Paradoxes of Motion and Space

Zeno's famous paradoxes of motion and space purport to show that motion is impossible (the arrow never moves) and that reality is not plural (space cannot be divided). In all discussions I have read on these puzzles a similar supposition is made: that points in space and instants in time exist.

Take the case of Achilles catching up with the tortoise. It is supposed that the gap between Achilles and the tortoise can never be closed because once Achilles has reached the point the from where the tortoise started it has moved on. But there is no starting point, halfway point, or point where the tortoise has moved to. Spatial points are approximations, convenient fictions imposed on the continuous fabric of reality by human minds.

In the case of the arrow which is at rest at each instant—there is no single moment of time. Again, the concept of 'instants' in time is a convenient fiction.

(see in this regard the work of Peter Lynds http://www.peterlynds.net.nz/)

Art, Perception and Indeterminacy

Paralysis. Oil on panel, 2005

This article considers the phenomenon of visual indeterminacy, which occurs when the sensory data gathered from the visual system cannot be integrated with semantic knowledge. A number of examples are given, including from the author's own art work, and some results presented from a scientific study based on them.

The implications for the operation of the mind and, in particular, the nature of aesthetic experience are addressed, and the distinction between the perception of visual forms and their cognitive interpretation is discussed. Arguments about the nature of aesthetic experience are then considered from some historical sources and interpreted in light of the distinctions between perception-cognition and form-content.

The paper concludes by summarizing the links between aesthetic experience, the operation of visual perception, and visual indeterminacy.

Read full article at Contemporary Aesthetics...

The Crucial Question

• Do you regard the perceiving mind as distinct from the world it perceives (trees, buildings, hats, etc.)?

• It is evident that the mind and world are not identical since we can imagine things that do not exist in the world (moons made of cheese).

• But if we accept that the mind and world are distinct, precisely at what point can they be separated?

• If you can’t identify at which point they become separated then you may be forced to conclude that they are continuous, effectively united.

• As we give this question more thought we are driven into accepting that the mind is both distinct from and continuous with the world it perceives.

• This in itself does not explain the relationship between the mind and world, but it is the best description we have of it, and if we want ultimately to arrive at an explanation it is preferable to have a better description to work with that a worse one.

• This is not a metaphysical question, or a least not exclusively so. It is a basic, practical problem that requires, and is amenable to, conventional scientific methods of investigation. The conventional scientific method, however, must embrace paradoxes, contradictions and ambiguities as essential components in our descriptions of reality, rather than logical flaws to be eradicated.

• There is a pragmatic imperative to arrive at a useful solution because all other problems relating to mind, consciousness, and reality supervene on this foundational question. Depending on which view you take you will make radically different assumptions and arrive at radically different conclusions.

• The world contains no boundaries other than those imposed on it by the mind.

• The mind cannot be separated from the world — they are identical with one another. So the boundaries apparent to the mind, which is part of the world, are also part of the world.

Painting and writing

Painting: A series of problems to be overcome.
Writing: You get better, but it doesn't get any easier.

World without mind

To doubt the existence of a world that is independent of the mind misses the point. Of course the mind brings the world into being, just as the world brings the mind into being: the case for a clear distinction between mind and world seems dubious. But it makes no sense to wonder about whether the world exists or does not exist without being perceived by a mind. 'It' neither does nor does not exist: categories such as 'existence' don't apply.

Variation and generation

Each new human is a variation of other humans, each new song is a variation on other songs, and each new painting a variation on other paintings.

Self supporting theory

It's risky to build one theory on the back of another (as aesthetic philosophers tend to do with Kant). For all its restrictions at least science demands we should test our ideas (even if in doing so we sometimes test for the outcome our theories lead us to expect). What philosophers can do is point out how complex phenomena are, which in many cases is far beyond the capacity of science to investigate. What science can do is show that what we might naturally assume to be the case is very often not; it forces us to reassess our intuitions.

How to stay ahead

It's tempting to measure one's progress against whatever is currently receiving attention. Just as our perception of reality is delayed by several hundred milliseconds (because of the time it takes the nervous system to process sensory signals) so what appears to be most contemporary is in fact already out of date. Better to look deep into the past and speculate far into the future, paying little attention to the present. You have to work very hard to remain interesting and unfashionable.

Paintings that look like photographs

• It is still impressive to see a painting that looks like a photographic depiction. But what is impressive? Imagine a machine that converted high-resolution photographs into oil paintings with great accuracy. How would we regard the resulting image — with more or less reverence than if the same image were produced by human hand? Most likely less because, it would be argued, it requires less skill and labour to produce the image by machine than by hand.

• (This argument would overlook the skill and labour embodied in the machine, which is still human skill and labour, albeit extended through mechanical means.)

• Comparing a two images of photographic precision — one generated mechanically and one by human artist — we would revere the one produced by the artist more than the one produced by the mechanical process. Why? because the human-generated one appears to contain more skill and labour. Thus what impresses us is the implicit skill and labour in the hand-crafted image, although both are visually identical.

• The quality that causes us to be impressed — the implicit human skill — is absent in the mechanically-generated, though visually identical, picture. This demonstrates the continuity between mind and world: we experience the world as ideas.

Between reality and representation

• All cognate (visual) experience is attended by memory. To sit on a beach and experience clouds, sand, water, rocks, is in each case to recognise these things and in so doing to draw upon memory resources, cognitive resources, that allow us to know where we are and what we are looking at.

• In this sense, looking directly at beach scene is no different from looking at a picture of the beach, insofar as each presents us with a set of visual cues that invoke associated memories, thus allowing recognition to occur.

• The enactivists argue the memory is 'out there', in the external world. The mistake here is to assume there is an external world.

• It would be wrong to suggest that memories are merely fixed units of information storage, which we simply 'call up' on cue. Memories are also being dynamically generated, 'on the fly' — our perceptual models are continually updated, adapting to new sets of cues.

Visual cues

• Presented with visual cues the mind constructs meaningful objects. The visual cues may bear little optical resemblance to the objects they depict, yet still decisively invoke those objects.

• In this sense, the process of identifying objects in the world is the same as identifying objects in a depiction: each presents a set of visual cues that the mind categorises as objects. We can be just as unsure or mistaken about how to interpret visual cues from the world as from pictures.

• The primary difference between seeing object in an image and in reality is that in reality we recognise objects more or less directly, that is without seeing anything else at the same time, whereas in pictures we recognise the object depicted, the medium of depiction (paint, ink wood), the vehicle of depiction (piece of paper, oil-covered canvas) — as well as other things: a Picasso collage, a cubist artwork, an modernist composition, etc.. In other words, recognition in depiction is multifold.

Artistic style influences perception

• Looking at a summer landscape on a cloudy day, seeing cows grazing and trees clumped in fields, after having looked at Constable oil sketches of the same subject, I was immediately struck by the way the landscape looked like the sketches.

• It is perhaps the case that each object or scene we recognise is an accretion or compound of numerous perceptions. When we recognise an image of a cow it is because we reference the accumulated experience of all the cows we've seen, likewise with a picture of a beach .

• It is perhaps the case that the most recent or frequent visual experience comes to predominate in our memory. So for example, if we spend a lot of time looking at Constable's images of summer landscapes of the British countryside then they come to 'stand in' for such a scene; they dominate the memory image. So when we come to look at the scene, say through a train window, we recognise objects (trees, clouds, cows) while referring to the most recent or frequent impressions.

• In a sense, the 'real' scene is just as much a representation as the oil sketch. Each is an image in which recognise particular entities, drawing on memories accrued over countless perceptual moments. The most recent or frequent experience determines the 'shape' of the memory that is brought into play when recognition occurs. I recognise the 'real' landscape at the same time as the Constable landscape - one is overlayed on the other.

Multifoldness in representation

• The visual system is a mandatory object recognition system. The visual field must be categorised into objects, this happens largely involuntarily and normally highly comprehensively.

• Although it is not known exactly how object recognition operates in the visual system, a great deal is known. It often occurs by 'perceptual grouping', that is, putting visual cues together to form clumps or groups that take on the value of object-ness.

• Normally all the visual data received by the system is categorised, assigned meaning based on memory, our vast accumulated experience since birth. It is fast and efficient, using a minimum of information to create a seemingly rich and accurate impression of the world (although easily prone to errors).

• All objects in the visual field must be classified. Once classified we make assumptions about them based on a massive storehouse of knowledge and experience (likely weight, texture, taste, volume, etc.). This is knowledge brought to bear from memory coupled to minimal visual data.

• When coming into the National Gallery, I recognise the gallery space, that I see a painting on a wall in a frame, that it is made of paint, that it is a cathedral and that it is a Monet. All these things I recognise (pretty much) simultaneously, one might take slightly more precedence over the other in terms of conceptual dominance, but none completely effaces the other. They all exist together.

• Thus the experience of looking at the painting might be termed 'multifold' (as opposed to 'twofold') since the object and environment are recognised at the same time the referential content is.

• One could say that the peculiar nature of pictorial representations is that one recognises at least two things at once (simultaneously). The material from which the picture is made and what it represents. If we are presented with sufficient visual cues then we have no choice but to recognise an object being represented. Yet we do not cease to recognise the substrate (except on very special occasions, i.e. Gijsbreachts and Gavin Turk).

• The peculiar nature of pictorial representations is that we recognise several things occuring coterminously, or coincidentally. When we see a fruit on a branch we recognise it as fruit in a straightforward way. When we see a representation of fruit on a branch we recognise the fruit, but also the medium of its representation — at the same time. We may also recognise the style, or the artist, or the significance of the picture, thus multiplying the richness of the aesthetic experience.

Not a part of the whole

The string becomes a knot, while remaining string. The knot is distinct but also part of the string, as well as being the string.

Boundaries

Divisions create conceptual difficulties. At its simplest one space becomes two, separated by a boundary, in this case a line. Three things are then present: the two spaces and the boundary itself. If the boundary has any width at all, then it also occupies space, with a boundary around its edge, which has no width and so occupies no space. If it occupies no space, then we cannot say where it is. Is the boundary part of the line or the space, or both? It cannot be part of the space because if the line is removed then the boundary disappears, so it must belong to the line. But what proportion of the line's width does the boundary occupy? None, since the boundary has no width. So even though the line itself is a boundary between the two spaces, it actually contains no boundaries in itself — at least none that occupy any of its surface area.

Externalism

Extended minds

Multiplicitous consciousness

Surely we are never conscious of one single thing at a time. To conceive any distinct entity is already to conceive a boundary, and any boundary creates two entities — one on either side. All thoughts must be multiplicitous, in the sense of containing more than one thing at a time; consciousness cannot be a monolithic unity.
(with thanks to Steve Thompson for pointing me in the direction of the original picture)

Art as intelligence

In appreciating art we respond to the intelligent arrangement of matter. It is not the material that is wondrous (art materials rarely are in themselves) but the evidence of a human mind embodied in the material's organisation. The greater the degree of intelligence the greater the art. From this it should be apparent that the mind is evident beyond the brain.

Absurdity as a virtue

The world is infinite, boundless, and indeterminate, yet is conceived by a mind that is divisive, limited, and compartmentalised, which leads to absurdities: contradictions, paradoxes, vicious circularities, self-referential regresses, these being generally eschewed by the rationalist European tradition of thought.

Attempts to arrive at a logically coherent explanation of our predicament that avoids these absurdities inevitably lead into philosophical cul-de-sacs. Better to accept the obvious conclusion: that contradiction, paradox, circularity and regress are essential attributes of the dynamic process of our conscious awareness, rather than being awkward or unwelcome anomalies.

Paradox of the Line

"A line segment can be divided, at least in thought, ad infinitum by halving it, halving the halves, and so on without end. So it must be made up of infinitely many parts. What is the size of these parts? If it is zero the line would have no length, if it some non-zero size, however small, the segment would have to be infinitely long."

From Paradoxes from A to Z by Michael Clark (Routledge, 2002)

Although the apparent absurdity here may appear to be the consequence of this being a purely conceptual problem (i.e. such a state of affairs could not exist in the real world, and is merely a philosopher's fancy) there is a valid sense in which the conundrum applies in real world situations too.

Think of a real line, drawn on paper or screen (like the one above). It appears to be of fixed and determinate length — something that would fit comfortably inside, say, and A4 sheet of paper. It appears such a line could be readily measured, but this is true only up to a point. If one zooms in on either end in order to locate precisely where it finishes, there is a problem insofar as the end will be 'fuzzy'. Whether made of ink or pixels, whatever material the line is constructed from will ultimately be composed of atomic and sub-atomic particles. Such particles, at the quantum level at least, have no absolutely fixed location. Indeed the more one zooms in to find the precise point where the material constituting the line disappears the less determinate the point will be. In other words, there is a valid sense in which the precise length of a physical line is indeterminate, literally of in-finite length, although it may fit easily inside a sheet of A4 paper.

Notes on the World and Mind

1. Science shows us that material objects have no absolute boundaries, and that reality at a sub-atomic scale is essentially indeterminate, insofar as the behaviour of quantum-level particles is probabilistic rather than deterministic.

2. We cannot determine precise boundaries around objects that appear to us distinct at our usual level of observation. Distinctions in the natural world are relative rather than absolute.

3. Consequently, the apparent distinction between ourselves and the world is not evident at the sub-atomic level (this is especially so if we take into account quantum non-locality).

4. If we allow that the conscious mind is (at least in part) a product of activity in the brain, and that the brain is composed of the self-same material that constitutes the fabric of the universe, then we accept that the material composition of the mind is continuous with the material around it.

5. If we allow that all structures appearing as objects have indeterminate boundaries, and moreover that in many respects they have no boundaries at all, then objects take on ‘extended’ dimensions, meaning effectively that they occupy an indeterminate (and possibly infinite) portion of space-time. Objects are continuous with what surrounds them.

6. If we accept the above we also have to accept that one of the basic attributes of the conscious mind is that it confers distinctions on the world — it renders the world as a mass of discrete objects.

7. We are so habituated to making distinctions that it seems entirely natural that the world is made up of bounded objects, while at the same time we know that such boundaries are an effect of our perception and cognition, not inherent attributes of the world.

8. The world is not inherently divided; the mind creates divisions; the mind is made from the same substance the world, so the mind is not divided. Yet somehow these divisions come into being (because we are conscious of them — they are real to us), even though there is no material support for them in the fabric of the world.

9. We arrive at a contradictory state of affairs: The world is not divided; the conscious mind is divided; the world and the mind are continuous with one another; it seems divisions do not exist and exist at the same time. Where are these divisions (that give rise to distinct objects)? One can say they exist in the mind, but the mind is made of material devoid of distinctions, including any distinction between itself and the world.

10. The situation can be expressed in the following paradoxical form:

The Paradox of Internalism
Internalists hold that mind and world are distinct because the mind exists in the brain and not in the world.
Yet clearly brains are part of the world (where else could they be?).
So mind and world are continuous.

The Paradox of Externalism
Externalists hold that mind and world are continuous because the mind is not confined to the brain but extends into the world.
Yet clearly minds are conscious while the world is not (otherwise doors would be conscious!),
So mind and world must be distinct.

Visual indeterminacy

Can you see what this is?

Taken from The Natural History of the Mind by Gordon Rattray Taylor (BCA, 1979)

Rattray Taylor claims, "I have shown this picture to scores of people, but have found no one who could see, without help, what it represented. Once they are told it shows a ... they usually have no further difficulty and then find it impossible to see the picture in the naïve way they did originally."

I was certainly one of those who couldn't work out what this is and it stands as a good example of visual indeterminacy, which occurs when we are presented with a vivid image that resists easy or immediate identification.

Between the Human and the Posthuman

Outline for a keynote to be given at the conference 'Between the Human and the Posthuman', Nottingham University in September 2007

In this presentation I will reflect on the fortunes of the term ‘posthuman’ since it first came to prominence in the 1990s, and what it might mean to us now.

I will look back to the period in the last decade when enthusiasm for new technology fuelled speculation about the potential of computers to augment attributes that had hitherto been regarded as uniquely human, such as creativity, imagination, intelligence, and consciousness. From computer science and science fiction came ideas about the enhancement, and even replacement, of humans with technology-based systems.

Looking at the intellectual landscape today we can see where some of those ideas remain influential and where some now appear misjudged. I will argue that in fact two quite distinct conceptions of posthumanism emerged in this period. One held that technology offered a way of overcoming human frailties and eventually supplanting us with a superior species. Another, which I will defend, sees posthumanism as symptomatic of a radical shift in our understanding about what it is to be human in the first place.

The limitations of human mind

"...the mind of man being finite, when it treats things which partake of infinity, it is not to be wondered at if it run into absurdities and contradictions; out of which it is impossible it should ever extricate itself, it being of the nature of infinite not to be comprehended by that which is finite."

Berkeley, A Treatise Concerning the Principles of Human Knowledge

Boundless

There is nothing before you as you do not begin
There is nothing after you as you do not cease to exist
There is nothing inside you as you have no boundary
There is nothing beyond you as you have no limit

• Do not think of the world 'out there' as something distinct from you. You are 'out there'. You are the world and the world is you.

• When Dr Johnson refuted Berkeley by kicking the stone he mistakenly assumed he and the stone were separate things.

Illusion

The Leaning Tower Illusion

Winner of the Best Visual Illusion Contest 2007

• What we see of the world is what we know of the world. Although the two images are identical the right hand tower seems to be leaning more "... because the visual system treats the two images as if part of a single scene. Normally, if two adjacent towers rise at the same angle, their image outlines converge as they recede from view due to perspective, and this is taken into account by the visual system. So when confronted with two towers whose corresponding outlines are parallel, the visual system assumes they must be diverging as they rise from view, and this is what we see."


(from http://illusioncontest.neuralcorrelate.com/)

Contradiction

Man A: You always contradict me.
Man B: No I don't.

If Man A is telling the truth then Man B is lying. But if Man B is telling the truth then Man A is lying. So they are both lying or both telling the truth. Or they are each lying and telling the truth at the same time.

The mind is the world

• If you accept a paradoxical solution to the mind-world problem then the consequence is a conception that is at once both very simple and beyond our capacity to conceive. The paradox being there both is and is not an external world that is both full and devoid of objects. Simple, yet inconceivable!

• The mind is a system that registers, records and retrieves differences, but in doing so creates those differences.

• One is relieved of agonising over the status of the mind-independent object if one accepts the coincidence of the mind and world. The mind does not reflect differences in the world, the mind is the differences in the world.

• Mind moves through distinction and association (how?). Understanding a sentence requires that we hold both the distinct concepts associated with each word and the combined meaning they produce together: “The big red hat’. In this we understand scale, object-hood, colour — each distinct yet all combined.


• The fact that a visual scene (like the one above) contains both discrete objects and a unified field is seemingly so obvious that we skim over it. But considered in its fullest implications this contradiction is excessively difficult to hold in our mind, which is perhaps why we skim over it.

• A collection: Something that is simultaneously a singularity and a multiplicity.

• It is important to discover how the brain sustains differences, i.e. how difference is encoded in the organic structure.

• There is a valid sense in which prior to human consciousness there were no stars, planets, trees, rocks, etc. (one of the objections often raised to point out the absurdity of idealism). Such objects only come into being at the point they are understood as objects by minds. Likewise, in the case of the tree falling in the uninhabited forest, there is not really a tree or a forest, nor any sound, since these attributes require a mind to exist.

• The error is to think existence precedes or transcends mind. Only if you hold on to this do you wonder how things can continue to exist when no-one is perceiving them.

• The mind is like a torch shining into the dark. Whatever falls into the path of the beam comes into existence. What we take to be the external object, however, is actually the reflected light originating in the mind. In a sense we only perceive the activity of our own mind (standard idealism). We have to abandon the idea that there is something ‘out there’ separate from the light reflected back to us (things in themselves). The light reflected is the object, it creates the object's existence — its 'thingness' — which is another way of saying the mind is the world.

External world

• To perceive is to remember, to recognise — know again. We cannot perceive what we don’t know or remember. Everything we perceive we will seek to categorise according to our memory. We have to learn to see. When we recognise an object in a picture we do so because we remember the object depicted, but we also recognise the substrate of the picture — the material it is made from —and it’s cultural context (old, modern, high art) as well as its meaning (fear, emotion, humour, sarcasm, violence). That is, we perceive and remember several things at once, but all are imagined.

• The Unity of Consciousness. If consciousness were unified we would not be aware of differences. Consciousness is the sum of distinctions.

• Perception is an act of imagination.

• There is no word or phrase that describes the state of reality as it really is, rather than as it appears. The world is both full of objects, things, systems, relationships, and at the same time it is completely devoid of these. It is not neutral, since neutrality implies neither one state nor the other, and since both states pertain it is not neutral.

• Because the mind is reality — is nature — not something separate, it has the same generative possibilities for creating novelty and the same structural limitations.

• When people argue about the existence or not of an external world, one has to ask ‘External to what?’ The head? The brain? Part of the brain (remember mind can continue even if parts of the brain are removed)? A group of cells? A specific cell…?

• A notion of externality would require some knowledge of the precise location of the perceiving subject. Since we don't know precisely where the conscious self is located (many assume the brain, but even here it is not known exactly where) we cannot know where the boundary between the 'internal' and 'external' lies. Nor do we even know if there is a boundary.