“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 unique space, as being, as it were, constituents out of which it can be composed; on the contrary, they can be thought only as in it. Space is essentially one; the manifold in it, and therefore the general concept of spaces, depends solely on the introductions of limitations. Hence it follows that an a priori not an empirical intuition underlies all our concepts of space.” (Kant, Critique of Pure Reason, A25)

There are multiple questions regarding the multiplicity of space, starting with the nature of space itself and what constitutes the notion of ‘real’, after these I can then discuss different possible spaces, such as dream, virtual, or our ordinary phenomenological space; if more than one of these is real then Kant’s above claims would be incorrect.

Our use of language might trick us into treating space as a ‘thing’ or ‘object, but it rather seems the case that space is that in which ‘things’ or ‘objects’ exist. Another temptation is to conceive of space as a container, but this metaphor also treats space as an ‘object’, albeit one that contains other objects. If space is a ‘thing’ then it would need space of its own in which to exist, and that space it’s own as well, creating an infinite regress. Thus I conclude that space is not an object.

Kant writes that we could visualise empty space; “We can never make to ourselves a representation … that there is no space, although we may … think that no objects therein are to be met with” (Kant 2000: 33). I disagree and hold we can’t imagine such without also imagining objects to act as points of referance.

If we attempt to imagine an empty space what we actually imagine is a space within a border, or contained within edges or other definite points; these objects create that notion of space. An empty cube or circle can be imagined, as can a space around a cube or circle, but nothing without any spatial relations at all.

We could visualise ourselves floating in nothingness and we would have an awareness of the space between our toes and head, or between our eyes and an outstretched hand, but nothing else without more points of reference. To demonstrate; imagine waking in a pitch black room with no knowledge of objects or boundaries around you. Such a sensory deficit would not create a sense of a gulf of space, but a complete unawareness of space beyond our body due to lack of material references. The same must be true of the sensation of floating in empty space, which is space without material references. In either case we would find ourselves with no conception of space except immediately around us.

Hence space is intrinsically tied to relations between objects. We require reference points to compare spatially, that is by angle and distance, or else we can have no concept of it. This means Space is entirely relational, existing as relations of distance and angle from one point to another.

To strengthen this claim I shall borrow from Leibniz; it seems meaningless to suggest that all objects could exist one inch to the right of where they are, as it would amount to no real change in relations between objects. Similarly as Leibniz wrote “'tis impossible there should be a reason, why God, preserving the same situations of bodies among themselves, should have placed them in space after one certain particular manner, and not otherwise …for instance, by changing East into West” (Leibniz 2003)

Kant writes that “The representation of space cannot therefore be borrowed from the relations of the external phenomenon by experience, but this external experience is itself first only possible by this stated representation” (Kant 2000: 32). This may be read to oppose my claim, but may make a point to which I would not disagree; that the organisation of things into spatial relations is not a learned process but innate. Our eyes do not perceive space, but the mind takes their images, along with all other sensory data, and correlates them into a three-dimensional grid automatically and without our assent. This is true for all people, and likely of animals, and seems to be biologically hard-wired into us. This does not change that what our minds are doing is drawing relations between objects.

Moving on with the assertion that space is ‘relations between things’, the new issue is whether there could be more than one set of relations between things, if not then all objects, without exception, must be spatially related to all other objects; one counter example disproves that there is only one set. A common source for such an example would be dreams.

Dreams are not spatially located in our normal world. If one asserts that the dreams exist within the mind, and the mind is simply the brain organ in action, and because the brain has a spatial relation to the rest of our world that dreams have spatial location in our world, I should say that they misunderstand the relation between the brain and the mind. The mind and the brain are importantly related and neurons firing in my brain may have some casual link to me experiencing some sensation or image, but no image is to be found among those neurons. An image is something seen, and neurons firing do not form a picture of a wine glass, thus a dream wine glass can not be spatially located in the brain organ. There is no spatial relation between a dreamed object and the bed I sleep on outside the dream. The dreamworld and the world I sleep in are spatially disconnected with no spatial means of travel between them.

Dreams then serve as an appropriate example of a separate set of spatial relations, that is, a separate space. This shows that Kant is wrong that we can only “represent to ourselves only one space” (Kant 2000: 33). However, dreams are not ‘real’ and it may still be true that there can only be represented one ‘real’ space, thus leading me to discuss what constitutes the concept of ‘real’ and whether there could exist a separate ‘real space’

I would like to begin by appealing to what would make us accept a reality as ‘real’ so as to see how we make the distinction.

Some people assert that this world is not real, but an illusion created by some being, like Descartes ‘Evil Demon’ (Descartes 2003: 22) or by some more modern version of the same. Despite the logical possibility of this no sane person takes the possibility seriously. I further suggest that even if this world was an ‘illusion’ spun by demon or God that we would not act any differently and still would consider this our ‘reality’. This suggests that our relationship with the world is an important factor.

Berkeley idealist philosophy relies on similar assertions. Berkeley’s reality, formed of immaterial ‘substance’, suffered from the need to separate the ‘realness’ of this world and the ‘falseness’ of the dream world despite their shared immateriality. To do this he explained our lack of concern for dreamworlds as via how ‘real things’ are “vivid and clear and … imprinted on the mind by a spirit distinct from us” (Berkeley 1988: 182) whilst dreams are not. What has been appealed to here is how our world contains constancy and is impressed upon us from outside (whether or not by a God). By this notion of ‘real’ the important factor is our ability to have an ongoing stable relationship with the world. Without the properties of being external or without constancy any world would lack any sensation of reality, and be akin to our more surreal dreams.

Hence I take for our criteria of reality the constancy of laws therein and an independence from our will. Dreams, as normally experienced, fail these criteria. However, there have been attempts to imagine a possible dream world which does not fail.

Anthony Quinton in Spaces and Times tries to imagine a covenant dream world. This coherance gives dreams a sense of reality so we would take them as seriously as the world we inhabit now. He writes that “Injuries given in England leaves scars in England, insults given at the lakeside complicate lakeside personal relationships” (Quinton 1962: 140) and even notes how publicity would be present in this other world, though that seems unnecessary as an non-public world with only a sole sentient being would still seem to deserve the title ‘reality’. Such a world we would consider ‘real’.

However, a hypothetical dream world can only establish possibly distinct real sets of spatial relations. We need to apply the notion of ‘real’ to other sets of spatial relations, such as in ‘virtual reality’ to have proven a multiplicity of spaces.

The Mirriam Webster dictionary defines ‘virtual reality’ as ‘an artificial environment which is experienced through sensory stimuli (as sights and sounds) provided by a computer and in which one's actions partially determine what happens in the environment’. It also contains a definition of virtual as ‘of, relating to, or being a hypothetical particle whose existence is inferred from indirect evidence’. In this sense we can consider virtual reality as not being presupposed to be false by considering ‘virtual’ to be synonymous with ‘false’. Such an objection would be purely semantic anyway

Virtual realities are related to our world similarly to dreams; its objects cannot be found by inspection of computers any more than dreams by inspection of brains. Virtual realities best dreams by possibly being regular, coherent and meaningful worlds that obey internal laws. They can be created in three-dimensional grids with objects that are spatially related and interact according to laws similar to this world’s, with such a world containing stability, permanence, and heavily resembling our own reality.

Most computer generated worlds are not immersive. Sensory data about these worlds is displayed through monitors and speakers and not direct to the mind, but our minds are quick to identify virtual objects and consider them real. Simple virtual realities like the Windows Desktop create virtual objects like ‘folders’ which form a structured world which we can explore and gain consistent results from according to internal laws. This set of relations between objects is not contained within our world, as it is not mirrored on the surface of the hard disc the folders are ‘contained’ in. A computer image has no permanence in this world, yet we talk of it being in a place within the computer reality in a non-metaphorical way.

In a full immersive virtual reality we would likewise consider the objects to exist even when not visible despite their lack of material substance in our world. Our minds would naturally create a mental map of the objects and plot spatial relations as normal.

There may still be asserted a distinction between this and our interaction with our own world, but I would suggest that the exact same process is occurring.

Our world is a reality formed of abstract objects. Sensory data is organised by innate processes into an internal world picture. That which is incoherent is dismissed as unreal, such as illusions. Our world is composed of objects that could not be known through sense alone, such as the cube which can not be visualised yet imagined (a cube’s eight sides cannot be seen at once), and hence must be abstract from sensory images. Science offers us a picture of the underpinning of this world through extension, mass and motion, but all of this is deduced from the way our mind organises sensory data. Hence these notions, including that of substance itself, are not learnt but created by the mind, merely a ‘form of phenomena’ to borrow the term from Kant (Kant: 2002: 34). Nothing differs here from what the mind does in a virtual environment.

That our world can be described by science in the abstract by mathematics and in such a way that we can no longer visualise what science refers to does not make us treat our mental picture of reality less seriously. Equally, in a virtual reality such a world could be described also in the abstract by mathematical rules, though in this case we have an explanation as to why those rules apply by reference to a higher reality. That we lack that explanation in this world’s reality should not be a reason to consider it more ‘real’.

In this world we do not know the organising force of reality and what determines the laws of physics. Neither can we explain them through reference to ‘matter’, as that is just an empty abstract concept, one our minds create just as quickly in virtual reality as here. The concept must be empty because if it contained anything more elementary it wouldn’t serve its role as an elementary substance or building block for our picture of reality.

I would also not like to end up in a regress where I conceive of worlds within worlds to infinity, nor would I want to evoke God as Berkeley does (Berkeley 1988: 178).

However, we cannot talk about what laws operate beyond existence as we know it. A sentient being in a virtual reality alien to our own may find ours’ inconceivable; similarly it may be in vain to stretch a mind designed for this one to thoughts of what kind of reality created it. Settling with the argument that there is no more reason to treat this reality seriously than a coherent virtual reality should we find ourselves stuck in one such a reality would be real, and thus there can be a multiplicity of ‘real’ spaces.

Kant, I. (2002) The Critique of Pure Reason, trans. F. Haywood, London: Living Time Press

Quintin, A (1962) Space and Times in Philosophy vol.37, University of Southampton PHIL 2002 box 3

Uchii, S. (2003) Leibniz-Clarke Correspondence, Date Accessed 11/04/2006.
Available from the World Wide Web: http://www.bun.kyoto-u.ac.jp/~suchii/leibniz-clarke.html

Berkeley, G. (1988) Three Dialogues in R. Woolhouse (ed) Principles of Human Knowledge and Three Dialogues, London: Penguin Books,

Descartes, R. (2000) Meditations in D. Clarke (trans) Meditations and Other Metaphysical Writings, London: Penguin Books

Merriam-Webster Online Dictionary (2005), Dictionary definition for ‘Virtual Reality’ and ‘Virtual’, Date Accessed: 05/04/2006.
Available from the World Wide Web: http://www.m-w.com/

Despite the above consisting of merely the work of a graduate, nor a post-graduate nor any professional academic, I felt it was important to provide proper referencing information for anyone who might possibly require it.

I do this partly because I used to find it annoying to read pages online and struggle to find the information I required in order to reference the article, and partly because plagiarism is a very serious issue in many educational establishments.

Hence for the sake of the possibility of someone needing it, here would be a typical format for referencing this article. You should check with your university department in order to get precise instructions of how to format your bibliography.

Hankins, J. (2007) The Multiplicity of Spaces and Reality of Virtual Spaces, Available from the World Wide Web: http://www.skeletalroses.co.uk/html/articles/metaphysics_spatial_multiplicity.htm