# The Porter Zone

Philosophical musings and more

# Introduction

In his essay (appropriately) titled ‘Ontological Relativity’, Willard Quine introduced the notion that there is no such thing as a fixed, standard ontology, but instead ontology must be relativised, so each individual has one or more ontologies unique to them, and that we use language as a means to (where possible) translate between them.  The key point in his argument was that it is impossible, purely by means of language for me to determine whether you and I ontologise concepts for which we have a common term in the same way.  That means that we cannot, as one may have thought, use language to establish a consensus ontology, as we cannot, purely based on language, derive a unique meaning for common terms.  To use Quine’s example, we may have an agreed term ‘rabbit’, and we may even agree on what it denotes, but we have no way of determining whether it should ontologise as ‘an animal of such and such a shape’ or as ‘a collection of such and such kinds of body parts’.  In the absence of a consensus ontology, we must therefore conclude that there is complete ontological relativity, a fact which is one of the starting points for my essay Against Standard Ontologies.

Now, Quine’s argument is very persuasive, but it depends largely on rather tendentious thought experiments, such as the infamous case of the rabbit Gavagai.  This is not to say that these thought experiments are invalid, but as they depend on somewhat unusual special circumstances to acquire their force, they inevitably lead to the question of whether ontological relativity is truly endemic, or whether it is purely a feature of extreme cases within the realm of possible ontologies, and that most of the time we can actually establish a consensus ontology.  Therefore, in this essay I shall present a formal argument based in the structure of language, that does not depend in any way on special examples, which shows that any reasonably complex language can and must exhibit ontological relativity.

# Argument

I am going to walk through the structure of language stage by stage, starting from the individual units of language and building up via grammatically correct sentences to sentences with truth value, sentences with reference to a model of the world and finally sentences that refer to the world as we perceive it.  In the process we will see precisely where ontology enters and why it must be relativised.

## About language and ontology

So we start from the basic units of language.  In English these are words, but in other languages (especially agglutinating languages) these might be lexemes that glue together to form words.  Therefore I will us the abstract term ‘element’ to refer to the basic atomic unit of language, that is to say the collection of basic units that can be combined and recombined to form utterances.

### Syntax

It seems to be a general fact that in all natural languages (at least all the ones we know about) elements combine to form utterances.  Utterances themselves generally consist of one or more segments, each of which is capable of standing on its own as a complete, formally correct unit of speech.  That is to say, these segments can be uttered on their own and be assigned a ‘meaning’ (more on that anon).  To see my meaning more precisely consider the sequences of English words:

1. The cat sat on the mat
2. He ate them because he

Here 1 can stand on its own.  It does not beg any questions.  However, 2 is incomplete, as we do not know what it was that he ate them because of.  I will call these basic segments sentences.   Thus 1 is a sentence and 2 is not.  The rules specifying whether a sequence of elements is or is not a sentence constitute the grammar or syntax of a language.  So syntax tells us how to build sentences from elements.

### Semantics

A grammatically correct sentence is all very well, but if we want to do anything with it we need to be able to tell its truth value.  That is to say, if a sentence can be seen as an observation about the way the world is, we want, given a source of information about the world to plug into it, to be able to tell whether that observation is accurate.  The next step gives us part of this information, in that given a grammatically correct sentence, the semantics of the language tell us how to derive the truth value of a sentence from information about a class of special elements within it: its predicates.

A predicate is a unit that predicates a property of an object (the thing can be pretty well anything, from a referenced thing in the world, to another predicate to a complete sentence) in such a way that the result of doing so is a truth value.  For example consider the following:

1. The grass is green
2. ‘All your base are belong to us’ is a grammatically correct sentence

Here 1 applies the predicate ‘is green’ to the object ‘the grass’, giving the truth value ‘true’, while 2 applies the predicate ‘is a grammatically correct sentence’ to the object ‘all your base are belong to us’, giving the truth value ‘false’.  Given a predicate one can, in principle, define its extension and antiextension, which are respectively the collection of objects of which it is true / false.

My assertion, which appears to be true of all known natural languages, and which goes back in philosophy to Alfred Tarski, is that once I know the extension and antiextension of all predicates in a sentence, and know which of these all objects in a sentence belong to, then the semantics of a language tell me how to derive the truth value of a sentence from that information and the structure of sentence.  Consider the examples:

1. The grass is green
2. The dog, which had long hair, was rolling in something that smelled horrible

1 is obvious: as noted above, we just check whether the object ‘the grass’ is in the extension of the predicate ‘is green’.  If it is then the sentence is true.  2 is more interesting; to see how it works, let me recast it:

1. There was a thing x such that x smelled horrible and the dog was rolling in x and the dog had long hair

So the sentence is true precisely when (a) the dog had long hair, and there is some thing x such that (b) x smelled horrible and (c) there is a relation of ‘was rolling in’ between the dog and x.  So the truth value of the sentence reduces to evaluation of three predicates.

### Reference

Now we have our predicates with their extensions and antiextensions.  At the moment we have a purely formal system of symbols that bears no relation to the world as we perceive it.  How do we know how to relate the objects in a sentence to objects in the world?  In other words, how do we know what ‘the dog’ in the sentence above refers to?  This actually turns out to involve three steps.  First we have to identify what the things are that our world consists of, then we have to describe each type of thing, so we can recognise it when we see it, then we have to identify which of the things we discriminate within the world is the thing referenced in our sentence.

For the moment we stick with the third of these steps.  Say we have correctly discriminated the world into a collection of things.  We then need to be able to look at that collection and relate objects within our sentences to those things.  This is what we mean by reference: a term like ‘the dog’ in our sentence above is said to refer if it corresponds precisely to a thing in the world that we have discriminated as being of the kind ‘dog’.  Reference is therefore, as we can see, absolutely necessary if we are to be able to make any sentence we utter concrete, in the sense of relating to the world we perceive.  Moreover, even with sentences dealing with purely abstract matters, if terms do not refer, that is, if they cannot be assigned to (abstract) things of specific, well-understood, commonly agreed kinds, then there is no way that I can understand your utterances, for there is no way that I can relate the objects in your sentences to anything in my conceptual world.  Thus without reference, language as a tool for communication is useless.

### Ontology

The final thing we have to deal with is the first two steps outlined above as preconditions for reference, that is to say building a conceptual model of the kinds of things the world is made of, then describing each kind of thing in such a way that we can discriminate instances of it within the world and ask questions about its properties (that is, assign it to the extensions or antiextensions of predicates).

This turns out to be the part of the structure which simultaneously is the most critical for evaluating the ‘meaning’ of sentences and the one about which we can say least.  The first of these claims should be obvious, in that if I divide up the world in a different way to you then you may utter sentences that, from you point of view, reference specific objects, and yet, from my point of view, those objects do not even exist.  A simple case of this would occur if I had been blind from birth, in which case colour terms would be entirely meaningless to me; words like ‘red’ and ‘green’ would be valid words, and I would even be able to determine the truth value of sentences like:

1. Green is a colour
2. An object can be red all over and green all over simultaneously

But those sentences treat ‘red’ and ‘green’ as objects of predicates like ‘is a colour’, not as predicates in their own right.  As predicates, they have no reference and hence no (anti)extension, so I genuinely have no way of answering as to the truth value of:

1. This dog is brown

As an additional subtlety, given the sentences:

1. Unripe tomatoes are green, ripe tomatoes are red
2. This tomato is green

Then if I were blind from birth, I could answer as to the truth value of 1, because I can learn these facts about the habitual colours of tomatoes, and yet I have no way of answering 2 other than asking someone else to do it for me.  Going the other way, say I were a human being and you were an animal with sonar-based senses (e.g. a dolphin).  To such an animal, objects properties go beyond their visible externals and include their internal constitution in terms of density, mass distribution, etc.  Thus your ontology would contain large quantities of information that simply vanishes on translation to mine; you would distinguish classes of objects that I saw as being identical. Ontology is inherently private.

## Analysis

We conclude from this that two speakers of a language can easily agree on syntax and semantics, as these are the mechanics of language, which depend only on the internal structure of a sentence and not at all on the outside world.  Reference begins to be problematic, for example consider the sentence:

1. Cicero was troubled by serious crime

Does ‘Cicero’ reference the American city or the Roman Senator?  In either case the sentence is true, so we have to deduce reference from context.  Thus reference depends not just on the sentence itself, but on the context in which it is placed.  This context has two aspects.  First, we can assign reference to particular terms by ostention, that is by (literally) pointing at an object while using the term we wish to assign it to, e.g. saying ‘This dog is brown’ while pointing out a particular dog.  This can be generalised to apply to a very wide range of cases.  It provides what we can consider the occasion specific part of the context by indicating those references that cannot be deduced from the sentence or from background knowledge.  So, second comes background knowledge or what Quine calls a conceptual scheme.  I do not need to have the term ‘dog’ in the sentence above defined for me because you assume that I know what a dog is.

How can you test that I know what a dog is?  The test is simply that you and I should agree on the contexts in which the term ‘dog’ can be used in a sentence and on the truth of the resulting sentences (at least in cases where we can both make sense of those sentences).  So if I were to answer ‘It’s not a dog, it’s a canary’ that would imply a failure of common reference. However,we can determine whether you and I agree on the class of objects referenced by the term ‘dog’, and if we do then we assume that we have a common reference.

As soon as we move onto ontology that breaks down entirely.  It may be that I break the world down in a way entirely alien to you, but have still been able to spot common features in things you reference as ‘dog’, and so can agree on the reference of the term, even if my ontology is entirely different.  For example, if I had the senses of a spider with eight eyes, complex chemical sensors (sense of smell) and very sensitive motion detectors, my ontology might classify all items based on whether they were moving or not, so I would consider a moving dog as distinct from a stationary dog, not out of perversity or choice, but simply because my brain was wired in such a way that all visual percepts automatically came to me with a motion indicator attached to them.  Again, if I were a robot which had eight distance sensors instead of two eyes, my ‘visual’ perception of the world would be as structures in an eight-dimensional space and would (as for the dolphin) include information about internal structures of objects, and again this information would be an inherent part of my perception, not just something tagged on to a more basic perception.  So if perception differs ontology will differ.

But now, none of us have the same perceptions as one another and none of us have the same conceptual schemes as one another.  You and I will be trained by common culture in how to break things down as far as reference goes, and in so far as our common neural anatomy goes, but as we move beyond reference into ontology, as ontology is always private, we have no way of telling whether we do, in fact, share an ontology or not, because our only tool for testing this claim is language, and language can only tell us about reference.  Therefore ontological relativity is necessary, not because we can prove it is true, but because it is necessarily impossible to prove that it is not true.

# 1 Introduction

It is a truism that lay persons rush in where experts fear to tread. We are too well aware of the many enthusiasts who insist that they have built a perpetual motion machine, that they can square the circle, and so on and so forth. Where philosophers have long concluded that there can be no such thing as a single standard ontology, non-philosophers ignore such minor issues and set about trying to build one (e.g. SUMO, see [4]).

Unfortunately, it is still the case that there can be no such thing as a standard ontology. As I will show in this note, at best there can be a number of local ontologies, each dealing with a small, well understood problem domain, where there is only one point of view. This latter criterion is crucial: if I am building ontologies in (say) robotics, I have to accept that the points of view of the robot’s designer, programmer and user are very different, not to mention the point of view of the robot itself. Thus each of these must involve a separate ontology.

I proceed by setting out the arguments for ontological relativity, the claim that multiple equally valid ontologies are endemic. Having done this I show that there are, in fact, very severe constraints on what a candidate ontology can look like, imposed not by a world-view but by the requirement for philosophical coherence.

# 2 Ontological relativity

An ontology is a (hopefully systematic) collection of types whose intersections are such that by applying subsets of the types in the collection to a thing we can reach the point at which we have a sound description of that thing, and some understanding of its structure. But this is immensely problematical.

## 2.1 Multiple Ontologies

Consider first the case of types of things whose existence is debated. For example, I may believe in angels, you may not. So, even if an ontology extended to include the category of ‘imaginary things’ we would end up categorising angels in different ways. Thus there is no way that even one ontology can be applied in a consistent and unambiguous way across all cases and individuals.

Now consider the case where I am a classical physicist and you are trained in quantum mechanics. Your conceptual world contains ideas such as ‘wave function’, ‘S-matrix’, ‘state vector’ and so on and so forth mine does not. Thus it is not a matter of our having a common set of categories but disagreeing as to how to categorise a thing; in this case you have categories that I do not even know of the existence of. Therefore either we must conclude that multiple ontological frameworks must coexist, or we must assert that progress will inevitably drive us to bigger and better ontologies, or we must become Platonists and assert that there is a single ‘correct’ ontology, but we have not yet discovered it all. Of these options, the second is dumbfounding in its arrogance and, less pejoratively, is merely a weak form of the third. The third is unprovable and also faintly worrying for all those of us who are not Platonists. Therefore multiple ontologies must coexist.

## 2.2 Coexisting ontologies

Third, we can do serious damage to the Platonist point of view. Consider Quine’s famous example from [6] where you and I see a rabbit, you say gavagai and I deduce that gavagai means rabbit. Which seems perfectly sound, until we consider the assumptions inherent in this deduction. I have assumed that you ontologise the world into things in the same way as me, so you look at what I think of as a rabbit and see a single thing. But you could use an ontology in which the basic unit is the body part, and then there are names for particular collections of types of body part, so gavagai actually refers to the components of what I would call a rabbit.

Quine showed that, in fact, there is no way of distinguishing by purely extensional communication whether gavagai means rabbit or ‘a particular collection of types of body part’, meaning that both ontologies are equally valid and the difference causes no problem in communication. It is therefore impossible to privilege one over the other; any attempt to do so would inevitably end up deriving from personal prejudice than any rigorous criterion. Thus, not only are multiple ontologies possible, they are endemic. In [6] Quine coined the term ontological relativity to refer to this concept that in fact there can be no preferred ontology.

## 2.3 Local ontologies

Therefore we must conclude that there is no global ontology that can be applied by fiat. At best there are local ontologies, tailored to specific problems or domains, between which we translate. This should not, of course, come as a surprise to anyone who regularly switches between vocabularies depending on context (e.g. technical, formal, informal).

# 3 Constraints on ontologies

## 3.1 Concrete vs Abstract

We need to be very careful with the formulation of the categories that make up ontologies, for the way we formulate them can depend on the precise world-view we want to adopt. Moreover, they can result in severe constraints being imposed on the resulting ontology. Thus any candidate ontology must be verified not just against its creators’ view of the world, but against meta-ontological requirements of coherence and consistency. In this section I demonstrate this fact by analysing one apparently safe top-level categorisation, into concrete and abstract.

### 3.1.1 What is concrete?

What, precisely, do we mean by concrete? The folk-epistemology denition that something is concrete if it is real is far from helpful, because if I am a Platonist then, as far as I am concerned, $\aleph_0$ is real, whereas if I am a constructivist I might assert that only finite integers are real, if I were an empiricist I might deny the negative integers, and if I were a strict empiricist I might wonder whether it is actually provable that the integer 472,533,956 is realised anywhere in the physical world. So the naive view founders on ontological relativity.

So say that a thing is real if it can be realised; that seems safe enough. A horse can be realised, so horses are real. But what about unicorns? The fact that no realised unicorns have been discovered does not mean that they cannot be realised, only that they have not been realised; there is a clear distinction between absence and impossibility. Now, we might decide to rule against unicorns because they are imaginary, but consider the case of the top quark. Top quarks have been demonstrated to be realised, so top quarks are concrete. But the top quark as a thing was hypothesised long before it was discovered, so what was its ontological status after its invention but before its discovery? If unicorns are abstract, so must the top quark have been, in which case it suddenly underwent transition from abstract to concrete upon its discovery. Thus either, once again, ontological relativity rears its ugly head, or else we have to accept the Platonic position that anything we can construct hypothetically is, in fact, concrete.

### 3.1.2 Types and kinds

In fact things get much worse. When we speak of things, do we consider a thing to be anything that is realisable, or does it have to correspond to a particular object. To put it more formally, can types and kinds be things? To return to my example, horse is actually a type, in that it consists of a collection of qualities that allow us to ascribe identity to one particular class of things. But surely types cannot be concrete, for (unless we are Platonists) surely the concept horse cannot be realised, precisely because it is, in the truest sense, an abstraction.

So let us suppose that all types and kinds are abstract. What, then is there left to be concrete? That question is very hard to answer, because once we have taken away all types, kinds and properties (for properties are merely a kind of type), what is left is formless, undistinguished stuff. Indeed, as Quine has pointed out ([7]), even proper names can be thought of as properties, as they are essentially predicates that allow us to distinguish one thing from the rest, and hence are a property held only by that thing. Even within the context of Kripke’s rather more Platonic universe, the rigid designator ends up as being a kind of label that picks out a particular thing ([3]), and is hence a property or type. Thus, once we have stripped away all types and kinds what is left is things that are undistinguished and undistinguishable, the unknowable thing in itself. The concrete category might well exist, but in as far as the purpose of an ontology is to enable proper categorisation of things, then it is useless, because it is not susceptible to categorisation.

Therefore it follows that when we are building an ontology, we might, if we so wished, make an initial division into concrete and abstract, but we would immediately find that at that point we had, at least in the concrete category, gone as far as we could go, and that all subsequent work must involve the imposition of structure upon the abstract. Therefore, any ontology that attempts to maintain a distinction between the concrete and the abstract while imposing structure on the concrete is incoherent.

## 3.2 Hierarchies and other structures

There is a common assumption among practitioners of practical ontology that ontologies must be hierarchical, that is to say that each type or kind is a specialisation of precisely one (more general) type or kind, and so on all the way back to a single root kind. Thus the categories that make up the ontology form a simple tree. This top-down approach is strongly rooted in pre-modern systematic philosophy (see [1] and [5] for examples) but it is not obvious how realistic it is.

### 3.2.1 Hierarchical models are not sufficient

Consider, for example the case of the platypus. A platypus is a type of mammal, but it is also a type of egg-laying animal and those two types cannot be placed in a hierarchical relation to one another. Hence, the type platypus cannot be derived from only one parent type. As a more conceptual example, the C declaration

```typedef union
{
long l;
double d;
} longdouble;```

creates a type which is simultaneously a type of long and a type of double; in fact it is polymorphic and can be taken to be of either type.

Consider also this problem. Say I decide that a relation is a type of thing within my ontology. So it must sit somewhere in my hierarchy. But any realised relation is a relation (one type) between one or more things (one or more additional types), and so the realised relation derives from at least two types, and may derive from any number. This is evidence of a certain problem with naive ontologies: if one tries to make an ontology all-embracing then it has to end up being self-describing, so meta-ontological structures such as relation become part of the ontology and end up being related to almost everything.

### 3.2.2 Recursive types

In fact, we can go further. Clearly any reasonable ontology must allow for recursive types. For example, in Haskell we might specify the type of (rather ironically) a binary tree as

data Tree a = Leaf a | Node ( Tree a ) ( Tree a )

In general, we can only define the type binary tree in terms of itself, and this is far from being the only example. A sound ontology has to allow for recursive definitions, but a hierarchy cannot.

### 3.2.3 Functional types

A classic example of a type that will not fit in any hierarchy is the function type, that is to say a type of things that change the type of other things. So, for example, transducers are a type of thing that convert one type of energy to another, e.g. microphones, which convert sound energy into an electric current. We can model this as

transducer :: a -> b

where a and b are the input and output types of energy. So this function type depends crucially on two types, the input and the output.

### 3.2.4 Conditional types

This is complex enough, but the example of the tree demonstrates just how far from being a hierarchy ontology can get. Recall that we defined

data Tree a = Leaf a | Node ( Tree a ) ( Tree a)

Here a is a parameter that can stand for any type. So this prescription tells me how to make a binary tree of type a. Continuing down this route, we can be more stringent, for example

data (Eq a ) => Set a = Set [a]

says that I can make a set whose elements are things of any type a that happens to belong to the type Eq. In other words, I am given a type of types (i.e. Eq) and from it construct a function

Set : : (Eq a ) => a -> Set a

This is a conditional type, in that it imposes a condition on a: if a is of type Eq then Set a is a type.

To make this concrete consider the types heap of sand, heap of bricks, heap of clothes. These fall into a pattern, in that though each of them is a type in its own right, underlying them is a more general type, the type heap. Each type of heap is formed by combining heap of… with another type from within a fairly wide class of types. So we combine a type (heap) with a type of types (types of things you can form into heaps) and derive a function (that takes a heapable type into the type of heaps of things of that type).

It need hardly be said that this is entirely incompatible with notions of hierarchical or tree-based ontologies. A more subtle structure, such as that found in typed lambda calculus (see [2]), is probably required.

### 3.2.5 Conclusions

So we conclude that a viable ontology cannot be hierarchical or tree-based. This is not to say that it cannot have a parent-child structure, but whatever structure we choose must allow that (i) a type may have multiple parents, (ii) a type may be its own parent, and (iii) the most general rule for deriving more specialised types from less specialised must accomodate at least function types and conditional types.

# References

1. Aristotle. The Physics.
2. H Barendregt. “Lambda calculi with types”. In: Handbook of Logic in Computer Science. Vol. II.
3. S Kripke. Naming and Necessity.
4. I Niles and A Pease. Towards a Standard Upper Ontology. 2008.
5. Proclus. The Elements of Theology.
6. W Quine. “Ontological Relativity”. In: Ontological Relativity and other essays.
7. W Quine. Set Theory and its Logic.

## Introduction

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

If 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.

As 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.

As 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

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.

But 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.

Next 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.

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.

Go 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.

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.

## It came from beyond an epistemic barrier . . .

Epistemic Barriers – this time in English!

1 Introduction

I admit it.  On Epistemic Barriers is (though I say it myself) a rather profound piece of work, containing some very important philosophical ideas.  Unfortunately, it is also profoundly hard to read.  I made the mistake of writing it in the impenetrable style of some of the philosophers I was critiquing.  Which was a mistake, in that complex ideas were made impossible by an overly academic style.

So this essay is an attempt to present the same ideas, but with a more transparent exposition.  That doesn’t mean that what I have to say will necessarily be easy to understand.  As I have already said, the ideas are quite deep, and as they deal with the bounds of knowledge (what is and is not knowable) they are inevitably going to be mentally stretching.  However, I will do my best to ease comprehension.  That means none of the quasi-mathematical language or excursions into Germanisms.

2 What is an epistemic barrier?

In this section I’ll introduce the concept of an epistemic barrier.  It’s quite a complex idea, so I shall approach it gently from, as it were, both directions.  So first I look at the facts relating to the mysterious mutual comprehensibility of all human languages, and then I look at those facts that limit mutual comprehensibility.

2.1 The enigma of mutual comprehensibility

If we look at our world, there is a certain very surprising fact that constantly stares us in the face, but is so commonplace that we don’t realise just how surprising it is.  What I refer to is the fact that, in spite of there being hundreds of languages spoken by people on this Earth, we have yet to find a language that is wholly incomprehensible (I am ignoring here certain dead languages, as the are special problems inherent in trying to decode a language with no native speakers and no obvious descendant languages).

Why do I say this is surprising?  Well, if two languages have arisen from different sources, and are sufficiently isolated (say one in Europe, the other in Australia), then there is no obvious reason why it should be necessarily the case that speakers of the two languages should be able to establish communications with one another, let alone that it should be possible to translate between the two languages.   We take this for granted, but, in actuality, the fact that all human languages seem to be mutually comprehensible is something of a mystery requiring explanation.

Now there are a number of competing explanations.  I will list those most relevant to my eventual goal, which is not mutual comprehension, but mutual incomprehension.  So the theories are:

2.1.1 All languages are essentially the same

According to this theory, there is only one way that a natural language can be formed, and thus any two natural languages must be mutually comprehensible, because they are simply realisations of the same underlying structure.

This implies that there is only one class of conceptual categories, and only one way of ontologising the world around us.  For if (say) multiple ontologies can exist, there is no guarantee that objects as described in a language using one ontology will correspond in any well-behaved way with objects as described in a language using another, and so mutual comprehension will be limited to non-existent.

Thus the theory imposes a very regimented view of reality and what is and is not permissible in terms of individual’s conceptual models of the world.  Indeed, it is almost Platonic, for the limitation to a single class of ideas and kinds of things is, in all but name, an acknowledgement of the existence of forms that all things (to a greater or lesser extent) realise.

Now, I do not consider this theory to be viable, for a number of reasons.  First, it is incredibly anthropocentric.  What reason do we have to believe that ours is the only viable way of anatomising the world and the world of ideas?  Surely, all human languages are mutually comprehensible, but what reason do we have to believe that ours are the only languages that exist?  Or that our planet is an exemplar for all those where language-using life may arise?

Second, consider the following thought experiment.  Say we discover a species of aliens who have evolved on or very near to a neutron star.  Due to the extreme nature of physics in such a neighbourhood, they sense quantum wave-functions directly.  So while we see (say) a stone as an isolated object, they sense a distribution spread across the whole of space-time.  In other words, our senses are local, while theirs are global.  Now, our entire world-view is predicated on objects being localised in space and clearly distinct from one another.  Indeed, the idea of predication, fundamental to all human languages, requires a clear concept of thing or things which clearly possess one or more definite properties.  But to our quantum creature none of this makes sense, as the world consists of an endlessly shifting mass of probabilities, with no clear barriers or delineations, and so their world-view, and therefore their language, must be alien to ours.  The only recourse, if we want to salvage the theory, is to say that language-possessing aliens cannot differ significantly from us in their physical environment and sensory apparatus, which is clearly absurd.

Third, the theory is logically circular.  For it argues that every language must take the form of something we recognise as a language.  Its evidence for that is that all the languages we know are recognisable as languages.  But we would expect nothing else; if a language were truly alien then we  could not necessarily recognise it as a language, so we would not know that it was there as a contradiction to our theory.  Thus the theory is unfalsifiable and, as such, worthless.

Before you ask, the reason why I spent so long on attacking an obviously flawed theory is twofold.  Well, it may be obviously flawed, but that does not stop it from being deeply embedded in our culture.  Indeed, the whole effort to communicate with aliens, whether in the form of pictures on space probes, signals beamed into space, or attempts to ‘listen in’ on alien conversations, is based on the assumption that alien languages are similar to ours, and that certain linguistic facts that are obvious to us will likewise be obvious to aliens (and vice versa).  One of my conclusions is, in fact, that this belief is false, and that therefore the enterprise of SETI is futile.

2.1.2 All human languages are essentially the same

This is a less ambitious version of the above theory, so it accepts that alien languages may differ wildly from ours, but still insists that human language is essentially wired-in, in the sense that it is inherent in being human.  So, though individual languages may be contingent things, there is a universal grammar that is built into our neural hardware, so to speak, and is specified by the blueprint for a human being (i.e. our genome).  This is the theory most closely associated with Noam Chomsky and his school.

I do not consider this theory to be viable, though it is harder to dismiss than the first theory, the argument against it depending on balance of probabilities rather than obvious flaws.  Though Chomsky and his followers point to the fact that we acquire rules about what is and is not grammatically correct without hearing (many) examples of incorrect usage, this argument has a number of flaws.  First it ignores the fact that, in fact, as children, though it is granted we do not usually hear solecisms, we are repeatedly corrected when we commit solecisms.  Second the phenomenon is more economically explained as being the result of our modelling the language we speak on the language we hear: this, after all is how we acquire dialect and accent, so why should it not be true for grammar?  Third, if, as Chomsky would like us to, we interpret this avoidance of grammatical solecisms as being evidence of hard-wired rules at work, how to account for the fact that said rules are strongly language dependent (so, for example, this sentence is perfectly correct in English, but, if translated literally into German, would be grossly incorrect)?  To posit that I am genetically an English speaker is nonsensical, but if we try to universalise the rules to the point where they apply to all known human languages, they become nearly vacuous.

This is the next point.  The universal grammar, as it is presented, exists at the very high level of specifying that verbs link noun phrases, and descriptions can be predicated of objects.  But are these really sufficient ideas to justify the theory?  And even if these facts are hard-wired into our brains, they are so minimal in their content that they do nothing at all to answer basic questions about language acquisition.  In other words, a universal grammar sufficiently general to account for all human languages is so vague as to be almost entirely without benefit to its owner, and as such it is more or less impossible to see how it could have evolved.

And finally, once again the theory is circular.  Say it is true that all the human languages we know follow a Chomskian universal grammar.  That could just be due to the fact that, used as we are to Chomskian languages, we cannot recognise non-Chomskian languages when we encounter them.  So the evidence that might falsify the theory is inaccessible to us, and thus the theory is unfalsifiable.

Note that this is not to say that there is no hard-wired aspect to human languages.  For example, there does seem to be a fixed sequence of colours, such that if a language has a word for one colour on the list, it must also have words for all the preceding colours.  However, this tells us nothing about language, and is more a feature of the human sensory system.

2.1.3 All humans are essentially the same

This theory can be seen as a subtler version of the previous theory.  Rather than saying that any features of language are hard-wired into human brains, we observe that human language is intrinsically a property of humans.  And as humans, we are (to a reasonable approximation) identical.  Thus we have similar senses and similar minds, and so see the world in similar ways.  And this means that an idea formed in one human mind cannot be alien to another human mind.  That is not to say that we could swap thoughts and expect to understand one another; rather that my thoughts should not be such that your mind cannot accommodate them, and vice versa.  And thus, human languages are susceptible to translation into other human languages precisely because they have the common feature of being languages of humans.

This theory can withstand all the arguments we have made against the other theories.  It is anthropocentric, but in a different way to the first theory.  That theory made man the measure of the universe.  This theory makes it clear that human languages are a property of humanity, but makes no pretensions to speak of the properties of alien languages.  Moreover, it is clear that this theory can be generalised, so that quantum being languages are mutually comprehensible, but, due to the extremely different conceptual and sensory apparatus of humans and quantum being,s it is a corollary of the theory that human and quantum being languages are not mutually comprehensible, just as we concluded above.

Moving onto grammatical issues, one of the great strengths of the theory is that it makes no claims about the structure of language; it is concerned with the structure of ideas.  Thus, such hard-wired features of the human sensory system as exist (e.g. the colour sequence) can be found reflected in human language, and some of these may influence grammar (e.g. the notion of predication, which depends on a distinction between things and properties that is meaningful to us, but may not be to the quantum creature) but they do not dictate grammar.

Finally, the theory is clearly not circular, because it makes no pretension to give a universal theory as to what make a language, or even what makes a human language.   Therefore we shall accept this theory of language and see where it takes us.

2.1.4 Epistemic barriers at last

In fact, it leads us on to our goal: the epistemic barrier.  As I have said, in my thought experiment with the quantum creature, there will be little or no conceptual common ground between me and it.  Because of this, there is no reason to believe that my mind could house its thoughts and vice versa.  So therefore, the theory of language says that with a very high probability, it should be impossible to translate between my language and its.  Or, to put it more simply, it will be impossible for me and the quantum creature to share ideas, not just because we speak different languages (as should be clear by now, language differences are a barrier easily overcome) but because of a fundamental difference in our conceptual worlds.

I will therefore say that in this case there is an epistemic barrier between me and the quantum creature.  More generally, I will say that two languages, or two conceptual realms are separated by an epistemic barrier if it is systemically impossible to set up a correspondence (e.g. translation) between them.  That is to say, the reason for a failure to translate is not (as with, say, undeciphered ancient human scripts) because we do not yet have the necessary key, but because it is fundamentally impossible that there ever should be such a key.

2.2 Barriers to mutual comprehension

Now let’s start from the other end, and look at the various barriers to perfect translation that exist.  It turns out that translation cannot be perfect, and there exist barriers of various kinds, ranging from those between individuals who share a language up to those between human languages.  But the common feature of all of these barriers is that we can still capture a predictable proportion of the original intent of a thought as it crosses the barrier.  This is abruptly lost when we hit an epistemic barrier, where something mysterious happens.  I shall discuss exactly what in the next section.

2.2.1 Barriers between me and you

In epistemology, the main reason for interest in translation theory is not because philosophers want to be able to translate their work into foreign languages.  The interest lies in the fact that the mere fact of human communication is an act of translation.  If you think about it, whenever you talk to someone, you assume that they will be able to interpret your words in the way you intended them, and similarly you expect that the intent you perceive in their words was the intended intent.  Thus, even if you are both speaking the same language, you are translating between two idiolects.

Now this is a potential source for loss of information and ambiguity.  For a start, languages do not all cut up the semantic space in the same way.  So, many languages do not distinguish ‘green’ and ‘blue’ as concepts, having instead a ‘grue’ colour concept.  So if you come from that background, your mind does not distinguish ‘green’ from ‘blue’, and even if you now speak English, you are likely (this seems to be what happens in practice) to use the words inconsistently, causing confusion for native English speakers.  Similarly, an English sentence that hinges on the distinction between ‘green’ and ‘blue’ may well be pretty meaningless to you.  Likewise, someone brought up speaking German who has learned English, may well find the way that native speakers treat snails and slugs as different kinds of animal somewhat strange.

But all this is quite cosmetic.  There is a more fundamental issue.  Consider the word ‘rabbit’.  Now, you and can talk quite happily about rabbits, and I can be absolutely certain that whenever you say ‘rabbit’ you are signifying a lop-eared rodent.  But do I know what ‘rabbit’ means to you?  The answer is ‘no’.  I can know precisely as much about your views on the word ‘rabbit’ as can be expressed using our mutual languages, but it is a truism that there are non-linguistic thoughts, and another truism that I can never learn your non-linguistic thoughts through the medium of language.  So what you take ‘rabbit’ as meaning, its emotional and other non-linguistic associations, are forever hidden from me.

So here is a (reasonably) small barrier.  That is to say, in conversation we use words, and we can be confident that whatever was the linguistic component of our intent when we framed them will be comprehensible to a competent colinguist.  But the non-linguistic part of our thought must remain private, or else be expressed in symbolic form, in which case we are actually inviting those who observe our symbols to substitute their own non-linguistic ideas for ours.  So ordinary, empirical statements translate absolutely, and as they form most of our discourse, that means that most of the time this person-to-person translation works perfectly.  But complex ideas with personal emotional connotations inevitably suffer some loss in translation: the loss of meaning, a loss that can only be rectified in a somewhat elliptic fashion through art.

2.2.2 Barriers between human languages

Now consider translation as we normally think of it, between two human languages.  Here there is again some inevitable loss of information, largely due to the simple fact that, as noted above, different languages slice the cake of meaning in different ways.  As noted above, colour words are a perennial source of confusion: for example, the Russian words голубой and синий both translate into English as ‘blue’ and yet, to a Russian they signify entirely different colours.  Prepositions and conjunctions are a particular minefield, as it seems that even closely related languages divide shades of meaning up between words in different ways.  Idioms are another place where translation often fails entirely: there is no simple English equivalent for l’esprit d’escalier or schadenfreude and so these expressions are generally carried across unchanged, and have even entered common English usage.

What is, however, more interesting is cases where it is not so much meaning that is the problem as connotation.  Thus, Gut bürgerliche Küche translates literally as ‘good middle-class cooking’, but whereas the latter phrase would have distinctly negative, even satirical connotation to one accustomed to British culture, in Germany it is an indicator that one can expect a good meal.  So translation between languages also requires a translation between cultures, and, if done incautiously, loses meaning given by cultural context.  This is, in fact, the direct extension of the loss of personal meaning in person-to-person conversation: now we are translating between cultures and the private information that cannot be expressed purely linguistically is precisely the baggage that any culture carries with itself.

Even more interesting, however, is the first hint of an epistemic barrier, that is to say the fact that there are cases where a language can express concepts that are untranslatable. One such is the German word gemütlich.  One can try to translate this into English, but attempts to do so generally end up with half a dozen vague and inadequate phrases.  But that does not mean that just because your first language is English you can’t know what it means.  I am perfectly aware of what gemütlich means, and can use it correctly, and yet I have no idea how to render it in my mother tongue.  Another such word is kitsch (German seems to be good at this game).

So what we have here is not quite an epistemic barrier, for I can form these untranslatable concepts in my mind.  This means that they are not systemically untranslatable, but rather simply that  over the centuries Britons have never felt the need to express the concept of kitsch, and by the time we did it was easier to borrow a loan word from German.  So this does not contradict our model of language; instead it shows that building vocabularies is not just a matter of slicing the cake, but also (sometimes) of accidentally missing parts of it (and lest it be thought that English is impoverished, English has distinct words dove and pigeon where German has Taube, snail and slug for Schnecke and so on).

Note finally, that much of my discussion has involved English and German, two extremely closely related languages.  The further apart two languages are, the more meaning is lost in translation (so English and German are both unable to express the Japanese system of honorifics without complex circumlocution).

2.2.3 Epistemic barriers again

So what have we learned about epistemic barriers from this discussion?  First, we see that language-to-language translation generalises person-to-person, and that the mechanism for information loss is the same.  Surely, more information is lost, increasingly so, as I have noted, as the languages and cultures move further apart, but essentially the information loss is controlled, and we can estimate (roughly) how much indeterminacy is introduced in the process of translation.

Second, we know what they are not, that is to say they are not just the consequence of gaps in vocabulary, or more or less complicated grammatical inflections.  If English speakers the world over were to decide that plof was the translation of gemütlich then that would be an end to that apparently untranslatable concept; the fact that we could not say succinctly what plof meant is neither here nor there: we happily and correctly use words like labile or liminal in spite of the fact that if asked what they meant we may well end up embarrassing ourselves.

So, say gemütlich involved a genuine epistemic barrier.  That would mean that it would be impossible for a non Germanophone to even comprehend what it meant, which is a much stronger statement than simply that there is no word for it.  The concept of gemütlich, rather than being merely elusive should be actually unthinkable.  Now this is a really strong statement, so let me put it more formally: two languages are separated by an epistemic barrier if some or all of one of the languages is inconceivable by speakers of the other.  Or, to put it another way: there is an epistemic barrier between me and some idea not just if I can’t understand it, but precisely when I cannot even accommodate it within my mind.   This will have very strong implications as regards our ability to discover alien languages.

3 What can we say about epistemic barriers?

3.1 Can we prove that they exist?

The simple answer to this question is no.  Let me expand on that, as the reason why is rather interesting.  So, how could I prove that an epistemic barrier existed?  There are two possible approaches: one is to identify an actual, concrete epistemic barrier, i.e. to find one that I can point at, and the other is to use a general argument that shows, on theoretical grounds, that such things must exist.

3.1.1 Finding a barrier

I’ll discuss the details of finding a barrier, in particular locating how close the nearest one is, later.  For now let’s stick to the rather crude question of whether I can find any way of detecting the presence of such a beast.  Well, there’s really only one way of doing it, and that is to find a genuine bona fide language that we cannot comprehend (at least in part).   So how would I do that?

Well, there’s one approach, which is that it might just happen that one day a flying saucer lands in Trafalgar Square, an alien emerges, marches down Whitehall and into Downing Street, where it nails ninety-five theses to the door of Number Ten.  Assuming that the alien was not an interplanetary juvenile delinquent or performance artist, we could safely assume that the theses constituted language and, assuming (as seems overwhelmingly likely) that we could make no sense of them, we would again probably be safe in assuming that they were beyond our comprehension.  So we would then have, for what it was worth, a genuine example of language from the other side of an epistemic barrier.  We would know nothing about said language apart from this fact, but it would at least establish the existence of the barrier.

Now before you laugh and suggest that this scenario is a little crude, the problem is that barring such a clear act, pointing at some thing, as it were, with a large sign saying ‘alien language’ we are more or less stumped.  The problem is this.  To recognise a language from the other side of an epistemic barrier, we have to know something about what things are like on the other side.  But we can’t, because by definition, such things are inconceivable by us.  To argue that there ought to be features of any alien language that we can detect is simply to revive the universal language or universal grammar models for language that I dismissed in the previous section, which would have the amusing consequence that in order to find an epistemic barrier one has to assert that they don’t exist!

This fact has quite amazing consequences.  If the only way to be certain that something is a communication in an alien language is to, as it were, catch aliens in the act of communicating it, then that means that alien languages, when seen blind, with no prior knowledge, cannot be distinguished as such.  In fact, we can go further.  Even if we do catch the aliens in the act, as their language is systemically incomprehensible to us, most likely we will be unable to detect any of its grammatical features (if, indeed, it has any) and so we will not be able to learn anything about the language, and hence not be able to spot even further instances of the same language.  Even looking for repeats must be called into question, as there is no guarantee that the language will handle repeats in the same way that our languages do (where repeated ideas leads to repeated text).

What this means is this: no matter how many hard instances of beyond the barrier language we may accumulate, we will never be able to learn anything about beyond the barrier language So whereas the bigger the corpus of a dead language, the higher the probability of decipherment, here a change in the size of the corpus has zero effect.

We conclude that no test can detect the presence of an alien language.  It is, simply by virtue of being alien, indistinguishable from noise.  And therefore a language from the other side of an epistemic barrier is in principle undetectable by any means available to us, short of catching an alien in the act of communicating it.  And thus, as I said above, efforts, like that of SETI, to detect alien communications are futile.  Even to assume that alien radio signals are modulated in a way we can recognise is an anthropocentric assumption too far.

So, barring a sudden intervention from on high, we are not going to be able to find a barrier.

3.1.2 Postulating the existence of barriers

Failing that, I can motivate a belief in the existence of barriers as follows.  I can easily conceive of a being (e.g. the quantum creature from the last section) so dissimilar to us in sensory apparatus and world-view, that it inevitably will suffer from a complete failure to communicate with us.  And this will not be a result of failure to try hard enough, but will simply be because the models of how the universe works belonging to us and the creature will be so different from one another that there is no way of mapping between the ways we divide up the cake of knowledge.   Indeed, it is arguable that we have separate cakes.  In other words, the failure to communicate will be systemic, inherent in our humanness and the creature’s alienness, so there will be an epistemic barrier between us.

But now, though I chose my quantum creature as a deliberately extreme example of an alien obviously separated from us by an epistemic barrier, if we consider any alien creature, then it will have evolved not just with different culture, but within a completely different biological, geological and so on and so forth context.  It seems extremely unlikely that its way of thinking about the world will match with ours.  And, as I noted above, different world-views lead to radically different languages, so I can hypothesise that any alien creature must be separated from us by an epistemic barrier (that is unless something highly fishy, like a bunch of super-aliens going round seeding worlds, is going on).

And that is enough.  Though I believe it is overwhelmingly likely that alien creatures exist, I don’t need that for this argument.  The mere fact that the existence of such a creature is not impossible (for if it were, then why are we different?) motivates my claim, that in all probability epistemic barriers exist.  For even if there are no aliens, the possibility of aliens, and with it the possibility of knowledge that I cannot comprehend, exists.

3.1.3 Predicting the existence of barriers

So it is extremely likely that epistemic barriers exist.  Is there any argument that I can use to prove that they exist?  The answer to that is a bit tenuous.  I can develop an argument (and will, see below), but it is somewhat tendentious and relies on a large number of fairly questionable assumptions.

The argument is essentially a rehash of that old favourite, the ontological argument.  It goes like this.  Clearly it is unlikely in the extreme that the extent of the realm of possible languages should be coterminous with the class of languages that my mind can comprehend, for to assert otherwise would be to assert, essentially that all information is open to the human mind, which would seem to be a rather questionable assertion (after all, my thought experiment of the quantum creature shows that it is clearly possible that information not open to my mind should exist).  Thus the languages that I can comprehend must be strictly a subset of all possible languages, meaning that there exist languages that I cannot comprehend.

Let us examine this.  It is actually reasonably sound.  The only contentious patch is the assertion that if I could comprehend all possible languages then I could comprehend all possible information.  But what if there are chunks of the universe that are indescribable in any language?  That would allow me to comprehend all languages without having to lay claim to godlike powers.  There are two ways of dealing with this issue, one Platonic, the other consisting of a mixture of information theory and hand-waving.

The Platonic approach asserts that if something is genuinely incomprehensible, in the sense that no mind exists, or ever has existed, or ever will exist, that can comprehend it, then it has no reality.  This is not as stupid as it sounds.  It is actually quite reasonable to say that given that (as Wittgenstein said) we must remain silent of that of which we cannot speak, and that (as observed above) not only must we remain silent, but we must also remain ignorant of its very existence, then for all our purposes it might as well not be there.  For if it had any effect we could detect then it would enter within the realm of things comprehensible by us.  This is a rather neat idea, but it has one flaw: once again we have proved that the barrier exists by asserting that nothing on the other side of a barrier can exist.  Back to the drawing board.

The second possible approach is as follows.  Let us assert that all that is can be expressed as information.  This is one of the basic assertions of information theory, and it isn’t too much of a stretch to assume that, even though its form may change, the basic principles of information theory are true throughout the universe.  But now, all information can be expressed as a code of some sort, and therefore we could, with a certain amount of hand-waving, construct a language, not necessarily comprehensible to us, that encoded this information.  Therefore all that is is comprehensible in some language (which may, admittedly, be a language that no-one actually speaks).  This approach is full of holes, but I believe it has some promise.

3.1.4 Constructing a trans-barrier language

That was the argument for the existence of barriers: suggestive, but, at present, inconclusive.   There is another constructive argument, in that I will try to present a recipe for building a language that we cannot comprehend.  Now, this is somewhat abstruse, in that it involves concepts such as meta-grammar, and it doesn’t add much to the overall argument, so those of a nervous disposition can happily jump ahead to the next section.

I aim, in a thought experiment, to construct an incomprehensible language.  But didn’t I say that we can know nothing of the grammar of a language on the other side of an epistemic barrier?  Indeed I did, but I said nothing about meta-grammar, that is to say the rules that the specification of the grammar must satisfy, or the grammar of the grammar.  It is entirely possible that all languages could share a meta-grammar, for the relationship between meta-grammar and grammar is a one-way street.  We know how to go from meta-grammar to grammar (though we can generate only grammars that we can comprehend), but there is no reason to assume that we can deduce the presence of the meta-grammar from a sample of incomprehensible grammatical language.

Say I define a meta-grammar (how I would set about doing this, I am not entirely sure, but this is, after all, a thought experiment).  So now I take a computer and I write a program that, given a meta-grammar, will use random decisions to build a grammar based on that meta-grammar (if I want to be really clever, I can actually write a program to write the program, thus introducing randomness into the grammar generating program itself).  And then I can use another program to generate ‘text’ in a random language conforming to that random grammar.  And then the programs delete themselves and all files used in the generation of the language, leaving only a corpus of ‘text’ in the language.

What I get is an entirely artificial language, which has a non-denoting vocabulary (so words have meaning relative to one another, but no meaning outside of the language itself; this is not a problem: the same is true, after all, of the languages of formal logic or of computer languages).  However, as it has been thoroughly randomised, I will assert that I will be unable to grasp the principles on which it works.  For, to continue the thought experiment, there is no particular reason why it should even conform to our notion of words.  Surely, it will have semantic units, but (say) a communication may be encoded so that the nth symbol is the sum of the nth semantic unit and all preceding symbols (such a language would have the property noted above of not repeating even if the content repeats).

This argument is incomplete, but it is, I believe, highly suggestive, and indicates a fruitful area for possible future research.

3.2 Can we find where one is?

I have produced a shaky but interesting line of argument that barriers do, indeed exist.  The next question, then, is can we ever see a barrier?  That is, can we ever tell the point of linguistic or conceptual development at which we will run into a barrier?  The simple answer is (again) no, but the reason why not is rather interesting.

In fact, what we’ll see is that epistemic barriers are very strange beasts.  They almost certainly exist, but it is entirely possible that their location depends on who it is that is talking.  Moreover, the are undetectable, being always infinitely far from us (so they, by their very nature, exist at the very bounds of knowledge), but we may, if we are very lucky, be able to make an educated guess about their existence.  In other words, in a suitable irony, the bounds of knowledge are themselves unknowable.

3.2.1 Epistemic barriers are not fixed objects

Think, for a moment, about the statement ‘some or all of one of the languages is inconceivable’ in my definition of an epistemic barrier between two languages.  What would it mean for part of a language to be conceivable by me and part not?  First of all, is it possible?  Well, we can imagine a hierarchically organised language, where each tier in the hierarchy extends the tier below and adds additional structure.   As a concrete example of this, consider the relationship between the specification of what a computer program should do, high-level programming code, low-level programming code and machine code.  So it is entirely conceivable that if we encountered such a language, we could comprehend the bottom tier(s) but not the upper ones.  So, yes, this is possible.

Having established that such a barrier can exist, what does it mean?  From my point of view, there is a barrier down the middle of the language, dividing the accessible and inaccessible parts.  But from the point of view of a speaker of that language there can be no such barrier: obviously they can comprehend all of their language, else it wouldn’t be their language.  So where I see a barrier, they see none, but they may see a barrier (say) somewhere down the middle of my language, or it may even be that I can comprehend some of their language but they can comprehend none of mind (and before you say that that sounds silly, that is precisely the situation with Finnish and Estonian: Finns can understand Estonian but Estonians cannot understand Finnish).  So the key point is that the location of epistemic barriers depends on where you are standing.

3.2.2 Epistemic barriers are invisible

Let me revisit the Platonic observation from the attempt at a proof of the existence of barriers.  I claimed that if some concept exists on the other side of an epistemic barrier from us, then we cannot know even that it exists.  This sounds rather mystical, but is quite simple.  If I am mentally unequipped to  handle the concept, then  I cannot conceive of it, so no I cannot know about it.

But what if, say, I could not conceive of the whole concept, but there was some part, or fragment, that I could conceive of?  In that case, I could be aware of the concept to the extent that my mind could house it, but I would have no way of telling that (as it were) higher forces were at play.  As with the language with a barrier down the middle, I may see holes in the ideas or communications, as I understand them, but I have no way of telling whether those holes are genuine or are caused by my inability to process that which is beyond my comprehension.

As epistemic barriers bound what is, for us, the totality of knowledge, there is no way of telling whether they exist, and we are locked in an epistemic bubble of our own making, or they do not exist, and we just happen to be privileged with the key to all knowledge.  That there is no way of distinguishing between these two possibilities is the reason why my attempt to prove that epistemic barriers did exist was so fraught with vagueness and complexity.  In other words, epistemic barriers are invisible.

There is a very neat real-life example of this phenomenon.  Quantum mechanics has wasted more ink in its short history than many disciplines.  One of the principal problems with it seems to be that some aspects of the theory can be more or less understood, using appropriate mathematical models, but other simply make no sense.  And the manifold problems with the theory as it stands (from Schroedinger’s cat all the way up to the grotesque nonsense of Feynman integrals) comes from an attempt to force something that is simply other into a human conceptual framework.  I therefore propose (without proof) that we are seeing indirect evidence of an epistemic barrier, in that we are making touch with a level of knowledge that is only partially comprehensible, and so we fill the gaps in our understanding with more or less baroque imaginings.

This suggests a possible way of detecting a barrier indirectly, rather like a black hole, by spotting its side-effects.  I will return to this below.

3.2.3 Epistemic barriers cannot be located

I can’t point and say ‘look, an epistemic barrier.’  But even if I can’t actually see the barrier, can I at least get some idea of when I am getting close to the bounds of the knowable?  Putting it like that, the answer is, as you should be expecting by now, no.

Imagine, for the moment, that I can describe the realm of ideas as some sort of map, so I stand on the middle of a plane, and as you move away from me, the points on the plane correspond to more and more complex ideas.  Now, given what I’ve already said, an epistemic barrier corresponds to a gap, where the plane is interrupted, and I have no idea whether things are resumed on the other side of the gap.  Can I tell how far away the gap is?

Okay, let’s say I can understand the ideas corresponding to some point on the plane.  Then it stands to reason that similar ideas should be comprehensible.  So if I walk a little way in any direction I am in no risk of falling into the chasm.  So what does this mean?  There are two possibilities: the plane goes on forever, or it has an edge but I can never reach it because the farther I get from my starting point, the harder it is to move away.  So in either case, there is no way in which I can get to the edge and peer over it.  Rather than stopping sharply, the plane corresponding to my conceptual realm will, as it were, peter out.

What this means is that, no matter how far I get in my journey, no matter how complex my language or concepts get, I have no way of telling whether I am going to bump into a barrier.  Because I can’t ever reach one, and no matter how close I might get, it always seems that I have plenty of space to explore.  So epistemic barriers are always infinitely far away.

3.3 Can any information flow across one?

Thus far I have concluded that epistemic barriers almost certainly exist, but they are rather elusive, being invisible and always infinitely far away.  For the purposes of this section, let’s say that one exists, and there is a whole treasure trove of information on the other side of it.  What I want to know is, just how much can I tell about what there is on the other side?

Now, obviously, this question is only meaningful in cases where we have languages that partially cross a barrier, so we can see part, but not all, of a concept.  In the case where no concept crosses the barrier, it must, almost by definition, remain totally opaque and, like a black hole, with which the analogy is very apposite, invisible.  And so, again, like a black-hole, we must look at cases where the mysterious something behind the barrier interacts, at least indirectly, with things that are within our conceptual realm.

This is where the example of quantum mechanics introduced above comes into its own.  Let us say that my proposal that there is an epistemic barrier preventing us from acquiring complete comprehension of the quantum realm is correct, but that some of the concepts are partially accessible.  So what happens?

Well, if we look at quantum mechanics, and especially quantum field theory, we get quite a clear picture.  Some parts of the theory are very well understood, so we can solve the Schroedinger equation for simple systems.  Moreover, we can make rather accurate predictions about many things, from the behaviour of transistors, to what happens when you smash particles together in a supercollider.

But what we do not have is any sound conceptual understanding of how we make these predictions.  The problem with quantum field theory is not just that the mathematics it is based on is sloppy.  The problem is that the mathematics simply doesn’t work, to an extent that you can actually make the theory produce whatever result you want it to.  The theory is based on a plethora of assumptions that seem to have no logical basis in physics, mathematics or anything, but which are required in order to get the ‘right’ answers.

Now this baroque complexity is, to my mind, rather reminiscent of the Ptolemaic description of the solar system, with its cycles and epicycles.  In other words, it is an attempt to describe that which cannot be described within the existing conceptual framework.  So, just like the epicycles, it can predict the right results, but that is not surprising given the rather large amount of fine-tuning that has gone into building the theory in the first place.

This leads me to another analogy, which is, I think the crucial one.  We humans are programmed to recognise faces, as recognising other people is a key survival skill.  And as such, whenever we look at any random-ish pattern, be it clouds, wallpaper or a carpet, we see faces.  We find patterns that are not really there.  Looking back at the example of quantum mechanics, it is hard not to conclude that the same is happening.  We have a collection of concepts that we can understand around the edges, but where understanding tails off into random noise when we approach the barrier.  And so the baroque complexities of quantum field theory are simply the equivalent of faces in the clouds: imaginary patterns that we trace in the randomness to fill in the gaps in our understanding.  We think that they tell us about the universe, but in fact they tell us about ourselves.

And this, I believe, is what will happen when we look at an epistemic barrier.  We will not see a barrier, but rather gibberish in which, being the pattern-seeking creatures we are, we will find patterns.  But we can expect such patterns to be unsatisfactory, and insusceptible to any deep understanding, because at best they are attenuated shadows of the the unknowable, and at worst they are nothing more than random nonsense dressed up with the trappings of reason, and as such our belief in them will eventually (as seems, regrettably, to be the case with quantum field theory) become a matter more of theology than epistemology, and so to derive its strength from faith and not reason.

Now that idea opens up a whole new, and very tempting possibility for philosophical exploration, that is to say, an examination of the epistemological location of the deity, but I believe that now is the time to bring this essay to an end.  We have seen that there are bounds on knowledge, but that those bounds are themselves unknowable, and moreover that though information may leak across the boundary, we will never be able to tell whether it is true air from another planet, or just images drawn on the clouds by our imaginations.

## 1 Introduction

In a recent essay I made some, in retrospect, rather excitable claims about the possibility that a potentially insurmountable epistemic barrier might be emerging as a kind of fault-line within our culture. I wrote, of course, while impassioned, which is never wise, and cooler reflection has led me to doubt my own conclusion. This essay is therefore an investigation of the whole question of epistemic barriers. It does this in three sections. First it takes a second look at my original argument (made in my piece The Other in Culture) which used Quinean radical translation to prove that epistemic barriers are impossible and examine it very carefully for hidden assumptions, which, it turns out, are rife. The next section then analyses these assumptions in order to see when they break down, the point being to answer two questions:

 (1) How dissimilar can two individuals be in culture and Weltbild and yet still not suffer from an epistemic barrier to converse? (2) How dissimilar do two individuals have to be before they do suffer an epistemic disconnect?

The second of these questions is, obviously, the harder to answer, involving as it does some extremely imaginative Gedankenexperimente: in fact a fully adequate answer can only really be achieved by approaching the barrier from the other side, which is clearly impossible, and so we have already found that there are facts about this area of enquiry that are in principal unknowable. If an epistemic barrier exists we can have no idea of what resides on the other side, or of how many further barriers may exist beyond it. Therefore question (2) needs to be reformulated less ambitiously as:(2’a) Is it theoretically possible for epistemic barriers to exist?

 (2’b) If they do, what, if anything, can we glean from communications issuing from the other side? (3a) Is there any way of proving the existence of an epistemic barrier? (3b) Is there any way of detecting communications emanating from the other side of an epistemic barrier?

Answering these questions leads naturally onto the final part, where I take up again the question from The Male Gaze Gone Wrong of whether there is, in fact, an epistemic barrier within Western culture, dividing the self-focussed culture of ego-reinforcement from the more old-fashioned outward-looking culture. My conclusion is that there is not, but there is a very hard problem in radical translation.

## 2 Terminology

Now, some of you will have already been put off by my rather specialised terminology. My article will rely on some key concepts that I will define here, simply so we all know what is going on, and you understand why I feel unable to use plain English. So, here we go.

• Epistemic Barrier: essentially a barrier to the free flow of knowledge between two parties. This is more than simply a language difference, because language differences can (in principle) be overcome by translation (see below). It is a systemic separation that cannot be overcome by any act of translation or representation, so on both sides knowledge exists, but the knowledge on each side is in principle unknowable by individuals on the other side. Obviously epistemic barriers are subtle and mysterious, if only because (as far as we know) we have never actually encountered one, and yet (as I shall argue below) they must exist. Their enormous importance arises from the fact that they bound the realm of the knowable, and so put us, as it were, in our epistemic place: we will not, can not know everything.
• Translation: means rather more in philosophy than everyday language-to-language conversion. Rather it deals with the communication of ideas from one source to another which may not share the original’s episteme (ontology, knowledge, beliefs, etc). Thus, in a sense, when I write these words and you read them, an act of translation is going on even if we both have English as our native tongue, because your episteme is naturally different from mine (we are not the same person) and so the meaning I place on these words as I write them may differ from the meaning you draw from them as you read them. Quine’s radical translation argument is an attempt to understand the limitations that are inherently placed on this translation process which derive from the fact that extension (truth value) is public, whereas intension (meaning) is private.
• Weltbild: has a wider meaning than any one English equivalent, hence my use of the German term. It is world-view, conceptual apparatus regarding the world, ability to derive information from the world, and essentially everything about how an individual experiences the world they live in. This differs from world-view in that it is not about attitude, it is something deeper and more inherent in our nature. Thus you and I may come from absolutely differing cultural backgrounds, and have no world-view in common, but we share a common Weltbild essentially because we are both (I hope) human, and so have a common way of being in the world, common senses, and common cognitive apparatus. This is crucial, so let me just ram it home: Weltbild is not about ideas, it is about the state of being in the world, one’s (to continue with the Germanisms) Sitz im Leben.
• Language: has a much wider meaning than natural language. It is taken here as being the entire conceptual apparatus we use to form, convey and analyse knowledge, so it includes natural language, symbolic languages (e.g. mathematics, logic) and other less formal modes of dealing with processing knowledge, such as imagery and symbolism. Thus my Weltbild is my epistemic state, while my language is the agent I use to act upon my Weltbild

## 3 Radical translation and its underlying assumptions

### 3.1 The Proof that Epistemic Barriers do not Exist

I will now rehash the Quinean argument for (at least limited) mutual intelligibility, with the intention of then proceeding to examine the hidden assumptions (if any) on which it rests. Readers of The Other in Culture may recall that there I used Quine’s example where you and I are trying to communicate and you are endeavouring to determine what I mean by the word ‘gavagai’, which you suspect inhabits the same region of epistemic space as your word ‘rabbit’. I shall not use that example here, the argument being more abstract, but it is useful to keep it in the back of the mind, in case the abstraction becomes overwhelming. Say you and I are communicating. Then, in endeavouring to understand what you say, the information available to me is:

• The sentences you utter
• The truth value you assign to them
• The collection of sentences I am able to formulate
• The truth values I assign to them

I also make two key assumptions:

• The principle of substitutivity: if S in your language translates into S‘ in mine then they should agree in truth value in all possible linguistic and epistemic contexts.
• A theory of truth: the rule whereby I can relate the truth-values of sentences in differing contexts to their structure and syntax and the truth values of their constituent objects and predicates.

The principle of substitutivity is fairly obvious: essentially it says that if S and S‘ correspond then one should be true or false precisely when the other is, and vice versa. This is little more than a statement of the principle of extension from set theory (if two sets have the same members and the same non-members then they are the same set). The theory of truth seems equally unproblematical, but in fact the meta-theory of theories of truth is immensely complex. Let it merely be said that there are many theories of truth, that it has been proven that no theory of truth can be complete (in that there will always be sentences that are neither true nor false), and that different theories can give rise to very different results. Those wishing to learn more should consult Understanding Truth by Scott Soames. So how to I apply these assumptions to the data available to me? I play a complex matching game, endeavouring to find correspondences between your sentences and a subset of the sentences available to me. This will, in general, be extremely hard, because if you happen to say (for example) Klaatu burada nikto, then unless I am given some clue as to your intention, or I have a very large body of your other sayings, pinned to precise epistemic contexts, I am not going to get very far in translating it. This is why when discussing radical translation we generally simplify the game by using ostensive sentences, that is, the sentence that you utter is accompanied by some gesture or other meta-linguistic communication that indicates that your sentence refers to some part of the epistemic context in which we both find ourselves. This reduces the number of sentences that I have to evaluate in order to guess at your intention. Obviously we start with very simple sentences like ‘there is a rabbit’ rather than with recitations of national epics! The goal of all this is to reach a point where you utter a sentence which is held to be true, and I am reasonably sure of what that sentence is. I do this by looking for substitutivity: that is to say, I seek out circumstances where your sentence is or is not true and compare it to my sentences in those circumstances. The correct sentence(s) should be substitutable into any context and give the right answer upon substitution. To cut out the technicalities (of which I will note only that they depend vitally on my choice of a theory of truth, because I need to be able to get from truth or falsity of sentences to truth or falsity of predicates and vice versa), we reach the point where you and I can form sentences and I will know that your sentence S will be true precisely when my sentence S‘ is true. The question now is, does this mean that I know what S means? And the answer is: most emphatically, no. I know the extension of (potentially) every term and predicate in your language (by which I mean I know its truth conditions and how to use it in the process of forming valid sentences). But as for its intension, which is that which makes it be true or not true in the first place, i.e. its meaning, there is no way I can know that, because all I have been able to use in my act of radical translation is truth values and substitutivity. So I know (it seems) little or nothing about meaning. For example, unless one lives in arctic regions the sentences it is daytime and there is sunlight are substitutable, but their meaning is clearly entirely disparate; one can distinguish them eventually, but that involves some quite deep analysis of pairs of sentences, and establishment of complexes of analogical concepts. That was a problem caused because we had not probed far enough before forming our translation model. So, now consider the German phrase gut Bürgerliche Küche. It translates straightforwardly as good middle-class cooking, and yet the meanings of the two phrases are entirely different. The German has strong positive connotations, while the English has, if anything, faintly negative connotations. Our different cultures create resonances that are simply not there in the words themselves, and can only with difficulty be established using substitutivity (to do so would be very complex indeed, requiring a comparison of emotional reactions, which immediately calls into doubt the validity of the translation process). Now consider the ultimate distinction: that between individuals. The sentence This is sweet is simplicity itself. And yet what does it mean? We can say This is triggering certain taste receptors on my tongue, but though the extensions of those two sentences are identical (they are completely substitutable), the second does nothing at all to illuminate the former. I know what I think sweet means, you know what you think sweet means; but how much of that can we communicate? The sensation of sweetness is too direct, too immanent for us to describe: rather than being decomposable into parts susceptible of discussion and analysis. It is atomic and thus indescribable, other than in terms of its presence or absence, even though it is a very intense sensory experience. What this means is that I can discern by radical translation, precisely as much of the meaning that entities and predicates have for you as you are capable of expressing linguistically and no more. But then, if you cannot express those missing shades of meaning linguistically, it is not only I who loses them, but also those who share your language. Thus in principle, anything you can communicate in your own language, you can communicate to me. Thus, if this argument does, in fact hold, there can be no epistemic barriers. Now, is this a realistic model? Yes. When you and I communicate, even if we do it in the same language, we have to assume that we assign the same truth values to linguistic units, which we verify by comparing the contexts they appear in, and also that we share a common way of building linguistic units (with truth values) into true sentences. We know nothing of each other’s internal state: only of that which can be discerned externally (and which can all be lumped together under the heading of ‘linguistic units’ with little violence) is available. And though this approach may be criticised for reducing everything to the black-and-white world of truth and falsehood, it is not clear that a more nuanced approach would work any better, given that by using truth-value and substitutivity I can translate adequately all that is expressible.

### 3.2 Assumptions of the Argument

Progressing through the argument, the hidden assumptions more or less scream for attention, but it is still worth discussing them. So, I will start by listing and defining them and then progress to a general discussion in which I aim to crystallise the key points that may permit the existence of epistemic barriers after all. Let me first of all, however, point out that it should be clear from the analysis above that the argument is extremely strong, and moreover it is supported by our experience of translation to date, that is to say the creation of mutual intelligibility between speakers of all known natural languages. It is therefore not surprising that the existence of epistemic barriers – systemic barriers to communication – is generally unsuspected or even denied. So, the main assumptions are as follows.

#### 3.2.1 Substitutivity

Substitutivity seems, at first sight, to be watertight, as is little more than tautology. But there is in fact a meta-assumption underlying it. That is to say, we assume that given languages L and L‘ then there should be a consistent translation relation between the two languages, so sentences S and S‘ are related precisely when they are substitutable. But what if it proves impossible to define such a relation? That is to say, what if it is impossible to find a consistent relation between S and any sentence(s) in ‘L‘, so S appears, to a speaker of L‘ to have no fixed interpretation, in spite of the fact that it is clearly meaningful to a speaker of L? In this case the principle of substitutivity is true but useless, because we have nothing to apply it to. If sentences are not substitutable then we cannot compare them across epistemic contexts, and so the whole enterprise of radical translation collapses.

##### Conclusion
• We must consider the impact on substitutivity of a failure of two languages to form a consistent translation relation.

#### 3.2.2 The Theory of Truth

The theory of truth is clearly an enormous assumption, with many ramifications. There seems to be a rather naive assumption that all communicating beings will use a two-valued Aristotelian logic, and yet we find that three-valued logics (where the values are ‘true’, ‘false’ and ‘undetermined’) are almost essential if we are to deal with truth in any rigorous way, not to mention some of the other standard logical paradoxes, while early Indian philosophers made use of the dialethic four-valued logics (‘true’, ‘false’, ‘neither true nor false’, ‘both true and false’). Though this may seem very abstract, ones choice of logic is a key determining factor in how one sees the world (or possibly the other way round) and so may limit ones ability to comprehend the function of sentences in an alien language. For example, if I use three-valued logic while you are rigidly two-valued, many of my statements must seem to you perverse or unaccountable, for deductions that to you are obvious are not to me, and thus substitutivity starts to fail. We can go further. The theory of truth, in that it is a way of deriving the relation between the truth value of a sentence, the truth values of its components and the sentence’s structure, makes some very fundamental assumptions about the structure not just of the known language (which is legitimate), but of the unknown language. It so happens that the languages we know of follow broadly the same syntactic structures (though there have been sporadic reports of such oddities as languages without verbs, they remain unverified) but to insist that all languages must be like human natural language and are formalisable within the languages of logic that we have so far discovered seems unreasonable. It can, and no doubt will, be argued, in rebuttal of this claim, that it is inconceivable that there should be a language that is not based on our categories, but there are two rebuttals to the rebuttal. First, and rather obviously, it is all we know, so obviously anything else seems inconceivable. Second, and more insidious, language shapes our episteme, what we can know and conceive of, is shaped by our Weltbild, that is to say the world of ideas that we and our imaginations inhabit, the way we ontologise the world around us, etc. If I do not have the epistemic apparatus required to conceptualise an idea, then I cannot conceive it. That sounds trivial, but it has enormous consequences. So if L has one syntactic structure and L‘ another, incompatible, syntactic structure, then substitutivity is bound to fail, and it will be impossible to establish a translation relation. This is simply because in translating from ‘L‘ to L we will be forcing L‘ into the structures imposed by L. As I indicated above, even when translating between two such closely related languages as German and English some information is lost. If we go to the extreme case of two languages with incompatible grammars, then information will inevitably be lost, as well as false information being created, because concepts expressible in L‘ will be inexpressible in L, and hence translate into nonsense, or fail to translate at all. Another way of saying this is that if I am to translate you effectively, then my language must be large and complex enough to be able to express any concept expressible in your language. This is not necessarily the case.

##### Conclusion
• Our language’s syntax shapes the way we approach and translate other languages, and limits the extent to which we can comprehend ideas expressed in alien languages.
• If I am to translate faithfully from your language to mine then my episteme must encompass yours (else there will be untranslatable concepts)
• Our choice of logic shapes the way we will model truth values.

#### 3.2.3 Kinds of Truth

There is another, even deeper, assumption relating to truth. In the discussion of theories of truth above, there is a hidden assumption that there is essentially one truth, but many different ways of finding it, so we did not question atomic truth: what it meant to apply a simple predicate to an object and to assert that the result is true. All of our discussion simply took atomic truth as read and dealt with the problems inherent in building from atomic truth to the truth (or otherwise) of complex sentences. But there is no guarantee that there is only one kind of atomic truth. For example, consider the atomic predication this stone is red. In our language, L, that means that the stone is coloured red at the precise instant that the sentence is asserted. If it had been blue five seconds before and was green five seconds later, that would not affect the truth of the assertion. But it is equally possible to imagine a language L‘, that takes into account the whole life of the object subject to predication, according to which, this stone is red required that the stone (to the best of the utterer’s knowledge) has always been red, is red, and will always be red. L and L‘ are both internally consistent, and so lead to sound theories for complex sentences which are in themselves consistent and as complete as any theory of truth can be, and yet they are utterly incommensurate. Consider for a moment just how alien L‘ is. We could see a red stone, and so assign the value true to this stone is red, and yet two individuals whose Weltbild is defined by L‘ could disagree as to whether it was red if (say) one of them had seen it before it was painted, while the other’s experience of it is limited to times after it was painted. Similarly, aL‘ speaker could assert that a traffic light was red and amber and green simultaneously without any contradiction. The apparent incoherence of truth in L‘ arises because the truth of sentences evaluated now depends on events at other times or epistemic places, and is a characteristic of intensional logics, such as modal logic or (as here) tense logic, but our logic in L is extensional, and so, from our point of view, L‘ is incoherent and nonsensical. In other words: the principle of substitutivity fails because L‘ is intensional. In fact, in this case we could save the situation because though truth in L is extensional, L contains intensional elements, meaning that we can express L‘ within it, and so a suitably modified form of the principle of substitutivity (with substitution into equivalent intensional contexts replacing simple extensional substitution) would be true. But, it is, of course inevitable that our language can contain encompass L‘; if it could not then I would have been unable to specify it so precisely. My point was to show that even a concept of truth very close to our own can result in an apparent collapse of the mechanics of radical translation. Generalising, languages which make use of such concepts as metaphorical truth, symbolic truth, moral truth or mythological / religious truth have the potential to be completely disruptive, because though I can broadly describe each of them as having an intensional truth function, now, unlike L‘, I cannot necessarily describe them in L, because their Weltbilde will contain schemata of cultural assumptions which are not identical to my own, and to which I have no access, as they are hidden behind a linguistic barrier. Thus such a language must be incomprehensible to me, as I have no common point of reference (which I did in the case of L‘) against which to evaluate sentences expressed in it (an elegant example of this is the Ancient Egyptian concept of Maat, which means – amongst other things – truth, but is more complex than extensional truth, including as it does concepts such as cosmic order, and is now rather mysterious because the cultural background that made Maat precise to an Egyptian was never written down, and hence is lost to us). So, even within the bounds of the describable, it is possible to imagine concepts of truth that are sufficiently alien that radical translation may break down. But there is no reason to assume that every concept of truth must be describable within our culture’s Weltbild. And with these indescribable concepts of truth, we have to assume that radical translation must fail, for if we cannot even describe the conditions under which a language marks a sentence as being true, how can we achieve any consistent translation from it to our language? As I hope I have demonstrated, the concept of truth and cultural baggage, or Weltbild are inextricably linked, so it is naive to assume that radical translation will work under all circumstances.

##### Conclusion
• Radical translation fails if the Weltbilde of the two languages do not have a common concept of truth, which means there must be sufficient commonalty of cultural background.

#### 3.2.4 Ontology

Another hidden assumption of radical translation is that the speakers of the two languages share, if not a common ontology then at least commensurate ones, so there is a discoverable rule that links objects in the two Weltbilde. That this is true should be fairly obvious: we cannot even begin to analyse sentences to discover structure and truth-value if we have no way of expressing or comprehending the objects referred to within those sentences. So, for example, a Weltbild whose ontology identified all things of a kind would prevent the formation of n adequate translation relation. And this would apply in both directions, because clearly the possessors of this Weltbild would have no concept of individuality or self, while our Weltbild and languages are predicated on the distinction between self and other. Thus, though we and they could possibly communicate very simple concepts (though even those may be fraught with complexity: so simple a sentence as it is not raining may fail, because to our interlocutor it is always raining somewhere, so it is always raining) any sentence involving quantification or individuals would fail to translate. This is now going beyond a difference due to one truth-function being intensional and the other extensional; we are reaching the point where the languages are simply too different even for us to be able to make such a statement: the concept of truth is simply other. Before it be said that this is merely a Gedankenexperiment, consider an even wilder Gendankenexperiment which turns out to be something of a parable. Say we are trying to communicate with a being who perceives not, as we do, macroscopic objects, but rather quantum wave functions. So, if I point and say rabbit this will be absolutely meaningless to the quantum creature, because as far as they are concerned there is always a rabbit everywhere, albeit with shifting probability distributions. So our ontology, which is based on precisely located discrete objects, and their ontology, which is (at a guess) based on shifting globalised objects with no clear individual existence, are so much at variance that it is hard to see how we could even begin to establish a translation relation. Indeed, as I have observed elsewhere, much of the vaunted ‘difficulty’ of quantum mechanics is likely to stem from a misguided attempt to force the language of the quantum creature into the straitjacket of our definitely non-quantum Weltbild. We should be impressed that we have achieved even our rather limited understanding of the quantum realm, which suggests that even if we can never truly understand a language on the other side of a barrier, we might be able to abscond with some crumbs of knowledge.

##### Conclusion
• Incommensurate ontologies can prevent the establishment of a translation relation.
• Though full translation across such a barrier is impossible, we may be able to achieve very limited and fragmentary partial communication.

#### 3.2.5 Meta-Linguistic Issues

Finally, there are a number of meta-linguistic issues that focus on two areas. FIrst, how do we know when an ostensive sentence is being uttered? And how do we know what are the objects being picked out? Or, conversely, how do we know that if we point at an object and utter its name, our interlocutor will understand out intent? The answers are simply we can’t, we can’t and we don’t. We have to make some behavioural assumptions as regards body-language or physical behaviour. And while this is all very well when dealing with other members of our species, or even closely related species, it would not work if we were trying to establish communication with (say) the quantum creature of the previous sub-section, to whom the whole concept of ostention would probably be meaningless anyway. The second issue is more insidious. For radical translation to work I have to know when my interlocutor thinks that what they are saying is true or false. I could assume that if they point at something red and utter hokak then they are asserting that it is red is true, but that is my assumption, and, for all I know, they could be saying it is not blue or even (plausibly) it is green, knowing that the assertion is false, for why should they not have an apophatic language which works by making false assertions? By assuming the truth value based on how my Weltbild dictates I use language, I am imposing the structure of my Weltbild on theirs, and so, if I do eventually arrive at a translation, I will seriously misrepresent what they are trying to say. And – here is the key point – there is no reason to assume that I would ever discover my mistake. As an example of this, consider Athanasius Kircher’s extraordinary ‘translation’ of Ancient Egyptian, which foundered on his assumption that the Egyptian conception of truth was allegorical rather than simply extensional.

##### Conclusion
• Radical translation relies on at least some common form of communication, if only at the level of body-language, so in fact before we start we already assume something out the other.
• We must not assume that our interlocutors use their language to convey meaning in the same way that we do; to do so only results in a translation that misrepresents them.

#### 3.2.6 General Discussion

There is little more that needs to be said. It is clear that radical translation will only work if the two parties involved have Weltbilde that are sufficiently close that concepts existing within one are expressible in the other. We have seen that it is entirely plausible that there should be Weltbilde sufficiently disparate that this is not the case, and thus that in these cases radical translation will fail, meaning that we will have discovered an epistemic barrier. The only crumb of comfort is the suggestion that some very low-level communication may be possible such a barrier, though inevitably information would be lost when passing even the simplest concept in either direction. We shall return to this in the next section.

## 4 On Epistemic Barriers

### 4.1 Language Shapes Episteme

I observed above that the structure of our language (interpreted in the widest sense as being essentially equivalent to Weltbild) limits what we are capable of knowing, and therefore shapes our episteme. A consequence of this is, naturally enough, that it is entirely possible that there should be things that we can never know because our Weltbild cannot contain them. That is to say that the existence of epistemic barriers is possible. Now this is a rather startling conclusion from what was, when first mentioned, treated as if it were merely obvious. Let us therefore examine how Weltbild shapes episteme, taking as our starting-point three examples: one from physics and two from mathematics. The example from physics is our old friend, quantum theory, specifically the infamous double-slit experiment. In this we shine a beam of electrons at a barrier with two slits in it and measure the density of electrons emerging from the other side. Now we assume that electrons are particles, because in other experiments they have behaved like particles. But in this experiment it turns out that they are behaving like waves, and apparently have the ability to pass through both slits at the same time. In our normal Weltbild this makes no sense at all: something either is a particle or a wave. When one switches to the Weltbild of quantum mechanics these problems go away: what was a sometimes a particle sometimes a wave is revealed as an entity in a vast (infinite dimensional) space, and it turns out that though there is a way to relate these entities to our Weltbild, it is neither simple nor very well-defined, so it is entirely possible for one entity to at the same time look like both a particle and a wave, depending on how you view it. Now to mathematics and the concept of higher-dimensional space. For someone not trained in mathematics, the idea of a space with four dimensions is utterly mysterious; they have no way of conceptualising it and no machinery with which to mentally take hold of it and analyse or envisage it. However, with sufficient mathematical training one reaches the point at which higher-dimensional geometry is seen as merely a natural generalisation of our three dimensions, and eventually one gains the ability to conceptualise geometry directly in terms of algebraic objects: every geometer will be aware of the moment where they stopped trying to draw pictures in their heads and started to think conceptually instead. So while mathematicians cheerfully talk about four, seven or even infinitely many dimensions, the lay-person is left floundering. Now consider something even stranger. For most lay-persons the concept of infinity in itself is rather troubling; indeed, the formal definition of an infinite set seems simply counter-intuitive. Thus the idea that there might be different kinds of infinity, with some larger than others is simply incomprehensible. And then when we move on to observe that given any infinite number one can always construct a larger infinite number, that therefore there is an unbounded hierarchy of infinite numbers which is itself infinite in extent, and that there are some infinite numbers so vast that they cannot be obtained by operating upon any of the infinite numbers smaller than them and yet even these numbers have others bearing the same relation to them as they do to smaller numbers, something akin to panic is likely to set in. And yet, with sufficient mathematical experience one can reach the point of being able to work with these ideas and to have some form of comprehension of what they mean. What lessons can we draw? The example of quantum mechanics shows a case where radical translation is perhaps failing, in that the translation relation is extremely ill-defined. In fact, it is entirely plausible that the quantum Weltbild is so alien to ours that it is on the other side of an epistemic barrier, and so our current difficulties with formulating a consistent, coherent quantum theory are inevitable given that, for us at least, comprehending the quantum realm is impossible. As another example of the pitfalls of this kind of inadequate translation, consider the case of the grammaticalisation of the Finnish language. Non-fennophone linguists approached Finnish as if it were Indo-European (which it is not) and attempted to systematise its syntax based on a Weltbild derived from the study of Indo-European languages. Thus we end up with a language in which apparently there are fifteen cases, four types of verbal infinitives, some of which decline (?), and syntactical rules so complex as to be nearly meaningless. As with quantum mechanics, difficulty is a consequence of badly-mismatched Weltbilde, and in both cases the result is that the language being translated from (the quantum realm, Finnish) becomes almost incomprehensible when translated. We simply cannot fit the ideas into our episteme because our language, our Weltbild does not permit it. A second observation from the quantum-mechanical example is this. The initial reaction to the double-slit experiment is a conceptual failure because we expect that something is either a particle or a wave. It cannot be both. So when something acts as if it is both then we have no recourse but to panic. But why not both? Largely because the concept that entities as we experience them are ‘real’ in some sense is deeply embedded within our Weltbild, and we do not expect ‘real’ things to be of two kinds at once. In spite of the startling ease with which it is possible to fool them, we believe our senses precisely because if we do not then what do we believe? Our animal inheritance tells us to act on what we sense and treat perceived things as being concrete. Thus the idea that a perceived thing is in fact only a representation of a larger and more complex reality, forced to take its particular form by the limitations of our senses, is not one that comes easily to us, let along the obvious conclusion that the entire realm of what we perceive is essentially a construct derived from outside reality (if there is such a thing) by our limited ability to translate from its language into one that we speak (in the widest possible sense). It is perhaps worth stepping back and taking stock, as we have entered some very deep waters. The conclusion I seem to have drawn is that what I am and what I know, so the totality of my Weltbild, limits what I am able to comprehend. Is this particularly surprising? I don’t think so. Just as people had no concept of micro-organisms prior to the invention of the microscope, if we do not have the machinery to detect something then we won’t. And if we have perceptual apparatus that can partially detect something, then we will perceive fragments of it which we will then translate as best we can, given that we are lacking some (maybe the crucial part) of the information required to make an accurate translation (think of what a foreign language sounds like to one who cannot speak it). But turning from senses to ideas, the two mathematical examples show that without the right conceptual toolkit certain areas of epistemic space are inaccessible to use, whereas once we have acquired the toolkit, we can navigate them with (relative) ease. Indeed, the example of geometry, where something in the mathematician’s head ‘clicks’ and they pass from having to try to model geometry using two or three dimensional analogies to being able to see directly the geometrical significance of the algebra, is a clear case of someone learning a language and reaching the point where they no longer need to translate back to their native tongue but can work confidently in the new language. So there are ideas that we are unable to grasp unless our language is expanded in an appropriate way (as a very mundane example, anyone who can speak German will know what gemütlich means, and yet it cannot be translated adequately into English), but then we will have difficulty translating those ideas back into the base language. In other words, we are seeing, not an epistemic barrier, but more a kind of epistemic one-way road: one can expand ones Weltbild to allow the conceptualisation of new ideas, but there is no way of taking ones new knowledge back home. In conclusion then, language clearly does shape episteme, in that it dictates what knowledge we are able to comprehend, and may render knowledge that lies beyond these bounds as nonsense. We can, in an irreversible process, expand our language to encompass new concepts, and hence expand our range of epistemic possibilities. Now, our base language is clearly not complete, where by complete I mean is capable of encompassing all concepts, or, to put it another way, it covers all epistemic space. So, as our base language is incomplete, why should the extension be complete? Clearly this is highly implausible, particularly as we cannot prove that a language is complete, for how can we prove that there are no ideas it cannot encompass, particularly in view of the fact that ideas alien to a Weltbild may well be entirely invisible from within that Weltbild? On the flip-side, we cannot, from within a language prove that it is incomplete, because to do that we would have to be able to conceptualise ideas that the language cannot conceptualise. Therefore we can only know that our language is incomplete once we have extended it. So we are in a state of permanent uncertainty as to whether there is or is not fresh epistemic space to be explored. Therefore we can never guarantee that there is not knowledge ‘out of reach’, and therefore epistemic barriers are not theoretically impossible, answering question (2’a).

### 4.2 The Existence of Epistemic Barriers

In fact, I can strengthen this. Introduce a relation between languages, so L < L‘ precisely when L‘ is an extension of L that grants access to greater epistemic space. Also, identify languages that are susceptible to perfect translation, so we are talking here of classes of mutually intelligible Weltbilde. Say that L is maximal if it is inextensible, so there is no L‘ such that L < L‘. Clearly a complete language C (if one exists) is maximal, but can a complete language exist? Let us restate the question: can maximal languages exist? Can a language have internal tensions that prevent it from being extended? Unless one takes a very essentialist view of knowledge, and seriously believe that there is, as it were, an epistemic terrain waiting to be explored, then the answer must surely be no. For example, some natural languages have highly restricted number systems, so it is impossible to count above some specific small number. So it would be impossible to express any truly mathematical concepts in such languages. But that does not prevent speakers of those languages from extending their epistemic range to include mathematics for the very reason that makes it possible for us to know of the language’s limitations in the first place: that is to say that translation between these languages and languages with unrestricted number systems is achievable. Certainly, individuals have to learn an unrestricted language at an early age, before the restricted Weltbild is locked in, but the point is that being a native speaker of (say) Mangarrayi does not place an irrevocable epistemic barrier in ones way. So, generalising from this, it may be than an individual natural language is inextensible, but that does not prevent it from being translatable into a more epistemically flexible language that can be extended. This leads to an interesting point. If the speakers of Mangarrayi had never encountered European colonists then an external observer might have thought that their language was inextensible and incomplete. But, as we know, it was extensible (this is where the distinction between the epistemic languages we are discussing and natural languages is crucial: the natural language Mangarrayi is inextensible, but the epistemic language of its speakers is extensible). This comes back to the point made above that we cannot make any predictions about the path forward; we can only look back. For all we know our current language may be maximal, but all the evidence suggests that it is not, for it has been extended before, and, as we have just seen, apparently inextensible languages can be extended, and moreover, just as we cannot prove that it is not maximal, we cannot prove that it is. All of which comes down to a strong argument for the in-principle non-existence of maximal, and hence complete, languages. We need a new definition of completeness. If the speakers of Mangarrayi had never met Europeans (or any other group whose language had a complex number system) they would most likely never have developed mathematical thought. And yet, clearly their Weltbild gave the potential for mathematics within their episteme (in the same way, anyone who understands simple arithmetic has the potential within their Weltbild for an understanding of transfinite arithmetic). Generalising, all we can know is where we are now and where we have been; we cannot know where we will go, because that is contingent on unknowable future events. Thus in speaking of epistemic potential, which is precisely what we are speaking of when dealing with epistemic barriers, we must consider as the completion of our current state that portion of epistemic space from which we are not separated by an epistemic barrier, which is precisely the union of all possible languages extending our current language. Strictly speaking this union may not itself be a language (the mathematically inclined can fill in the details if they so wish), for clearly not all of its constituent parts need be mutually intelligible, but it is a member of a larger category of things that I will call language*, whose precise structure I will not bother to elucidate overmuch, beyond noting that every language is also a language*. So, a language* is *-complete if it is the union of all languages extending some language. Call the complete language* derived from a language in this way its *-completion. Clearly this is inextensible (which shows that it is not itself a language); we can also prove that any extensible language* is a *-completion. Let C be inextensible in language*; it contains some language L. Then C must contain the *-completion of L, because if there was some language L‘ that extended L but was not contained in C then we could extendC by adjoining L‘ to it (this extension is legal precisely because L‘ is the extension of something already in C). So all inextensible elements of language* are *-complete (note that going to the larger category of language* allows us to make statements that are unprovable, or simply untrue, of languages simpliciter). So we can now formally state what it is for there to be an epistemic barrier between two languages: it is simply that their *-completions are not equal. Or, in other words, the potential epistemic spaces, given the two languages as starting points, are distinct: there are ideas accessible in one that are inaccessible in the other. So we can divide languages into epistemic classes, which are languages which have the same *-completion, and hence which are potentially intercomprehensible. And now, here is the point (at last) of all this formalism: there is no a priori reason why there should be a unique inextensible language*. In fact we can know little about the category language*. For example, the only members of language* we can know are the languages simpliciter that are comprehensible to us; to know a non-trivial language* we would have to know an infinite series of languages, which would require us to predict unknowable future events, so it is very hard to determine the characteristics of a *-completion. Now, De facto the only elements of language* we know are those in the same epistemic class as our own. Anything else is either a language, which cannot be comprehensible to us, as it has a different *-completion, or the limit of a series of such languages. Putting this together, we conclude that there is no way we can determine what is an inextensible language* or how many of them there might be. This means that though the concept of language* is theoretically powerful, we cannot, say, use it to discover alien *-completions and inspect them to discover the form (if not the content) of languages on the other side of an epistemic barrier. Which is interesting, because, though it is clear that we cannot understand a language on the other side of an epistemic barrier, we might have hoped to at least be able to recognise one as being a language. This suggests that even that is not possible, a point to which I shall return. So, if a language lies on the other side of an epistemic barrier, then, by virtue of it having a different *-completion to our language, there can be no point of contact between it and any language we have or might some day have. We must remain forever mutually unintelligible and unrecognisable. Thus I am close to answering question (2’b) in the negative, and to giving decidedly discouraging answers to (3a) and (3b). Answering these questions solidly is the purpose of the next section.

### 4.3 Seeing Across the Barriers

This section takes stock of what we have seen already and then tries to answer one complex question (which has questions (1), (2’b), (3a) and (3b) inherent within it), that is: what, if anything can we know about languages and interlocutors on the other side of an epistemic barrier? I shall discuss this under three headings. First, what could we do if confronted with something that we knew was a communication, but which emanated from the other side of an epistemic barrier? Second, can we detect epistemic barriers? And third, assuming that the communication were not served up to us on a plate, is there any way we could detect communications from the other side of an epistemic barrier? That is, not translate them, but simply know that they are there.

#### 4.3.1 Dealing with Epistemically Alien Communications

Suppose that we have, somehow or other, obtained access to source of information emanating from the other side of an epistemic barrier. Let us not inquire as to how we could do this, and how we could know that that was what it was: those issues are the subject of the next sub-section. The purpose here is to examine question (2’b): having obtained this source of information, what can I do with it?

##### 4.3.1.1 An Analogy

Let me start out with an analogy. Suppose that when we looked at the world, what we saw was pixellated. What I mean by this is that our visual system would divide up the world into cubes, and then within each cube we would see, not detail of the things within it, but a shade of grey whose brightness depended on the amount of ‘stuff’ in that cube, varying from black (empty) to white (completely full). To give some idea of what I am talking about, here are two images.

Elizabeth Vigee Lebrun
Elizabeth Vigee Lebrun pixellated

The left-hand image is what we usually see; the right-hand image is the result of pixellating over 16×16 squares, so every square of 256 pixels is averaged to a single shade of grey. As you can see, if you have seen the original picture, you can spot the parts of the processed picture that correspond to the hat and Madame Vigee Lebrun’s decolletage, hand and (with a little imagination) easel (for some reason her head is largely lost). But that is the point: you are using the original picture as a guide to discern features in the pixellated version. What would you be able to determine about the image if you had only the pixellated version to go on? Well, there’s one way to find out. Look at the next image.

Mystery object

Here we have nothing to go on. If one felt very brave one might hazard a guess that the square was a person, with the white blob at the top being their head, and the truly adventurous might hazard that the mass of white on the right-hand side of the square was something that the person was holding. And that’s about as far as we can go. Certainly there is nothing to indicate that this is, in fact, a pixellated version of the infamous Madonna with bared breast, said to be a portrait of Agnes Sorel. Now the point of this is not just to show how easy it is to see what you already know is there (though that does, undoubtedly play a part in the translation process when dealing with languages that are within your epistemic class, and so which are, to a greater or lesser extent, familiar in their structure), but rather to draw an analogy to the problem of communicating across an epistemic barrier. We on our side of the barrier are, with respect to the alien speaker of the far-side language, in the position of the viewer of pixellated images relative to the viewer of the whole image (though, counter-intuitively, the same will be true of the alien with respect to us, so there is a key distinction between the analogy and the epistemic situation in that in the epistemic case both parties lose information). That is to say, much of what is being communicated will appear to us to be total nonsense, as we cannot apply any form of the substitutivity principle, meaning that translation fails, or worse still, we may not even realise that it is there. But, if we work on a coarse-grained enough level, we may be able to abstract a very partial, fragmented and distorted notion of what is going on. So it may be possible to extract some knowledge from the communication, but there is no guarantee that it is anything that the original speaker would recognise should it be possible for them to examine it, which, of course, it is not.

##### 4.3.1.2 Some Translation Theory

This, last observation leads into what starts as an aside, but becomes crucially important to our argument. Say my language is L and yours L‘ and we have established a translation from L‘ to L. There are only two ways for you to verify the accuracy of my translation of one of your communications. First, you can translate it yourself, and compare the two translations, but then any distortions inherent in the process of translation will remain invisible, as they will apply equally to your translation and mine. So the test whereby you examine my translation into L and consider it as a communication in L is worthless precisely because you have then (unconsciously) taken on my Weltbild simply by electing to use L. So, the second approach is for you to translate my translation back from L into L‘ and then compare it with the original. But this is a notoriously risky business, even with closely related languages: any text distinguishing between pigeons and doves or slugs and snails will become quite garbled in the course of the round-trip from English to German and back again. Also, there is the completely undecidable question of whether the difference between the original and the doubly-translated version arose in the original translation from L‘ to L or the second translation from L to L’. Undecidable because in order to make that judgement we need to have a reference point in both languages, hence a guaranteed ‘correct’ translation of the original information into L. But it is precisely the ‘correctness’ of the translation that we are trying to determine. Therefore, there is no way of judging the correctness of a translation. The best we can do is to seek to reduce the ’round-trip’ distortion in both directions (so L‘ -> L -> L‘ and L ->L‘ -> L). Thus a best possible translation is one that minimises this error (quantified in some pre-determined way), which I will call the epistemic differentiation. Note that as it is the minimum over all possible translations, the epistemic differentiation is not a measure of the adequacy or otherwise of any one translation (indeed, there may not be a realisable best possible translation): it is systemic, a measure of the epistemic distance between two Weltbilde as expressed in their languages, with 0% corresponding to identity and 100% to complete isolation. So, for English and German, the epistemic differentiation is tiny: there are only a few concepts, such as those I have mentioned in passing in the course of this essay, that either do not translate at all or do not translate uniquely. For English and Japanese the epistemic differentiation is far greater, as English cannot express the relative social standings of speaker and spoken-to. But that is not to say that translation between English and Japanese is bad, rather it is the best possible given the epistemic distance between the two Weltbilde. So we must give up entirely on the idea of having perfect, or even good, translations: a translation can lose 98% of the information in the original communication and still be the best possible. If we now take L and L‘ to be on opposite sides of an epistemic barrier, then the epistemic differentiation will be close to or equal to 100%. If it is 100% then there is nothing more to be said: communication between the two Weltbilde is impossible. Say it is at 99.6%, and let us assume that we have a translation that achieves the minimum distortion set out by the epistemic differentiation (I do not propose to discuss how we might make such an optimal translation: for the purposes of this Gedankenexperiment let us simply assume that we have), so we can extract, in a way such that it would be recognisable to the speaker of L‘ if only we could work out how to translate it back, 1 part in 256 of the original information (exactly as is the case with the pixellated version of Agnes Sorel above). Then there are two conclusions to be drawn from this discussion. First, as we saw above, even at this extremely high epistemic differentiation, some information can be extracted. Second, this is, to all intents and purposes, a perfect translation of L‘ into L as it is the best possible translation we will ever achieve given the distance between our respective Weltbilde. So it is perfect given the constraint of our different Weltbilde; we need to relativise our concept of quality of translation.

##### 4.3.1.3 Need the Epistemic Differentiation across a Barrier always be 100%?

Here we enter into very murky territory. There is a simple and concise answer: ‘no’. The definition of an epistemic barrier was a barrier to translation. Taking that as a starting point, let us consider this more carefully. If there is not a total barrier to translation between L and L‘, but there is a very high systemic epistemic differentiation, of the order of ninety-something percent, then does this count as being an epistemic barrier? Consider what I, as a speaker of L can ever glean from L‘ under these circumstances. I may gain some vague general notions, but I will never be able to tell how much of them is inherent in the communication I am trying to understand, and how much is simply my mind constructing artefacts from my own Weltbild in order to make sense of what is, essentially, senseless garble. Because if I can tell then that means I somehow have a means of telling whether my translation is correct or not, so in fact I have available to me a better translation than the one I am already using, so I just use that instead. Going back to the visual analogy, when you look at the pixellated Agnes Sorel, you can begin to read all kinds of things into it, but they have as much reality as the faces that we see in the clouds; they are artefacts resulting from our minds trying desperately to find the familiar among the unfamiliar. The point of this, is that under such circumstances, I cannot honestly say that I understand L‘; all I can really say is that when I encounter a communication in L‘, it puts certain ideas into my mind, but I have no real idea how many of them are strictly conveyed by the communication. Now, I can say, quite justly, that this is true of any translation, but when the epistemic differentiation is small, then at least the two languages are close enough for some form of dialogue to develop. There will come a point at which, with increasing epistemic differentiation, we cease talking to one another, and start talking past one another. Once we are in the talking past mode, though we may each of us understand some small part of what the other is saying, there is no way of verifying our understanding, as that would require a translation of greater fidelity than we are capable of. Which means that communication between such widely separated Weltbilde is strictly one-way, and its accuracy is entirely unverifiable: the ideas I gain from you could be inherent in your speech, or they could be faces in the clouds; I have no way of telling. This seems to me like a very fair description of an epistemic barrier. Thus, in response to question (2’b) we have to say that we may be able to glean something from a separated language, but we can never know how much of what we gleaned was really there, or to put it in a slightly more disturbing way, the best possible translation into our language need not contain any concept recognisable to the originator of the communication. So we conclude that given a Weltbild we can arrange other Weltbilde on a scale, with those permitting perfect translation, whose epistemic differentiation is close to 0%, at one end, and those with which no adequate intercomprehensibility is possible, with epistemic differentiation close to 100%, at the other. We will obviously agree that no epistemic barrier separates us from the Weltbilde whose epistemic differentiation from ours is small, and I have just argued that for a ‘sufficiently large’ epistemic differentiation, there is an epistemic barrier.

#### 4.3.2 Finding the Barriers

So, turning to question (1), where does the barrier set in? It turns out that we cannot even know the answer to this question. What I have just described is the classic setup for the sorites paradox. Briefly, a sorites paradox considers a problem where I have a class of things, and a function that assigns to each of those things a number in some specified range. I then have a predicate that applies to numbers, and which is false at one end of the range and true at the other. The other features that are required to make the sorites paradox complete are two assumptions: that there are no gaps in the values that the function can take and that the truth-value of the predicate is locally constant (it does not change if the value is changed by a small amount). Now it is fairly easy to see what happens: start with an object with value at one end of the range, where the predicate is true, and apply the local constancy to progress to the other end, where the predicate is false. Thus unless one of the conditions breaks down, true=false. Therefore one of the assumptions breaks down. Let me give two examples, one classical, one directly relevant to our discussion. In the classical case the things are collections of grains of sand and the function assigns to a collection the number N of grains in the collection. The predicate is then ‘is a collection of N grains of sand a heap?’ The two assumptions become the assertion that for every Nit should be possible to find a collection of precisely N grains of sand, which is trivially true, and that adding or removing one grain does not change a collection’s ‘heapness’, which is intuitively obvious. In our case, the things are languages, the function assigns to a language its epistemic differentiation from L, and the predicate is ‘is a language with epistemic differentiation n separated from L by an epistemic barrier?’. So, the first assumption is that for all n there should be a language with epistemic differentiation n from L, which is not at all obvious, while the second assumption is that a small change in a language should not tip it over the edge to the other side of an epistemic barrier, which seems reasonable. So, we have established that languages and epistemic barriers form a sorites paradox, and so the two assumptions break down. There are two possibilities. The first is that in fact the range of values assignable to objects does, in fact, have a gap, so there are forbidden values. As noted, there is no a priori reason, in the case of languages, why this should not be the case. The second possibility is that the local constancy of the predicate breaks down somewhere, which, in the absence of a gap, means that somewhere there is a sharp boundary between true and false, heaps and non-heaps, epistemically commensurable and epistemically separated. But clearly we don’t know where this is, else we would not have asserted the local constancy of the predicate. As as we don’t know where it is, there must be some range of values, within which it lies, where the behaviour of the predicate is unknown to us. But now say we somehow discovered precisely where the boundary was. Then we could find intelligible languages arbitrarily close to unintelligible languages, and so we could, with arbitrarily small error, approximate a language which is separated from us by an epistemic barrier. So it is not, in fact, separated from us by an epistemic barrier, as the error in translating it must be arbitrarily close to that involved in translating a mutually intelligible language. This is a contradiction. Therefore, there may be a barrier, but we can never know where it is: there is a region of epistemic space about which we must forever remain ignorant even as to whether it is or is not intelligible, so this is a form of second-order unknowability. Thus, in essence, we are back with the gap. There are some values of epistemic differentiation about which we can simply say nothing at all; values below this range correspond to mutually intelligible languages; values about the range are separated from us by an epistemic barrier. So the answer to question (1), about knowing how far apart we can be before we hit a barrier, is a very firm ‘we have no way of knowing’.

#### 4.3.3 Listening out for Aliens

After the long hard slog of the last sub-section, this should be something of a relief. We now turn our attention to questions (3a) and (3b) which are about proving the existence of epistemic barriers and of languages on the other side of them. Obviously, if the answer to question (3b), on detecting epistemically separated languages, is ‘yes’ then then answer to question (3a), on the provability of the existence of barriers, is also ‘yes’. However, it should be clear from the discussion in the previous sub-section that there is no other way of proving the existence of an epistemic barrier. The sorites paradox argument showed that we can never find one by going looking for it; all we can find is things that we can comprehend, which are de facto on our side of any putative barrier, and things that we cannot comprehend, which are either nonsense or languages on the other side, and we have no way of telling which. And even if we identify something as being a communication in an epistemically separated language, all that that tells us is that there is a barrier, it cannot (again, using the sorites argument) tell us anything about the nature of that barrier or its location. Thus, the barrier, even if its existence is proved, must remain a rather hazy, ill-defined entity, rather like a quantum wave-function (which analogy raises the fascinating possibility that perhaps detailed knowledge of epistemic barriers is separated from us by some kind of second order barrier). Thus the only hope of salvaging any form of positive answer to either question is to find a way of detecting epistemically separated languages. At first sight, our only hope might appear to be if a space-ship landed in Whitehall and an alien got out and nailed ninety-five theses to the door of Number 10, Downing Street. Such a clear ostensive association with a bona-fide alien presence could, if we assume that we were not simply on the receiving end of alien humour, or maybe even garbage disposal, be taken as being pretty strong evidence that the theses were expressed in an alien language. So, if the received communication failed to show any of the signs we would expect of communications that have not been deliberately obscured (observe that encryption can be thought of as the deliberate establishment of a transient epistemic barrier between two communities that otherwise share a Weltbild) then our degree of confidence that they originated from behind an epistemic barrier, and hence of the existence of epistemic barriers, is precisely equal to our degree of confidence that we can recognise languages in our epistemic class when we see them, even when we have never previously seen the language in question. As this is something that we seem to be extremely good at (consider how easy it is to distinguish noise from language, even incomprehensible language, when turning a radio’s tuning dial), therefore we conclude that if an alien committed a demonstrably ostensive act relating to some collection of information and the information had none of the properties normally considered to distinguish language, then we could conclude that we had the elusive epistemically separated language. The question then is, if we were presented with exactly the same information, but without the context of an ostensive relationship to an alien presence, would we be able to say that it was epistemically separated language, as opposed to, say, random noise? The answer has to be no. We just said that it had none of the properties normally considered to distinguish language. So it will have no natural-language or mathematical properties, which means that it is, to all intents and purposes, random. We cannot it distinguish it from random noise, because in order to prove that it wasn’t a currently indecipherable language emanating from within our own epistemic class, we had to remove all properties that we are capable of distinguishing; any evidence of such a property conveys information expressible within our language. Thus, if we are rigorous in our effort to ensure that the putative alien language is truly alien, and not merely mundane but incomprehensible, the act of ostention is the only means by which we can distinguish it from random nonsense. One could question whether we need to be this rigorous, and that we must (in the spirit of the preceding sub-section) allow that alien languages may have some properties, just very tenuous ones. But here again the sorites paradox bites home. It may be that an alien language has some very elliptical property that conveys only a tiny amount of information to us, but we then cannot establish a simple test for alienness, because to do so would require knowing we to draw the line between our epistemic class and the alien, and we cannot, because we do not know where the epistemic barrier is. All we can do is to assert that totally alien languages will be indistinguishable from random noise, and that less remote (but still alien) languages will have some tenuous properties. But from our side of the barrier we cannot say what those properties are, or how strong they can be unless we first have to hand an example of an alien language manifesting those properties, for to predict these qualities of alien languages on purely theoretical grounds would be tantamount to predicting the location of the barrier. So we can only start to detect tenuously non-random alien languages if we have, by way of a boot-strap, an example of a tenuously non-random alien language. And the only way to break out of this loop is via an ostensive act: some extra-linguistic evidence that clearly marks out the information as being an alien communication. Thus, until the day dawns when an alien does land its space-ship in Whitehall, we have to accept that the answer to both parts of question (3) is ‘no’. Note, by the way, that this means that the SETI programme of listening out in the hope of hearing alien communications is fruitless. Even so (apparently) universal a property of communications as modulating radio waves is more likely than not, a feature of our Weltbild and hence not necessarily a feature of alien communications. Adapting the argument above, SETI will only succeed once a friendly alien has told them what to look for.

### 4.4 How far away are the Barriers?

Looking at the argument so far, we seem to have reached a generally pessimistic conclusion. We can say that there is good reason to believe that epistemic barriers exist, but barring exceedingly unlikely events (the ostensive alien) we cannot prove that they exist, and under no circumstances can we determine where they are. It is possible that we may be able to glean some limited information from languages on the other side of a barrier, but we cannot prove that the information so derived was part of the intent of the originator and is not just an artefact of our Weltbild (or worse, our imagination). So, on the whole things look pretty gloomy. There are whole realms of knowledge that will be forever forbidden to us simply by virtue of our nature; anyone seriously believing that they can arrive at a theory of everything might as well pack up and go home, as might the theorists of alien contact. Having reached this generally pessimistic conclusion, let us look again at question (1) where it turns out there is a (small) amount of good news. We can’t actually know where a barrier is, but we can know something about the island of epistemic space around us: though we cannot precisely delineate its coast, we can at least get some idea of how large it is. And the answer to that is quite surprising. First, every human natural language yet discovered fits within one epistemic class; though some languages are more flexible or more complete than others, translation relations have been established in every case where speakers of a language exist and in some cases where the language is now dead. Now, on the universal scale, one species on one planet may not seem like much, but given the sheer diversity of human culture, and the extent to which some groups have been physically isolated, it is rather impressive that simply being human, with the common somatic and mental apparatus that implies, is enough to guarantee a commensurate Weltbild. In fact, we can go further. There is a long history of deeply flawed work on communication with non-human apes, but there are now the beginnings of evidence that it is possible to establish a limited translation relation with chimpanzees, though the work done to date is not sufficiently precise for the nature of the relation to be clear. More impressively, it has proved possible to establish a relatively complex translation relation, including positional grammar, predication and symbolic sentences, with bottle-nosed dolphins. While we might expect our very close relatives, who share a basic body-plan with us, to have some elements of a Weltbild in common with us, it is rather impressive that we can communicate at all with animals who inhabit a three-dimensional world, vice our two dimensions, have senses that we have not and have a body plan very different from ours, let alone being able to formulate a basic generative grammar. And finally, the remarkable case of Alex, the Grey African Parrot suggests that it is possible to establish some form of intercomprehension with a non-mammal (and again an animal with a very different body-plan from our own). Thus, wherever the epistemic barrier surrounding us is, it is clearly not as close as one might think.

## Conclusion

In The Other in Culture, I used the radical translation argument to rebut the claims of some special interest groups that gender or sexuality or some ill-defined racial category is sufficient to guarantee separation. Though the original argument has now been shown to be incomplete, the current analysis shows that my conclusion still holds true. We have seen that an epistemic barrier results not in subtle shifts and biases, but in total incomprehension. As the best that the special interest groups can lay claim to is subtle shifts and biases, unthinking prejudicial language and the like, that means that there is no epistemic barrier, and therefore the radical translation argument holds true. In The Male Gaze Gome Wrong I, somewhat incautiously, suggested that the split in western culture between the older communitarian spirit and the more modern culture of self-affirmation was the beginning of an epistemic barrier, citing as evidence the fact that it appeared to be, if not impossible, then at least extremely difficult, to establish any form of translation relation when dealing with concepts of eroticism and sexual attraction. In view of the fact that our Weltbild not only transcends culture and age (we can take it back to the fourth millennium BCE), but apparently even species, it is, I would suggest, unlikely that this is the case. That is not to say that our Weltbild is not undergoing considerable change, or that we do not have a very hard translation problem on our hands in relating the two cultures (exacerbated, I suspect, by the fact that the two groups use words like ‘sexy’ to mean two very different things). Both of those facts are true. But, as I said in the original essay, because we are one species we have one Weltbild, and therefore one epistemic class. Humanity is not epistemically divided.

## Further Reading

This may seem a rather strange reading list, but by far the best treatment I have found of this subject is to be found in a number of works of science-fiction emanating from Central Europe. Thus, with no more ado, my suggestions for further study are as follows.

# What is the ‘other’?

The ‘other’ is a key idea in what is commonly known as post-modern thought. Writers such as Lacan made it into a key tool in the analysis of culture, where it essentially defined as applying to any group that society chooses to marginalise, wishes to exclude or subordinate. This has led to some rather strange conclusions, such as Foucault’s notion that mental illness is a label used by society to render ‘other’ those it wishes to exclude.
Passing on to more sensible applications of the theory, it has borne fruit in the concept of multiculturalism, where we acknowledge that ‘other’ groups exist and create a situation where none is forced to adopt a majoritarian (or ‘other’) culture, but where the fruits of all the existing cultures are available to them.
Unfortunately, there are negative applications too. The ‘other’ has been turned into a political tool, with the ideal of supporting the political aspirations of groups that are identified as being ‘other’. As people sufficiently broad-minded to support all ‘other’ groups are exceedingly rare, this generally turns into an excuse to support some ‘other’ groups and ignore others, the choice being based on personal preference. So, in this situation the ‘other’ theory becomes an elaborate way of giving personal prejudice the veneer of philosophical justification. Also, self-identified ‘other’ groups have tended to use the concept of being ‘other’ as a tool to assert their political presence. This has led to the concept of ‘other’ separatism that I will discuss below.

# A definition of ‘other’

Before I start analysing the consequences of identification as ‘other’, it is worth seeing whether the rather woolly definition given above is philosophically meaningful. I will therefore show multiple cultural communities can come to exist even within one apparent cultural group. That is to say, how it is that within one ‘culture’ that official culture may be the majoritarian culture, that of the majority, but there will be minority ‘other’ cultures. The consequence is rather startling, as it directly contradicts established wisdom on the nature of the ‘other’.
I use an evolutionary model to show how subgroups can coalesce out of the majoritarian culture over time. Say we have a population of individuals within a group, who vary statistically around the mean. This is not to say that there is such a thing as a ‘normal’ person; rather there is a purely notional concept of a ‘mean’ person, who is, in a sense, the statistical average of the population as a whole. Obviously such a person need not, and most likely will not, exist. Now assume that there is a common culture across the group. This can consist of any form of information that can be passed from individual to individual, with errors creeping in en route. Provided that the strength of communication between individuals is (statistically) uniform across the population. In that case then the culture will preserve itself as a unity, though it and its mean value will change over time.
Now suppose that there is a subgroup of the population such that communication links between members of the subgroup are always stronger than those between members of the subgroup and individuals outside the subgroup. Then changes in the passed information are retained within the subgroup, and the averaging-out effect of the wider group is reduced. So, after not very long, the cultural information within the subgroup will have begun to diverge from that within the main population (the biological analogue to this is groups of animals that become to a greater or lesser extent isolated from the main population and eventually speciate, e.g. Darwin’s finches).
Translating this concretely, we find indeed that marginalised groups tend to communicate more within-group than without, whether due to persecution (religious minorities, homosexuals), discrimination (women, people of non-majority skin colour) or choice (closed sects). And these tend to be the groups that we think of as ‘other’. So, we can draw from this analysis two key points about ‘other’ cultures:
• There is nothing essential about ‘other’ cultures, so there is no inherent aspect of an individual that marks them out as ‘other’; it is entirely possible for a majoritarian individual to be part of a minority ‘other’ culture if they happen to have closer ties to members of that ‘other’ group than to majoritarians.
• There is nothing special about the membership rules for ‘other’ cultures; just about any assemblage of people can form a non-majoritarian culture, so long as they have unusually strong within-group links.
• ‘Other’ groups need not arise from exclusion by majoritarian society; they form as a result of preferential attachment, and this need not arise purely from exclusion: it can be a result of choice.

These facts are incredibly important, as the theorists of ‘otherness’ would have us believe the exact opposite. In particular, they undermine the notion that the ‘other’ is the excluded and disempowered.

One could, of course, try to come up with some definition that means that some ‘other’ groups (e.g. women, homosexuals, non-majority skin colour groups) are the real ‘other’ while others (mainstream Christians, aristocrats) are not. But then that depends on a value judgement, and not any well-defined criterion. Being ‘oppressed’ is a popular criterion, but it has the problem that while we should clearly (that is, if we happen to be liberals) stand against oppression, and aim to undo it and its effects, that has nothing to do with culture. To assert (as one hears from time to time) that oppression somehow makes the resulting ‘other’ culture more authentic is special pleading; the judgement is based not on anything inherent in the products of the culture but on the imposition of an external idea. So, any such judgement, being based on personal choice, must be capricious; in fact, it usually seems to be a function of the commentator’s political views. But a definition of other that (essentially) boils down to “‘other’ is what I say it is” is meaningless.
Hence, the only meaningful definition of ‘other’ is, it turns out, a non-majoritarian cultural group. One may form a personal ranking of said groups based on one’s political and cultural preferences, but one should not mistake this preference for a general theory.

# Monoculture, polyculture, multiculture

## Many world-views

Let us start the argument by considering Christian theology. There are different schools of Christian feminist theology applying to latina women, black women and white women. Now, if they are Christian then they must all be referring to one God, and yet they take radically different views of what that God is. That is to say, it is entirely plausible that one’s starting point in discovering God will depend on ones sex and race, and that the questions one asks will also be so contingent. But the end-point should be discovery of truths about the one God, which means that these truths should remain true regardless of ones sex or race. Moreover, the same applies to majoritarian theologians, which implies that their theology cannot be rejected out of hand.

But, of course, that is precisely what those who define themselves as ‘other’ do do: they reject majoritarian theology as being somehow tainted and arrive at pictures of God that seem more like pictures of themselves than of any universal deity. Of course, they could assert that their God is not universal, in which case the argument stops here, but in that case they are not Christian, which they say they are, so let us continue. Consider specifically the rejection of majoritarian theology (the same argument applies to the necessary rejection of differing ‘other’ theologies). The only intellectually tenable way of doing this is to assert that (say) Aquinas was mistaken, because he had the world-view of a man in a male-dominated culture, and that world-view has been shown to be, or is taken to be incorrect. But in that case, what guarantee is there that a feminist / womanist / latinista theologian’s world-view is any better? The hidden assumption in the preceding statement is that majoritarian thinkers’ world-view is flawed whereas that of the particular ‘other’ to which the theologian making the argument belongs is not.

## Rejecting majoritarianism

The frequently rehearsed argument justifying this rejection is as follows. (1) The ‘other’ group has been oppressed by majoritarians, and now they have thrown off the shackles of that oppression; (2) they reject being forced themselves to act and think as majoritarians; (3) they assert that the majoritarian world-view is not useful to them; (4) By extension, they assert that the majoritarian world-view is not useful at all, and that any product of it is of no value to them; (5) depending on how relativist they are, they either (5a) assert the existence of an epistemic barrier between their culture and majoritarian culture, or (5b) assert that majoritarian culture is entirely worthless. Now let us analyse this. Step (2) is trivially correct; it is not a matter of logic, but of justice. Step (3) is, as I have hinted above, questionable, as it may be that not all aspects of the majoritarian world-view are pernicious, but it is certainly the case that they should start from their own world-view and see whether there is anything useful to be gained from adopting parts of the majoritarian view, and not vice versa. Step (4) is where the argument breaks down; it and step (5) are not logical or philosophical statements, but political, being the starting point for a power-grab of greater or lesser extent (depending of which of (5a) or (5b) is chosen). And, as one would expect of political statements, they have no basis in observed fact, but are emotional statements designed to resonate with those who feel anger against majoritarian culture.

Therefore the argument in favour of rejecting the majoritarian culture is unsound. However, consider its consequences. Deploying (5b), the ‘other’ group silences the majoritarians and becomes the new majoritarian culture. But then different ‘other’ groups can do the same to that group and each other, until in the end everyone is silenced. Deploying (5a) and fractioning from majoritarian culture leads to a regression of smaller-and-smaller non-communicating monocultures, which continue to fraction until they reach the end-point of one-person cultures, and hence silence. Or the argument can be dismissed, in which case it is necessary to accept that all groups, including ‘other’ and majoritarians, have a part to play. So either everybody’s views should be taken into consideration or nobody’s should.

To say that nobody’s views should be considered is, of course, the end state of deconstruction, but it is something of a counsel of despair. We can do better than that. Say we have a number of schools of theological thought, each of which sets out from some world-view (and bear in mind that even the majoritarian culture is hugely fractured in this respect). What we could do is to have a big fight, with the strongest group getting to decide what is true. That is what is said to have happened in the past (though a quick look at the sheer variety of theological ideas espoused by majoritarians suggests that the true position is somewhat less black and white), and it is clearly not an acceptable approach. So, instead we could announce that each ‘other’ group has its own version of Christianity, that they are all equally valid, and that to try achieve consistency between them is disallowed, as it dilutes their status as ‘other’. That is essentially what we have now. It is a position much beloved of post-deconstructionists, who revel in a false ‘diversity’ of ‘truth’. False because in fact the logical consequence of their position is that there should be a number of totalitarian groups within each of which only one ‘truth’ is permitted. True diversity can be achieved only if all accept that they must listen to the views of those who are our ‘other’, regardless of how ‘other’ we may consider ourselves to be.

## Quine’s rabbit

So how can we listen to the ‘other’, for it is surely true that something obviously true within one world-view can be not obvious at all in another? The following is a highly condensed version of an argument of W.V.O.Quine. Say you and I have no langage in common, and I note that whenever you see a rabbit you use the word ‘gavagai’. What do I do? I could assert that it’s your culture and I have no right to interfere, in which case we are off down the road to island monocultures with no intercommunication save the occasional sling-shot. Or I could conclude that ‘gavagai’ means rabbit. Now it may actually be that in your culture you discuss animals not as wholes, but as a collection of body parts, so ‘gavagai’ refers to a collection of two short legs, two long legs, a body, two long ears, etc. Now there is no way that I could ever know that ‘gavagai’ conveyed much more information than the word ‘rabbit’, for I would hear ‘gavagai’ for rabbit, I would take words for individual body parts as referring to those parts, and so on. But this means that though some meaning would be lost in translating from your language to mine, the part that is lost is precisely that which you cannot express linguistically. And, similarly in translating from my language to yours (to assume otherwise is a form of inverted chauvinism).

Before anyone objects, I am aware that this is a purely linguistic argument. I am not thereby denying the possibility of meaning conveyed by numinous states. However, that meaning becomes culture, which is a shared public thing, only to the extent that it can be communicated, which requires expressive ‘language’ of some form, whether it be natural language, symbolic language or the emotional languages of art. Therefore, within this broadened scope of ‘language’, it follows that those ideas that a group can communicate internally using the expressive means available to it, can be translated and communicated externally. To deny this implies not only that intercommunication between cultures is impossible (a commonplace of neo-deconstructionism), but also that cultures cannot intracommunicate, so individuals are locked inside their own heads. So there are no epistemic barriers between cultures, or, to put it another way, contrary to what a university acquaintance of mine once claimed, the lyrics ofBohemian Rhapsody do not hold secrets that can only be understood if one is gay.

## Putting the rabbit into action

In the case of a feminist theologian talking to Aquinas, this means that though Aquinas may not appreciate the feminist’s private meaning (or she his), they can be confident that they understand one another in as far as they limit themselves to the expressible. Which means that if the feminist theologian disagrees with Aquinas, they can identify which of his premises she takes issue with, though he may not be able to explain to her why he believes it (because he cannot explain that even to himself). And at this point they can have a discussion, which might lead to each of them understanding the other better.

So I am not denying the value of differing perspectives, far from it. I am saying that in academia as in culture, we need the input of many different world-views, as they are the only way we can become aware of unjustified cultural assumptions that shape our thinking, and begin to understand what is baggage that we can let go and what is real core belief that we cannot. Or, in a wider context, what is assumption about the way art should be that can be challenged, and what is essential to our artistic identity. We can only do this if we have a cultural marketplace, where artefacts are valued based on their merit, not their tribal adherence. As soon as we start privileging certain artefacts on the basis of their ‘other’ status, or asserting that there are epistemic barriers between groups, we are taking the first step on the road to the isolated monocultures.

## Multiculturalism or death

So to conclude this part of the argument, I am arguing for multiculturalism, in which we do not destroy individual cultures or preserve them in aspic. Rather we allow them to join to a wider discourse in the hope of producing greater. The alternatives are not pleasant. In monoculturalism one group gets to assert its pre-eminence and suppresses all ‘other’ cultures. This has been tried and found wanting. In polyculturalism we defend many small totalitarian cultures in the only way we can, by retreating from contact with one another. And once that has been done it will happen again, with each of the small cultures fractioning into smaller cultures, until we achieve the end-state of the deconstructionist programme: six billion cultures, each consisting of one individual locked inside their own head. That way lies silence and death.

## Appendix: epistemic barriers

I argued above that there are no epistemic barriers between groups. The argument was elementary, but relied on a certain amount of hand-waving. There is a much more powerful general argument which does, however, assume a certain amount of philosophical machinery, namely knowledge of the sorites paradox. I present this argument here, but it does not affect the argument, so readers may, if they choose, skip to the next section.
Briefly, the outcome of the sorites paradox can be stated as follows. If I have a population of things to each of which I can assign a parameter (age, gender, sexuality, race, etc), and two types such that:
1. Things at one end of the range of the parameter are of type 1 and things at the other end of type 2
2. If thing A has one type then so do all other things with parameter value sufficiently close to that assigned to A

Then one of the following is true:

1. The two types are identical
2. The range of parameters can be divided into two regions that are clearly separated from each other

Let the population be the human population parameterised by some variable used to define groups as ‘other’ and let the types correspond to communities of intelligibility, so within a type individuals are mutually intelligible. Then the preconditions are met (clearly a small change does not effect intelligibility) and so one of the two outcomes is true. In outcome 1 the two types are identical, so the whole population is mutually intelligible and there is no epistemic barrier. In outcome 2 there is an epistemic barrier and the population can be divided into two groups, one of type 1, the other of type 2, with a clear gap between them in terms of values of the parameter. But the standard variables – gender (not sex), sexuality, race – are all extremely malleable, so this gap is unrealistic. Therefore there is no epistemic barrier. To put it more succinctly: we are one species; an epistemic barrier would require us to be two or more.

# The danger of being ‘other’

## Cultural isolationism

Increasingly, self-identified ‘other’ groups announce that majoritarian culture is of no value to them, and that their own culture is all they need. As such, cultural products of members of that group are asserted to adhere to different norms to those of other groups, and so cannot and should not be held to the same standard. In extreme cases it is even argued that non-members cannot appreciate or comprehend the group’s culture. This is the cultural equivalent of the fragmentation of Christian theology discussed above.

Now, the end-result of this agenda, if taken in its strong form, is obvious: every person is their own culture and communication is impossible, so all that is possible is silence and death. So, if it is obvious, why do the ‘other’ separatists not realise this fact? There seem to be three possibilities
First, the ‘one big push’ approach. The idea is that all that is needed is to destroy majoritarian culture, and then everyone will be happy. Apart from the fact that this is incredibly destructive, it forgets the fact, by their own logic, if majoritarian culture is and can be of no value to them, then ‘other’ culture is and can be of no value to majoritarians: there is a key principle at work here, that everyone is someone else’s ‘other’. So the consequence would appear to be that majoritarians have no right to exist. So, say we remove the majoritarian culture and do – something – with the majoritarians. Why should the remaining ‘other’ groups not start to bicker and fracture, which one would have thought more, not less, likely, in the absence of the oppressor. The idea, espoused by theorists of the ‘other’ that their shared experience of oppression will make them more reasonable, more amenable, ‘better, is simply a statement of faith, and it has no evidential basis (indeed, the fact that feminist theology comes in White, Black and Latina forms, and Latina theology has two violently disagreeing sub-factions suggests, on the contrary, that, to coin a phrase, ‘other’ individuals are human, all too human). Therefore, this theory cannot be taken seriously.
Second, the ‘monocultural other’ approach. The idea is that while the majoritarian view does not represent the entire population, hence ‘other’ groups form, the ‘other’ groups are each uniform in culture and therefore never form their own sub-‘other’ groups. But people are inherently variable, and so these sub-groups will form unless there is some mechanism to prevent that from happening. There is a commonly expressed belief that members of ‘other’ groups are somehow more cooperative than majoritarians, but this is simply a restatement of the ‘shared experience’ idea demolished above. Another belief is that those who disagree with the set of cultural beliefs that the writer considers to be authentically ‘other’ are not really ‘other’ at all (e.g. culturally majoritarian women are said to have subordinated themselves to the patriarchy); ironically this is the kind of exclusion that it is claimed led to the creation of the ‘other’ group in the first place. The only way to achieve the required uniformity is to impose it, which requires totalitarianism. Therefore, this theory cannot be taken seriously.
Third, the ‘multicultural other’ approach. The ‘other’ group accepts internal variation and adopts internal multiculturalism. This could work, but then why not multiculturalism across the entire population? There are two possibilities. One can assert that the majoritarian culture is inherently incapable of sharing with other cultures. Apart from being an exceedingly pejorative assertion, on a par with saying that ‘all men are sexists’ (which, regrettably, is not something I made up), this seems to ignore the fact that cultures are malleable things, and so it is entirely possible for majoritarian culture to reform, should it be given a reason to do so. So this possibility is based in prejudice, not fact. The other possibility is that one refuses to make the compromises required of any culture (see above) if it is to enter into multicultural cohabitation, so one insists on the purity of one’s isolated culture. This is simply selfish. So the ‘multicultural other’ could work but is insufficiently ambitious, and the only plausible reason for not extending it to full multiculturalism is an isolationism that means that the members of this ‘other’ group have turned majoritarians into their very own, marginalised, ‘other’.
So out of all that argument, it seems that the reason why ‘other’ separatists do not see the consequences of their position is based either in delusional beliefs about human nature, delusional beliefs about their own ‘superiority’ and prejudice against their own ‘other’. In other words, all the qualities that they rightly criticise in majoritarian culture. And this is because of the key point they miss: whatever our cultural categorisation, we are human, and so share essential human nature, including both the positive traits and the negative, one of the foremost of which is tribalism. Why tribalism is so fundamental a human characteristic is a question for another day.

## Isolationism and art

So far we have seen the isolationism is incoherent and unsustainable. But let’s, for the moment, pretend that an isolationist cultural group, or even individual manages to sustain existence. There is actually an insidious danger inherent in defining oneself in terms of being ‘other’ that means there is a very high probability that art produced by any individual who so identifies themselves cannot be great.
Why should this be true? At first sight it sounds like a pejorative statement, but it is not. I repeat again, we are dealing with an individual who entirely identifies themselves and their cultural activities in terms of being ‘other’. That is to say, they accept a cultural definition of their ‘other’ group, and, essentially, say ‘this is what I do; here and no further’. So they have made a conscious decision to limit the toolkit available to them in creating art, both technical and expressive, to that hallowed by the current definition of what their culture is.
Before I explore why this prevents great art, consider for a moment what majoritarian art with the characteristic of defining itself in terms of the artist’s majoritarian culture is like. There is a very simple answer: academicism. Composers like Cherubini, so loathed by Berlioz, painters like Landseer and Munnings are what you get: solid, competent and completely without any spark that takes them beyond competence and into greatness. Because, basically, defining yourself entirely in terms of a culture – any culture – means that you can never do anything new.
And so, back to the main argument. As I have observed elsewhere, great art always has something of the other about it. But the point is that that isn’t the ‘other’ the creator belongs to; rather it is other to that ‘other’. So to create great art, the artist has to transcend their culture and go beyond it. But if the artist is self-defined by their ‘other’ status, that is what they cannot do. And so they cannot create great art.
This is, by the way, one reason why the proliferation of different ‘other’ schools of art is not entirely a good thing. By promulgating the view that ‘other’ art does not need to be measured by the same standards as ordinary art, they essentially absolve the artist from the need to strive for greatness, because quality is measured not in terms of how their work transcends their ‘other’ status, but in how it conforms to it. Hence a new spectre appears: not only do the ‘other’ groups become monocultures, but those cultures will with and die, or at least end up irrelevantly preserved in aspic, while individuals who seek greatness desert the ‘other’ for the mainstream.

# One metaculture, many cultures

So, to conclude, there is nothing essentialist about culture. To say, as I have heard one critic say, that male writers cannot write convincing women characters, and indeed, should not be allowed to do so (I wish I were joking) is nonsense. To switch ‘other’, Thomas Mann could write convincingly about an elderly ephebophile in one book and an exuberantly heterosexual young man in another. Stravinsky could write brilliant jazz-inflected music without diminishing jazz or his own art.

The analysis above showed that there is only one stable situation, which I will now give a new name. What we need is a metaculture, within which many cultures exist. Each of us exists predominantly within one of those cultures. But rather than being told that that is where we must stay, and that appropriating ideas from other cultures is oppression or imperialism (take your pick) we should have in front of us the whole toolkit making up the metaculture, and be able to appropriate what we need from it. And then if we create something new, it doesn’t become the property of our culture, it becomes part of the metaculture.

So we celebrate the diversity of people, not as members of homogeneous groups, but as people, and allow each to form their own personal cultural toolkit that they use and extend as they reach for the one other that really matters – that of transcendance. That is the individual’s personal culture, and it, the selection of tools and the way they are used, reflects the individual’s nature. Some may prefer to stick broadly with the tools of a particular culture, and to extend and enrich that culture, others may prefer to create fusions of many cultures, and to create new things that belong only to the metaculture. Both approaches are equally acceptable. But to say that one can only use the tools that the doctors of cultural theory have hallowed for one’s use, based on one’s officially identified status as ‘other’ (or not) is fascism.