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.