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Dreams, Phantom Limbs and Virtual Reality: Challenges to the Singularity of Space?

Notes: A Neurobiological diagnosis with aesthetic, cultural and philosophical implications.
Part 2: Displacements of the Imaginary and Virtual Schemata

In the Transcendental Aesthetic of The Critique of Pure Reason, Immanuel Kant stated the a priori necessity of the singularity of space, “we can represent to ourselves only one space; and if we speak of diverse spaces, we mean thereby only parts of one and the same space … these parts cannot precede the one all embracing space … they can be thought only as in it”. In this paper I will review and criticise arguments against Kant’s claim, based upon the notion of ‘dream-space’, ‘virtual-space’ and ‘phantom-space’ and investigate the degree to which any of these putative ‘alter-spaces’ refutate Kant’s claim regarding the a priori necessity of the singularity of space.

When I first began to discuss the ideas to be presented in this paper I must confess that I was more than a little taken a back by the reaction of the partner of one of my friends – an amputee who suffers phantom pain – and who was outraged at the prospect of academic reflection on the ‘aesthetic, cultural and philosophical implications’ of something that was so personal and traumatic to him. To paraphrase a comment from one of the attendees at the recent Goldsmiths College conference on Phantom Limbs , ‘phantom limbs don’t instill a pleasant reminiscence of a mystical past but a simple, fucking excruciating, aching present’, the reality of which in one sense seems somehow devalued by mere metaphorical talk of aesthetics, culture and philosophy. Conversely, in a recent paper by Janet Sternburg I was surprised to learn that her own use of the phantom limb metaphor – in a letter to the NY Times to describe, not the annihilation, but an active absence of the ‘Two Towers’ from the New York sky line post 9/11 – had also prompted vigorous negative responses; with a least one reader writing to question her use of a ‘phantom’ metaphor to describe the horror of a city where body parts were still waiting to be discovered and identified…Although sharing common outrage these two responses to the use of the phantom limb metaphor reflect almost opposite polarities: one questioning its ability to reflect the subjective pain of the individual; the other questioning its ability to reflect the objective horror of a society. It would seem that at heart both commentators find the term ‘phantom’ in some sense pejorative; somehow demeaning of their own experience. By reifying the functionality of the metaphor in aesthetics, culture and philosophy we appear to subjugate what to these commentators is the essential characteristic of their experience – that is, its phenomenology. Nonetheless I wonder if the true root of their disquiet lies not in the syntax of a phantom word, but the semantics of a real pain.

And yet, from the perspective of the core ideas outlined in this paper, the use of phantom as a metaphor to describe some aspects of a disembodied pain is well chosen; suggestive of the opening of a meta-physical bridge into another space; a space not contiguous with the everyday space which we normally inhabit. A space that we cannot directly reach – for example by the laying down of measuring rods from a ‘real’ here to the phantom there – and yet a space which has its own internal normative consistency – as a phantom pain may have position, extent and location on the phantom limb etc.

It is in this sense, in the context of spatiality, that phantom limbs have much in common with both virtual and dreamed bodies; for with these spaces we also cannot lay down measuring rods from a point here to a virtual point there, albeit that objects in these realities also share with phantom limbs primary qualities of position, extension and location.

This apparent discontinuity – between phantom (and virtual) space on the one hand and the three dimensional world in which we live – challenges the Kantian thesis of the a-priori unity of space and time which claims, ‘we can represent to ourselves only one space; and if we speak of diverse spaces we mean thereby only parts of one and the same space’. The degree to which such alternative conceptions of space undermine Kant’s core thesis forms the subject of this paper.


In the Transcendental Aesthetic Kant claims that, ‘there are two pure forms of sensible intuition, serving as principles of a priori knowledge, namely, space and time’ and that ‘the form of inner sense is time; outer sense being space ’. For Kant, the existence of these forms is an a priori necessity, ‘… for in order that certain sensations be referred to something outside me … and similarly in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space is presupposed ’.

Having defined the necessity of the form, Kant ascribes three important properties to space:

  • Space is singular: ‘Space is not a discursive … general concept of relations of things … We can represent to ourselves only one space; and if we speak of diverse spaces, we mean thereby only parts of one and the same space … these parts cannot precede the one all embracing space … they can be thought only as in it’.
  • Space is infinite: ‘Space is represented as an infinite given magnitude … all the parts of space co-exist ad infinitum’.
  • Space is (empirically) real: ‘We assert, then, the empirical reality of space, as regards all possible outer experience’.

But for Kant, the concept of space reaches beyond its simple empirical reality; for although the empirical reality of space as the pure form of all outer experience is pre-supposed, the true form of space, ‘as something that underlies things in themselves’ must of equal necessity remain unknown and unknowable. Kant thus asserts the Transcendental Ideality of space where, ‘… objects in themselves are quite unknown to us, and that what we call outer objects are nothing but mere representations of our sensibility, the form of which is space ’.

In the second section of the Transcendental Aesthetic Kant makes three analogous claims for time, the ‘necessary representation that underlies all intuitions.’ Time is: singular, infinite and (empirically) real, but in its pure form, time, like space, is far more mysterious. This essay unfolds the logical necessity of just one of these six claims for space and time; Kant’s claim that space is, a-priori of necessity singular :- ‘we can represent to ourselves only one space; and if we speak of diverse spaces, we mean thereby only parts of one and the same space’.

But before examining alternatives to Kant’s thesis on the singularity of space, the metaphysical foundations which underlie our general concept of space need careful consideration. In particular we need to be clear over what exactly constitutes our concepts of location, object and ‘identity of object’ (the necessary conditions for an object M at time T1 to be defined as the same object M’ at some other time T2).

In the classical era, Aristotle defined the primary place of a material object as its ‘enclosing surface’, an imaginary piece of rubber tightly stretched over each object. The location of the enclosing surface thus defines the location of the object. The 17th century Empiricists typically defined material objects as objects possessing the ‘primary qualities’, with John Locke defining these primary qualities as those which are, ‘utterly inseparable from the body, in what state so ever it be … solidity, extension, figure, motion or rest, and number’.

More recently, in his book, ‘Spaces & Times’, Swinburne links the concepts of object and place such that:
“… at every instant of time every material object which exists at that instant occupies some place, and where ever any material object is or, it is logically possible, could be, is a place … A place is identified by describing its spatial relations to material objects forming a frame of reference. Any set of material objects which over a period of time retain the same spatial relations among themselves may form a frame of reference.”

Anything which can properly be said to have such a place Swinburne defines ‘a spatial thing’. Further, spatial things (or places) are spatially related (in the same space) if and only if they are at some distance from each other; the converse of which fundamentally implies:

  1. Two or more spatial things which are not some measurable distance from each other must be in separate spaces.
  2. These definitions of object and location lead Swinburne to assert two propositions concerning place and object:
  3. No two material objects can have the same primary place at the same temporal instant.
  4. No spatial thing can have two different primary places at the same temporal instant.
  5. The ‘necessary truth’ of [2 & 3] lead Swinburne to claim that any argument ‘leading to a denial of [2 & 3] must be rejected’. For an object M at time T1 to be classed as identical to M’ at T2, Swinburne states:
  6. The properties of M and M’ are, apart from the properties of spatial relation, similar …
  7. M and M’ are spatio-temporally continuous; there must be a continuous spatio-temporal path linking M and M’.


Man, Kant claims, acquires knowledge of objects only indirectly via information received from the senses, hence this information does not describe ‘the object in itself’, merely its apparent empirical reality.

In 1968 Ivan Sutherland opened the technological door into a novel reality that had long been predicted in works of science fiction. For the first time technological advances, such as those from Sutherland, enabled mapping of virtual data directly onto the senses; decoupling the perceived subjective sensation from the natural environment. Such ‘virtual data’ could be gathered from a remote source – effectively immersing the subject in the remote environment (telepresence) – or could be mathematically generated by computer, effectively immersing the user in a completely artificial, ‘virtual’, reality (VR).

In parallel with technological developments in VR, the last four decades have also witnessed the explosive growth of a wide area computer communication network, the internet. From its earliest conception as the potential communication arm for the American military/government in the event of nuclear strike; through its birth as ARPANET which initially linked just four sites in America; before finally reaching its current mass ubiquity as the multi-media orientated World Wide Web (WWW).

The internet is important in the context of Multi User Virtual Reality, (MUVR), as it provides a low cost, convenient communication channel enabling multiple users to simultaneously interact within the same virtual world. For example, within a MUVR a virtual book placed on a table by one user, could be picked up and examined by another.

In 1984 William Gibson, in his seminal novel Neuromancer, coined the term ‘cyber-space’ to refer to the alternative world he predicted would develop through globalization and integration of computer mediated communications and large MUVR. And although the core of Gibson’s dystopian vision still lies in the future, cyber-space is already creating a sense of sociability, space and world amongst its users. For example Froy observed that the social interaction which occurs in Newsgroups, IRC’s and multi-user games, defines tight knit virtual communities, which only come together in cyber-spatial locations (such as fantasy worlds and fantasy cafes) and notes that many of these communities have maintained membership over several years.

Much contemporary cultural theory, art and fiction examine what is perceived as the disembodiment of the subject in cyber-space; Froy described Thomas ‘overthrowing the organic body’, Benedikt foresees ‘humans ridding themselves of the ballast of materiality’. In Neuromancer the arch cyber-punk Gibson himself graphically defines the cybernaut’s ability to transcend the body in this way, ‘online… inside the system. I’m not in the meat anymore’. And it is this liberation from the human form that has specifically excited some none able-bodied commentators, who in large MUVRs see both a potential liberation from their physical bodies together with the opportunity to reduce isolation.


Although the phenomenon of phantom limbs has been known since antiquity, the phenomena had been shrouded in mystery and the first clear clinical description of phantom limbs was not given until 1872. After the American civil war in which thousands of soldiers underwent amputations, reports began to emerge of strange phantom sensations in the limbs that had been surgically removed, prompting the Philadelphia physician Silas Weir Mitchell to coin the phrase ‘phantom limb’ to describe these mysterious sensations. Indeed Mitchell was so surprised by the strangeness of the phenomena that, for fear of professional ridicule, he published his account under a pseudonym in the popular journal ‘Lippencott’s Journal’ in place of a more conventional peer reviewed scientific article.

That the fervent description of a ghostly appendage, invisible to the rest of humanity, may be a bridge to another space was suggested by the experiences of Admiral Nelson. Lord Nelson, after loosing his right arm during an attack on Santa Cruz de Tenerife, experienced intense phantom limb pain, including the bizarre sensation of invisible fingers digging into his phantom palm and this experience led him to claim that though the empirical reality of his pain he had ‘direct proof’ of the existence of the realm of the soul, ‘… for if an arm can survive physical annihilation, why not the whole person?’ Hence the Kantian thesis of the a priori unity of space and time does not remain unchallenged.

In his 1962 essay ‘Spaces and Times’ Anthony Quinton claimed that, by examining our concepts of a spatial entity, its extension and spatial relation to others, we see that ‘the unity of space is not involved in the conception of a spatial thing’. His challenge to Kant’s concept of space was constructed around the concept of a dream-space in the form of a clever ‘Quintonesque entertainment’. In his invention Quinton describes a situation where we go to sleep in our bed one space and wake up in an alternative dream space (e.g. by a lakeside) – and vice versa:

“Suppose that on going to bed at home and falling asleep you found yourself to all appearances waking up in a hut raised on poles at the edge of lake. A dusky woman, whom you realise to be your wife, tells you to go out and catch some fish. The dream continues with the apparent length of an ordinary human day, replete with an appropriate and causally coherent variety of tropical incident. At last you climb up the rope ladder to your hut and fall asleep. At once you find yourself awakening at home, to the world of normal responsibilities and expectations. The next night life by the side of the tropical lake continues in a coherent and natural way form the point at which it left off. Your wife says, “You were very restless last night. What were you dreaming about?” and you find yourself giving her a condensed account of your English day. And so it goes on.”

Life in both locations appears equally real and Quinton has no reason to claim that objects in one reality have any spatial relations to those in the other, for no matter how hard he searches each reality he can never discover evidence of the other. Similarly, as Bishop suggests, large scale MUVRs also present a challenge to Kant’s thesis:

“Quietly unnoticed by most of the world, thousands of tanks have been battling each other in a grim struggle for control of ‘the free world’. Day after day, tanks roll across countryside and through the wreckage of towns, warily hunting their prey. Hundreds of tanks have been destroyed, and large many cities laid waste in battles joined by many thousands of NATO personnel. But where on earth did these men fight?”

The above description is not that of massive covert military action by NATO, but a description of SIMNET, an ongoing US military training programme for tank crews. In nine remote sites 250 tank simulators each containing four crew members engage in virtual warfare over hundreds of square miles of battlefield. Each of the tank simulators provides a fully realistic experience for its crew, with the simulation tilting and swaying as the virtual tank moves across pot holes and through rivers; shaking with the nearby impact of virtual high explosive. But this battlefield is not located on earth or any other place in the everyday universe.

Furthermore, it is clear from Ramachandran’s description of the phantom limb phenomenon that objects in the ‘phantom realm’ also appear to exist in an alternate space with its own normative topographic laws. For example, in his online casebook, Ramachandran describes how he can interact with a limb in phantom-space simply by tracing its continuous outline on the surface of the patient’s skin:

… I came to meet Tom [Sorenson, who lost his left arm above the elbow in a car accident]. I called him up right away and asked whether he would like to participate in a study. Although initially shy and reticent in his mannerisms, Tom soon became eager to participate in our experiment. I was careful not to tell him what we hoped to find, so as not to bias his responses. Even though he was distressed by “itching” and painful sensations in his phantom fingers, he was cheerful, apparently pleased that he had survived the accident.

With Tom seated comfortably in my basement laboratory, I placed a blindfold over his eyes because I didn’t want him to see where I was touching him. Then I took an ordinary Q-tip and started stroking various parts of his body surface, asking him to tell me where he felt the sensations. (My graduate student, who was watching, thought I was crazy.)
I swabbed his cheek, ‘What do you feel? ‘You are touching my cheek.’ ‘Anything else?’ ‘Hey, you know it’s funny,’ said Tom, ‘You’re touching my missing thumb, my phantom thumb.’ I moved the Q-tip to his upper lip. ‘How about here?’ ‘You’re touching my index finger. And my upper lip.’ ‘Really? Are you sure?’ ‘Yes, I can feel it both places.’ ‘How about here?’ I stroked his lower jaw with the swab. ‘That’s my missing pinkie …’

It is apparent from this description that touching topographically related places on Tom’s skin opens a gateway into his phantom world, evoking precisely localised, and topographically consistent, sensations in his phantom hand.
In ‘Space and Time’ Swinburne specifies that any set of objects which over a period of time retain the same spatial relations among themselves may form a suitable frame of reference for a putative alternate space. Hence, by describing spatial relations to ‘material’ objects within each space, it is possible to form suitable reference frames in dream-space, virtual-space and phantom-space. Thus ‘lakeside and huts’, ‘hills and mountains’, ‘hands and elbows’ each form a frame of reference which in turn can be used to locate other transient objects within each corresponding space, (e.g. lake dwellers, enemy tanks, phantom itches etc.). It follows that if logical coherent, alternate spaces such as these pose a fundamental challenge to Kant’s thesis regarding the a priori singularity of space.

Clearly one of the first questions to be asked of a putative alternate space concerns its logical consistency. For example, Quinton’s use of a first person narrative set in dream-space has historically been criticised for introducing extraneous problems of personal identity. An inconsistency will clearly arise if Quinton’s body is in two spaces at once; yet in the situation where Quinton is awake at Lakeside his body is asleep on Earth – and vice versa – hence there exist two bodies at any one time and this clearly contradicts [3], Swinburne’s third criteria for spatial things.

And although in his article, ‘Times & Spaces’, Hollis outlines how Quinton’s myth can be amended such that, following ingestion of a mysterious drug, Quinton’s body, Q, vanishes from Earth, appearing at the Lakeside for a few hours, before returning to earth as Q’ at some later time, quite apart from the bizarre physics involved, this move brings its own problems of personal identity.

A simple dualist solution to the problem of inconsistency, discussed by Swinburne, is that Quinton ‘in entirety’ consists of two parts: ‘Quinton res cogitans’ and ‘Quinton res extensa’. In this vision, although there are two Quinton bodies (one on Earth, one at the Lakeside) there is only one complete Quinton (consisting of mind and body) – either on Earth or by the Lakeside – at any point in time. In fact, as several commentators on virtual/cyber-space suggest, the core of Gibson’s seminal vision, indeed the very notion of jacking into cyber-space, implicitly represents and buys into, just such a ‘sustained mediation’ on the Cartesian dichotomy.

Unfortunately it is apparent that there is an even stronger inconsistency in the location of the SIMNET tank crews. For in a virtual battle the tank commanders physically interact with their tank simulators; it is the sense data presented by the simulators that opens their window onto the alternate virtual-space. But clearly the soldiers’ physical bodies (and the mechanics of the simulators) never leave one of the nine training centres physically situated across America and Germany, again contradicting [3]. It is apparent that there is a serious inconsistency if the internal elements of the simulator – the crew, seating, buttons, dials, screens etc – are both in the virtual space and the real world simultaneously; and this inconsistency cannot so easily be resolved by enforcing a strict Cartesian division of mind and body.

Conversely it is clear that there is no such inconsistency with the conception of phantom-space; although phantom limbs have a very real existence for their perceiver, ex-hypothesi, they have no material existence in the everyday world.A second objection relates to the grounds on which we establish the ‘empirical reality’ of the alternate spaces. Acting alone Quinton has no grounds for establishing if either of his experiences, on earth or in dream-space by the Lakeside, are real.

By making Quinton’s experiences part of an orderly, consistent wider public experience, such that, “we suppose that the dreams of everyone in England reveal a coherent order of events in our mystical lake district and let everyone have one and only one correlated lake dweller whose waking experiences are his dreams”, Swinburne asserts that Quinton ‘would have every reason to say that both spaces were real’.

Similarly grounds for belief in the virtual-space of the tank battle come from the soldiers’ senses, the logical coherence of their experience and from the shared public events in this large scale MUVR, (as tank crews often discuss their virtual experiences as part of their day to day lives). Furthermore, each battle (and the tank commander’s actions in it) are rigorously analysed by instructors and discussed in depth during lengthy debriefing sessions. Living full, shared lives in the everyday and virtual-spaces, tank crews thus have every reason to believe that both constitute ‘real’ spaces.

Conversely phantom limbs provide an inherently subjective, first person phenomenal experience, which fundamentally is only loosely sharable by others through the study of brains scans and via listening to subjective reports. Clearly phantom-space is not a publicly accessible space in the manner that SIMNET is, nor as shared as Quinton’s communal dreaming. However, this lack of spatial community is offset by the regular reinforcement of first person phenomenal sensations which acts to ground locality.A third objection to the alternate conceptions of space relates to spatio-temporal continuity. Williams insists that such continuity ‘is a necessary condition for the identity of material objects of all types and in particular of personal identity’. Wherever a material object M leaves one space S1 to appear in a different space S2 there is a spatio-temporal discontinuity. Strict application of Williams’ principle would imply that [M at S1] and [M at S2] cannot be the same object.

What then of Q, the drug quaffing traveller into Quinton’s dream-space? On returning from Lakeside Q’ insists that he is the same man who took the drug and disappeared several hours earlier. On questioning, his appearance, memories and behaviour are suitably coherent. However it is only the first person account of Q’ that provides us with evidence for such continuity and this ‘lends colour to Butler’s classical objection that memory, so far from constituting personal identity, presupposed it’.

But what if Williams’ conclusion is false? In his 1960 thought experiment Coburn describes how a man called George appears to suddenly vanishes and a man exactly like him appears a moment or two (Dt) later. It would seem reasonable to say the two people are one and the same person, (consider what happens as Dt tends to zero). However, on the strict application of the Williams’ principle, George is gone for ever and an impostor is now in his place. This seems absurd and indeed Williams eventually modified his principle of identity to allow George to so reappear, under the condition that the new George behaves exactly like the old and turns up at exactly same place, (before any other entities appear also claiming to be George).

But what would Williams say if George turned up a small distance (DD) away from the point he vanished? Again common sense would suggest that we ascribe the identity of George to the new figure. Only if a second ‘perfect’ George appears simultaneously (George II) would we not know what to say. In that situation we may be forced to alter our concept of personal identity to include spatio-continuity as a necessary precondition for personal identity, as it is not at the moment.

Hence the fact that people cannot be spatio-temporally continuous relative to a previously identifiable frame if they pass between two spaces does not constitute an objection to the possibility of such spaces so long as there are no serious difficulties about re-identification (of the George II type).

In fact Swinburne observes that, ‘we would realise this more obviously if it was a regular feature of our universe for people to disappear and people exactly similar in appearance, behaviour and ability to report past happenings to turn up immediately afterwards elsewhere without having traversed what is, relative to earth, the intervening space’. Although such a situation is not (yet) a feature of our universe, we are all familiar with the concept as it has been popularised in the Science Fiction universe of Star Trek. A fourth objection simply queries how we know the (three) putative new spaces are not actually part of Kant’s all encompassing singular space?

Considering Quinton’s dream-space; for his myth to function at all he must be certain that the two locations he visits, Earth and Lakeside are not both located in the same space. Quinton can only provide the unsatisfactory mechanism of exhaustive search to try to establish this. However it is apparent that a search of length T days which has not located Lakeside on Earth, does not preclude such a discovery on day (T+1).

There are two simply solutions that meet this objection:

Lakeside is a special closed space, such that after a finite time all of it can be completely explored.

Lakeside has very different Laws of Physics. If the Physics of Lakeside were significantly different from that on Earth it would entail less change (and hence be more plausible) to imagine being in a different (non Earth) space than to adapt all our everyday notions of the world.

Conversely, because the virtual-space of SIMNET is a computer generated, unlike Quinton’s myth we can be certain that the spatial locations are not located anywhere on Earth without recourse to exhaustive search or by appeal to the consistency of physical laws. Clearly the virtual-spaces of the tank battles satisfy all Swinburne’s criteria for place, (the fixed objects within it, mountains, rivers etc., together form a frame of reference, which in turn can be used to locate other transient objects (enemy tanks, lorries, guns etc.), although there is clearly no path, such that we can lay a series of measuring rods, one after the other, from a point in Earth to the site of a virtual battle and hence the two locations must of necessity be spatially unrelated.

It is similarly apparent that phantom-space, ex-hypothesi non material, is not located anywhere in the physical universe. Clearly phantom-space also satisfies Swinburne’s criteria for place, (the fixed locations in it, for example fingers, elbows and hands etc., together form a frame of reference, which in turn can be used to localise other transient objects, aches, pains etc), although there is clearly no path, such that we can lay a series of measuring rods, one after the other, from a point in Earth to the site of a phantom limb and hence these two locations must also be spatially unrelated.


This paper has examined the one of Kant’s six claims on space and time, ‘that we can represent to ourselves only one space; and if we speak of diverse spaces, we mean thereby only parts of one and the same space … these parts cannot precede the one all embracing space … they can be thought only as in it’, in the light of three alternate spaces: dream-space; virtual-space and phantom-space.

Although all three alternate conceptions of space discussed in the paper exhibit regular normative spatial features in their topology, (for example, virtual, dream and phantom spaces are all characterised by the correct application of spatial predicates to fixed ‘material’ objects within them) and satisfy many of Swinburne’s criteria necessary to qualify as independent spaces, it has been shown that none consistently satisfy all such criteria or fit within Kant’s original conception of one all encompassing space.

However taken together, dream-space, virtual-space and phantom-space, suggest a possible modification to Kant’s Idealist conception where ‘… objects in themselves are quite unknown to us, and that what we call outer objects are nothing but mere representations of our sensibility, the form of which is space’. For the three alternative spaces discussed clearly provide multiple forms – arenas – for [shared] interactions of mind(s) and Ideal unknowable objects: everyday space provides the sensorium with one such ‘space’ of things; dreams, virtual reality and phantom limbs provide the sensorium with other such spaces. If so, the empirical reality of these multiple spaces provide novel refutation of one of Kant’s a-priori knowledge claims – that space is, of logical necessity, singular.

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Mark Bishop Department of Computing, Goldsmiths College, University of London