The Porter Zone

Philosophical musings and more

Monthly Archives: March 2011

Conceptual art is when . . .


We all know them when we see them.  Works of art then when you look at them create a kind of inner ‘what the?’ question, and which only begin to make sense when you read the little essay provided by the artist.  Or worse yet, where one comes away with the distinct impression that the whole purpose of the exercise was not to create an arresting image or object, but to let you know just how clever the artist was in coming up with that essay.

The thing is, we know it when we see it, but apart from applying the rather vague catch all of ‘conceptual art’ we often can’t work out what exactly it is that would make one want to say that Michael Craig-Martin’s oak tree is not good art, whereas Marcel Duchamp’s readymades are.  There is a terrible risk of falling into the ‘I don’t know much about art, but I know what I like’ trap, and arbitrarily consigning whole movements to the dustbin without justification.

So, in this essay I’m going to have a go at defining a fragment of an aesthetic theory in the hope that it might be able to disinguish good conceptual art which I see as pieces where a concept is used to create good art, and bad conceptual art, where the art itself is incidental to the concept.  My approach is going to be first, to put together a tentative definition, and then to explore it using a highly selective and random selection of pieces.

Aesthetics for conceptual art


What is conceptual art?  This question is surprisingly hard to answer.  Dictionary and encyclopedia definitions are far from helpful.  Wikipedia defines it as art in which the concepts or ideas involved in the work take precedence over traditional aesthetic and material concerns.  That sounds good, but there’s the problem that in fact it could be taken as applying to quite a lot of art that is definitely not considered to be conceptual.  So, for example Kasimir Malevich’s suprematist works are actually the working out on canvas of a very sophisticated theory, and the theory drove the composition, not notions of aesthetics.  So is this conceptual?

Malevich Yellow and Black

The obvious answers are yes, by the definition, and no, because it is traditional painterly art and, moreover, it stands alone: one does not need to know anything about suprematist theory to appreciate it.

And this is the problem.  Even naive art, indeed, especially naive art, has a concept that over-rides traditional concepts of aesthetics.  For example, what distinguishes Alfred Wallis from the endless bad seascapes painted by enthusiastic amateurs is that his vision, his determination to represent the reality of his inner eye rather than the mundane reality of the empirical world, is communicated so vividly in his work.

Wallis St Ives

So, once again, according to the definition, Wallis is a conceptual artist, but in any other sense he is a very traditional artist, who represents the world as he sees it, that not necessarily being the same as how we would see it.  And carrying on along these lines, we might as well say that Goya was a conceptualist, for often it seems that traditional aesthetics were the last thing on his mind:

Goya Saturn  

So that definition doesn’t work very well.  I am going to try to replace it with a definition which will, I hope be a bit more precise, even if it cannot be expressed so succinctly.  

It seems that the key point should be that the artist has an idea or concept.  This idea may be formal, in the sense of being a way of mustering materials to create a thing, or it may be expressive, in the sense of being an idea that the artist wishes to use art to illustrate.  But in either case, the idea drove the creation of the art; the artist followed the idea wherever it led, even if the result was not conventionally beautiful.  So, while traditional art may be driven by the urge to express an idea, more often than not the artist will force the idea to accommodate to conventional ideas of aesthetics, that does not happen here.  

In other words the art is theory-laden, in that it is the working out of a theoretical idea, whether that be formal or expressive.  So, in a sense, there is an element of detachment of the artist from the work, in that it is not an immediate outflowing of the unconscious mind, but a result of deliberate artifice, knowingly constructing the art work according to theoretical principles.

This is, I believe, a reasonable definition.  Clearly Goya and Wallis painted straight from the unconscious, unfettered by theory.  Malevich is more difficult, and I suspect that it may be impossible to rule his suprematist work out from any reasonable definition of conceptual art.  But that is not necessarily a problem, and so, having now a reasonable understanding of what conceptual art might be said to be, let us move on to constructing aesthetics for it. 

Conceptual aesthetics

Art does not work by appealing to the intellect.  Good art is art which speaks directly to the viewer’s unconscious mind in a way that makes them see the world in a new way.  Going back to Alfred Wallis, he makes the viewer see houses and ships not as nicely laid out items with proper perspective, but as complex things, whose features he sets out in detail, which interact with each other and the world as wholes, and so buildings are not partially hidden or distorted with perspective, but are set out as the forms of buildings, and one perceives St Ives as more than just a place, but as a community.  So he expands reality and changes our view on it.

But this is, I think, a critical point.  If one has to look at a piece of art, then ask oneself ‘but what does it mean?’, that is to say, if one has to engage with it intellectually, can it be said to have succeeded?  I think the answer is no.  If there is no unconscious, visceral factor to the piece, so the only engagement is intellectual, then it is essentially either a technical demonstration of the means of production, in which case it is no different from a technical drawing, or it is pure narrative, in which the use of a visual form to convey it is purely incidental.  In other words, the means of production, or the intended message, obtrudes between the art and the viewer.  Instead of a process of self-discovery resulting from communion with the art work, the viewer finds themself being told what to think by the artist. 

And so I propose this form of aesthetics for conceptual art.  The key to whether it is successful as a piece of art (no qualifying adjective) is that it succeeds on its own.  The viewer does not need to understand the concept (formal or expressive) to appreciate the piece.  In other words, the artist may have been driven by the concept when creating the art, but the end goal was to create a work of art, not to illustrate an idea.  And that is a crucial idea, so I will say it slightly differently: great art uses an idea, bad art illustrates an idea.   

Applying the theory

Let us see how this theory works out in practice.  I’ll start out with some examples of good conceptual art, and then progress to what one might term the ‘silly’ examples, the things that we recognise as being bad, but can’t quite say why.

Duchamp’s ‘Fountain’

The obvious starting point is with Marcel Duchamp’s readymades, which are about as conceptual as you can get.  Now the reading of these that one hears too often is that Duchamp was essentially playing a game, whereby he found random objects and put them in galleries with the intention of saying, as it were, ‘Oh aren’t I clever for telling you that a urinal is art?’

Duchamp Fountain

But Duchamp’s motivation was more complex.  It was well put by Beatrice Wood:

Whether Mr Mutt (Duchamp originally submitted the piece under the pseudonym ‘Mutt’) made the fountain with his own hands or not has no importance. He CHOSE it. He took an article of life, placed it so that its useful significance disappeared under the new title and point of view – created a new thought for that object

Duchamp was interested in showing that ordinary objects could be objects of aesthetic value in themselves; that even the mundane things could be art.  So we are not meant to look at the urinal and see Duchamp, we are meant to look at it and see a thing of interest and beauty in its own right.  It stands alone, independent of the viewer’s knowledge of Duchamp or his aesthetic theories.  All it asks, indeed all that Duchamp asked, is that one views it without preconceptions.

Bridget Riley

Bridget Riley’s work (especially her early work) has to be labelled as conceptual, as very often an entire piece emerges from rigorous working out of one or more formal ideas involving (nearly) repeating geometrical structures.  And yet they have an impact far in excess of what would be expected if that was all they were:

Riley Cataract 3

There is an almost vertiginous feeling to her work, making one, as it were, fall into the painting and creating the illusion of structure that simply isn’t on the canvas, but is created by our unconscious minds.  So Riley’s art is very much more than just the formal idea she used to create it, and indeed, by virtue of the way reaction to it is caused by how it interacts with our brains, our reactions are entirely outside of her control.  She provided the conduit, but the message is entirely our own.

‘Silly’ conceptual art

Here I’ll mention two fairly controversial examples.  First one that can be dismissed very quickly.  Michael Craig-Martin’s ‘An Oak Tree’ constitutes a half-full glass of water.  To quote from the Tate Gallery description of the piece:

 While this appears to be a glass of water on a shelf, the artist states that it is in fact an oak tree. Craig-Martin’s assertion addresses fundamental questions about what we understand to be art and our faith in the power of the artist. The work can be seen as an exploration of Marcel Duchamp’s declaration that any existing object can be declared a work of art. In his accompanying text, Craig-Martin provides the questions as well as the answers, allowing the simultaneous expression of scepticism and belief regarding the transformative power of art. 

Oak Tree

This is the artist obtruding between the piece and the viewer with a vengeance.  Without the explanation, the piece is meaningless.  One is tempted to suggest that the purpose of the exercise is not to create a sense of discovery in the viewer but rather to create the idea that Michael Craig-Martin is very clever.

Now on to an even more controversial piece, the infamous ‘Piss Christ’.  To summarise, Andres Serrano photographed a small crucifix submerged in a yellow fluid; the controversial bit was thay the yellow fluid was his own urine.

Piss Christ

Over the years artists have used any number of strange and often unpleasant media to create their work, so if Serrano had used urine because he wanted that precise visual effect that only it could provide, then that would have been fine.  But instead he decided to share the fact with the world, and at that point, inevitably, the artist and his technical means took centre stage.

Now, what makes this different from ‘An Oak Tree’ is that actually the image is visually interesting.  The play of light across the cross, combined with its penetration into the fluid creates a curious lambency that is artistically effective.  And so, ‘Piss Christ’ could stand on its own as a viable piece of art.  Unfortunately, the artist chose to turn it into an example of the ‘look at me’ school of conceptualism, and as such ensured that his artistry will forever be hidden behind his technical means.


What is human?


‘What is human?’ as a question is something that has eternally fascinated thinkers and writers.  Put less poetically, what we are looking for is some way of defining what that sense of humanity’s uniqueness that we all feel actually means: a specification of what it is about us that makes us special.

Until recently, the religious answer, that we were special because we were made in God’s image, was considered adequate, but it could not survive the twin hammer-blows of the Darwinian revolution and increasing knowledge of just how sophisticated animal behaviour can be.  In the twentieth century it became briefly popular to define humanity in purely biological terms, but the consequences of that trend were so terrible that such a definition is no longer admissible (and in addition, as I shall show below,  it would also be entirely meaningless).

And so we are left with a tricky question.  As we learn more about natural animal behaviour, one by one the old uniquely defining characteristics of humanity turn out to be shared with the most unlikely species.

Writers have contributed to this discussion with suggestions that humanity is a property of more than just homo sapiens sapiens.  Philip K Dick, in his story ‘Human Is’, concludes that an alien is more human than the man it is masquerading as, because it, unlike him, is capable of displaying caritas. Likewise, Stanislaw Lem, in his satirical story ‘The Great Washing Machine Tragedy’, elegantly demonstrates how it is completely impossible to find a definition of humanity that would not extend to a self-aware robot.  Similarly a recurring theme in ‘Star Trek’ has been the question of where the line is to be drawn between (say) human and machine.

It should not surprise readers that I will come down firmly in the Dick – Lem camp, and not with those frightened individuals who seek to maintain the myth that there is something about homo sapiens sapiens that is uniquely special.

The goal

The goal is to find if there is something about homo sapiens sapiens that makes us unique.  Something that sets us apart from all other species, confirming the comforting idea that we humans are hot stuff, and are somehow different from other animals.  If it turns out that there is no such criterion, the secondary goal is to find some criterion that is usable (in the sense that we can actually apply it) and whose consequences, though they may involve defining humanity rather more widely than we would have expected, are not obviously stupid.

There are basically two approaches to definition: either it is something about what we are, or something about what we do.  This can be rephrased as saying that humanity is either biologically  or behaviourally determined.   We now examine those two approaches.

Biological approaches

A biological definition is somehow dissatisfactory, as finding our uniquely human attribute in some strand of DNA as opposed to some aspect of our behaviour does seem to rather miss the point.   However, there is a more insidious problem than just being a bit boring.   If humanity is defined as ‘is a member of homo sapiens sapiens’ then this is formally identical to the criterion ‘is a member of sturnus vulgaris’, which defines the common starling.  And while it is clearly true that each species is unique in the sense that it is different to all other species, this is at best a triusm and goes no way at all towards finding a way to mark out one species (ours) as being unique in the stronger sense set out above.  And so a purely biological definition cannot be used to set us apart from all other species.

Behavioural approaches

The problem of finding a clear criterion

Therefore we have to look to behaviour.  What behaviour or groups of behaviours are characteristic of homo sapiens sapiens but of no other species?  This question proves to be singularly hard to answer.

Back when things were simple, humanity was distinguished by any number of criteria.  So there was man the toolmaker, the problem solver, the long-term planner, the self-aware, the possessor of culture, and so on and so forth.

And then Jane Goodall went to Tanzania and saw chimpanzees using tools.  Since which evidence of tool use among non-human animals has blossomed, so now even some birds are known to deliberately make and then use tools.  As for being a problem solver, there is now very strong evidence for problem solving in apes, elephants, cetacea and birds.  Most embarrassingly of all it turns out that portia fimbriata (a spider) is capable of solving complex problem and modifying its behaviour to deal with new challenges.  So some of the feats we are most proud of can be replicated by an animal that doesn’t even have a brain (in our sense).

What used to be considered a defining characteristic of humanity is a theory of self, that is to say that humans are capable of ascribing identity and self-awareness to others than themselves, and of differentiating the world as they know it from the world as others know it.  Well, now it has been demonstrated that so do chimpanzees, ceteaca and elephants.

Finally culture.   One key aspect of culture is individuals voluntarily co-operating for the greater good to achieve something they could not do on their own, and sharing the reward.  That was meant to be uniquely human.  Chimpanzees do it.  Dolphins do it (indeed, some of them go one stage further and enter into partnerships with humans).  So do some spiders.  So, on to the next aspect: altruism.  Surely that is uniquely human?  Well no: it is well attested in elephants and apes, and there are well documented cases of cetacea taking action to protect humans from predators.  And finally, the vertical transmission of skills and knowledge down generations is clearly demonstrated in cetacea, where hunting skills tend to be possessed by specific groups, and we even see clear evidence of adults teaching young.  Indeed, some whales even have vocal ‘dialects’ that can be used to  distinguish local groups from one another.

So, basically, it is annoyingly hard to find any behavioural characteristic that we proudly think distinguishes us from the animals that is not, in fact, shared by some other, often embarrassingly simple, animal.   We have, it appears, only one card left in our hands.

Homo orator

That is to say, language.  It seems, through all the blizzard of evidence of animal capability, that our linguistic capabilities remain a constant.  In fact the situation may not be as clear as all that, but this is our last best option, so let us examine it.

First, a definition of language is in order, because if we are too loose we run the risk of being able to say that (say) cats have language, while if we are too rigorous we might rule ourselves out.  So I shall define a language to be a system of sentences which can be generated from a finite set of words using a finite set of grammatical rules, such that I can form sentences of arbitrary complexity.

Let’s explore this a bit.  First notice that I have nothing to say about the semantics of language, that is to say whether the sentences I have constructed mean anything.  A good reason for this is that it is useful if our definition can include languages that we cannot translate.  That is to say, if I come across an unknown language, I want to be able to say whether it is or is not language without having to wait until it becomes translatable, and that means that the definition can involve only syntax.

The only other aspect of the definition that may cause surprise is the stipulation that I can form sentences of arbitrary complexity.  This is, in fact, one of the key defining features of human language.  For example, what differentiates our language from, say, the vocal signals of a prairie dog, is that we are not limited to a fixed expressive range consisting of distinct units.  In spite of, like the prairie dog, having a finite number of basic units (in our case, words) we can combine them to form new expressive units, to the extent that it is often said (with only mild exaggeration) that every human utterance creates a new sentence, never before spoken.

So, the proposed criterion for humanity is this: if we define language in this way, then only humans are possessed of language.  Clearly every known human natural language complies with the definition, so the question now is, does it work to rule out animal communication systems?

Are we really alone?

So, does the criterion work?  At first sight it seems promising.  Many animals have communication systems based on sound, light, scent or posture, but in nearly all cases these are collections of simple gestural signals along the lines of warnings, threats and invitations.  None of these constitutes a language.

The only cases that need special attention are elephants, chimpanzees and cetacea.  Elephants can be dealt with very quickly: so little is known about their communications (which have only recently been discovered) that we simply cannot say whether they form a language or not.

Chimpanzees have a rich vocabulary of vocal and gestural signals, there is no evidence of any grammar, and it does seem that the signals are discrete units in themselves, rather than being part of a greater whole.  Moreover, experiments in which efforts were made to teach basic language to chimpanzees (and other apes) have always foundered on the problem of grammar.  It seems that our cousins can handle basic subject-verb composition and simple predication of a property of a thing, but cannot comprehend the recursive structures that allow human languages to build sentences of arbitrary complexity.  So they have a concept of grammar, but it is too limited to generate more than a finite number of simple sentences.

Problems develop when we look at cetacea, and here I will concentrate mostly on one species: -the bottle-nosed dolphin – largely because it has been at the centre of most language-related research.  The starting point for this discussion has to be the extraordinary work done in Hawaii, where experimenters developed a genuine language, with a limited vocabulary and a grammar capable of generating sentences of arbitrary complexity, and taught it to dolphins.  The dolphins understood complete sentences, and were able to carry out specified tasks, and even answer questions.  So clearly the dolphin is capable of language.

Now the question is, do dolphins use that capability in the wild?  Here there are no clear conclusions, but there are some suggestive facts.  The prime point I will make is that dolphin ‘chatter’ is immensely complex, but in a special way.  It is neither a simple collection of calls, but nor is it the ever-varying but ultimately stereotypical song of hump-backed whales.  Rather, there are distinct elements that can be recognised and that recur, but the context and pattern of those elements is always changing, so, in essence, all utterances are unique.  This is, as we noted above, a crucial feature of human language, and is highly suggestive of the hypothesis that these dolphins do, in fact, have language according to our definition.


For various reasons, researchers seem to fall over in their haste to claim that dolphins do not have language.  This often reads most peculiarly, as papers in which clear evidence of linguistic capability is presented then end with a ritual, and unsubstantiated, assertion to the effect that language remains man’s alone.  There are, I believe, two reasons for this: one good, one bad.

The good reason is simple enough.  In the 1960s (when else?) there was a regrettable phase when some rather over-excited researchers made wild claims for dolphin intelligence and linguistic capabilities, including even the assertion that they could understand human speech!  This was, of course, debunked, but it is still the case that the ‘Flipper’ version of dolphins holds sway in the public consciousness.  Therefore, ever since, researchers have been eager to not make overly excited claims.   As a result, they seem to often err too far in the other direction, and to try to find ways of explaining away clearly intelligent behaviour as simply reflexive activity or mimicry.

Thus when one population started a strange fashion of wearing a sponge on their rostrum, researchers, desperate to avoid admitting that dolphins might have the concept of fad or fashion, came up with somewhat wild-eyed theories about how this might give some advantage in hunting, even though no evidence for this hypothesis has been forthcoming.  Likewise, it is apparently inadmissible to say that dolphins’ extraordinary appetite for sex can arise because they enjoy it – clearly recreational sex is a human-only thing.  In dolphins it is all about expressions of dominance.

This leads on to the bad reason, which is, I believe, fear.  Basically, we want to be uniquely special, set apart from all animals, to find a scientific justification for holding dominion over them.  And yet, one by one, we have seen the differences between us and animals vanish.  Language and culture (and fashion and recreational sex are cultural activities) are the last bastions of our human uniqueness.  If we admit, as a cold-blooded look at the evidence suggests we should, that even these characteristics are not unique to homo sapiens sapiens, what then?

Towards a definition

In spite of these concerns, it is clear that language is the best bet for a definition of humanity.  I’ll now examine some language-based definitions.  First one that successfully isolates homo sapiens sapiens, but which is philosophically untenable, then one that goes too far in the other direction, and has the problem of being utterly unusable, and finally an attempt at a synthesis of the two, which concludes with a definition of humanity that is wider than just homo sapiens but which has the advantage of being both clear and easy to apply.

Linguistic communion

The first definition is simplicity itself: we define humanity as the community of beings which possess language and with which we are able to communicate using natural language.  So we are now, for the first time, introducing semantics into the discussion: it is not enough just to possess language, we must have shared semantics.

So, can we go home now?  No.  This definition has some interesting problems.  At the moment we cannot converse (much) with bottle-nosed dolphins, though it is reasonably clear that they have some form of language.  So, for now, they are not human.  Now suppose some Champollion of the future deciphers delphine; at that point the dolphins abruptly become human.  That is somewhat unexpected: one would expect the scope of what is considered to be human to remain reasonably constant over time.

Things get worse.  The definition shares the fundamental weakness of the biological definition, because it basically says that a being is human if it talks like homo sapiens sapiens, so instead of the definition telling us that we are human, we tell it that we are human and then use ourselves as the yardstick.

Then it goes from bad to grotesque.  Imagine we discover a previously uncontacted tribe, who speak a wholly new language (something that has happened often enough in the past, and may happen again).  By this definition they are not human.  But they are homo sapiens sapiens too, so one could equally well say that according to the definition, they are human and we are not.  There is nothing in the definition to break this deadlock.

And so, this definition, though promising, breaks down because its definition relies on just too many imprecise notions.

Linguistic capability

So, let us go to the and propose the following: the criterion for humanity is linguistic capability.  So humans include homo sapiens sapiens, dolphins and (for all we know) aliens from planet Zog. This is perhaps a broader definition than we would like, but it is at least nicely unambiguous.

Or is it?  I now need to introduce the concept of an epistemic barrier, of which I have written at length elsewhere.   In brief, an epistemic barrier is an insurmountable barrier to communication or comprehension, so while (on current evidence) we can translate between all human languages, the hypothetical alien from planet Zog’s language (if it were on the other side to a barrier) would be incomprehensible to us.  And this is not just a matter of our not having tried hard enough or of not having found the trick.  The barrier is systemic: we cannot ever understand the language, because to do so would require us to be the alien and not ourselves.

One of the key features of an epistemic barrier is this.  Languages that are not separated from us by a barrier can be identified as languages and (potentially) translated.  However, for languages on the other side of a barrier, not only can we not translate them, we cannot recognise them: they are essentially indistinguishable from noise.

This is the sentence of death for this definition.  If we cannot identify these separated languages, then we cannot tell who is language capable and who is not.  Therefore the definition is unusable, and so valueless.

The via media

There is a potential compromise definition which comes from the flip side of the point about epistemic barriers: any language that is not separated from me by an epistemic barrier should be identifiable as a language, by means of detection of a functional grammar, even if we cannot translate it.  This is why I made my definition of language above purely in terms of syntax.

So define humanity as the property of being capable of using a language from which we are not separated by an epistemic barrier.  Consider the problems with the earlier definitions.  Defining something as human depends on linguistic capability, not on understanding, and so we don’t get the problem of species suddenly becoming human.  Also we don’t have the undiscovered tribe problem: we may not speak their language (yet), but we know that it is a language.  Finally, the solution to the epistemic barrier problem is built in to the definition.  A being, like the alien from planet Zog, that speaks a language on the other side of a barrier is inhuman, which is as it should be.

The only possible problem is that there still is a tacit assumption that our bubble of languages is somehow special, but we can even remove that by adapting a two-tier classification.  Thus all language-capable beings are sapient, and they are divided (by epistemic barriers) into linguistic groups, one of which happens to be the one we presumptuously call the ‘human’ group, though it could equally well be called ‘delphine’, or (better) more neutrally, ‘Terran’.


So we have a well-formed definition.  It includes us and rules out the alien from planet Zog, which is good.  Rather unnervingly, evidence suggests that, though it rules out other apes, it does not rule out some dolphins,  but if that is the price for having a sound definition, so be it.  It seems this our days of sapient uniqueness are over.

Appendix: the definition of ‘language’

For those who are interested, I present here a rigorous definition of ‘language’ in place of the rather vague definition used in the main body of the essay.  Note that (a) this is not necessary in order to gain an understanding of the main argument, and (b) the definition requires some mathematical sophistication (specifically, comfort with the notion of infinite cardinals).  Therefore, if you are happy to take on trust that the definition can be made rigorous, should cease reading now.

Definition of a language

Recall that I informally defined a language as a formal system which has a finite vocabulary, a finitely expressed grammar and which is capable of expressing sentences of arbitrary complexity.  The first two parts of this definition can be made rigorous, but for the third we need either a way of defining complexity, or an alternative criterion.  It is this latter approach that I take here.

So,  here is the definition:

A language is a formal system consisting of:

  • A finite vocabulary of symbols
  • A grammar consisting of finitely specifiable collection of rules for building statements from the symbols

such that the class of statements constructed from the vocabulary with the grammar is not denumerable.

In the case of a natural language the symbols are words, the grammar is the rules defining the syntax of the language, and the statements are sentences.  At this point note the following fact: this definition of a language is solely concerned with syntax.  Statements in such a language will be syntactically correct, but need not be semantically correct.  For our purposes in this essay, this will suffice.


Consider the definition in light of what we expect of a natural language.  It has three parts:

A finite vocabulary: natural languages have a finite number of words.  A language with an infinite number of words could not be comprehended, so we would end up using a finite subset of the vocabulary, hence reducing to the finite case.

A finitely specifiable grammar: the rules determining the grammar of the language can be written down as a finite statement in some metalanguage (we will generally use a mix of formal logic and English).  Again,  a language whose grammar is not finitely specifiable cannot be wholly comprehensible, and, indeed, cannot have arisen naturally, for how could the rules have ever been defined?  And so, again, we would end up using only a finitely specifiable fragment, and so we are back in the finite case.

Uncountably many statements: from these finite resources I can build not just infinitely many, but uncountably many statements.  This is not immediately obvious.  I therefore present below a general argument relating denumerability to bounds on the complexity of statements in the language.  After that I give three examples, working up from set theory, through first-order logic, to natural language, showing that in each case the language in question complies with my definition.

Complexity = non-denumerability

The purpose of this argument is to motivate the relationship between my original requirement of being able to express statements of arbitrary complexity, and the new requirement of the language being non-denumerable.  For the purposes of this discussion I shall consider the complexity of a statement to be the number of parameters required to specify it uniquely within the language.

Suppose that I have a language in which the class of statements is denumerable.  A simple example is the language with a vocabulary of one symbol (say ‘*’) and the simple rule that ‘*’ may or may not be followed by another ‘*’, so the statements are strings of ‘*’ of arbitrary length, and can therefore be encoded as integers.  As every statement in the language corresponds with a single integer, all of the statements have the same complexity, and so the language cannot express statements of arbitrary complexity.

Now consider the language which has two symbols ‘*‘ and ‘_‘ and the rules that the first symbol of a statement must be ‘*’, that ‘*‘ may be followed by ‘*’, ‘_‘ or nothing and that ‘_‘ must be followed by ‘*’.  Then statements consist of strings of ‘*’ separated by underscores, and so correspond to arbitrary lists of integers.  The class of such statements has cardinality equal to the continuum (as the set is a strict superset of the power-set of the integers).   This language can express statements of arbitrary complexity, because I can impose no upper limit on the length of the list of integers required to specify a statement.

Generalising to arbitrary non-denumerable languages: if such a language has an upper bound on the complexity of its statements, then its statements can be placed in a one-to-one correspondence with n-ples of integers for n < N for some fixed N.  This is impossible, therefore the complexity of statements in the language is unbounded.

Therefore the requirement for a language to be able to express statements of arbitrary complexity is equivalent to non-denumerability.  As non-denumerability is a precise criterion (unlike the rather vague ‘complexity’) it is to be preferred.

Example: set theory

In any standard version of set theory I can start from a vocabulary consisting of the empty set and some connectives, and, with the aid of a finitely specifiable number of axioms, build a language whose statements are the proper class of sets.

It can be shown that the statements include a countably infinite set.  But now I can construct the power-set of that set, and this is non-denumerable.  But every element of the power-set is itself a set, and so is a statement in the language.  Therefore the language is non-denumerable.

Example: first-order logic

Now consider first-order logic, in which I have a vocabulary consisting of a finite number of predicates, a finite number of unbound variable markers, standard connectives (quantifiers, logical operations, etc) and brackets.  Moreover, the standard axioms for first-order logic are finitely specifiable.

Here the key observation is the fact that I can build new predicates from old.  For example, suppose that my language has one predicate x Px.   I can immediately build predicates

(x1,…,xn) Px1 & … & Pxn

for all n > 0, and so the language contains a countable infinity of predicates.  I construct statements by selecting collections of predicates and binding their variables using the connectives.  Therefore the cardinality of the class of statements is at least that of the power set of the set of predicates, which is the continuum.  Therefore the class of sentences is non-denumerable.

So, first-order logic constitutes a language according to the definition, which is exactly what we would expect, given that it abstracts key features of natural language.

Observe that in first-order logic I can use it to build predicates of arbitrary complexity. Given a one-variable predicate, I can construct a more complex one-variable predicates from it, e.g.

x Px ⇒  x P’x ≡ (∀y) (Qxy ⊃ Py)

(where Q is some two-variable predicate).  Now take the definition of P‘ and write P‘ in place of P, to get a new predicate

x P’’x ≡ (∀y) (Qxy ⊃ P’y) = (∀y) (Qxy ⊃ (∀z)(Qyz ⊃ Pz))

I can repeat this process indefinitely, creating an infinite tower of predicates of arbitrarily increasing complexity.   Therefore, given any sentence containing the predicate Px, I can substitute for x Px a predicate of arbitrary complexity to obtain a sentence of arbitrary complexity.

Example: natural language

Natural languages have finite (though very large) vocabularies, and a finitely expressible grammar.  A critical defining feature of all known natural languages is the property known as embedding.   This is the linguistic version of the ability to substitute predicates of arbitrary complexity for simple predicates in first-order logic.

A clause embeds in a sentence if it can be substituted for an individual word in that sentence in a syntactically correct way.  So, given any sentence in a natural language we can replace any adverb with an adverbial subordinate clause, e.g:

he ate quickly ⇒ he ate as though he feared the food may be snatched from him

And similarly for nouns, verbs and adjectives.

As with first-order logic, by using repeated embedding I can form an infinite hierarchy of arbitrarily complex clauses.  But now, a sentence is a collection of clauses joined together with connectives.  Therefore the class of statements has at least the cardinality of the power set of the integers, and so is not denumerable.  Therefore the definition is effective.

Charlie Sheen, Societal Roles and Transgression


In recent days it has been very hard not to be aware of Charlie Sheen and his curiously uninhibited life-style; indeed the media coverage of his each and every action or utterance has been such that even one so generally ignorant of popular culture as I has (eventually) noticed that something excitingly strange was going on.  And I was struck, rather forcibly, by the nature of much of the commentary on Mr Sheen, which, I felt exposed certain structural features of our society.  And, indeed, of any sufficiently large society.  So that is what I am going to write about.

Now, before you get all happy and excited, I am afraid that I do not intend to delve into Mr Sheen’s unconventional sexual arrangements or to attempt to understand what it says about his psychology that he describes his concubines as ‘goddesses’.  Nor do I intend to discuss ‘tiger blood’ or a drug habit that Hunter S Thompson might have envied. No, this is going to be a simple philosophical piece about societal roles, and what transgression of said roles means.

The reason, before we go on, why I shall not delve into the ‘goddesses’ (and that double entendre was entirely unintentional) is not that I have any objection to discussing attractive women (rather the converse), but simply because they are just one of many symptoms that go to mark out Mr Sheen as a role transgressor.  Likewise, I shall make no moral judgement about his behaviour; the details of what he does are unimportant for my argument: all that matters is that (in a telling phrase) he is a ‘bad role model’.  

Societal roles

What are societal roles?

We all play out roles.  Some roles are very explicit and deliberately assumed, like the doctor’s bedside manner, but the roles that are really interesting are those that we don’t think about.  So, for example, there are gender roles or stereotypes.  Men, we are told, are emotionally null, logical, aggressive and goal-oriented, while women are nurturing peace-makers, concerned with feeling and emotion.  Men like to get drunk and watch sports.  Women gossip and talk about their children, while men talk about sport and exchange crude sexual banter.  Likewise students are radical drunkards who take drugs by the ton and have sex with everything that moves; their parents are conservative conformists with empty lives of quiet despair; their grand-parents are (depending on which stereotype you’re using) either sclerotic, racist, sexist fascists or wild party animals.  There are even roles based on jobs: secretaries are air-headed young women who wear very short skirts and plunging necklines and are generally assumed to be sexually available to anyone who asks; anyone doing anything faintly scientific has no personal skills, has dubious personal hygeine, looks strange, is probably male and will never, ever get off with a girl.  And so on and so forth.

Now, in daily life we will normally deploy one or more roles at any time (so the aggressive executive who talks corporate-speak by day might morph into a party-animal male by night).  And that’s just fine for those people whose psychological make-up makes them comfortable with the existing portfolio of societal roles.  But say somebody doesn’t?  What is to be done by (or with) a man who loathes all sports, doesn’t enjoy being drunk and who finds sexist banter offensive?  Well, what generally happens is that the unhappy individual builds a protective shell which enables them to function socially by appearing to fit their expected role, while protecting their true self which is hidden underneath.  It need hardly be said that this is not necessarily psychologically healthy.  And in very rare cases, an individual (like Oscar Wilde, Aleister Crowley, Katharine Hepburn, Freddie Mercury or Mr Sheen) decides to ignore the roles and be in public what they are in private.  So they become transgressive.

Where do they come from?

I’ll come back to being transgressive in a moment.  Before that, let’s see where roles come from and why it’s so important to society that people act them out.  In small, static societies, like, say, a pre-industrial revolution European village, where one may encounter at most a few dozens of people, and new people arrive only infrequently, it’s possible to interact with people on a basis of knowing them as individuals.  That is to say, if the list of ‘people I know’ is small and changes slowly, I can interact with each person based on my detailed knowledge of them.  However, in large, dynamic societies, like a major metropolis, one can encounter hundreds of people on a regular basis, and the roster of people one interacts with is constantly changing.  And in this case, one cannot rely on knowing everyone well.  So, if society is not to fall apart, it is necessary to have a relatively simple way of classifying people one encounters casually so that one knows how to relate to them.  And thus societal roles are born.

So, we can see why it might be good to have stereotypes or roles that help you relate to people you don’t know very well.  How do we get from that to people actually living the role?  Well, it turns out that there’s actually an advantage in acting the role too.  Because if you don’t clearly signal to someone how they should treat you, then they won’t know how to interact with you at all, and most likely anything you might have hoped to gain from encountering them will be lost.  So, just as you seeing someone else acting out a role helps you relate to them, which is good for you, you acting out a role helps them relate to you, which is also good for you.  

This means that there is a feedback loop, which has three main drivers.  First, that the roles should cover sufficiently much of the available space that most people should fit in at least one, second that there should be a relatively small number of roles (so everyone can learn all of them), and third, that they should be clearly identifiable, so you know which one applies when.  So the first driver promotes creating lots of very specific roles, while the second driver counteracts that by driving their number down, and the third driver ensures that they are fairly generic and clear-cut.  And that is precisely what we see: the roles are almost Platonic, extracting the essence of the normative behaviour of their respective group.

When do they break down?

Now, you’ll note that I said that the first driver was to cover nearly everyone.  Clearly any categorisation as crude as subdivision into a small number of roles cannot hope to cover everyone.  But, given that society has a huge investment in the roles, largely because its smooth functioning is predicated on their continued effectiveness, there is pressure for even those individuals who are not covered by any of the roles to conform to some role.  And usually that is what happens, the end-result being that the aberrant individual becomes just a little less well-adjusted than they might be.  But sometimes people transgress.

So what happens when an individual transgresses, and so insists on behaving as they want to, rather than how society says they ought to given their categorisation?  Well, it’s fairly obvious, really.  If you don’t fit, society doesn’t know what to do with you, and there are two things that can happen.  The easiest approach is to marginalise you – squeeze you out – so you become isolated from the mainstream of society: in a rather exact analogy, this is like the formation of a pearl around an irritant.  And, not surprisingly, we find that a lot of non-stereotypical people live alternative lifestyles and are more or less divorced from mainstream society.

But some individuals, whether it is due to the extreme nature of their transgression, or simply because their sheer ability makes them impossible to ignore, cannot be marginalised and rendered safe.  They are a threat to the stability of the system of roles, because if one person can get away with transgression, then the precedent is set for others to follow and simply be themselves.  Organisms (and we can view society as a meta-organism) tend to respond to threats in one of two ways: retreat or attack.  In this case, just as with a body responding to infection, there is nowhere to retreat to, so the only option is to attack.

And this, regrettably, is precisely what we see: Wilde and Crowley were vilified and hounded during their lives to an extent quite disproportionate with their (really rather tame) exploits.  Indeed, what are arguably Crowley’s worst acts (his irresponsible imperilment of fellow mountaineers) tended to be ignored entirely in favour of hysteria over his largely harmless magickal activities.  Hepburn was just too great a talent and too popular post 1940, but the near-terminal collapse of her career in the late ’30s and the post mortem revisionism that she is now subject to are clear evidence of society objecting to someone who defiantly created her own role.  Freddie Mercury was vilified in his lifetime, but he was loved by millions, so the forces of normativeness had to wait until after his death.  Mr Sheen is no Hepburn or Mercury, so he is attacked as a lunatic, etc, etc, etc and, of course, an unfit role model.

Which is where we came in.  Transgressive individuals suggest the need for new roles to add to the existing system.  But the system has huge inertia, and is (as we noted above) resistant to creation of new roles.  And this is its great weakness.  For transgressive individuals should be seen as a safety value.  They point to failures of the normative typology, and hence ways it could be improved.  And if the typology were the result of intelligent action that is, no doubt, what would happen.  But, of course, there is no intelligence at work, just an emergent structure deriving from the chaotic interactions of millions of individuals.  So, unfortunately, unless the millenium comes, we have to live with a society in which we are pigeon-holed into roles which fit some of us better than others, while only the occasional individual braves society’s ridicule by being themself.