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.

Of Simples and Samples

Simples!

Wittgenstein’s observation in §43 that “the meaning of a word is its use in the language” (see previous post) comes in the middle of a discussion of the role of ostensive definition and the reasoning behind so-called logical simples. The explicit target here is the thinking in his earlier work, the Tractatus Logico-Philosophicus. That, however, can be seen as indicative of the general problems faced by philosophers when they attempt to construct theories based on conceptual misunderstandings (and the problems can be very great indeed – I have heard a philosophy lecturer state that, if only she had the nerve, she would come right out and declare fiction to be impossible). In other words, it’s a particular example of a common type of mistake.

It’s useful, then, to pick through the argument just to see the sorts of problems which can arise from a seemingly unobjectionable starting position. But Wittgenstein’s discussion of these confusions also brings into focus two hugely significant aspects of his philosophy: the distinction between description and rules, and (following on from this) the “free-floating” nature of language-games.

Let’s trace things from the beginning: Augustine’s description of language acquirement (§1) suggests that “the words in language name objects – sentences are combinations of such names”. This picture (which is not so much a theory as the soil from which a theory might grow), can give rise to a further notion: “Every word has a meaning. This meaning is correlated with the word. It is the object for which the word stands”. Once this is accepted, the task becomes how to explain various features of language which seem puzzling given this initial conception.

One such problem is how to account for the meaning of words signifying objects that have ceased to exist. Take, for example, “Carthage was destroyed”. This sentence surely has a meaning, and yet how can it? – Its subject-word, “Carthage”, has no correlative object to be its meaning. But now the thought occurs that “Carthage” is a word for a compound object, and the destruction of Carthage involved the disordering of its constituent parts. So the word “Carthage” can be analysed into more “fundamental” words naming those constituent parts and thus – provided the constituent parts haven’t been destroyed – “Carthage was destroyed” retains meaning.

But what are the constituent parts of Carthage? The buildings? The bricks? Molecules? Atoms? Well, each of these can be destroyed and if that happens then “Carthage was destroyed” loses meaning. So the analysis must continue down until we reach the ultimate constituents, and these must be ultimately simple – hence “simples”. They must be indestructible and therefore indescribable (because a description signifies a combination of elements and a combination can be destroyed). Obviously, we have no idea what these simples might be. Nobody has ever seen one. Indeed, it’s hard to imagine how they could even be physical – they are, it seems, logical objects and they are logically necessary: they must exist or else meaning is impossible.

At the same time, however, it makes no sense to talk of simples existing or not existing. Why not? Precisely because their existence is a necessary grounds of meaning. If simple X did not exist then the word “X” would have no meaning and the sentence “X does not exist” would mean “… does not exist” – that is, nothing at all. And if you cannot meaningfully say “X does not exist” then you cannot meaningfully say “X exists” either – “X exists” tells you nothing because its opposite is not possible.

Now, if simples are indescribable, how might we refer to them? One tempting answer is that it will be achieved by ostensive definition: by pointing while saying (or thinking) the name: “This → is what I mean.” Indeed, it’s hard to see how else a connection might be established. Such pointing needn’t be physical; it could be mental pointing or even, perhaps, logical pointing. Whatever form it takes, however, it is hoped this act of ostensive definition will create a completely clear, unmistakable link between word and object. The word is “pinned” to the world and that is how language becomes meaningful.

This was (roughly) the sort of argument put forward by Russell and the young Wittgenstein. In the Investigations, however, he mounts some powerful arguments against it.

First off, he points out that the notions of simplicity and complexity require a context (a use) to give them meaning (§47). What count as the “simple components” of an object depends on the reason for dividing it in the first place – it is the activity that gives the words their purpose and hence their meaning. Think of categorising chess pieces: you might say there were 32 basic components or only 6 (pawn, rook, knight, bishop, king and queen), depending on your reason for categorising them. Talk of ultimate simplicity is an attempt to use language outside of any context, and this renders it meaningless (“philosophical problems arise when language goes on holiday” §38). It is like trying to specify the rules indicating when a “goal” has been scored, but not just in football (or rugby, hockey, etc), but in any possible game.

Samples!

Next we come to the notions that simples can only be named and must exist. Wittgenstein shows these claims to be thoroughly confused.

How might we make sense in practice of the claim that simples can only be named? Here’s one way: imagine a language-game describing sequences of primary coloured dots. The words “R”, “B” and “G” stand for the colours and a report might be “R, G, B” (●●●), “B,B” (●●) or even just “R” (●). (This is an amended version of the game Wittgenstein introduces at §48.) In this last case we might say that the reporter simply names the basic element “R”. What else can he do? But this way of putting it covers up a crucial distinction, because in this context “R” is still a report – it is not merely naming. When the reporter was being taught the colour-words and the teacher said “R”→● that was an example of mere naming. But the two cases achieve completely different things. The report “R” describes a possible state of affairs (and excludes all the others) whereas the teaching of “R” neither describes nor excludes; it sets up a rule for the use of a word. Without the rule the report isn’t possible, but the rule by itself says nothing – indeed, it only counts as naming if it is preparation for a subsequent use of the name. The two activities stand on different logical levels but are linked internally (by which I mean the link is conceptual rather than empirical).

A similar thought holds sway regarding the necessary existence of simples. At §50 Wittgenstein draws our attention to the linguistic role of samples. Consider, for example, the colour sample used by the shopkeeper in §1 (you see now how carefully the phrase “five red apples” was chosen?). Is the sample red or not? It’s tempting to reply “Of course!” but there’s something odd about that, because the sample is the means by which it is decided whether or not an object is red. So what is our basis for saying the sample is red? Do we look at it and compare it with itself? Obviously that’s nonsense, so the answer to “is it red?” seems to be both yes and no. Or neither. It is not the sort of thing about which “is it red” can be meaningfully asked.

As with simples, it can easily seem like something mysterious or occult is going on here, but actually what we’re running up against is (once again) the grammatical status of samples in the language-game. The colour sample plays an analogous role to the teacher’s definition “R”→●. As such, it provides a rule governing the use of colour words in particular cases. Or as Wittgenstein puts it (§50): “The sample is an instrument of the language, by means of which we make colour statements. In this game, it is not something that is represented, but is a means of representation.”

Thus it turns out that the seemingly occult nature of the sample amounts to this: if we had not set up the rule “this→● is ‘red’” then the word “red” in “five red apples” would have no meaning. And on the same basis, saying it makes no sense to assert that “X does not exist” is really just an odd way of saying that if we hadn’t named this simple “X” then “X exists” would be meaningless. “What looks as if it had to exist is part of the language. It is a paradigm in our game; something with which comparisons are made.” Philosophical Investigations, §50. [Edit: This isn't very clear, is it? Hopefully, this post makes a better fist of spelling it out. - Phil, 2/10/11]

A failure to distinguish between a description and a rule has led to a statement about grammar being taken for a statement about the world. (And it is easy to overlook this distinction when you start from the assumption that the essence of language is to describe states of affairs by combining names. “The decisive movement in the conjuring trick has been made, and it was the very one that seemed to us quite innocent” §308.)

And we can also see from this that ostensive definition doesn’t “pin” language to the world. It creates rules for the use of words within a language-game. A word has no meaning if it has no use, not because of the non-existence of an object. So, for example, we have a use for “Jones” even when the bearer of the name is dead. “Jones is dead” we say. We can imagine things being otherwise (think of the “unpersons” in Nineteen Eighty-Four) but that just shows that whichever language-game is adopted, its rules are not forced upon us by the a priori logical structure of the world (for there is no such thing). And it follows from this that a language-game cannot itself be true or false. Only statements within the game can be true or false – according to criteria that are also contained within the language-game.

You must bear in mind that the language-game is so to say something unpredictable. I mean: it is not based on grounds. It is not reasonable (or unreasonable). It is there – like our life.

On Certainty, §559