Truth Predicates - further on Kripke etc.

Perhaps this is a clearer exposition:

Consider two cases:

(A) The traditional case -

This is the 'hierarchy of languages' case, in which each successive meta-language in the hierarchy can be used to articulate a theory of truth for the language below.  At the bottom, we must have a language - L0 - which has no truth predicate.

The problem is that we then only have behavioural grounds for regarding L0 as a language.  This is because we cannot agree with speakers of L0 that we know how to speak their language.  Such an agreement embodies an agreement about how to tell the truth in L0, and L0 does not have the resources to do this.

Unfortunately, this means that we cannot unambiguously identify L0 as a language, because this would require drawing an unambigous conclusion about the intentional states of its speakers - about the rules they were following.  Kripke himself has shown the incoherence of this.

We don't, strictly, have definite grounds for attributing any intentional states at all to the speakers - any regularities we may have identified in a finite set of observations may be accidental.

It is, however, possible that the only interpretation of the behaviour of the 'speakers' of L0 that we can practically manage (that is computable for us) is one which attributes intentional states to them.  We still have a problem about which intentional states to attribute.

So - being sure that L0 is a language, and being sure whether we can correctly translate it, are both out of reach.

Davidson and Quine have also made this observation in a different context, in discussions on translation and the indispensability of a 'Principle of Charity' for the reduction of ambiguity.

(B) The 'natural language' case -

Consider this statement:

(B1) 'I never know how to tell the truth in the language I am speaking'.

If it is true that I do not know how to tell the truth in the language that I am speaking, then B1 cannot be a statement to this effect, since I don't know how to make these statements.

B1 can, however, be false - and must be false, in fact, in any intelligible language game.  This gives us:

(B2) 'I sometimes know how to tell the truth in the language I am speaking'

This must be true.  It also must be a case of my successful truth-telling (included in the scope of the 'sometimes').

Now think about:

(B3) 'We both know how to speak this language.'

This must have the consequence that we would (to some minimal extent) share judgements about the truth and falsehoods of assertions in our shared language.  So we can both make B2 type statements, and we would agree about the application of the truth predicate in B2.  We must, obviously, agree that B3 is true.

If we are learning a language from native speakers who do not share our 'meta-language', then we might test our success by checking with the native speakers that they agree with us about statements like B3, made in the object language.

If they learned our meta-language, we would expect them to agree with us about truth attribution in the meta-language, including the truth value attributed to the translation of B3 (and, to some extent, to the elements of our translation schema).

Notice that in this case, we cannot be in doubt about the intentional states of the speakers without also being in doubt about whether we have correctly made statement B3.

If we are not speaking the same language (if we have made a gross, but not yet obvious, mistake about how to speak the language), then we do not know how to say we are both speaking the same language in that language.


So, unlike case (1), we can unambiguously attribute intentional states, and we can unambiguously identify the language, in judgements we share with other speakers of the language.

What is the point of this?

Well, there is this apparent antinomy:

According to the traditional approach, we cannot tolerate a truth predicate in the language to which it applies without generating liar type paradoxes.

But it is clear from the 'natural language' approach that we can only unambiguously identify something as a language if it contains its own truth predicate.  This is because we need to be able to share explicit judgements within the language or, at least, with speakers of the language about whether we are speaking it correctly.

This has deep consequences for the kind of thing we can regard as a theory of truth.  The traditional approach assumes that a theory of truth is reductive - that the truth predicate for a language can be rendered in terms of, say, set theory, but only in the meta-language.

A natural language theory of truth - and I am arguing that this is the only approach which avoids the Kripkean ambiguity catastrophe - must be recursive.  We do not at any point dispense with the truth predicate, but we find cases where it can only be attributed in one way without generating incoherence (as in  B1), and build outwards from there.

This does not generate a catastrophe in any way which can be rendered intelligible (as I have argued elsewhere in this blog).

I think this approach also has the useful outcome of neutralising liar type paradoxes.  I'm less sure about this, but I think it would be harder to construct a catastrophic liar example within a recursive account.

We can still say, of course, things like 'This statement is not true' - but we only show ourselves to be confused about how to speak here.  There is no underling classification of the kind which generates the liar because there is no reductive theory about whose reliability we can ask intelligible questions.