Private Languages. Again ... ?

Drawing a few strings together:

We can only give a recursive account of what counts as a language - we point to the language we are using now, as a root, and we show that other things could also count by offering translation schemas (Davidson).

This is not a completely straightforward business.

As we speak, we change the language we are using - any change is possible within the bounds of intelligibility.  These bounds, themselves, can partly be described in terms of rules: but not entirely - we have to do a lot of experiment and exploration as well.

If we could articulate all the rules of intelligibility, the question whether our list of rules was intelligible would generate a paradox.  We might be tempted to avoid this by expressing rules in a 'meta-language', but this creates another problem.  An entirely formal language (one fully defined in terms of specific rules) is subject to an indefinitely large number of interpretations, and it is only by interpreting the language that we give it semantic content.  We can only avoid having to choose between paradox and ambiguity by accepting that the rules of intelligibility cannot be completely written down in any language at all.

This is OK, though.  Exploring the world and exploring what we can say are closely integrated activities - this is especially clear when we consider our explorations of what we can say about our explorations.

But it does create a problem:  if we cannot bound our language by rules, if we cannot fully articulate what we count as our language, then what definite test can we apply to a proposed translation of a potential language into our one?

The answer to this question looks evasive.  Although there is a real problem about agreeing a translation schema, it is not an essentially different problem from the kinds of problems we face in agreeing how to talk about other things.  If we can agree about anything, and if we can make sufficient sense of the idea of a translation schema that allows for some successful cases, then we can agree about a translation schema.

We can explore, in a partly rule bounded way, what would 'count' as a successful translation of Dolphin into English, just as we can explore, in a partly rule bounded way, what would count as a reasonable explanation for the Aurora Borealis, or for the dishes remaining unwashed.

(We might, after all, learn some things from our attempts translate Dolphin that taught us new ways to speak in English that had a bearing on what we were prepared to count as a successful translation of Dolphin.)

What we cannot do, though, in any language, is say 'Dolphin is a language, but one that we will not ever be able to translate' - we can attach no meaning to 'language' in this statement that would allow us to distinguish language from anything else.  We might as well say that stones can speak.  (See Ursula le Guin's short story 'The Author of the Acacia Seeds').

So, the first problem with a private language is that either (a) there is a translation schema for it, and it is therefore not, after all, private or (b) it is not a language.

A general problem with an argument of this kind might be that we do not need to explicitly judge that something is a language before we speak it.  This is addressed by a similar argument to the one I suggested in Truth Predicates and related posts.

In summary, we have a problem with identifying a candidate L0 as a specific language, since we only have behaviour (or symbol lists or whatever) to go on.  No finite set of these can be used to unambiguously attribute an intentional state (such as meaning something) (Kripke).

This doesn't render the idea of a language generally ambiguous, however, unless we are committed to some reductive account of what a language must comprise.  Since we know we are speaking to one another now, and since we know (roughly) what we are saying to one another, this doesn't matter.  We can construct a recursive account instead.

But we can only explicitly judge that we are speaking to one another (i.e. we can only say so) in a language which contains the equivalent of its own truth predicate.  This is because to say 'we speak the same language' is as much as to say 'we speak the same language, and we speak it properly'.  Since L0 has no truth predicate (by definition), users of  L0 cannot say this.

This means that any identification of L0 as a language will always be provisional and corrigible.  There will be no guarantee that if we learn to 'play the L0 game' that we will be speaking a language.

Another way of putting this is that although we might suspend judgment on whether having a language is essentially to do with sharing it (which would beg the question under consideration), it is clear that judging that we have a language requires shared agreement if it is to be intelligible.  A truth predicate in a private language would be redundant in exactly the way predicted by Ramsey.  A truth predicate in a shared language allows us to explicitly agree, in a restricted sense, what it is that we are sharing.  It allows us to ask and answer questions like 'what do you mean by ...?' and 'do you think it is true that ... ?'.  Neither of these arise in a private language.

It seems likely, in fact, that all rules about how to speak a private language would strictly be redundant, since they would only report what the speaker already knows in order to speak the language.

Which brings us to what, I think, was Wittgenstein's objection.  Even if the rules were stated, the user of a private language could have no way of knowing whether they did apply to the language, since any method of checking this would be no more secure than his confidence that he was using the language correctly in the first place.  He would need to be able to judge that 'I am following the rules' didn't break any rules, which he could not securely do.

He could not intelligibly form the judgment 'I am speaking my private language properly'.

We can compare this with the equivalent judgement expressed in a shared language, where either (a) the judgement can reliably attribute an intentional state (of knowing that we are speaking the same language) or (b) there is not, after all, a shared language - we have misunderstood what is being said.

Going back to the translation issue raised at the beginning, however, it seems possible that Wittgenstein took for granted that we would not have difficulty recognising a language.  This is implicit in his discussion of the 'slab/block' game near the beginning of PI.  As I indicated previously, if any L0 can only be corrigibly identified as a language (unlike a language which contains its own truth predicate), then Wittgenstein cannot establish that the 'slab/block' team are speaking to one another.

As Kripke points out in 'Rules and Private Language', his paradox not only renders the idea of a private language unintelligible, it has catastrophic consequences for identifying anything as a language given the traditional (broadly Tarskian) account of what a language can be.  His mistake here is not to recognise that the context of such a judgement will always be from within a working language - one which contains the equivalent of a truth predicate which does not require a reductive account, since the same context provides the root for a satisfactory recursive account.