 112). If it is impossible to dissect a space into disjoint nonempty subsets of places, that is one sense of being connected - although I am oversimplifying a bit. If any two places in a space can be connected by a path, that is another sense of being ‘connected’; and finally, if any closed curve in a space can be contracted to a point, that is yet another sense in which a space can be said to be ‘connected’. Path-connectedness is stronger than the first sense of ‘connectedness’, since path-connected spaces are ‘connected’ in the first sense, but not all connected spaces are path-connected. I am being deliberately vague as to the difference between places and points. This is an issue in itself, but the intent of my vagueness is to allow a natural introduction of the concept of a ‘neighborhood’, which I will describe as all the places contained in a stretch of space in any direction from a given place. Perspective space will be said to be “simply connected” for the somewhat technical reason (cf Mendelson [TP] p 114) that no two neighborhoods, the union of all of which constitutes the entire subspace that is a single perspective, intersect within the complement of that subspace - those two neighborhoods themselves being part of the larger space, i.e. the space of nature. But now that we have disclosed the connectness of perspective space, something must be said about the property of separation in such a space. This is an important property to consider since it is fundamental to the concept of measurement.
Our ability to measure by successively laying down a meter stick from place to place depends on places being at some distance. Let us suppose that a space is “metrisable” when and only when such an activity (that of finding distances) has a meaningful outcome. Felix Hausdorff had shown that if a space fails to satisfy certain axioms of separation that space is not metrisable (cf Patterson [TOP] p. 50). Not only was Russell familiar with Hausdorff’s set theory, he would only a few years after Hausdorff’s most significant work make important use of it in defining a spatial ‘point’ (AM chpt. XXVIII). The salient fact is that in a private world the separation of places required for metrisability cannot be part of the data. In terms of Russell’s perspective space, two perspectives are required if we are to have a concept of separation, but for a private worlder only one perspective can be given.
Because within a perspective the neighborhoods of other perspectives cannot be given, no two given neighborhoods are distinct, and so the axiom(s) of separation cannot be satisfied; and because of this, no sense can be attached to ‘distance’. Even if we had measuring devices that did not depend on motion or change of perspective, say tape measures, in private worlds they might vary from world to world without effect on what we take to be the distance between two places in public space. It is only if movement is possible that two places are separated in perspective space since only then do disjoint neighborhoods avail themselves, and only then is a metric possible. This has the consequence that measurement is possible only in a space where movement is possible, a view held even by Poincare:For a being completely immovable there would be neither space nor geometry; in vain would exterior objects be displaced about him, the variations which these displacements would make in his impressions would not be attributed by this being to changes in position, but to simple changes of state. (“The Value of Science” p. 248)Russell’s later remarks tend to suggest that because my eyes are not in my visual field changes in orientation need not affect topological relations; that is, the order of things is unaffected by such changes in eye movement thereby allowing “common sense to ignore the subjectivity of visual position” (HK p. 263). He implies by this and other remarks that while the parts of a visual field have spatial properties the separation of parts of a visual field does not imply separation in the space of nature. More clearly stated, the important point is that spatial changes are possible for the later Russell even when there is no corresponding spatial change in the space of nature. Russell appears, then, to move away from the idea that the space of a private world just is the perceived part of a single perspective, saying that “if there is a space which contains both it (an ordinary table - sb) and my perceptual space, then in that space the physical table must be wholly external to my perceptual space” (HK p. 221). By “external” he here appears to mean something like the relation that obtained in his earlier formulations of his theory of space between a single perspective and natural space.
We have now reached two conclusions: first, the space of a private world, unlike perspective space itself, is not metrisable, that is, it fails to incorporate the possibility of a concept of distance; but, second, like perspective space it is connected. The first conclusion (the one about metrisability) I will use to elucidate an important difference between Russell and Wittgenstein on privacy; the second I will soon make use of in solving the problem of the elusiveness of the self: a solution which at the same time offers the prospect of shedding light on why we cannot be presented with the objects of the mental acts of others. But before I do this, there is one other matter that needs straightening out.
Some philosophers - Berkeley and C. D. Broad - as well as some philosophically minded physicists, such as Poincare and Reichenbach encouraged the identification of what we might call “perceptual space” with the space of a private world, that is, the space constituted by a perceived perspective. As long as a single perspective is understood as part of the space of nature Russell can be seen as rejecting such a view. Thus in his last major philosophical work, he speaks of the “serious error, committed not only by common sense but by many philosophers” of “supposing that the space in which perceptual experiences are located can be identified with the inferred space of physics...” (HK p. 220).
To get at what Russell had in mind consider that in the space of nature railroad tracks usually run parallel, rail never touching rail. Yet, our actual experience upon peering at a lengthy stretch of track “down the way” is that of tracks appearing to meet at some point. If we take Russell’s view, then there is a threefold distinction to be made. First, there is perceptual space in which the tracks meet; then there is the physical space in which the tracks actually exist and do not meet; and finally there is the perspective that defines the private world of the experiencer - and here too “aspects” of the tracks fail to meet. Considerably later than his original 1914 formulation of perspective space Russell introduces percepts in the description of what I have been calling “perceptual space”, saying that “...subjective space is that which appears in our percepts when we view the world from one place” (HK p. 264). These percepts appear to be constitutive of the “visual field.” There is much to be said about the relation of causation and space that cannot be said here.
There is, however, one further distinction among spaces that Russell merely touches upon but which is very instructive to examine, even if only briefly. It will be useful to borrow a word Russell uses in a different context and speak of “wild” spaces. Its relevance to the problems that concern us can be clarified for our limited purpose by making use of a recent metaphor which we owe to Hillary Putnam (RTH chpt. 1). I must emphasize that my intent is not to address the numerous problems Putnam’s metaphor can be used to illustrate but only to make use of it as what Dennett has called an “intuition pump.” Imagine, then, that we have a brain in a vat which is being induced to construct the mere experience of being at some perspective. How is this perspective different from the space of a private world? It must be kept in mind that within a private world there can be no change in perspective on Russell’s theory. While there may be an imagined change of perspective, there may be no change in the perspective of the self that does the imagining; but if in actual space there is change in perspective, then there is a change of position or perspective of the self, whence an asymmetry between vat-space, or “wild space” and the space of a private world in Russell’s sense of “private world.” It should be born in mind that in rejecting the Kantian notion that there is only one space and affirming subjective or psychological space(s) Russell is not denying that mind enters into the very determination of the space of nature. As late as 1948 he averred that points in space-time are classes of events some of which might very well be mental (HK p. 223).
We are now ready to see how these distinctions and what we have said about connectedness come together to answer the question, “To what do we attribute the elusiveness of the self?”
The Core Thesis: A Need To Spatialize Privacy: We have already seen that the activity of measurement in a private world is without meaning or result. But isn’t this as much as to say that there is no private metric; and if this makes sense, and I think it does, doesn’t the impossibility of a private metric tell us something about other private exemplars that might be alleged by extension to concepts besides properties of space, such as that of pain? And what of the self and its place? It seems that the problem of the elusive self can be explained away as a consequence of the fact that the space in which the self is located is a space other than that of the private world of the physical objects of our immediate acquaintance, even though the space of the latter is, strictly speaking, a subspace of the space of nature. More exactly stated: the place of the self and the place of the objects of acquaintance are not path connected, that is, there is no path joining a place within the space of the perspective of a private world and the space of nature. This is in fact the proposal I want to pursue. I want to claim that instead of thinking of privacy mentalistically in terms of a special kind of relation to a subject, we instead think of it as a property of a perspective, that is, as a property that supervenes on a topology. Embolden by these prospects I go even further, extending this notion to a philosophical account of why the experiences of others are private to them. There can be no path joining the place of an object of the immediate experience of another to any point that is in the space of my private world. Let us now take some care in what it is exactly that Russell took the self to be and then pursue the question where this self might be found.
In 1914, Russell distinguished two senses of ‘self’ (EW p.81). One sense was that of the subject of awareness; the other was the self as “the whole assemblage of things that would ... cease...if our lives came to an end.” The self as subject occupies a place in natural space, for Russell. The self in this second sense is not to be found; “it is not part of the data” (EW p. 81). I will refer to this second sense as the “Cartesian” sense and the former as the “non-Cartesian” sense. It should be kept in mind that the Cartesian “self,” in this the second sense, is the self that Descartes’s cogito is designed to prove.
Where Exactly is the Self? But now we must go on to ask, “Where exactly is the self?” Some may think it more appropriate to ask, What is the nature of this question? The kind of question this is was brought out by Gareth Evans who believed that the identity of persons is determined spatio-temporally (VR 211). Evans notes the curious fact that “a subject can know that he is in front of a house simply by perceiving a house” (VR p.232). The nature of the question we ask, then, is a factual one: Where is the place of such a subject? Russell here is admirably, and perhaps surprisingly, direct:Since the mind is correlated with the perspective to which our sense-data belong, we may regard this perspective as being the position of our mind in perspective space. If, therefore, this perspective is...inside our head, there is a good meaning for the statement that the mind is in the head. (ML p.120)The place of the self, then, for Russell is not within a private world or perspective, but in some sense within the space of nature. Elsewhere (AM p. 336), Russell makes explicit his doubts that “the mind occupies a single place in physical space.” But this is not a repudiation of its occupancy of physical space, rather it is consistent with the notion that the mind is located in an area of the brain and not a point or even, perhaps, a circle of zero diameter! Nor would it be inconsistent with this position to regard the place where the mind is as “specious” just as the present was, and still is by some, regarded as specious rather than punctual.
It cannot be emphasized too strongly that the self of which Russell is here speaking is the first sense just mentioned, not the second or Cartesian sense. Having developed for the first time the principles of analytical geometry DesCartes understood space as well as anyone of his generation and yet he made the self a substance independent of extension. By contrast, Russell, a geometer at heart, placed the self in space. The objects of awareness, too, are in space; they are not sense data in the sense we’ve come to understand in the works of Moore, Broad or Price; the mind says Russell is not a “bag” full of experiences (ML p. 98). This distinction taken in concert with Russell’s views on the nature of space contain some important consequences for a proper understanding of certain controversial passages in Wittgenstein. Let us take a look at two of them.
There is, I believe, good evidence that Wittgenstein’s own views on the nature of the self were strongly influenced by Russell, especially in the _Tractatus_. At one place, Wittgenstein says:I am my world. (The Microcosm) (T 5.63)and slightly thereafter,The subject does not belong to the world rather it is the limit of the world. (T 5.6320)There is a remarkable similarity between Wittgenstein's view of the self and the "microcosm" and that of Samuel Alexander who commented,I am my own microcosm (SPD vol. 1. p. 110) ... in this microcosm ...time...is laid out in spaceWe can now understand these cryptic remarks if we think of Wittgenstein as accepting the Russellian idea that the space of a private world, in Russell’s sense, is the interior of a point in the space of nature. “The limit of the world” is, then, the smallest neighborhood containing the entire space of a private world. Where he departs from Russell is in his acceptance - or so it is made to appear - of the self as a Cartesian self, and it is this fact that creates a dilemma if we try applying Wittgensteinean ‘privacy’ to Russellian private worlds.
Was There a Private 'Private Language Argument'? Sometimes it is a good idea to defend a radical theory just to see where the chips may fall. One such theory is that behind Wittgenstein’s argument against the possibility of a private language are considerations having to do with the physics and the geometry of the space of nature. I will briefly entertain this theory, as I believe it has something to offer of philosophical substance if not historical fact. Wittgenstein may have changed his views in the Philosophical Investigations on the nature of the self, but he retained an appreciation of the question of space in relation to it. Thus,One might say: Surely the owner of the visual room would have to be the same kind of thing as it is; but he is not to be found in it, and there is no outside. (PI 400)If Wittgenstein had spoken of the kind of space the owner of a visual room occupies instead of what kind of thing such a person is, then Russell and Wittgenstein would have stood a chance or reconciling some of the profound differences between them. Alternatively, there is the real possibility that Wittgenstein wanted to expose problems with the standard Cartesian view of the mind rather than to address Russell’s rather idiosyncratic theory, which outside of a few commentators such as Samuel Alexander (STD) received little notice.
We shall next consider how one might make the case that Wittgenstein harbored a private private language argument. To do so most convincingly, I believe, it is necessary to lay stress on the likelihood that Wittgenstein’s private language argument was shaped in significant ways by his thoughts on the physics of his day, thoughts which were filtered through what Russell had said in presenting his theory of perspective space.
Perspective space must differ from the space of a private world if for no other reason than that according to Russell (AM p. 338) perceptual space possesses properties relativity theory denies to actual space or perspective space. A further complication (the consideration of which is beyond the scope of this paper) is the relation of space and matter. Following his original formulation of the theory of perspective space, Russell became engrossed in the consequences of the theory of relativity. For example, in Human Knowledge: Its Scope and Limits (HK p.220) he insists that ‘distance’, following the special theory of relativity, applies between events rather than objects. This is not in evidence in the earliest formulations of his theory of perspective space. Moreover his decision in The Analysis of Matter to define points in space in terms of event quintets and his indecision as to whether space is continuous certainly must be kept in mind as we investigate his earlier view; but these new considerations may have been compelled by the very ideas which may have been operative in Wittgenstein’s thinking, if our conjecture of a private private language argument has any credibility.
At the heart and soul of the later Wittgenstein is the idea of language as practice. The philosophical foundations of language are institutionally ordained by conventions that have their basis in human activity, not monads. How different Russell and Wittgenstein seem! Yet, if we examine the role of convention in the thinking of some physicists we see that our old friend “metric space” is what underlies our having distances to measure in the first place. This is where Wittgenstein’s discussion of the meter stick in Paris can be seen to entail among the few unheralded lessons to be taught by his now famous argument, although the problem of defining a ‘meter’ appears to have been anticipated as early as Leibniz (SEL p. 203). We have seen that within a Russellian perspective or private world there is no available conception of a separation between points, and furthermore that there can be no measurement of distance. We already know that at a perspective in physical space measurement must be regarded as without a point. Hans Reichenbach is supportive of this idea as central to understanding what was then the new physics. He remarks,...a definition of a unit at only one space point does not render general measurements possible. (Reichenbach. PST. p. 17.)What I wish to claim is this: the very nonsensicalness of a private metric which we find in Russell and which is made explicit in Reichenbach is extended by Wittgenstein to all private exemplars for terms in natural language - all of which terms must have some public meaning. Indeed the parallels between Wittgenstein and Reichenbach are nothing short of striking, as when Wittgenstein likens appeal to inner criteria to the imagined results of imagined experiments (PI 265). This after Reichenbach had spoken of imaginary measurements. In fact, a measurement can be thought of as an experiment, a human practice, designed to discover facts about distances. Further, wouldn’t a private measuring stick be much like Wittgenstein’s “beetle in the box,” which each of us might carry about to do our measuring? What is required by the public nature of measurement? As Reichenbach suggests,...the requirement of uniformity would be satisfied by carrying around a measuring rod carried around at random (PST p. 17).Is this not like having a measuring rod at each and every perspective? As long as it served its function, none at all really, would it have a part in the “game” of measurement? This raises the question of what that function is and whether it can be fulfilled privately. It is difficult to believe that the parallels to Reichenbach are merely coincidental. There are additional reasons for believing this is unlikely. Consider one of Reichenbach’s comments on the nature of congruence in physical space, wherein he discusses the meter stick in Paris.It is logically impossible to determine whether the standard meter stick, is really a meter. The highest refinement of our geodetic instruments does not teach us anything about this problem, because the meter cannot be defined. It is arbitrarily defined by the unit and the question whether it represents this unit has lost its meaning. (PST p.28)The similarity to Wittgenstein’s often cited view seems obvious enough:There is one thing of which we can say neither that it is one meter long, nor that it is not one meter long, and that is the standard metre stick in Paris. (PI 50).Remarks such as these by Reichenbach have very strong Kantian overtones. Reichenbach, like Poincare, Broad and others, held to a fundamental distinction to be between “private” (Cartesian) and public space, a distinction that had to be bridged by construction. Russell was more circumspect and could easily have obviated Wittgenstein’s cogent criticisms of privacy in the Cartesian sense by distinguishing not only between private and public space but between public space and its subspaces, creating a three fold distinction where before there had been only a two fold distinction - a distinction not so easily discerned in Russell’s later work but present none the less. Russell was drawn to this by a complex interaction of two influences: his realism, which tended to falter, and his respect for Hume. In a more general and, therefore less precise, sense of ‘realism’, Wittgenstein hoped to rediscover a realism with respect to natural language after the perceived collapse of his picture theory of meaning and its attendant metaphysical implications.
Whether Wittgenstein actually had a private ‘private language argument’ is a question that cannot be resolved, but once the scientifically minded Wittgenstein is fully appreciated belief in the possibility of exhuming such a philosophical artifact of the revolution in physics will receive less resistance. I can now state my two main conclusions; first, the elusiveness of the self is owing to differences between the space of nature and the space of private worlds: and second, nonintrospectability of the experiences of others is owing to the properties of and relations between the space of the one doing the introspecting and the space of the objects of the immediate experiences of others. This approach possesses the advantage of relating two problems not obviously related.
Summary and Conclusion The question of the elusiveness of the self was raised in view of Hume. It was suggested that by spatializing privacy we might explain such elusiveness. We next saw how Russell hoped to accomplish several things by his theory of perspective space, and we made an effort to state Russell’s views on two special topological features of such a space, viz., separation and connectedness. It was then argued that the self was elusive because it was not in a space connected to that of the objects of acquaintance. In addition, we gave some reasons for believing that unlike Russell’s notion of self Wittgenstein in his attack on the possibility of a private language moved the discussion to a more generally understood conception, that is, what I have called a Cartesian idea of the self. The possibility was raised that there might have been a private “private language” argument, and in the process we related metrisability, which we had seen to be impossible in a Russellian space of a private world, to Wittgenstein’s discussion of the meter stick in Paris. We, then, observed how philosophers such as Reichenbach had earlier arrived at somewhat related conclusions in considering the measurement of spatial intervals.
Russell’s theory of perspective space was formulated before Einstein’s theory of General Relativity, although it was inspired by the Special Theory. In exploring the implications of this theory in relation to the elusive self I have favored Russell’s earliest formulations. In his later theorizing, Russell developed a theory of space that attempted to take into account what were then new developments in quantum theory. Although he would revise and qualify his view on privacy he would retain a belief in perspective space and thereby reaffirm his ever lasting kinship with Leibniz.
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