Languages and Truth - a clearer exposition ... maybe ...

The 'brick slab' language, and Tarski's object languages (which avoid paradox?) are only languages by stipulation.  There is no behvioural or reductive test for something being a language that doesn't fall foul of Kripke's paradox.

If we want to be able to say 'these people are speaking a language', then we need to have a concept of truth, because we need to be able to say 'these people are speaking a language properly'.

If we find someone speaking a language 'improperly' it is because they can do otherwise.  A noisy dog is not a deficient speaker of English.  Only an English speaker can lie or make mistakes in English.

For someone to be a speaker of a language they need to be able to tell the truth in the language (whether or not they actually do).  When we attribute the capacity to speak to someone, we also attribute the capacity to tell the truth.

When we agree that something counts as a language, we are saying (with Davidson) at least that it is translatable.  When we say that what we are using now (in this conversation) counts as language, we are saying something that, if it can be speculated explicitly (within this conversation), must be true.  It's falsehood is inconsistent with its explicit speculability.



So:

The statement 'we are using a language' is reliably true if it occurs in a conversation in that language, because its contrary (in the context of that conversation) would be unintelligible.  Kripke's problem makes any behavioural or material ground for the judgment that we (or others) are using a language radically unreliable.

We might judge of others that they are using a language, but until we share that judgement with them in a conversation it remains subject to Kripke's paradox.

Also, since any judgement that a language is being used includes a judgement about it's being used properly, such a judgement depends upon a judgement that it is possible to tell the truth (since this is part of the judgement that the language is being used properly).

The judgement that we have correctly translated a language used by third parties is (Davidson and Kripke) radically unreliable without some 'Principle of Charity'.  However in the context of any shared conversation with the natives - using either or both languages - this radical unreliability is ruled out a priori since 'we may have radically failed to interpret your language' (expressed in either language) would not, if it were true, mean what it appeared to mean to all participants in the conversation.  It would entail that there was no conversation of which it could be a part.

The 'slab and brick' game, and all games in which paradoxes have been excised (languages without truth predicates), the judgement 'we are speaking a language' cannot be formed, because they cannot contain their own truth predicates.  Because of this, they can only be identified as languages by stipulation or on material or behavioural grounds - and so these identifiecations are vulnerable to Kripke's problem, or are arbitrary.

Solving the problem of paradox this way comes at the price of rendering any judgement that we are using a language radically unreliable.

On the other hand, living with paradox allows us to make a priori, and incorrigible, judgements that we are using a language.

And worse:  it is the possibility of these judgements that gives sense to the word 'language', whether we use it to refer to the tools of our present conversation, or whether we use it to speculate about other possible conversations - corrigibly or otherwise.  The meaning of 'language'  depends, necessarily, on being able to point to 'what we are doing now, in speaking to one another'.  To call something a language, corrigibly or incorrigibly, is to rely on a concept which can only be rendered recursively, with a root in what we are presently doing when we speak to one another.