Truth and Meaning

I think a puzzle for Davidson's approach is that we couldn't work out how to speak a language from a truth theory for the language on its own.  Since a truth theory for a language only allows us to distinguish true from false sentences of the language, it can only teach us what to assert and what to deny.  It is hard to see how context can get in here.

I don't mean just the kind of context that disambiguates indexicals, or gives sense to 'occasion sentences', but also the conversational context, the context that makes a certain utterance 'appropriate'.

Is there an important difference, here, between having a theory of truth for L and having a list of all the true sentences of L?  Isn't a theory of truth (as envisioned by Tarski and Davidson) just a way of generating such a list, or determining whether an arbitrary sentence is a member of it?

How would we make a transition from having such a list, or such a test, to being able to speak L?  We may not be able to give a full account of meaning in terms of use, but we can't give an account that denies its relevance.  If we don't know how to use an expression, we don't know what it means.

We can be confused by the fact that we might learn to speak French from a theory of truth for French written down in English, but we would oly be able to do this if we can, as well, transfer certain principles of appropriate use from the English context onto the French expressions that we have learned.

Even if these principles were, themselves, articulated in both English and in French, they would not be part of the hypothesised theory of truth for French.

A priori tautologies

On second thoughts, logically a priori statements are slightly interesting, because the rules that they ultimately depend on are only intelligible within practices which, themselves, are at least partly 'hinged' upon non-tautological a priori statements.

It is not possible to articulate a logic without a language to articulate the logic in, and the possibility of this language, if it is considered by its speakers, must be the subject of an a priori judgment.

The necessity of logical laws follows from the a priori possibility of the language in which they are entertained.

Distinctive definition of 'A Priori' ... tidying up

An 'a priori' statement is one which, though not a logical theorem, cannot be false in any playable language game.  Whether we call logical theora a priori is a matter of taste, but they are certainly not interestingly a priori.

Among necessary falsehoods, we can recognise hypotheses about the impossibility of language in general, claims which are Moorean 'paradoxical' etc.

There is room for us to argue about whether some particular statement is a priori or not - for "Neurath's Boat" type reasons, and because there is an open question bar to a general theory here.  Whether some statements are a priori may be a matter of linguistic experiment - of 'doing philosophy', perhaps.

Composition

Clearly, some 'concepts' are, at least partly, compositional.

We can't conclude from this that:

(a) we can recognise compositionality from particular structural features, or

(b) that the meaning of a composed 'concept' is exhausted by an account of its composition

This is partly because we can't sideline idiomatic uses.  'Brown suit' has a content which cannot be discovered from 'brown' and 'suit', because to wear a brown suit means something different than to wear a grey suit.  Or a pink suit.

It is possible that compositionality (ugh) is not even that important - that it sort of helps us along, but more as a kind of mnemonic than because we need it.

'But' the grammarians say 'how do you account for our indefinite capacity to construe meaning from a finite set of components?'.

The answer is in two parts:  what is the evidence that we have this indefinite capacity?  It doesn't exist, because an indefinite capacity can't be demonstrated.  It can only be a potential account - and an unlikely one, given our finite condition.

The second part is that even if we settle on requiring a rule-based account of human 'language' behaviour, this need not be a grammatical account.  A finite computational engine can produce speech-like behaviour from non-grammatical components - e.g. a list of sentences linked to a list of appropriate reponses.  Even were such an engine to do a little humanish parsing, this need not be its only method.

Dyslexic people sometimes have difficulty discriminating individual words - since they don't have the resource of a reliable capacity to decode or concoct written sentences, they are more dependent on phonetic elements.  For instance, they are more likely to think that common complex expressions - 'Just now', 'Good day', 'How are you' - are single words.

Most of us, even if not dyslexic, can remember similar errors from childhood.  I remember hearing 'Here we go round the' (... Mulberry bush) as 'Helligo rounda'.  The fact that it didn't have any clear meaning didn't especially distinguish it within my limited experience, and even adult literate reflection can't make a lot of relevant sense out of the first line of this nursery rhyme.

(Mulberries don't grow on bushes, for one thing.)

The compositionality argument has two parts:

(1) There are cases where we can deduce the meaning of an expression from grammatical rules and the 'meanings' of its parts (word meanings, in particular).

(2) We need some story about how we can decode expressions we haven't heard before.

But this is pretty ramshackle.  As above, (1) is rarely possible in a completely satisfactory way.  And (2) ignores lots of other resources we might draw on - particularly context, including any preceding linguistic exchange.

After all, that's how we start 'decoding' in the first place ...

Turing cognitivism

The halting problem has a structural similarity to the Goodman/Kripke paradox insofar as the fact that the machine has not yet halted cannot count as evidence that it will not halt.

Also, the demonstration that a human mind is like a general cognitive engine - a Turing machine - would have to include a demonstration that it was following the rules of such a machine, and Kripke has shown that this demonstration cannot be conclusively constructed.

So, curiously, it seems that if my mind is like a Turing machine, there is no finite way in which I could demonstrate this.  It would not be a computable issue.

The proposal that the mind is a kind of Turing machine can only ever be a kind of assumption of cognitive science - a 'false heuristic'? - and not part of a deductive cognitive theory.

'Meaning is Use'

We could confuse two views:

(1)  If we know how to use a word, then we know it's meaning.

(2) We give the meaning of a word by giving an account of its use.

The first seems unexceptionable.

The second is much more problematic.  To give an account, we are already depending upon some un-articulated meaning/uses.  Why should some of these be more 'obvious' than others?  Why, apart from a specific context of enquiry (a specific question, or specific ignorance) should some be based on others?

Also, we do not learn use meanings from such definitions - although these may aid us in some specific circumstances.  We learn them through practice, through experiments with use.

Also, approach (2) is confusing with respect to meaningfulness in general - knowing how to talk preceeds knowing that a certain articulated use of a word is correct.  It's perfectly easy to imagine a restricted language game in which the meaning relation didn't exist - in which no accounts of meanings were ever given.  As with the 'slab, brick' game, we might construct a theory of the meanings of the words in such a language.  But giving a type (2) theory in terms of uses rather than representations does not avoid the difficulty that Wittgenstein used this game to illustrate:  we cannot say that the users of the game share our theory of their meanings.

If we play chess with someone who cannot speak, can we say that they are following the rules of chess?  Kripke would say: only provisionally, and they might be following any number of other sets of rules which produced congruent behaviour in the games we had actually played with them.  Wittgenstein might say that they were not following rules, but just playing chess.  And that we might be wrong about that.

When we make a (1) type judgement - that we know how to use a certain word -  we are exposed to Kripke's scepticism about what we might mean by it unless we make it in a shared conversation which 'works'.  To ask whether this shared conversation might rest upon unrecognised Kripkean ambiguities is to ask whether it is, in fact, a shared conversation - a question which cannot arise within it.  When I say 'I know how to talk to you - I know what we mean by what we say', I am not saying something than can be refuted (shown to be false) by some behavioural evidence because a consequence of my being wrong would not be that I had said something false, but that I had not said anything meaningful - and so not anything at all.

So 'meaning is use' turns out to be a warning, not a theory - and, in particular, a warning against the semantic role of type (2) articulations.

Why should we expect unexamined heuristics to be false?

Here are some reasons why they might be:

(1)

Given Nature's indifference between functioning heuristics, and the likelihood that the ratio of successful false heuristics to successful true ones is likely ot be high, the probability that an unexamined heuristic is false must be high.

(2)

There is a sense in which all all language users share a specific false heuristic:  that they somehow live in the same world, and that this is why their shared language makes sense.  In fact, they only think they live in the same world because their shared language makes sense.  It is only in a shared language game that this question can arise, and it is only because the shared language game works that we can sustain the illusion of some pre-linguistic shared world.

(3)

Why would we articulate a tacit heuristic?  In normal conversation, this would only happen if a difficulty had arisen:  if interlocutors discovered that just pointing to a practice did not resolve a dissonance.  In this case, the interlocutors have discovered that they are unintelligible to one another, and need to modify the game to recover.

Except in the case of a simple grammatical or computational error, this process would have to result in at least some interlocutors abandoning heuristics as they articulated them.

(4)

The work of interrogating a heuristic falls outside the discipline the heuristic underpins - settling issues of its truth or falsehood is unlikly to be relevant to the discipline.  It might shed light on whether the discipline as a whole made sense, but this is not an issue routinely raised by practitioners, who can point to their own successful (?) practices in support of their intelligibility and who can therefore relegate heuristic 'housekeeping' to philosophers.  Their (reasonable) presumption might be that practically inconsequential inconsistencies in the underlying heuristics must be addressable.

An efficient intellectual division of labour would lead to disciplinary heuristics being simplified, since more generally defensible underpinnings would incorporate complexities which were practically irrelevant.

Pointing to Practices

While we can 'point' to practices which underpin our thought and talk, we should be careful about how we use this in our explanations.  In empirical or anthropological explanations, this pointing is possibly helpful and probably harmless.

If we are looking for a justification for the kind of thinking and talking we are doing, then this pointing may not be helpful.

We can be deceived by something here:  often we do point to an unquestioned practice in order to 'justify' something, in ordinary talk.  I think this is often just to remind an interlocutor of a shared committment, however, so it really only counts as a hypothetical justification:  "Remember that X implies Y" is OK if someone has temporarily forgotten the relevance of X and its status as a fundamental.  So the form of the argument is: if we are having the conversation I think we are then you must see that Y is unavoidable.

But, of course, it may exactly be X or its relevance that are in play; and there may exactly be confusion over the nature of the conversation.  Regress beckons ...

Some might argue, from here, that we should review what we mean by 'justify', to bring it more into line with pointing at shared committments.  This move is exposed to an open question objection unless the shared commitments are unavoidable - if they must be shared by anyone having what could count as 'a conversation' at all.  In this case, confusion stops the conversation; we have no tools for exploring or explaining it.

Moral certainty

If I was subjectively certain about something, and was unable to see how I might be wrong, would I have a proof? We would suppose not, although this is the context of Cartesian anxiety.

What if no-one else could see how I might be wrong either? Even after considerable discussion and investigation?

At some point, out investigations would convince us that we could only be wrong if we had made some general mistake about the possibility of demonstration - about how to talk intelligibly about the object of my certainty. Might this also be a mistaken conclusion?

This kind of structure of doubt applies to groups as well as to individuals, but it has a limit. If we can pose the question, and make no more assumptions in our proof than those that are required to make the posing of the question possible, then we have a different kind of demonstration - it's structure is 'we know the answer if we can ask the question'. (Some obvious questions - 'can we ask questions?' - can be answered very directly this way.)

Can we have a hypothetical attitude to our participation in a conversation? We obviously can't express this within the conversation ("I'm not sure whether we are actually able to talk to each other") because we would be saying that we didn't know what the meaning of this sentence token was. If we were, we could not seriously express the doubt (or we'd by lying if we pretended to - another way to end the conversation ...)

We obviously can't 'privately' ask a question that we can't ask publicly. This would require a private language. We can be 'mad' - we can fail to engage in conversations in a humanly recognisable way. Or we can appear to talk nonsense to any potential interlocutor.

No one could say of our madness:  'they suffer from Cartesian anxiety', except provisionally, and perhaps poetically.  The only positive demonstration of such a thing would be our articulation of it, which would prove it false.

Signal Content

If we ask what a signal (or the state of a machine) 'means', we are attributing an intentional state to the machine, to the originator of the signal.

If we examine how an actual example of a homeostatic mechanism behaves, we do not find intentional states - just physical circumstances.  We cannot (Kripke) 'decode' a thermostat (i.e. an actual physical device) unequivocally in terms of temperature maintenance.

We might talk about 'correct' and 'incorrect' signals, without attributing intentionality to the machine or the signal, but we would still have to make this judgement in terms of the overall function of the machine - and therefore in terms of the intentions of its creator or designer.

We can say 'at this point, line 4 should go high'.  If it does not, then this is a malfunction - either a mechanical failure, a design failure, or a poor mechanical implementation of a design.  (Are these all different?).

If we say 'line 4 high indicates that the lift door is open', and we find line 4 high when the door is shut, can we say that line 4 gave an 'untrue' signal? We can say the signal was incorrect.  If we say that the machine says the lift door is open when it is shut, then we can say the machine lied, or was mistaken, but this goes along with attributing intention - we make a normative choice here about the status of the machine; we treat it as an interlocutor.

Articulating tacit rules

Attributing conformity with a tacit rule to a non-interlocutor is always corrigible (Kripke).  Articulating a tacit rule we 'discover' we have been following changes if from being tacit - and also changes the way we talk.

Imagining that before we articulated the rule we must, indeed, have been following it is to make exactly the corrigible attribution we might make to a non-interlocutor.  When we move from tacit to articulated, we also move from corrigible to incorrigible.

Can we say that we moved from less clear to more clear meanings?

Evolution

Nature is indifferent between a successful heuristic and a true theory; but we cannot be, or our justification for saying so could be that this comprised part of a successful heuristic.

It is incoherent - for instance - to try to support our belief that the future will, in some way, be like the past by saying that it is a component of a successful heuristic.  "It's been OK so far" isn't a ground for complacency just because we've got away with it up until now ...

Truth telling and its effects ...

Telling the truth is not free.  Some can afford it better than others.

Our reflections on the price we are prepared to pay cannot be articulated in the language game in which the moves under consideration are to be made.

They might be articulated in another context - perhaps a privileged context, such as an academic discussion.  Such a discussion will have a different price list.

It is only when there is no context in which we can render ourselves intelligible that we are finally damned; that we become completely incoherent, and unable even to say so.

Patterns

Children are often given mathematical puzzles that involve working out how to continue a sequence of numbers.  Wittgenstein focuses on this kind of situation when discussing rules and mathematics.

There can, of course, be no 'right' answer to how to continue any finite sequence, since there will be an infinte number of potential rules that its generation might instantiate.  Given this, it is odd that children are - generally explicitly, and always implicitly - told that there is a 'right' answer.  Valid, but peculiar, rules will be rejected (e.g. suggesting that the sequence '2, 4, 6 ...' instantiates listing even numbers in the odd hundreds and odd ones in the even hundreds).

This is an essential part of teaching mathematics - this weeding of peculiar rules.  In fact, a sound intuition about which rules would be peculiar is a component of 'mathemtical ability'.

A child that is being given this mathematical training is getting two signals from the teacher with each exercise: one is the list of numbers, and the other is a reassurance that there isn't something 'tricky' going on - that this list really is a sort of message, a hint that some simple and obvious solution is the 'correct' one.

We handle numbers using manageable rules - which comprise a subset of the formally possible rules.  All the mathematical 'observations' made by humanity so far comprise a finite set, and so could instantiate an infinitely large number of mutually incoherent sets of rules.  We have selected from these the humanly manageable ones which appear to be coherent.

We have no way - we could have no way - of demonstrating that the set we have selected is the only possible one.  Such a demonstration would depend upon a set of rules which would have to have mathematical meanings.

If we had two sets of rules which were internally consistent (and so were consistent with all our 'observations') but inconsistent with each other, we could only choose between them on the basis of an observation we had not previously made - but the generation of mathematical 'observations' is a rule-driven business ...

Maybe we cannot state a complete set of rules, because we modify their meanings as we do mathematics - because doing mathematics is partly a matter of resolving rule ambiguities.

And that's apart from any open question issues which would arise.

Private Languages

Maybe this is the Private Language Argument:

Suppose I told you 'I have a private language, which I can use when I am thinking things to myself'.  You might ask 'What do you say to yourself, in your private language?'

I could answer in two ways:

(1) I could give you  a translation, in our shared public language, of what I say to myself.
(2) I could say that my private language was not translatable into a public language.

I could not, of course, simply give you a 'raw' private utterance, with or without a translation.  This would be to render the private language public.

(1) Is what we presently have.  If I tell you what I am thinking, I am doing as much as this - but this does not demonstrate that I have a private language:  It only demonstrates that I can use our public one.

(If we could conclude from our use of a public language that we 'must' have some private 'language of thought', then what would we have to conclude from our use of this private language?  That we must have an even more private language of proto-thought?  What kind of explanation could this possibly provide?)

If I want to demonstrate the possibility of a private language by an argument produced in our public language, I would need to have a way of pointing at the private language in a way which showed (a) that it was a language and (b) that it was not a public language.  But I can't point to it if it's private, and I can only show that it's a language if it can be spoken.

With respect to (2), the idea of a language which is in principle untranslatable is  (obviously) incoherent for Davidsonian reasons.  How could we know it was a language?

Evolved Function

There are two ways of describing an evolutionary process, just as there are two ways of describing a computational proces: (a) from an intentional perspective and (b) from a mechanical perpsective.  It is mistake to think that when we understand one we understand the other; and it is a bad mistake to think we can reduce the intentional to the mechanical.

It is possible that we may be able to 'reduce' the mechnical to the intentional, in the sense that we cannot understand rule following (and so mechanism) except in terms of a system falling under the scope of some intentional concept.

We can only render the evolution of function (an intentional category) intelligible by referring to higher functions.  If longer legs aid survival by allowing higher escape speeds, we 'explain' longer legs in terms of the function of speed ,whose relevance is the function of escape, whose relevance is the function of survival.  If we didn't understand what survival was, or why it was 'desirable', this explanation would have no force.

We could tell a different - much more complex - story about about the macrobiology of evolution, involving reproductive chemistry, the coding options available within DNA sequencing, genotype/phenotype relationships, protein folding and structure, environmental factors etc.  We can't, at present, tell enough of this story to be able to completely describe many large scale functional behaviours in terms of detailed mechanisms.  Even when we can do this, however, we will not be able to 'render' function as mechanism except by stipulation.  And this would expose our accounts of function to mechanical failure - just as if we tried to define a logical operator in terms of what a particular electronic digital component did.

In my last post I said we should think of machines as elements in a conversation between their designers and users.  When we discover a 'natural machine' we don't recognise the normative aspects of attributing function, and so we arrive at the argument from design.

And maybe this is lucky - especially if it is our visceral normative attributions which prevent us, on the whole, from seeing each other as machines.  Excessive intentional attribution is probably less dangerous to us than deficient intentional attribution.  From a functional point of view.

Talking Machines

We should think of a machine as part of a conversation between its creators and its users.  It's like the mechanial parts of our talking activity - the noises, the physiology, the writing technology.  They might break down, they might take different forms, but their character is given by their intentional content.

A machine's character is also given by the intentions of its creators, and the 'sharing' or 'communicating' these with its users.  It is not given my any physical description.

This applies most clearly to 'ideal' machines, such as Turing machines.

A real computer is part of a complex conversation between 'programmers' and 'users' - or, more correctly, between different classes of users.

The 'limitations' of these machines can only be given, in any intelligible way, in terms of the 'limitations' of intentional ascriptions - of 'rule following'.  If we say that there must be some rule which underpins the possibility of intentionality, we are making a mistake.

OQ Arguments, and Crispin Wright's 'dilemma'

For any potential source of knowledge (the reliability of our senses, religious inspiration, scientific method), we cannot both (a) have it as an empirical fundamental and (b) show it to be reliable.  These two are mutually exclusive, because any demonstration that our knowledge of (b) is reliable has to be based on some other fundamental.

We also cannot say 'this must be accepted without demonstration' because we have to explain the 'must'.

The Scope of a Rule

To speak, we must (a) attribute rule following and (b) attribute belief in natural laws (the 'rules' which the world follows).

Some of these rules have an indefinte scope. This can make it sound as though their scope precedes and exceeds the scope of language - of what we can talk about. We can only imagine such a thing by considering the possibility of a world that we cannot (in principle) talk about, but which, nevertheless, follows the rules. Whatever the value of this as a metaphysical speculation, we can't test it.

A specific case is the rules we presume to underpin the possibility of language itself. We imagine that logical and mathatical laws have a wider scope than simply guiding how we speak. This belief is associated with the kinds of things we say about them - among which are statements like 'these laws have indefinite scope'. Such a statement is true with respect to any testable case, since such a case must be articulable. Also, to qualify it would suggest that there was some articulable case in which they did not hold.

But its generality and lack of qualification do not need to extend to 'things we cannot talk about'. And there can be no rule that defines the boundary between what we can talk about and what we cannot.

When we explore this boundary, we generate paradoxes. This does not mean that the exploration is invalid or absurd. It means we must be careful about the conclusions we draw from these explorations - and about what we mean when we talk about them.

All the objects in the metaphysical world beyond the reach of speculation are paradoxical.

Conclusions drawn from the indefinite scope of our rules of intelligibility will also be paradoxical, since they depend upon speculations about these objects.

Meaning sneaks into the incompleteness and inconsistency proofs at the level of the rules themselves.

Worlds without people ...

Suppose we imagine a world - perhaps this world at a different time - without any people in it, so that 'there is no language in that world' is true. What are our grounds for saying that this, or that anything at all, is true in this 'non-linguistic' world? Only that you and I, now, can agree about it - and can agree about what any such world would be like.

We cannot say that there might be some other world, that we cannot imagine or agree about, and yet that there is some definite thing that must be true about it. What kind of thing could a truth that no-one could ever agree about be?

Barry Stroud

It may be a contingent matter that there was no language at the time of the dinosaurs, but only we can say so. We cannot imagine the truth of some state of affairs separately from the possibility of expressing it except by imagining a conception of it that cannot be translated into our conception. If I think 'at the time of the dinosaurs, there was no language' I am imagining being transported to that time and having no-one to talk to. What else could I be imagining? That some invisible, even non-existent, person was similarly transported ...

The dinosaurs could not know that it was true that they had no language.

If I say to you 'There was no language at the time of the dinosaurs', what non-linguistic 'fact' about the time of the dinosaurs are we expressing that makes that time different from what we would say of it in any case? We say a lot of things about dinosaurs, but we don't say 'and there was no language then'. What would this add if we did? We don't wonder whether they could talk to one another, and so go to find an expert who can tell us.

And it is not whether there was language at the time of the dinosaurs that is important, it's that we can, now, talk about the dinosaurs. This is no different from talking about anything else - including things that happen now, contemporaries of our linguistic abilities.

If I say something about the time of the dinosaurs, I am not concerned about whether what I say was true then, but with whether it is true now: and the only conception I can give to whether it was true then is whether I would say now that it was true then ....

What is it, exactly, that was true then except what we agree about now? And If we don' t have that agreement, how do we identify the thing we might have agreed about?

Private Language Questions

This is the real power of the Private Language Argument:

The question 'Is it possible to ask questions?' can have only one answer if it is a question. We might imagine, however, that it is something we could wonder about, non-linguistically. It would be like wondering whether it was possible to talk.

What would this 'wondering' be like?

It could be like privately articulating the question 'Is it possible to ask questions?' We could wonder whether any previous public questioning and answering we had done had really 'worked' - whether it had comprised real questions and answers. It's hard to separate this question from the question whether we had really been speaking at all in the past - whether we had understood what anything we thought we were saying meant. This is incomprehensible, but it has a specific incomprehensibility here: we could not know what we were 'privately' doing by asking ourselves 'Is it possible to ask questions?' as this private act depends upon the validity of the public practice of speaking - which we wish to query, or about which we have become sceptical.

What the PL argument says is that there cannot be some private language in which we could comprehensibly articulate these queries - e.g. about the possibility of asking questions or about whether it was really possible to talk to people.

The PLA can be reformulated in Davidsonian terms:

If some private language were to count as a language, we would have to be able to interpret it, or translate it, into the public language in which we are conducting our enquiry. I think this is what Wittgenstein meant by saying that otherwise we would not know what rules we were following or whether we were following them correctly.

If we can only render the concept of a rule intelligible in terms of intentionality (which I've argued for earlier), and we can only reliably attribute intentional states to interlocutors (from Kripke's paradox), then this result is what we would expect.

Another perspective on this: how would my (or your) having a thought in our private language be represented, and how would our thought be attributed to us, in the public language of our enquiry? If I say of someone that they have articulated the possibility that it might rain in their private language, then I might as well be saying of them that they thought it would rain.

I could say of someone 'she thinks in Polish', and imagine her thinking the Polish sentence for 'I think it will rain'. I can imagine her inventing a language which can be translated into our language, and using that language to say something that would translate as 'I think it will rain'. I cannot imagine her thinking it will rain, but somehow representing this in a language I cannot translate. Such a language might as well be random - have no rules, but just mean whatever she took for the moment it to mean. She might think it would rain, attach this thought to a noise, a colour, an unpleasant memory, her confusion about linear programming algorithms, and any of these would do. Anything at all could 'stand for' her thought that it would rain, and so anything could be 'translated' into our language of enquiry as 'I think it will rain', and different things could be translated so at different times. There could be no rules in this translation schema, and so it could not even be reliably applied from one occasion to another.

If we translated:

'X, on occasion Y translates from our language of enquiry into "It will rain" in Sophie's private language'

into Sophie's private language, we could not know whether our translation was correct.

And if we could not know whether our translation into Sophie's language was correct, we could not know whether the translation of any such statement back into our language of enquiry was correct, and so we could not know what anything in Sophie's 'language' meant.

Linguistic Rules and Bush Tracks

It's a mistake to think that because we can discern linguistic rules a language user must, in some sense, know what these rules are. This is like saying a train knows where the track is.

A language user may have a quite restricted kind of linguistic competence, and still be able to function - and to appear to function well.

Imagine someone who knew, say three thousand sentences and was competent in selecting the occasions on which to produce them. It might take considerable study to be sure that this was a case of rote learned responses, rather than what we might think of as full linguistic competence.

What is more important, though, is that these rote learned sentences would sound as though they had been constructed according to grammatical rule - whereas in fact they had just been memorised.

This isn't to say that there may be no such thing as grammatical rules, or other linguistic rules. It is to say that these rules are a tool of the linguistic student, not of the speaker. We should know this from the opening examples from the Investigations - the builders. The rules appear when we analyse, interpret, or translate the builders linguistic behaviour. We do not have grounds for saying that the builders are intentionally following these rules of grammar that we have discovered.

Grammatical rules are rules of linguistic behaviour, not of meaning or truth. We discover them as we discover 'laws of nature', and so these discoveries are subject to the same Goodmanesque or Kripkean uncertainties.

Hume, Is->Ought, Open Questions ...

Hume's paragraph on deriving ought from is suppresses the methodological rule by which he selects 'is' statements.

This rule is, of course, normative - and so Hume cannot allow it to be deduced from factual statements. It can, however, be induced - as his method for selecting facts.

This leaves him with a dilemma if asked to respond to an explicit statement of the rule: He can either (a) deny the validity of the rule (which undermines his is-ought insight) or he can (b) accept it as implied by his fact selection process, if not by the 'facts' that he selects. In the second case, the selection method must either include or imply the rule 'no value statement can be a fact', rendering the argument circular.

If the rule depends on the fact selection process, it doesn't depend on the facts. Does this leave the argument intact (though weakened by circularity)? The scope of Hume's 'facts' is narrow: arguably only the direct evidence on which natural science depends. Most 'social facts' include value statements or value commitments, from which 'oughts' can be deduced (as in Searle's argument).

Rules and Arithmetic

Maybe the exact statement which (indirectly) generates the contradiction is:

"The rules have greater scope than what we can describe"

which must come out as:

"The rules have greater scope than the language which gives them sense".

Rule based proofs

Suppose we have a set of rules for constructing proofs for a system, and the rules could (in principle) be used to construct a proof of the validity of the system. And suppose that we have a proof-computational analogue of validity, as Gödel has. But we add one more thing: the system we are working with is a 'language', and our concept of a rule is grounded in the intelligibility of this language - so that we give an account of 'rule' in terms of some actual rules, and we we give an account of these recursively (or transcendentally) as I've indicated elsewhere in this blog. (We show that the failure of one of these to be a rule would be inconsistent with the intelligibility of the language.)

Would we then be trying to ground the intelligility of the language (it's capacity to test validity) in the intelligibility of the language (upon which the rules of demonstration ultimately rest)? And, if we were, why would this circularity produce a contradiction, rather than just be vacuous or invalid?

Maybe because these are the only two options - vacuous circularity or inconsistency. Although that's a bit vague and long-range.

Arithmetic is a good subject for this kind of investigation because of its capacity to model an indefinite range of rules and representations. It's because it can do this that it generates the incompleteness and inconsistency theorems.



The cycle I'm thinking of looks something like this:



(1) It is possible to state a rule, because we couldn't speak otherwise - it is a consequence of intelligibility

(2) Some of the rules we must be able to state are rules of logic and of arithmetic

(3) We can use these rules to specify a general theory of validity

(4) A demonstration of validity is, essentially, a demonstration of intelligibilty...

What happens as we go around this circle?

Maybe we discover that either (a) we stop meaning anything (we execute the recitations of a machine) or (b) the meanings change as we iterate.

(a) would be a result of being able to give a complete behavioural account of what was going on (which we could only do in a 'meta-language'). Once we've done this, we can't constrain the meaning of the behaviour we have described.

(b) means the rules change as well. To change the meaning of a rule is to change its consequences - what can be deduced from its truth. This means that we don't get a 'closed' system of proofs.

(This is all consistent with (i) the current conversation being the top of the meta-linguistic hierarchy and (ii) unspecifiable constraints on meaning, allowing developmental change - especially as we change meta-linguistic perspective.)

How could we say that the 'meanings' of the rules (Peano plus logic?)that Gödel employed changed?

Or is it the meaning of 'validity' which changes?

His computations might be 'meta-computations', since he - in some sense - demonstrates that they are 'in principle' executable, but does not execute them.

This is like saying that a rule we use applies outside of any possible scope of use. That it is 'universal', where this includes things we can't talk about as well as things we can.

Counting

It's easy to imagine a counting system which functions for some particular set of circumstances, but doesn't work 'in general' (e.g. the 'one, two, many' system occasionally attributed to some 'primitive' people by anthropologists).

Does this mean that we can ask the question whether our counting system might be like this, and that we might discover (in some future) that it didn't really work in some particular, presently unimaginable (undescribable) circumstance?

The best answer to this question would show that the question could only be asked if our counting system did not suffer from this defect. This would avoid the problems associated with giving a general account of counting (Peano/Gödel), or with 'defining' counting in terms of the system we presently use.

Gödel's method, which shows that Peano's calculus can be represented arithmetically, suggests a route to an answer: if our question can be represented arithmetically, and would only make sense if this was the case, then we might regard it as answered.

There are loads of bear traps, though - 'making sense' being an obvious one. But if we think of 'making sense' in terms of practical interpretation (the playability of the game), then there is still a possibility of a transcendental demonstration.

Would we be saying that only a person who counts the way we do could understand the question the way we do? Along with a Davidsonian attitude to conceptual schemes, this might work (so long as we avoid trivial solutions, e.g. that part of the understanding included a certain kind of generalisability of our counting method).

We would need to avoid any tacit reference to an 'ideal' counting system - one which is at the top of some abstract hierarchy in which, say, arabic numerals are above roman or greek numbering systems; or in which 'more' abstract rank above 'less' abstract systems.

(I think I can only deal with (a) games which are playable, and (b) potential games which are not - and there is no final method for discriminating between these. But, of course, the playability of a game, e.g. a question asking game, can have general consequences.)

Gödel's proofs depend upon demonstrations of indescribable worlds - no 'practical' arithmetic would encounter his numbers. There are many things we might think we could do with numbers (e.g. rank them, perform certain algebraic operations on them) which are not possible with Gödel's examples. They aren't quite as minimally articulated as we might think a 'number which is indescribable' would be - we have some elements of their descriptions.

(Some objections to Cantor's proofs arose from their consequence that there were indescribable numbers?)

Is it OK to say that we can't ask any questions of an indescribable collection? Does it matter if it only contains numbers? Can we make this restriction, given the representational power of numbers?

Perhaps the possibility of speculation depends upon arithmetic being constrained in a way which (a) cannot be fully articulated, and (b) avoids Gödel's consequences.

We can allow such a constraint as (a) because it is the kind of constraint implied by the possibility of a theory of truth for our language. There must be some constraint, but we cannot fully articulate it.