We can only attribute intentional states incorrigibly to an honest and competent interlocutor. All other attributions of intention are corrigible (Kripke).
If I am theorising about a language, I am hypothesising about rule following - I am attributing intentional states to the users of the language. If I do this in a 'meta-language' which I do not share with the users of the object language, then my attributions are always corrigible - I can never be sure they aren't quadding.
The only sense we can make of the idea of a tacit rule, is that it is a rule which can be stated in a meta-language. Tacit rules, therefore, can only be identified provisionally (they are like hypotheses from behaviour). If I make a tacit rule of my language explicit, however, this ambiguity disappears. Between interlocutors, the possibility that I may not be stating the rule I appear to be stating is incoherent.
If we think of the rules of logic as being like the tacit rules of a possible language, we can see that the statement of these rules in a meta-language can only be provisional.
But if we state a tacit rule in the object language we do something to the language: we render the provisional definite. This must change the tacit rules of the language - it must change the way it can be described in the meta-language.
An accumulation of changes like this will produce a game very unlike the game we are presently playing. If it can be 'translated' into the game we are presently playing, then the rule changes must, in a a sense, be trivial. if it can't, we have no grounds for calling it a language.
But we can only show this by explicating the rules, and by changing the game ...
Monday, October 26, 2009
Sunday, October 25, 2009
Knowledge and intention attribution
We can only incorrigibly attribute intentional states to honest and competent interlocutors. If you say that you believe it is raining, then I can only doubt whether you believe that it is raining by also doubting either your honesty or your linguistic competence. If this doubt is radical, then I can't question it within the game we are playing - I can't say to you 'I don't think you know how to talk', if that's what I seriously think.
If you say to me 'I know it is raining', the situation is no different. You can tell a lie here (dishonesty) or make a mistake (incompetence), but no particulary difficulties arise.
The difficulty arises when I try to (a) take you seriously as a competent and honest interlocutor and (b) entertain the possibility that you might be wrong. It's another 'Moorean paradox' - I'm trying to interpret your use of 'know' in the 'usual' way, but at the same time believe that you are wrong. In addition, I can't say to you 'You know, but you are wrong' - if I want to retain the usual meaning of 'know'.
The mistake here is to believe that a hypothesis can always be articulated in the language in use, and - of course - the hypothesis that the 'language' can't be used can't be articulated in the language.
The puzzle about the incorrigible status of 'known' facts arises from the circumstance that hypotheses about errors here can't be articulated in a game shared with those making the errors. Which isn't such a deep puzzle. When an interlocutor insists on 'know' and 'false' together, we can't play the usual game with these pieces. Just as 'believe' and 'false' don't work in the context illustrated in Moore's paradox.
We can allow 'know' to entail 'true' in the context of a playable game, because a failure of this entailment would require a change of the rules, not some more metaphysical adjustement of the 'underlying reality'. It is the game which 'breaks down', not the world.
If you say to me 'I know it is raining', the situation is no different. You can tell a lie here (dishonesty) or make a mistake (incompetence), but no particulary difficulties arise.
The difficulty arises when I try to (a) take you seriously as a competent and honest interlocutor and (b) entertain the possibility that you might be wrong. It's another 'Moorean paradox' - I'm trying to interpret your use of 'know' in the 'usual' way, but at the same time believe that you are wrong. In addition, I can't say to you 'You know, but you are wrong' - if I want to retain the usual meaning of 'know'.
The mistake here is to believe that a hypothesis can always be articulated in the language in use, and - of course - the hypothesis that the 'language' can't be used can't be articulated in the language.
The puzzle about the incorrigible status of 'known' facts arises from the circumstance that hypotheses about errors here can't be articulated in a game shared with those making the errors. Which isn't such a deep puzzle. When an interlocutor insists on 'know' and 'false' together, we can't play the usual game with these pieces. Just as 'believe' and 'false' don't work in the context illustrated in Moore's paradox.
We can allow 'know' to entail 'true' in the context of a playable game, because a failure of this entailment would require a change of the rules, not some more metaphysical adjustement of the 'underlying reality'. It is the game which 'breaks down', not the world.
Rules and Gödel
If we were trying to interpreting a language, we would test interpretation hypotheses to see whether they led to contradictions.
A contradiction should result in rejection of the interpretation hypothesis which entailed it.
Part of this hypothesis, in the context of a logical proof, is about the meanings of the rules. Perhaps, in logic, there is nothing apart from the meanings of the rules.
Will there always be an interpretation which avoids contradiction? Yes, but possibly not always a constructive interpretation - an interpretation which allows novel constructions from the same elements. But of course constructive interpretations must include interpretable rules of construction ... and about what count as 'elements' and 'composites' etc.
Do Gödel's proofs show us that all 'closed' rule based interpretations must be incomplete or contradictory? He and Turing have ruled out computational approaches to certain questions.
But the contradictions just throw us back to the incompleteness hypothesis - that our interpretations cannot protect us from future re-interpretation. Any definite interpretation must leave open the question of its own reliability.
Here is a rule of interpretation:
To you words
understand must vertically,
this read not
rule, the horizontally.
On the basis of what further rule do we demonstrate that we have a correct interpretation of this one? Only that we have avoided contradiction? What rules demonstrate the contradiction?
Phenomenologically, we can have a Wittgensteinian 'Aha!' moment, and know how to 'go on' ... but this is epistemologically irrelevant. It just tells us what a competent language user might feel on such an occasion. It doesn't tell us anything about justification. To try to say, as W seems to, that it's a mistake to think we need justification here is just to introduce a novel kind of justification strategy (a strategy which I, for one, don't have any 'Aha' feelings about ...).
He might say, instead, 'to ask for more is to ask for a justification of justification' - and this is right as a global position, but is not right with respect to particular justificatory strategies, which always seem to be revisable (Quine). What we need is a demonstration that unless this strategy works then no strategy would work - RAA. This seems more elusive ...
A contradiction should result in rejection of the interpretation hypothesis which entailed it.
Part of this hypothesis, in the context of a logical proof, is about the meanings of the rules. Perhaps, in logic, there is nothing apart from the meanings of the rules.
Will there always be an interpretation which avoids contradiction? Yes, but possibly not always a constructive interpretation - an interpretation which allows novel constructions from the same elements. But of course constructive interpretations must include interpretable rules of construction ... and about what count as 'elements' and 'composites' etc.
Do Gödel's proofs show us that all 'closed' rule based interpretations must be incomplete or contradictory? He and Turing have ruled out computational approaches to certain questions.
But the contradictions just throw us back to the incompleteness hypothesis - that our interpretations cannot protect us from future re-interpretation. Any definite interpretation must leave open the question of its own reliability.
Here is a rule of interpretation:
To you words
understand must vertically,
this read not
rule, the horizontally.
On the basis of what further rule do we demonstrate that we have a correct interpretation of this one? Only that we have avoided contradiction? What rules demonstrate the contradiction?
Phenomenologically, we can have a Wittgensteinian 'Aha!' moment, and know how to 'go on' ... but this is epistemologically irrelevant. It just tells us what a competent language user might feel on such an occasion. It doesn't tell us anything about justification. To try to say, as W seems to, that it's a mistake to think we need justification here is just to introduce a novel kind of justification strategy (a strategy which I, for one, don't have any 'Aha' feelings about ...).
He might say, instead, 'to ask for more is to ask for a justification of justification' - and this is right as a global position, but is not right with respect to particular justificatory strategies, which always seem to be revisable (Quine). What we need is a demonstration that unless this strategy works then no strategy would work - RAA. This seems more elusive ...
Thursday, October 08, 2009
Tacit Rules
I've already posted a slightly turgid argument for the incomprehensibility of an 'external' (to our language) theory of truth, based on the impossibility of interpreting the language it was rendered in (referring to Quine and Davidson, radical translation, and what counts as a language).
A much simpler idea has occurred to me:
The idea of a tacit rule really only makes sense if it can in principle be rendered explicit. Rules have to be statable.
The obviousness (?) of this is reinforced by some reflections on Kripke's rule-following paradox. If it's hard to give a tractable behavioural account of the criteria for having followed a statable rule, what content is left for the concept of an unstatable one?
Consider, also, that we can only get rid of the catastrophic ambiguities which Kripke's paradox generates in the conext of a working language game - where a capacity to agree about rules follows from the playability of the game.
A 'theory of truth' for our language would be a complex rule which was, in prinicple, unartculable. It wouldn't, in any manageable sense, be a rule at all ...
A much simpler idea has occurred to me:
The idea of a tacit rule really only makes sense if it can in principle be rendered explicit. Rules have to be statable.
The obviousness (?) of this is reinforced by some reflections on Kripke's rule-following paradox. If it's hard to give a tractable behavioural account of the criteria for having followed a statable rule, what content is left for the concept of an unstatable one?
Consider, also, that we can only get rid of the catastrophic ambiguities which Kripke's paradox generates in the conext of a working language game - where a capacity to agree about rules follows from the playability of the game.
A 'theory of truth' for our language would be a complex rule which was, in prinicple, unartculable. It wouldn't, in any manageable sense, be a rule at all ...
Wednesday, October 07, 2009
Speaking to the rules, logic ...
If we want to write down the logic of a language, we write it down as though the capacity to follow rules - and these specific rules - precedes the possibility of the language.
However, Kripkean ambiguities about whether someone (a speaker of a language, for instance) is following rules are only resolved between interlocutors, and within a playable language game. The judgement that someone is following a rule is always corrigible unless they agree, as an interlocutor, about the rule they are following - at this point a doubt about whether they are following it implies a doubt about their status as an interlocutor, since it would imply incompetent or dishonest use of the language.
We can explore this 'from the inside' by finding rules which could only be rendered ambiguous by risking the playability of the game - e.g. the discusion about whether 'P' and 'P' mean the same thing (below).
But even this exploration is possible, so long as it involves 'second order' investigations - 'mad' questions about hinges can be asked, and this circumstance, itself, examined. And so on. If we try to tidy all of this into a hierarchy of types, we simply create a new 'mad' object of enquiry, which is the theory of types itself, and where statements about it might fit into its hierarchy.
I think what is wrong here is exactly the conception that rule following somehow precedes, rather than is implied by, the possibility of language. Precedes, that is, in some fundamental metaphysical sense. And this is exactly the conception that Kripke's argument undermines, and that Wittgenstein also denies.
It may be true that we can only speak if we can follow rules, but this does not mean that some 'independent' conception of rule following can be formed. We demonstrate rule following in our talk, but only our capacity to talk allows us to articulate it.
But:
While this suggests that we shouldn't be surprised that we get into trouble when we try to render truth-telling in terms of following rules, does it actually explain the necessity of the related paradoxes? I feel that it does, somehow, but can't find a way of articulating this.
However, Kripkean ambiguities about whether someone (a speaker of a language, for instance) is following rules are only resolved between interlocutors, and within a playable language game. The judgement that someone is following a rule is always corrigible unless they agree, as an interlocutor, about the rule they are following - at this point a doubt about whether they are following it implies a doubt about their status as an interlocutor, since it would imply incompetent or dishonest use of the language.
We can explore this 'from the inside' by finding rules which could only be rendered ambiguous by risking the playability of the game - e.g. the discusion about whether 'P' and 'P' mean the same thing (below).
But even this exploration is possible, so long as it involves 'second order' investigations - 'mad' questions about hinges can be asked, and this circumstance, itself, examined. And so on. If we try to tidy all of this into a hierarchy of types, we simply create a new 'mad' object of enquiry, which is the theory of types itself, and where statements about it might fit into its hierarchy.
I think what is wrong here is exactly the conception that rule following somehow precedes, rather than is implied by, the possibility of language. Precedes, that is, in some fundamental metaphysical sense. And this is exactly the conception that Kripke's argument undermines, and that Wittgenstein also denies.
It may be true that we can only speak if we can follow rules, but this does not mean that some 'independent' conception of rule following can be formed. We demonstrate rule following in our talk, but only our capacity to talk allows us to articulate it.
But:
While this suggests that we shouldn't be surprised that we get into trouble when we try to render truth-telling in terms of following rules, does it actually explain the necessity of the related paradoxes? I feel that it does, somehow, but can't find a way of articulating this.
Thursday, October 01, 2009
Mathematics and the World
Maybe this is how to say it:
What we find is not that there is some mysterious isomorphism between certain mathematical structures and 'the world'; but that there is a quite intelligible isomorphism between these structures and the tacit (or even explicit) 'grammar' (in the Wittgensteinian sense) of any descriptions of the world that we find we can agree about.
It isn't that the world is mathematically structured in some imponderable way, but that we cannot describe it without using mathematics. And our descriptions come to us so naturally (as competent language users) that we think they, themselves, are isomorphic with some 'phenomenological' structure (our internal sensory and cognitive environment) which seems (to us) to produce them. We forget that we do not share these phenomenological environments, except in the sense that we succeed in sharing our descriptions; communicating our 'observations'.
What we find is not that there is some mysterious isomorphism between certain mathematical structures and 'the world'; but that there is a quite intelligible isomorphism between these structures and the tacit (or even explicit) 'grammar' (in the Wittgensteinian sense) of any descriptions of the world that we find we can agree about.
It isn't that the world is mathematically structured in some imponderable way, but that we cannot describe it without using mathematics. And our descriptions come to us so naturally (as competent language users) that we think they, themselves, are isomorphic with some 'phenomenological' structure (our internal sensory and cognitive environment) which seems (to us) to produce them. We forget that we do not share these phenomenological environments, except in the sense that we succeed in sharing our descriptions; communicating our 'observations'.
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