Drawing the Line: Family Resemblance Concepts

So far (§§1-64) Wittgenstein has been chipping away at the Augustinian picture of language, showing that it doesn’t provide us with the essence of language. All attempts to delineate or shore up its features have only led to confusion or nonsense (metaphysics, for example). Finally, at §65, Wittgenstein’s interlocutor snaps:

You make things easy for yourself! You talk about all sorts of language-games, but have nowhere said what is essential to a language-game, and so to language: what is common to all these activities, and makes them into language or parts of language.

Let’s consider the interlocutor’s frustration in more detail. After all, what is it about the concept of language that might lead him to claim it must have an essence? It hinges upon an understanding of the term “concept” which might be put as follows:

A concept picks out a particular group of things that all have a common factor (or factors). For example, generosity, bravery and humility are all called “good” because they all have something good about them. But what is this quality of goodness? That is to be revealed by a logical analysis of the sub-concepts “generosity”, “bravery”, etc. And what is thereby revealed will be goodness in its pure or ideal form; it will be the essence of goodness.

Following on from this, it seems reasonable to expect that concepts must be exact. If all objects with the factor Φ fall under the concept P, then object x either has Φ or it doesn’t. It’s either in or it’s out.

It’s clear then, I think, why the interlocutor demands an essence of language: since items x, y and z all fall under the concept-term “language” there must be some quality Φ they all share and is the reason they are grouped together in this way. So what is quality Φ? If the Augustinian picture isn’t the essence of language then what the hell is? Typically, Wittgenstein’s response is a rejection of this question:

 Instead of pointing out something common to all that we call language, I’m saying that these phenomena have no one thing in common in virtue of which we use the same word for all – but there are many different kinds of affinity between them. And on account of this affinity, or these affinities, we call them all “languages”.

Philosophical Investigations §65

To demonstrate this, he asks us to consider the concept of “game”. From board-games to guessing-games to bouncing a ball against a wall, there is no one thing (or set of things) that all games have in common. Instead, “we see a complicated network of similarities overlapping and criss-crossing: similarities in the large and in the small” (§66). These similarities he christens “family resemblances”, and says that the various things we call “games” form such a family (§67).

This account denies that either commonality or exactness are necessary features of our concepts. The members of the concept “number” (cardinal numbers, negative numbers, imaginary numbers, etc) have no one thing in common, but it is clear what we call a number and what we don’t. To that extent it is an exact concept (though there’s always the possibility that it might be extended by a development in mathematics). But with a concept like “game” not only might there be extension, but the current members cannot always be clearly identified. Is throwing a ball against a wall really a game? Or seeing how long you can hold your breath? With such borderline cases there may be no right or wrong answer – we could just say “it’s up to you”.

But now (the interlocutor may object) it seems the concept is in danger of losing coherence. If you replace commonality with resemblance then can’t everything be linked to everything else by a web of resemblances? What’s to prevent everything from finding a place in the concept? Moreover, how can a concept function if it isn’t exact? If we don’t know which objects fall under it then surely we don’t know what it means? So even though commonality and exactness might not appear to be there, in some way they must be or else the concept is unviable.

Wittgenstein first tackles the question of exactness. He admits that the use of a word like “game” is not everywhere clear, but denies this necessarily makes it unviable. As he points out (§68), tennis is a perfectly playable game despite the fact that there’s no rule about how high to throw the ball when serving. In the same way, the concept-word “game” fulfils its purpose even though it’s not always clear whether something is a game or not. Of course, it may sometimes be helpful to draw a clear boundary (Game Theory, for example, uses a specific definition of “game” for the purposes of its research) but that is something we do as and when we need to. It is an invention rather than a discovery.

Moreover, not only is a clear definition not always necessary, it is not even always preferable. When a mother tells her child “go out and play” would it always be better if she specified exactly which games she meant (supposing she could)? Mightn’t it sometimes be best to let the child make its own mind up?

At §71 Wittgenstein moves on to the notion of essence, which he raises in the context of how we explain family resemblance concepts to others. This, he points out, is often done by giving typical examples, together with a similarity-clause (“and so on”, “and similar things” etc). We expect this explanation to be taken in a certain way: most of the time (we hope) the other person will “draw the line” in the right place from now on. Of course, here we are at the mercy of his ability to understand – but that is true given any explanation or definition we might provide.

Such an explanation is not an incomplete expression of my knowledge – as if I had a precise definition that for some reason I couldn’t articulate. Here Wittgenstein is combating the temptation to suppose that understanding our explanation “means to have in one’s mind an idea of the thing explained, and that is a sample or picture” (§73). This sample would be the essence or ideal form of the concept. Wittgenstein’s point here is not simply that we don’t have such a sample, but that the sample could not possibly do the job required of it.

What, for example, would be a completely general representation of “redness”? A sample like “●” is not unambiguous; it might be taken as a sample of that specific shade of red. Alternatively, if it’s supposed to be a sample of a specific shade, what’s to stop it being taken as a general sample of redness? The requisite type of training is required to make it one or the other (eg: “When I hold up this→● bring me any red object”) but that’s precisely what is lacking here. Without this training the sample might stand for redness, a shade of red, or even “not red”. It could stand for anything, and so it stands for nothing.

Similar difficulties arise if essence is viewed in terms of a definition – as if our rough explanation might be used as the raw material for constructing a precise one. For a start, this would put us in a very strange situation: in explaining (eg) games we (somehow) consult a definition we are not aware of having and which we are (somehow) unable to articulate. The other person then uses our rough examples to (somehow) formulate this same definition – without realising he’s doing it – and is then unaware of having it and (somehow) cannot articulate it.

Even if we accept this situation, we’re still faced with the problem that no definition can be completely clear or stipulate how we should proceed in every possible case. Take, for example, a proposed definition such as, “Games are those things we play according to certain rules”. For absolute clarity, don’t we need a further analysis of the words “things”, “play” and “rules”? And won’t that analysis throw up yet more terms to be explained? There seems to be no end to the process (cf, the seemingly throwaway remark in §1: “Explanations come to an end somewhere”). As Wittgenstein comments (§87): “It may easily look as if every doubt merely revealed a gap in the foundations; so that secure understanding is possible only if we first doubt everything that can be doubted, and then remove all these doubts.”

But still (it might be objected), even if we accept that an essence cannot guarantee coherence, how is it maintained in a family resemblance concept? Why doesn’t everything leech into everything else in a blur of affinities? The point here is that we distinguish between pertinent affinities and superficial ones. War is similar to a game in many respects; however, we don’t call it a game (though we may accuse someone of treating it like a game) because this similarity is not as pertinent as the one between war and a quarrel. It is important that we don’t confuse “let’s play war” with “this means war!” and so we have drawn a conceptual boundary-line between the two. In other words, it is the activity in which the concept is embedded that dictates where its boundaries lie. And where no boundary is necessary then none need be drawn. The boundary does not come built in to the concept so that we have to discover its contours (like discovering the molecular structure of salt); it is dictated by use – and that is something invented by us.

This is why we do not have to combat every conceivable doubt before a concept can be declared viable. As Wittgenstein puts it: “an explanation may indeed rest on another one that has been given, but none stands in need of another – unless we require it to avoid a misunderstanding – one, that is, that would arise if not for the explanation, but not every misunderstanding that I can imagine” (§87).

We can (and often do) use words without fixed definitions. We may even alter our definitions “on the hoof” if required (§79). And this is fine so long as it doesn’t make our language-game unplayable. It is the language-game (the activity) that dictates whether or not a concept is coherent – not an Ideal Form which is supposed to reveal the common essence of our concept words and provide them with completely clear boundaries. For the Ideal can do no such thing. It is neither possible nor necessary. “The signpost is in order – if, under normal circumstances, it fulfils its purpose” (§87).

Well, perhaps the interlocutor still has one last question: “If the explanation of ‘game’ doesn’t provide a sample or definition or formula, then what does it provide? Surely the pupil gets something? After all, he understands! Before he didn’t know and now he does know. So what’s in his mind now that wasn’t there before?” This leads to questions about what it means to “know” or “understand” something. Wittgenstein has already flagged up the issue (in §81) for further consideration. And it will get a lot of further consideration, because it involves confronting what is perhaps the really deep illusion here – the one that stands behind (and sanctions) illusions concerning logical simples, essences and ideal forms.

The Death of Metaphysics

A couple of posts ago (“Of Simples and Samples”), I attempted to explain the distinction Wittgenstein makes at §50 between the different linguistic roles played by (on the one hand) a means of representation, and (on the other) the thing represented. This is an absolutely crucial point with far-reaching consequences for philosophy and, to be honest, I don’t think I really nailed it. So let’s have another go.

I’ll start with a language-game (based on the one at §48) which hopefully gives a rough idea of the general approach found in works such as the Tractatus.

Imagine a world made of the following, utterly simple elements: ●, ●, ●. We shall name them “R”, “B” and “G”. If any two elements appear next to each other they are said to form a compound object. For example, we shall call ●● the compound object “p”, and ●● the compound object “q”.

So a state of affairs such as: “●●  ●●“ can be described by the proposition “p, q” and this proposition can be further analysed into “RB, BG”. The most elementary proposition would simply name an element: “R”. It would mean something like “This →● is R”.

We can say of p and q that they exist (or don’t exist), and also that they have (or have not) been destroyed. But we cannot say either things of R, G or B because existence and destruction are only to be thought of in terms of the combination or non-combination of elements. So words such as “existence” and “destruction” only operate at the level of compound objects, not at the level of elements.

A report of the total destruction of everything might be: “R, G, B”, representing the state of affairs: “●  ●  ●“.  In such a case nothing of which we could say “it exists” does exist, and everything of which we could say “it has been destroyed” has been destroyed. Of course, the elements are still there – they must be, or else it would be impossible to describe the state of affairs. But we can say nothing at all about them – not even that they exist. All we can do is name them. (Here the scenario’s limitations should be borne in mind; ●, ● and ● are not actual examples of utterly simple elements. For instance, they have both area and shape.)

This act of naming, however, is crucial because it is the means by which language is connected to the world. It is a form of what might be called “ostensive identification” linking name and object at the most fundamental level possible, and allowing us to see with complete clarity whether what we say is true or false. The statement “This →● is R” either correctly picks out the element ● or it doesn’t.

In the Investigations, Wittgenstein sums things up as follows:

What does it mean to say that we can attribute neither being nor non-being to the elements? – One might say: if everything that we call “being” and “non-being” consists in the obtaining and non-obtaining of connections between elements, it makes no sense to speak of the being (non-being) of an element; just as it makes no sense to speak of the destruction of an element, if everything we call “destruction” lies in the separation of elements.

Philosophical Investigations §50

He then makes the same point in a slightly different way: “One would like to say, however, that being cannot be attributed to an element, for if it did not exist, one could not even name it, and so one could state nothing at all about it.”

It is this second formulation he goes on to consider, and he does it by way of a comparison with the standard metre in Paris. In Wittgenstein’s time this was a rod of platinum-iridium which served as the authoritative sample of the length “1m”. (It has since been replaced by a definition involving the speed of light, which can be found here; this does not affect the argument.) Wittgenstein points out that, in an important sense, we can say neither that the standard metre is or isn’t 1m long. This is because “being 1m long” depends on matching the length of the standard metre, and a sample cannot meaningfully be measured against itself.

This might seem mysterious, but it actually just reflects the peculiar role of the sample in the language-game. It is a rule by which we establish the convention “1m”. Or, as Wittgenstein puts it: “it is not something that is represented, but is a means of representation” (§50). Without it we could not talk about things being (or not being) 1m long.

It could be put like this: “The standard metre is 1m long” looks like a description (which could be true or false), but in fact it is the expression of a rule governing the use of the phrase “1m”. It is not an empirical statement, but a grammatical one.

So although we might be tempted to claim that the length “1m” must exist or else we couldn’t even say “nothing is 1m long”, this would be confused. What has to exist (if we are to play the language-game we play with the word "1m") is part of the language: the means of representation. And the means of representation (the rule) will be neither true nor false, because it doesn’t describe the world; it defines a concept governing the use of a word (and in the case of the standard metre it is internally linked to a whole cluster of other concepts involving length and measurement).

Hopefully it is clear how this analogy relates to the case of elements. The meaning of “This →● is R” appears to rely on an intrinsic quality of the world – a quality which must exist (eg, the element ●). But actually its meaning depends not on the world but on the rule governing its use. This point can be easily missed because the rule takes the same form as the statement, making it look as though there were only statements. The statement “This →● is R” is a successful application of the rule “This →● is ‘R’”. And the statement “This →● is R” is false because there is no such rule as “This →● is ‘R’”. So the claim that (eg) “red must exist” boils down to the fact that if there’d never been a red-coloured object then we couldn’t have the rule “This →● is ‘red’”. (Hence, 15^th C. Europeans could not have a rule governing the colour-word “carmine”, because before Spain conquered the New World and brought back dyes made from cochineal insects, Europeans had simply never seen the colour before.) What do exist are red objects. But, from the point of view of meaning, what must exist is a rule.

This insight in turn gives us a clearer view of the confusion over “existence” and “destruction” in my initial language-game. There I said that “existence and destruction are only to be thought of in terms of the combination or non-combination of elements”. What sort of statement was that? An empirical one? No. It was a rule: a definition that governed the use of “existence” and “destruction” in the game. And it was this rule – not any necessary quality residing in objects – that made it impossible to talk of elements existing (or not existing) or of their being destroyed. It may look like a statement about the world to say, “we cannot assign existence or non-existence to elements”, but it’s actually a restatement of the rule. As such, it is part of the means of representation, not something that is represented.

So was the rule the right one? Well, imagine while playing with Lego you decide that only two (or more) bricks stuck together count as “existing”. Would that be the right rule? It seems not so much right – or wrong – as pointless. Language has gone on holiday.

Statements such as “simple elements must exist” are metaphysical. They claim to reveal a priori necessary truths about the world. If Wittgenstein is right (and there are many who would say he is not), then such statements are revealed as essentially empty. Insofar as they have any meaning, they are misleading expressions of the rules of our language – and rules are neither true nor false. Aside from that, they are merely examples of a subtle (and extremely tempting) form of nonsense, a shadow cast by grammar.

Wittgenstein, Names, Meaning and Use

The first 45 sections of the Investigations touch upon a wide range of topics, but their central concern is to combat the picture of language suggested by the quote from Augustine in §1: “the words in language name objects [….] Every word has a meaning. This meaning is correlated with the word. It is the object for which the word stands.”

Wittgenstein’s first criticism of this account is that words do far more than simply name objects. The language-game he outlines in §2 (where a builder calls out “slab”, “block”, etc, and his assistant brings the appropriate objects) demonstrates this by its very primitiveness. Since our language goes way beyond the basic functions allowed for in Augustine’s description, his version clearly doesn’t capture the whole picture (a point Wittgenstein makes explicitly at §3-4).

In §8 Wittgenstein extends the building language-game to include number-words, colour samples and the words “this” and “there” – ie, examples of the sorts of features left out of Augustine’s account – and then (at §10) makes the following remark:  

Now what do the words of this language signify? – How is what they signify supposed to come out other than in the kind of use they have? And we have already described that.

The terminology here moves from “name” to “signify” – and the italics show that this is not meant to escape our notice. Why introduce this new term? Well, “signify” is akin to, but not identical with, “name”; it is broader, more diffuse – we can either say, for example, that the word “ring” names or signifies the object I put on someone’s finger; but while that ring can signify my love, it cannot name it. So (the thought goes) although we may concede that words do more than name, perhaps we can still show that something similar is going on by adopting “signify”.

Wittgenstein’s response to this rejects such a move. In fact, he seems to consider it an example of what he elsewhere (§254) calls a “typical expedient in philosophy” – in this case, using a flexible term (or form of words) to shoe-horn different activities into the same category. Thus, although it is possible to say both “’X’ signifies the number…” and “’Y’ signifies the colour…” this does not make the use of number-words and the use of colour samples the same any more than the word “ring” signifying a ring is the same as a ring signifying undying love. In a specific context “’X’ signifies the number…” could be useful – ie, it could remove a particular misunderstanding – but here it is part of an inappropriate imitation of scientific reductionism, blurring the facts rather than revealing an underlying connection. Indeed the fact that it is possible to represent markedly different activities using the same basic sentence-structure is one of the linguistic features that tempts us to assume there is such a thing as the “ultimate essence” of language. For me, Wittgenstein debunks this spurious type of assimilation rather effectively when he says (§22):

We might very well also write every assertion in the form of a question followed by an affirmative expression; for instance, “Is it raining? Yes!” Would this show that every assertion contained a question?

Notice also how Wittgenstein’s immediate response to the question at §10 is to bring things back to the matter of use. This is a recurrent pattern in the Investigations: a particular notion (or theory) of meaning leads to puzzlement at which point we are urged to consider how the relevant word or phrase is actually used in various situations.

Why does this help? Because words are like tools (§11) and language is what we do with those tools. And so “what does this word mean?” is akin to “what is this tool for?” or “how is it used?” And, as with tools, the answer may not be as straightforward as you think. Consider a hammer: I can use it to knock in a nail, or pull a nail out, or smash away an obstruction or stop my instructions blowing away in the wind, or even as an ornament (but I can’t use it to glue a tile to the wall – not everything is “up for grabs” and it is significant that there are limits to the flexibility of language as well as hammers).

It follows from this that explaining meaning is not a matter of forming a reductive hypothesis but of painstakingly describing what we already know: how words are used. This insight will form the basis of Wittgenstein’s whole approach to philosophy.

The importance of use is glanced upon at various points in the Investigations’ opening sections until, at §43, he more or less lays his cards on the table:

For a large class of cases of the employment of the word “meaning” – though not for all – this word can be explained in this way: the meaning of a word is its use in the language.

And the meaning of a name is sometimes explained by pointing to its bearer.

I must admit, I have always found this crucial passage troubling. In fact, thinking about it often produces precisely the sort of “mental cramp” Wittgenstein mentions in relation to such questions as “What is meaning?” (The Blue Book, page 1).

I shall describe my confusion not simply to highlight my own dimness – though that’s always worth bearing in mind – but as an example of how infuriatingly difficult it is to break free of the misleading conceptions of language “which send us in pursuit of chimeras” (§94). Academic commentators such as (the excellent) Peter Hacker tend to make it look dauntingly easy: this is why the Augustinian picture of language doesn’t work, and this is the Wittgensteinian version we should replace it with. Job done. All I can say is that I’ve been studying Wittgenstein on and off for over twenty years and I still sometimes find myself falling into the same old traps. It is a comfort, however, to realise that Wittgenstein himself seems to have had a similar problem. Again and again in his later works he complains about how hard it is “to keep our heads above water” (§106) and only days before his death he commented “I do philosophy now like an old woman who is always mislaying something and having to look for it again; now her spectacles, now her keys” (On Certainty, §532).

Anyway, on with the philosophy. I have no difficulty with the general message of §43 (that meaning is use), but there is a further aspect to it which often sends my mind reeling, namely: what sorts of words does its caveat (“though not for all”) refer to? Take a moment to read the passage again, consider it, and see what you think.

It is all too easy to suppose that Wittgenstein is saying there are some types of words whose meaning is somehow “untainted” by any particular use. Such words would, so to speak, “carry their meaning with them” from situation to situation. It should go without saying that this is a startlingly un-Wittgensteinian conception (and that alone ought to alert us to the possibility that we’ve taken a wrong turn).

All the same, this reading seems to be confirmed by the final sentence of §43. Isn’t Wittgenstein here saying that in the case of proper names (eg, “Jones”) the bearer is the meaning of the name? That would at least provide an example of a word which carried its meaning with it, but it would also directly contradict a point Wittgenstein has emphatically made just three sections earlier:

It is important to note that it is a solecism to use the word “meaning” to signify the thing that ‘corresponds’ to a word. That is to confound the meaning of a name with the bearer of the name.

Philosophical Investigations §40

Either we conclude that Wittgenstein has made a remarkable blunder and started arguing against himself, or we go back and think more carefully about what he’s actually saying in §43. So which is it?

Well, after a lot of thought, I realised this: §43 is simply about the different ways we explain the term “meaning”. It says we do not always explain meaning in terms of use. It does not say that there are some words whose meaning is totally independent of their use. One might reword it as follows:

“In most cases the employment of ‘meaning’ can be explained as a reference to the use of the word in question. A description of use is what we mean by ‘meaning’ in such cases. But even when it is not done this way – eg, where a name’s meaning is explained by pointing at the bearer – it is still not the case that the bearer is the meaning.”

Or, to put it in the form of a dialogue:

A: What is meant by “meaning”?

B: Most of the time the meaning of a word is its use in the language. But in this case I explain the meaning of “Jones” by pointing to him, thus →.

A: So he → is the meaning of “Jones”?

B: No! He is a human being. How can a human being be a meaning? No object can be a meaning because meaning is not a thing. He → is the bearer of the name “Jones” – in other words, he is the person I want you to bring when I say “fetch me Jones”.

Or, finally, to express it as a grammatical distinction: One does not say, “Hello, I am the meaning of the word ‘Jones’.” One says, “Hello, I am Jones.”

Even as I typed them out, I could feel my grasp of the above points squirming to get away from me. There is something eerie about how difficult it is to keep these (seemly simple) conceptual distinctions in focus. Again, this was something Wittgenstein often remarked upon:

 [Philosophical problems] are solved through an insight into the workings of our language, and that in such a way that these workings are recognized - despite an urge to misunderstand them. [...] Philosophy is a struggle against the bewitchment of our understanding by the resources of our language.

Philosophical Investigations §109