We can imagine a language which doesn't have certain self-reflective capacities - e.g. which doesn't have an explicit truth predicate. This is because we would still be able to translate this language into the one we are presently speaking.
(We can't, of course, translate - or, therefore, imagine - a language which did have a truth predicate, but whose truth predicate worked in a significantly different way from 'ours'.)
Some language-like games might not be able to have a truth predicate. The introduction of a truth predicate (which would have to, again, be isomorphic with 'our' truth predicate) would render them unintelligible. Bargaining games are like this - when a salesman swears that everything in the brochure is true, we know he cannot be using 'is true' in the same way as, say, a logician or a natural scientist. On the other hand, the bargaining game would be unplayable if it was complemented by a logical or natural-science-style truth predicate, because this game depends upon a certain amount of conventional dishonesty. The extent of this dishonesty is explored by the participants in the game, but not explicitly explored - it is explored practically, by finding out what moves 'work' and what moves don't. Salesman do not make good philosophers, but this does not render the bargaining game intrinsically corrupt.
What would render it corrupt would be dishonest practice on the part of any players. I'm going to give a definition of this here which I'm not sure I can fully support, but which I think is roughly right:
Dishonest practice is practice which exploits the expectations of other players in a way which sacrifices the playability of the game to the instrumental aims of the practitioner.
Since the bargaining game cannot include a truth predicate, and since it is hard to construct a normatively self-reflective game without a truth predicate, it is possible that the bargaining game cannot be used to explictly adjudiate on honest practice. To test any practice against the definition, we would need to make a judgement about the objects and consequences of moves within the game - and particualrly about whethe a move rendered the game unplayable. This last, I think, would definitely require self-consious reflection on the possibility of truth-telling.
This raises a tricky moral issue: Can we, from outside, using a language with the capacity to articulate truth related issues, adjudicate on the language of the bargainers, which does not? We would be presuming to be able to translate this language, while knowing that we could not discuss the quality of this translation with the bargainers - we could not ask them whether the translation was correct.
We could, of course, learn to play the game. If we had an appropriate facility with it, we could then reflect on this facility using our native meta-language. This looks tricky: the character of our engagement would be different just because we had access to the meta-language. A physicist discussing mass with a weights and measures inspector does not participate in the weights-and-measures game in the same way as another inspector would.
This may be harmless. We certainly wouldn't want to say that the physicist and the weights and measures inspector didn't understand one another - we wouldn't want to say that they weren't able to play this game together. We would, however, find that their game became more difficult if it developed in a certain self-reflective way. There would be some truths about mass that they could only share by changing the game.
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