Paradigm shifts, perspective, impressionism, epistemology


What I want to talk about today is Kuhn’s concept of paradigms and paradigm shifts.  This much-misunderstood theory of science is often popularised as claiming that science progresses not by orderly development and deduction from evidence, but rather as a form of beauty contest, with current orthodoxy being that which happens to be most popular.  It need hardly be said that this view is rather popular with those who wish to claim that science is merely another form of culturally-derived dogma, and has no special epistemological status.  However, it is entirely at variance with Kuhn’s position.

Kuhn claimed that the paradigm at any moment is the world-view that scientists use when attempting to understand the universe around them.  At intervals that paradigm shifts and a whole new world-view arises, which supersedes the old one by being better at describing the universe.  But this new world-view requires a new set of conceptual apparatus; in Kuhn’s, again often-misunderstood, words, it is incommensurable with the old world-view, in that there is no easy mapping between its world of ideas and that of the old.  And so its acceptance is not an immediate process, as there is a need for familiarisation with and translation to the new way of seeing things.  Thus the sociological aspect of the theory does not question the nature of scientific truth, but is about how people react when their world-view shifts, forcibly or otherwise.

This set of ideas, particularly the notion of incommensurable paradigms, is rather tricky (which is why it is so widely misunderstood), but it is very reminiscent of  my concept of epistemic barriers, for they too describe world-views which are so different in the way they describe the universe that there is an effective barrier to communication between them.  So my goal in this essay is to explore this relationship with a view to providing a clear statement of what it means to say that there is, has been, or is about to be a paradigm shift.

I am aware that part of the problem with popularisation of Kuhn’s theory is that it is not clear to the lay-person why (say) the shift from pre-relativistic to relativistic physics was such a jolt, and little attempt has been made to explain it.  Therefore, my discussion will take examples from the history of art, specifically two major changes, that is the introduction of perspective and impressionist approaches to colour.  Both of these are paradigm shifts, and both can be described very naturally as sudden expansions of the formal language of art.  So once again we will see a link between paradigm shifts and epistemic barriers.

So this essay is organised as follows: first I will talk about my two examples, giving the art-historic background.  Then moving to looking at them in terms of the flow of ideas, I will draw out the key features of the transitions that they embody in order to arrive at a model for what a paradigm, and a paradigm shift might look like, and what incommensurability might mean.  Having established Kuhn’s terms, I will then look at them in terms of the theory of information flow provided by the concept of the epistemic barrier, with a view to reformulating Kuhn’s terms within its epistemological language and thus making a precise definition possible.

Paradigms shifts in the plastic arts

Example 1: perspective

Egyptian HuntingIf we look at early art, though there are occasional attempts at creating a three-dimensional effect, the artists generally seem intent on communicating an idea that on producing a perfect reproduction of things as they are (or, rather, as we perceive them to be).  The goal was a poetic truth rather than the literal truth of the senses, so art was not a scene, but rather a collection of image that conveyed the ideas that the artist considered important.

For example, consider the fine piece of Egyptian art reproduced here.  At first it looks like a typical hunting scene.  But then, why are the three figures of wildly varying size?  And why is the lady wearing the Egyptian equivalent of evening dress while on a hunting trip?  And what sort of person takes his pet duck with him when he’s going out to hunt – other ducks?  And, of course, the answer to all these questions is that if you even ask any of those questions you are looking it the image with the wrong mind-set.  In this case, we’re lucky in that the image comes (as you can see) with commentary, so we know the artist’s intent.  However, be reassured that this is not an exception; rather the, to us, unconventional conventions it displays are the norm across Egyptian art (and yes, it does say that the duck is a pet).  So, the piece is intended to show how manly and generally spiffing is the man who is the central figure, what a fine man he is, as shown by his vigour in hunting.  It’s his tomb and his afterlife, so he’s bigger than his wife, not because she was a midget, but because he is the subject of the piece, and therefore the most important object in it.  Now she’s all dressed up because obviously you want to look your best in the afterlife, don’t you?  This is an art of idealisation, not representation.  And as for the duck: well, obviously he was fond of it and wanted it to be with him in eternity.  All of which means that the image is not a picture of a real event; it represents the hero’s aspirations for the kind of afterlife he wants to live.  Hunting (in the form depicted here) was, of course, a pastime of the upper classes, so it is very clear that he has no intention of being a mere labourer in the land of the dead; he will live the life of the elite, as an obvious corollary of which he has a sexy trophy wife  and a duck he loves very much.  Note that, by Egyptian ways of thinking, even if his wife was not, in reality, a sex-bomb, the mere fact of her depiction as one within the tomb would make her one in the land of the dead.  So the image is not just a statement of desire; it is a magical machine that makes that desire a reality.  The image contains a wealth of information that our mind-set puts us in danger of losing, leaving only incomprehension.

Alfred WallisAs a second example, consider this piece by Alfred Wallis, the famed naive painter of St Ives, discovered by Ben Nicholson.  Naive art is another field where perspective is used only rarely, but it is a grave mistake to think, as do some of the more patronising among us, that this stems from technical incapability.  In the case of Wallis, as with le Douanier Rousseau, ability was not an issue because perspective was not a part of the world view they presented.  They did not represent things as they were, they presented them as the ideas they embodied.

Looking at the painting, to our eyes, accustomed as they are to art which simulates the third dimension, there is something weirdly wrong with Wallis’ composition.  If we take it at face value, we have a number of normal-sized houses in the midst of which is a positively Brobdingnagian building.  Vertically above this a giant thing that can only be a headland, only we are seeing it from above, which is impossible, juts out into a strange sea, a sea which embraces the roof of the mansion and has waves whose swell is larger than the boat which appears to be suspended in mid air.  Now, I am not satirising Wallis here; rather, I am trying to represent in words just how unsettling his image appears if one approaches it from within a mind set that expects to see correctly worked-out perspective everywhere.  But now we need to consider not how this looks to us, but how it looked to Wallis.  Start with the headland: this is a feature of St Ives known as ‘the Island’; Wallis knew what shape it was, and what mattered was showing it in its true nature.  In this he followed the same principle as the Egyptians and much pre-modern art: what mattered was presenting the essence of the thing rather than the way the thing looked.  The giant house is a real building in St Ives that Wallis often painted; again, as with the Egyptian piece, its size is exaggerated because it is the focus of the piece, and it has to be large so we can see all the fine detail that makes up its essence.  In addition, Wallis has conflated the topography of St Ives so as to bring together a house and a headland that are actually separated by a length of beach, but that is no matter, because the painting is about the Island and the house, and not the beach, so the beach is reduced to a bare minimum.  What matters is that the two key ideas are seen together, associated, as they clearly were, in Wallis’ mind.  And finally, the other houses, less significant, are real houses near the central house, but rearranged (and they are arranged differently in each painting featuring the central house) so as to create specific emphases and structures around the focus.  Therefore, for Wallis the space of the image is not simply a replica or simulacrum of the three dimensional space of St Ives; rather it is a conceptual space, in which he arranges ideas of things, rather than the things themselves, so as to create the overarching idea that constituted his vision for the piece.  In this, his approach is almost identical to that of the Egyptians: art communicates an idea by showing things as they should be, or need to be, rather than as they are.  Space is the servant of the artist, not the master.

Dora MaarAs a final example I want to look at the process of unlearning perspective that occurred in the twentieth century.  This is one of Picasso’s many portraits of Dora Maar, and it is immediately apparent that though perspective is present, in that there are some three dimensional effects, each segment of the image has its own vanishing point, its own rules, its own three dimensional space, and these spaces are related only by the image’s internal logic; there is no over-riding reality, at least not in any photographic sense, though one can (and I will) argue that there is a higher reality at work.

The key to understanding this painting is the realisation that Picasso was not painting a woman badly, or deliberately distorting her.  He did not start from her face and say to himself ‘how can I make a funny shape out of that?’  Instead he saw her head and upper body artistically as a number of geometric units, each of which has three-dimensional form, but existing distinctly from one another.  As an analogy to aid understanding, consider Quine’s famous example of the rabbit.  You and I see a rabbit run past and I say ‘gavagai’.  You naturally assume that when I say ‘gavagai’ I mean ‘rabbit’, but in fact, I might mean by it ‘an assembled collection of specific body parts’, and you would have no way of knowing that my meaning was different to yours, because whenever I say ‘gavagai’ you will say ‘rabbit’ and vice versa.  Likewise, you or I might see a woman as a single three-dimensional object, but to Picasso, looking at her as an artist, she was a toolkit, a menu of individual three-dimensional components that he could turn into an artistic object.  But, unlike the case of the rabbit, we can see into Picasso’s world via the images he made for us, even though they present us with a grave conceptual challenge.

And so, Picasso takes this ensemble of components, each independently having three-dimensional form, and has then attempted to represent them as he seems them in a two-dimensional medium, in the hope of communicating to the rest of us something of his vision.  But now, as each component is an individual, they have their own three-dimensional structure, and their own perspective when rendered into two dimensions, and so there is no unified perspective or view-point.  This means that we seem to see a congeries of units of the woman, each seen from its own view-point and with its own perspective, but that was not necessarily part of Picasso’s intention.  The intension of this painting is the vision of Picasso’s artistic eye, that vision of a form of forms, each a living thing in its own right, and how those forms interact to create what the rest of us see as only one form.  It gives us a glimpse into Picasso’s reality, showing the form behind the outward appearance.  And so, again, it is more than just a woman, it represents the complex of ideas created in Picasso’s mind by gazing on that woman, the execution of which requires a move away from traditional perspective-based art.

Example 2: impressionism

Cezanne Bathers

Another convention of modern Western art has been the use of colour in a ‘naturalistic’ way, representing things as having the colours we see when we look at them, so skies are blue, grass is green and dandelions are yellow.  Like perspective, the whole purpose is to give art a greater realism, so its business is clearly that of representing objects as accurately as possible in just the way that the eye would see them, so as to leave no ambiguity about what it is that the viewer is looking at.  And just as the cubists smashed perspective, aiming to represent the idea of the thing, rather than the outer form of the thing, so the impressionists smashed the tyranny of chocolate-box colour.

As my first example, I want to look at Cezanne’s Bathers.  One thing is obviously missing from this piece: perspective; depth is created by masses of colour lying in superimposed planes rather than by any formalistic use of vanishing points.  As a result, a ‘normal’ sense of depth is missing, instead we feel the image as hanging in a space of its own creation where form is defined by colour rather than any conventional geometry.  And looking again, we see that even forms have severed their link with the objects they represent; the three foreground women have utterly unrealistic shapes, as does the woman standing at the left, but their point is not to create photorealistic images of naked woman.  Anyone could do that.  What Cezanne did was to use paint and colour to show the mass and the depth of bodies as things seen in light, with their exoteric or real form only the starting point of his attempt to portray their sheer physicality.

GainsboroughBut now look at the use of colour, especially in the sky and the trees on the left-hand side.  In the trees we see something quite revolutionary: colour is no longer a decoration or property of the forms depicted, it is the forms.  The forms and shapes of the trees have dissolved, leaving behind only patches of colour, and yet in this totally non-realistic depiction we sense the depth, the mystery of the woods and feel an emotional effect far greater than anything a strictly realist depiction could achieve.  As an experiment, look at the picture of Gainsborough’s Mr and Mrs Andrews which I have deliberately rendered in greyscale.  Something is lost, but the composition and its structure and out knowledge of its forms remain intact, as does the interesting contrast between the general pastoral tone and Mrs Andrews’ manner of comporting herself.  Now try to imagine the Cezanne in greyscale; instead of a complex of emotions and ideas, the greenery would evince only muddle.  So Cezanne has achieved a breakthrough in that now colour and form are one and the same.  And, even more importantly, paint and form are one and the same.  Cezanne’s colours are not applied in naturalistic shapes, they are applied in the shape of his brush.  The medium, the technique, the artist, the idea and the content are merging into one another.  The same, of course, is true of the sky.  Those extraordinary dark blue blobs have no ‘real’ function, but they create a sense of the depth and emotional complexity to be found even in a clear sky that no photographic or ‘accurate’ depiction could.  Art has shifted from simple representation to being a way of communicating ideas that could never put put into words.

MatisseNext I want to look at one of Matisse’s portraits of his wife, noting that we are now squarely into neo-impressionist territory.  As with the previous example, colour has become almost entirely non-functional; it is plausible that Mme Matisse was wearing a green blouse, but it is not at all plausible that the green of the blouse should spill across onto part of her neck.  And looking closer at the greens, on the blouse and the chair-back we see that there are two groups of green – strong and weak – and Matisse moves between them in a way that makes no sense at all in terms of the play of light or shadow, but which creates a kind of depth without actual physical depth, for of perspective there is not a trace.  Also worth noticing is the way that on the left hand side the chair-back is solid, in that there is a mass of white-green between the spokes of the chair, while on the right hand side we see straight through to the mysterious blue background.  So while the left hand part of the chair is  massive block that seems to cohere with the background, the right hand part floats serenely in a mysterious space that seems to have dimensions completely unlike the three we are used to.  This dichotomy is, of course, paralleled in the depiction of Mme Matisse’s body, where the left side is dark and heavy and seems rooted in the chair, while the right side is lighter and floats in front of the chair, it’s lightness emphasised by the massive black triangle of the collar.

And between these two mysterious spaces, one earthbound and unified, the other light and clearly separated into distinct things, lies the face.  Passing over the fact that it is grey, the key thing here is that Matisse has made no effort to actually portray his wife.  What we see is, instead an idealisation of femininity, a Platonic essence of woman, created from a minimal structure of lines and curves, with no detail or redundancy.  The face could never be that of a real woman, and yet in it we see all real women, rendered with a serene beauty that any degree of realism could only spoil.  And so we see this face, reminiscent perhaps of the strangely inhuman sculptures of the Cyclades, unifying weight and lightness, darkness and light, mass and space in one perfect expression of what it is to be human.  No representational painting, let alone do it without use of allegory or imagery: Matisse creates his luminous image purely out of masses of colour, and thus stands at the ne plus ultra of Impressionism, the last point at which any vestige of representation was possible.

Once again, therefore, we see that by passing beyond simple realism the artist can convey sophisticated concepts without the need for labels or subtexts.  Matisse was not painting his wife, but the idea that the image of his wife created in his mind, and doing that required going one step beyond the conceptual realm of the artistic conventions of his day.  To those versed only in those conventions, his work must seem mysterious, even nonsensical, but once one accepts that he has no ambition to realism, and thus that his painting is not a failed photographic portrait but a successful conceptual portrait, meaning and ideas become available that one could, before that acceptance, not even know were there.

Gwen John

As my last example, I want to take Gwen John’s Terrace in Moonlight, Meudon.  This is at the opposite extreme of impressionism to the Matisse, in the here, rather than colour crystallising into forms, forms dissolve into mark on canvas.  We can see the painting in three ways.

First there is, indeed, the view of a terrace, with a mysterious sky against which rise stones on the horizon.  This image is deeply puzzling because the objects we think we see – the tree, the stones, the path trees, seem to exist in isolation from one another.  Rather than being unified to form a field of view, they hang, suspended in no-space and apparently superimposed with no concern for order or realism.  Indeed, they seem to have even something of the Egyptian approach to depicting objects, each seen face on, so as to emphasise its individual nature, and coexisting only by virtue of those relations which the artist decides to imbue them with, rather than those forced on her by mundane reality.  So, on this level, where on the right hand side we see what we could take as two trees, one passing in front of the other.  But that is not what we see: we see a single entity that bifurcates, standing proud above the plane of the wall and ground, while other ‘trees’ lie within that plane.

Second, we see forms, limned by black lines which fade in and out of existence.  So there is a horizon, there are the blobs that may be rocks, the wall and the massive triangle of the central tree.  These seem to begin to make an effort at breaking up the unity that is the mass of colour, and turning it into what we might perceive as recognisable objects, as if the true reality is the colour, and the forms are that which our minds, schooled in thinking of solid three-dimensional objects, try to impose on it by way of structure.  And yet, as I noted, the lines are not uniform.  In places they almost vanish, and at times they become huge swathes of black.  As a result, none of the forms of the imposed order have any deep reality.  They merge into one another in an endlessly shifting symphony of colour where form leaches into form, one moment of which John has captured for us.  Therefore the painting, in spite of being a representation of a wholly static subject, is dynamic in the extreme, being but one glimpse of an ongoing conceptual process.

Third, we see the mass of colour, no longer the subtle gradations of representational art, or even the complexes of colour of Cezanne and Matisse.  Rather we see colour at its most elemental, reduced to brush-strokes, each of which conveys nothing in itself.  So in one instant we see hundreds of isolated, meaningless brush-strokes, but in the next we see them come together to makes those forms that we, with the guidance of John, discover within them.  We see an emergent structure that is not present in its parts, and yet is present in their totality, just as there is nothing in any one cell that can be seen as being human, and yet in their communion humanity is born.  John has emancipated colour, so now her message lies not in the way that colour serves the forms, but lies in individual marks on canvas, each clearly identifiable as a mark on canvas, and the ‘subject’ of the painting is not the ostensible subject, but rather the way that John uses it to create near abstract structures that play off our ideas of reality in order to help us take the plunge into the deeper realities lying in the gaps between the marks.  One might say that whereas the surrealists tried to use photo-realism to depict the results of their  delvings in the unconscious, John shows us the royal road to understanding the unconscious and making it part of ourselves.  Realism is left far behind.

Paradigms, paradigm shifts, incommensurability

What is a paradigm?

Rather than state Kuhn’s definition and then try to force my examples to fit it, what I want to do is explore the artistic examples described above and look at them for something that one might call a paradigm.  This approach has to dual advantage of both validating Kuhn’s approach, by showing that unprejudiced examination of art history can reconstruct it, and critiquing it, by indicating places where it needs to be sharpened or modified.

In the cases I have described there are clearly several views as to how one should look at art and what the function of art is.  For example, you could look at the Matisse portrait and observe that people don’t have grey faces, dismissing it is obviously not being a good portrait.  Likewise you could look at the Wallis piece and complain on any number of grounds: that the scales of things are wrong, that the land is hanging in mid-air about the house, that boats tend to be larger than waves.  And so on for each of the paintings I have discussed.  In each case you would be missing what I have claimed is the true content and intent of the painting, but that’s not what matters here.  I am not claiming divine revelation, so your objections on grounds of irrealism are just as valid as observations about the paintings as are my rhapsodies to irrealism.  You would have a valid, consistent, coherent world-view according to which the only piece of art that I have discussed that is successful is Mr and Mrs Andrews, just as I have mine, in which all of the pieces are successul in their own way.

So it seems there is not one overarching theory of aesthetics: we seem to have three:

  1. Realism.  Art is an attempt to render the world as we perceive it in as precise a way as is possible given the constraints of the medium.  Certain artifices (e.g. perspective) are agreed on as tools that are used to achieve this.  Art is judged based on its ability to do this, as well as by qualities that the artist conveys by their arrangement of the objects depicted.
  2. Formal irrealism.  Art is an attempt to render the ‘thing in itself’, the reality underlying the outward appearance of objects.  The objects are arranged and portrayed in such a way as to represent those of their features that the artist wishes to emphasise, and their relations to one another.  Art is judged based on its ability to connect to the viewer at a visceral level, creating a vision of the thing in itself.
  3. Structural irrealism.  Again, art is an attempt to render the ‘thing in itself’, but now objects lose their individual status, merging together to form larger structures, and are portrayed in such a way as to make those structures emerge.  Art is judged based on its ability to show the wider reality that underlies the thing in itself.

The key point here is that each of these theories is quite sound in itself.  It is not that realism is right and formal irrealism wrong, or vice versa.  Rather, each provides a valid way of looking at and understanding art.  Call such a body of theory a paradigm.

What is a paradigm shift?

So we now know what a paradigm is: it is a way of looking at something, art in our case, but it could be physics or theology or whatever, that makes sense, is internally consistent, and provides a comprehensive model for understanding what you see.  So what happens when the world changes, when a Cezanne starts to paint masses of colour rather than things, or you first discover a Wallis?  The realist paradigm worked pretty well until the final decades of the twentieth century, but then it began to break down as more and more painters started to reach beyond its bounds in the attempt to represent a message that no longer lay in the interaction between the viewer’s cultural apparatus and the way the things depicted were shown relating to one another, but in the things themselves.

Mr and Mrs AndrewsGo back to Mr and Mrs Andrews.  His carefree posture with gun and dog shows that he is trying, perhaps a bit too hard, to be at ease as a member of the landed gentry, but the slight, but definite, dissonance between the countrified setting and her dress raises a question about how successful this is, a question reinforced by the slight, but definite, ‘come hither’ quality in her expression.  Gainsborough quite neatly fulfils his commission and lampoons pretension at the same time.  But none of this is really inherent in the image itself.  The painting tells us a story, but it does this by making us think about things outside of it: our expectations for country gentlemen, for well-mannered wives and so on.

A Battery Shelled

Compare this with Wyndham Lewis’ A Battery Shelled.  Now the painting exists in and of itself: it represents a mysterious world with a crumpled ground in which part-human figures labour while super-sized humans look on while the cosmos exists as mighty structures in the sky, if it is a sky, indifferent to the insects beneath.  Lewis is not interested in showing us some things and then pointing out to us some of their more interesting features.  He has captured a moment and is trying to convey to us the emotional content of that moment directly from his painting.

What then is to be done?  There are three possibilities for dealing with this defection of artists from the established paradigm.

  1. Ignore them.  This is very, very easy to do, but helpful only if the movement away from the established view is brief and a return quickly follows.  All that happens as a result of ignoring them is that those doing the ignoring end up in their own little ghetto, isolated from future developments and unable to comprehend them.  And this is, to be honest, exactly what we have seen in some cultural conservative circles in art, with the likes of the ludicrous Alfred Munnings bravely proclaiming that post-realism was just a passing fad.  It also happens in, say, physics, where there are still cranks who proclaim that Einsteinian relativity is all wrong.
  2. Try to accomodate both points of view.  This seems very tempting, but it is doomed to fail.  The reason is fairly easy to see: what kind of aesthetic theory is there that can simultaneously embrace Gainsborough, Wallis and John, all of whom have their own great merits?  How can one reconcile commentary through accurate depiction with blazing a way to the immanent other?  Any such theory would end up being so general and so attenuated that either it would be useless, or else it would, by force majeure turn into several separate theories masquerading as one, in which case we are in the third scenario.
  3.  Accept that the paradigms are both equally valid.  In this case we accept that Gainsborough, Picasso, Matisse and all the others are great artists, but no one body of theory can be used to approach all of them.  We need a new paradigm to understand the new art, different from the old one.  That does not make the old one invalid, as it works perfectly for realist art, but it fails to work for the new art, and that is where we need a new paradigm.  In fact, if we look at option 1, it is clear that it is just a special case of this option, consisting of those individuals (of whom there will always be some) who refuse to acknowledge the new paradigm.

Looking at the process that has occurred, what happens is something like this.  We started in the realist paradigm and carried along, most of the time able to exercise option 2, extending the paradigm to incorporate new developments.  But there came a point where artists, in their quest to represent their vision, moved so far away from the realist model that option 2 was no longer available: the disparity between what they painted and what the paradigm expected was just too great to be accommodated.  And at this point a paradigm shift happened: the only way to describe the new art sensibly was to create an entire new paradigm that acknowledged that it was separate, and was a new kind of art, different from realist art.  The paradigm shifts when facts on the ground force the acknowledgement that existing descriptions no longer work, and that a whole new way of looking at things is required.

What is incommensurability?

So, let us say a paradigm shift has occurred, so I now have two paradigms (for sake of argument): realism and formal irrealism.  Above I wrote some words about three formal irrealist pieces; the question is, are my words meaningful within the realist paradigm?  Well, obviously their semantic content remains, but the answer has to be no: the criteria I am using to make my judgements simply have no meaning within the realist paradigm.  Viewed from within realism, Wallis’ paining is simply bad, and everything I have to say in its defence is simply meaningless.  Indeed, following up on that point, it’s not just critical language that becomes meaningless when we switch paradigm; the art itself becomes meaningless.  Without the irrealist concern for the thing in itself, the Egyptian tomb painting is incomprehensible.

It’s not hard to see why this happened.  Remember that I said that a paradigm shift happens when the existing paradigm is stretched to the point where it can no longer contain everything within it and yet remain coherent, so all it can do is split asunder.  So a paradigm shift occurs precisely when it is no longer possible to present a single viewpoint within which everything we are looking at is comprehensible.  Which, inevitably, means that after the paradigm shift, one of the paradigms cannot comprehend the other, for if each can comprehend the other then there would have been no reason for the shift to occur.  So a paradigm shift creates a barrier to comprehension in at least one direction.

This makes sense.  If I a come to a gallery with a conception of art based on Gainsborough, and find myself confronted with Picasso’s portrait of Dora Maar, then it will indeed be incomprehensible to me.  Now note that I am not saying that this means I will inevitably dislike it.  No, the point is that it will be something entirely outside of my current conception of art.  That doesn’t mean that I cannot feel the shock of the new and discover the new paradigm within myself, merely that I will have to do so, that or decide that I want no part in it.  What I cannot do is look at it and appreciate it on the same terms that I would appreciate Mr and Mrs Andrews.  So the realist and formal irrealist paradigms are incommensurable.

In this case we have concluded that it is impossible to describe or appreciate art of the new paradigm from within the old paradigm.  The obvious question is, is this always the case?  What (if any) are the rules governing incommensurability?  Well, say we have two paradigms, A, which is the parent, and B, which is the child.  Clearly each can comprehend itself.  Also we have seen that at least either A cannot comprehend B or B cannot comprehend A.  Can we say any more?

It turns out we cannot.  There are three possible cases:

  1. A fails to comprehend BB comprehends A.  The process of forming a new paradigm certainly involves additions to the vocabulary, whether of art or science: new tools, techniques, concepts.  However it is not so clear that it requires one to reject what one already knew before the paradigm shift.  It is entirely possible to view realist art from, say, a cubist perspective, looking beneath the surface to the work of art as a thing.  It can bring fresh insights and fresh ways of executing realist art.
  2. A comprehends B; B fails to comprehend A.  Once the perspective paradigm shift had occurred, earlier art, like our Egyptian example, would be more or less incomprehensible: certainly much of its meaning would have been lost, because its notion of art as symbol of deep reality would have been incommensurable with the realist paradigm.  However, there is no obvious reason why realist art should not be comprehensible from within the older paradigm.
  3. A fails to comprehend BB fails to comprehend A.  In this case that comprehended both of them but which they could not comprehend.  There is some evidence suggesting that such situations can occur; I will discuss some possible examples below.

Therefore it seems that all cases are possible, and so the concept of incommensurability needs to be refined to take account of information flows.

Paradigms and epistemic barriers

Epistemic barriers demarcate paradigms

I discussed the concept of an epistemic barrier at length in another essay, but for convenience I will recapitulate the key notions here.  An epistemic barrier arises between two communities when their conceptual schemes are so much at variance with one another that reliable communication between the two communities becomes an impossibility.  Note that this is nothing to do with the language used to communicate, but is about the concepts that are being communicated.  Indeed, it is entirely possible for an epistemic barrier to exist where no linguistic barrier exists.  Community A might have within its group world-view concepts that simply don’t exist in community B‘s world-view and which therefore could not be communicated to community B in any language.  It is not so much a matter of only being able to know things you have a word for, as of only being able to know things that you are prepared to know about.  That is to say, you need, as it were, a mental pigeon-hole of the right shape to fit an idea if it is to be successfully communicated to you.

Now this is not to say that any new idea creates a barrier.  Obviously many new facts exist that fit entirely within our conceptual framework and do not require a major change in the way we ourselves conceive of knowledge.  As above, the barrier arises precisely when the new ideas are so far from those we are used to that they simply cannot be expressed in terms of those that we are used to, and so cannot be communicated using existing terms.  What is required to comprehend them is a substantive conceptual shift, a deliberative act of extending the world-view.  Our usual, incremental process of assimilating new information will not work.

All of this will look very familiar, for the good reason that this is just a slightly more abstract way of looking at the ideas we’ve gone over above.  The merit of this approach, however is that it lets us study more precisely what happens at the points of intersection, where paradigms abut one another, and how information does and does not flow between them.  Moreover, the definition of an epistemic barrier is, in philosophical terms at least, reasonably precise, in that it can be modelled quite precisely, whereas that of a paradigm is, perforce, somewhat woolly, as it ends up having to assert, more or less, that we know a paradigm shift when we see one.  In fact, as I will show below, this is not necessarily true.

So we can (at last) define a paradigm more or less rigorously, by saying that it is a region in epistemic space, that is to say a collection of ideas and concepts, and its boundaries, that is to say, the points beyond which one cannot go without a change of world-view, are defined by epistemic barriers.  Of course, this definition is complicated by the impossibility of firmly locating a barrier.  For if one could say where the barrier was, that means one could tell precisely how far one could go conceptually, which means one would then know precisely what one couldn’t know, which is impossible.

This systemic vagueness is actually quite reasonable in terms of what we know about paradigms in real life.  For example, Mr and Mrs Andrews is clearly realist, the Picasso portrait is clearly irrealist, but what about this Cezanne landscape?  Is it realist or cubist?  It seems to be one of those liminal cases that could be claimed as either.  In general we can tell which paradigm most art belongs to, but there will be a group of works that could be in one or the other, and it is impossible to come up with a consistent classification.  This well-known vagueness, which applies in all fields, not just art, this difficulty of classifying the liminal cases, is precisely the real-world evidence of the philosophical claim that the location of an epistemic barrier is unknowable.

The anatomy of a paradigm shift

One advantage of the epistemic barrier approach is that instead of seeing a process where paradigm B replaces paradigm A, we can look at paradigms as areas of epistemic space separated from one another by epistemic barriers, seeing them in the round, so a paradigm shift is less about creating something new than about finding a way to explore a region of epistemic space that was previously accessible.

So, the starting condition, before the paradigm shift occurs, is that I am sitting in some region of epistemic space, which is to say that I have a collection of thoughts and concepts that I am able to frame in my mind and communicate with others who are in (roughly) the same place.  Now, as we’re discussing the case in which a paradigm shift occurs, that means that somewhere in my neighbourhood there is an epistemic barrier, though I can’t say precisely where, as described above.  Of course, nobody stays in the same place epistemically; we learn and think and expand our knowledge and the range of concepts within our world-view, and this means that my location in epistemic space shifts.  Now say I happen to shift towards the barrier.  At some unknowable point I will cross the barrier.  This is important, so it’s worth considering in detail.  The epistemic analysis allows us to understand what happens in much greater detail than the simply binary apposition of the paradigm approach.

Initially I am safely within the same world-view as my peers: I am in paradigm A.  Now, as I extend myself, gradually I will find myself entertaining more and more concepts that I cannot share with my peers, and I may start having difficulty understanding them, because my new thought-patterns render theirs increasingly incomprehensible.  So a conversation with one of my erstwhile peers may be like talking on a noisy phone line, with more and more noise occurring, until eventually mutual comprehension breaks down, at which point the paradigm shift has occurred, and I am now in paradigm B.  But the point to note is that there is no clear dividing-line, no clear point at which I can say ‘there we became incommensurable’.  Rather, in one or both directions, communication degrades gracefully from perfect to non-existent.  And likewise, mutual communication with those already on the other side of the barrier now becomes possible.

That’s what it looks like to me.  What does it look like to those I have left behind?  There are two cases, depending on whether the barrier is total or partial.  The distinction is based on whether the barrier applies to all or part of one’s world view, and hence affects all or part of communication with those in paradigm A.  The point here is that in some cases, for example artistic judgement, the fact that I and you are now separated by an epistemic barrier on matters relating to art does not force us to be separated when discussing, say, physics.  The barrier in this case affects only those parts of our common epistemic space that deal with art, and does not impede communication on other subjects, and so it is partial.  Based on day-to-day experience, where most people share a common core epistemic space, but otherwise sit one one side or another of various partial barriers in a mix-and-match kind of way, we would expect this to be perhaps the norm.  And yet consider the apparent total disconnect that seems to exist between majoritarian culture and, say, adherents of all-embracing belief systems that aspire to cultural isolation, or the gap between the majoritarian world-view and that of those suffering from extremely severe mental illness.  Here we seem to be close to finding a total barrier, which precludes any meaningful communication.

So, in the case of a partial barrier, what happens when I cross it is simply that, on topics that the barrier controls, I become incomprehensible, but on other topics you can still understand me.  This raises the interesting possibility that I may, therefore, be able to help you to, as it were, peek around the edge of the barrier, by using whatever analogical or metaphorical language I can to describe the other side.  This is, in a sense, how education works.

In the case of a total barrier, something much stranger happens.  As I cross the barrier, I will, like a station on a wandering radio receiver, tune out until, epistemically speaking, I vanish: all possibility of communication with me from your side of the barrier is at an end.  In this context, note that friends and family of those who adopt exclusionist belief systems or suffer from extreme mental illness often talk of their loved one being ‘taken away’.  Very often this is put down to the ill intentions of those with whom the individual now aligns themselves, and many in the ‘anti-cult’ movement claim that those they oppose deliberately separate their ‘victims’ in order to increase power over them.  In fact, a more plausible explanation may be simply that the ‘taking away’ is just the natural consequence of passing beyond a total epistemic barrier: where no communication is possible, none will occur.


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