Ramsey's Ladder, again

Maybe I've said this before:

We want to preserve the first rung, but not the rest. We want to leave S meaningful, or rather usefully meaningful (!) where S="X is true"; but we want to leave "S is true" vacuous.

Rules, of course, work like this. If S="It is a rule that X", this means something. But to say "It is also a rule that S" is vacuous. We don't have a 'master' rule that says we must follow the rules. To propose something as a rule is just to propose that it should be complied with (with contextual qualifications, and under agreement).

If statements of truth values are, or are importantly like, statements of rules, then statements attributing truth or falsehood to statements of truth values will always be vacuous.

The traditional liar paradox is a statment about the truth value of itself: "This statement is false" contains a statement about a truth value. Taken as a rule, it is simply incomprehensible: there is no answer to the questions 'What way does this rule require us to talk?'.

And it only appears to be consequential if we allow the rule that we should follow the rules ...

Is it true that we should tell the truth (generally, with appropriate caveats etc.)? It's vacuously true, in a playable game. Its falsehood can't be a move in a playable game.

And:

"We should always talk as though this statement is false" is incomprehensible at the first level - it simply cannot mean what, at first sight, it pretends to mean. It tells us to do something that is logically impossible. (What it appears to mean is something that would falsify an interpretive hypothesis, in the Davidsonian sense).

Cartesian Anxiety

Our central phenomenological terror is not that our perceptions might deceive us, but that our friends might:

The inexpressible hyperbolic doubt that we are always talking at cross purposes.

Pace Dante, the gates of hell bear no intelligible warning.

Interpreting behaviour

We often re-interpret or misinterpret behaviour. Kripke shows that there can always be more than one intentional description of the same behaviour.

It is natural to think, here, of there being (a) the behaviour and (b) a set of interpretations. But we shouldnt make the mistake of thinking that there must, therefore, be a way of describing the 'uninterpreted' behaviour. The only descriptions we may have might be interpretations, and the 'sameness of behaviour' might only consist in our agreement that the interpretations are interpretations of the 'same' behaviour.

We may demonstrate this 'sameness' by identifying key aspects of the situation ('navigation markers') - such as time, place, actors etc. - but these are not descriptions of behaviour, and might not include anything which told us what was actually happening.

We might imagine, also, that some mechanical descriptions of limb movements and interactions with objects might somehow 'capture' the raw elements without introducing an interpretation. Computer simulations are based on models which encode this kind of information, but they are extremely difficult to interpret as 'descriptions' - they contain a great deal more information than our normal descriptions, and it is organised in a way which is hard for a human being to decode.

While the possibility of this modelling language might have been predicted from our judgements of sameness (and the existence of the 'navigation markers') , it certainly hasn't played any important role in producing judgements or demonstrations of sameness.

Also: it isn't clear that any such language really could capture all of the things which contribute to our actual arguments for sameness (where these are produced). The navigation markers relevant to a particular demonstration may be idiosyncratic, and missing from the the encoded description. We may not refer to time and place or personae but infer these from some other data which are not generally included in the descriptions encoded in the modelling language.

So what we have is just interpretations and the judgement of sameness. And we can make this judgment reliably - it would be incoherent to suggest that we don't. We also produce intelligible arguments for sameness which do not depend on 'full descriptions', or anything like these.