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