Tacit Rules

It's tempting to think of tacit rules as just rules we haven't stated - as though they are still in a cupboard somewhere, just not having been taken out and looked at yet.

This metaphor is misleading, though. Is it a tacit rule of chess that the normal rules stay the same at least until next Wednesday? Or next Thursday? We can ask an indefinte number of questions to which 'rules' like this might be answers.

The fact that 'normal' interlocutors know most of the answers to these questions (when asked) is like the fact that they give commensurate answers to questions about their immediate perceptions. They just know how to talk - or so we would say in any shared game with them.

Rationality

To explore a subject, to theorise about it, is to discover what is intelligible to say about it. Sometimes we demonstrate intelligibility by showing that we can continue playing the game, and sometimes we can say why a certain move is or is not intelligible. A consequence of the open question argument is that we cannot give a general account of what would make any statement intelligible or not.

We are sometimes confused by the fact that false statements seem to be intelligible. What is not intelligible, however, is to agree that a statement is false but to 'assert' it - to play it as though it were a legitimate move in the conversation.

Exploring rationality is, however, exploring this kind of intelligibility. A theory of rationality asks what we can intelligibly say about intelligibility. This threatens to generate open question problems. We can avoid this by giving a recursive account - by pointing to examples of intelligible moves and showing how the intelligiblity of others can be illustrated or demonstrated from these.

It is different from other kinds of account of alethial or epistemological processes, though - for all of these, we can say (of any metaphysical, physical, or formal theory 'X') either 'X is true' or 'We can talk as though X is true'. These are more or less equivalent, and the second is not inconsistent with 'We can talk as though X is false'. Where X includes an essential element in any account of intelligibility, however, we cannot talk as though X is false. Also 'We can talk as though we can talk' in tautologous, and is not a simile.

We think that we have two things - rationality, and how to talk. This is partly because we believe we have a pre-linguistic, or sub-linguistic rational process that we have phenomenological access to. However, we can only bring these processes into the game by giving an intelligible account of them - by showing that they can be represented as rational processes. In this context, sensory phenomena are no different from any others.

To be able to speak is to be able to speak intelligibly - to be able to tell the truth (whether or not we exercise this ability). It is always unintelligible to 'seriously' claim otherwise. It is not possible to know what such a claim might mean, since to take it seriously is also to render it unintelligible.

The world, one way or another, must be the kind of place in which intelligible conversations can take place. While we might imagine some other world, we cannot imagine living there.

To say that the world is like this is to make a fairly complex empirical claim, since the possibility of intelligibility implies the possibility that a fairly complex game can be played - the one we actually play when we talk, with all its certainties and uncertainties, clarities and ambiguities, concrete claims and abstract structures. It also must allow - perhaps require - that we play this game 'from the inside'. We must respect the constraints imposed by open question considerations, and much of what we do when we explore what can intelligibly be said will feel like empirical discovery.

Language and thought

We can attribute intelligible thoughts to someone on the basis of their behaviour, or on the basis of what they say about them.

In the case of behavioural attribution, we always have Kripkean ambiguities. If someone explicitly claims to believe something, we can only doubt whether they do by doubting whether they are an honest and competent interlocutor. This doubt, if it is radical, cannot intelligibly be expressed in any conversation with them, since it is exactly whether we can have a conversation with them that we doubt.

A belief attribution can be incoherent for different reasons. The belief might be incredible, in the context of the behavioural evidence. It might be incoherent in the conversational context - e.g. a self-attribution of the kind instantiated by Moore's paradox: If someome persistently appears to claim to have a belief which we cannot intelligibly attribute to them, our conversation with them breaks down - we no longer know what they are talking about.

I think there are beliefs that cannot be attributed to anyone because to have the mental equipment to have the belief would also make the belief incoherent. A belief that it isn't possible to talk might be like this. Someone who had this belief would have to (a) understand what people thought they were doing when they spoke to one another and (b) believe that they were failing.

It would only be possible to meet criterion (a) if one knew how to talk. We might think this could be like knowing how to cast a horoscope, without believing the outcomes. But to know how to talk is to know, very generally (with a certain acceptable error rate), what is true and false - what it is appropriate and inappropriate to say. (b) cannot be an appropriate thing to say in any playable language game, so a person who knew how to talk (in the relevant context) would also assert that (b) was false. Someone who believed it wasn't possible to talk, but knew how to 'mimic' talk in this way, would sound as though they believed it was possible to talk - they would sound just like everyone else.

We might say 'but they would be lying'. This claim is not ruled out, but finding grounds for it is complicated by the fact that it depends upon certain interpretations which have an irreducably normative element to them. It is not simply a 'matter of fact' whether someone is an honest interlocutor or not, particularly where the evidence of their dishonesty is not acknowledged in any conversation we have with them.

Chinese beetle consciousness ...

I'm not sure if this is even a partly original metaphor ...

Suppose you are in a prison, in solitary confinement. You are entirely restricted to a cell with no access to the outside world except for a window you can look out of, and a small hole through which you can send and receive messages to and from other prisoners.

No one lives outside the prison.

Suppose you look out your window and see a tree, and send a message to other prisoners asking them what they see outside their windows. Some say 'a tree' and some say 'nothing'.

You might imagine that some of the prisoners look out the same side of the prison as you do - where the tree stands - and others look out the other side - where this is no tree. But you might also imagine many other possibilities consistent with the answers that you have received.

You might ask further questions to choose between these possibilities.

What if you ask other prisoners where they live, and they all answer 'a cell'. What would this mean? Is 'a cell' the same kind of place that you live, or is it just a name for the place that a prisoner lives?

What questions could you ask that would help you to answer these questions? What if different prisoners' cells were different in some respects, but were still called 'cells'? How different could they be?

What if there were no prisoners, but only computers, scanners, and printers on the other sides of the holes in the walls?

Some speculations can be checked with other prisoners, and some cannot - can only be entertained in the conversation we are having now, and not in any conversation that would be possibly among the prisoners. (If you send a message saying 'are you computer?' and get the answer 'no', would you know more than you did before you asked?)

We should not be deceived, though, by the possibilities which we can entertain in our present conversation, nor into believing that we can intelligibly speculate - within it - on certain of its constraints.

I might ask you where you live, and you might (reassuringly) say 'here, in my consciousness ...'

Consciousness

I can't imagine what it would be like to be my cat.

I think I can imagine what it would be like for me to be my cat - what it might be like to be a human person in a cat's body, perhaps with some specific and recognisable cat-like desires and capacities. Would my eyesight be the same but more acute? What about hearing and smell?

Would I only have a cat brain, unable to think very clearly about what I am imagining? (!)

When I imagine being you, I really only imagine what it would be like for me to be you. For me to be standing where you are standing, to have some of your physical characteristics. Perhaps also some of your capacities.

Suppose you have no idea what I'm talking about: would I have to imagine that as well? How would I do that?

The 'mystery' of consciousness arises from thinking that things are not like this; from thinking that I can 'really' imagine being you. This is what makes us think there is something 'commensurate' or 'similar' going on here - that your consciousness is 'like' mine.

But if I imagine being you, in some complete way, I would also be imagining not being me - I would be imagining having no idea that I had ever been me; perhaps that this problem had never occurred to me.

'Consciouness' is a mystery if I think that by attributing it to you I am attributing what I think of as being me to you - if I think you are 'just like me' but with some different interests, capacities, understanding, and senory inputs.

I can imagine being me, with these differences, but I can't literaly imagine being you.

What is the world like?

This is a question.

It is the kind of place in which questions can be asked, the kind of place about which we can talk. Which gives it some empirical structure.

It is also like something we can say about it - if we say 'the world is real' then we can say 'it is as though the world is real'. Everything that 'is true' can also be a way that we can talk. We can say 'there are objects', and 'we can talk as though there are objects'.

When we say 'but what is the world really like?' we seem to be asking for an answer which cannot be re-rendered in this hypothetical form. The grammar of this leaves only one possibility: 'We can talk as though we can talk'.

We might also be asking for an answer which validates our capacity to ask questions and give answers, but this is confused. If I don't know whether I can ask questions and get answers, I wouldn't know whether a proper questioning and answering had taken place when I try to ask.

Truth and Commercial Language

Here's a (draft of a) paper I'm hawking about the academic wilderness ...

"Commercial language and the pursuit of truth: How to answer an ancient question"

It's an overview. It also needs de-coloquialising. (!)

Recursive roots and wild speculations ...

Re: my earlier post on this -

"There is some theorem of arithmetic" is probably equivalent to "arithmetic is consistent", which more or less falls with the second incompleteness theorem.

Although maybe we have the wrong idea about what arithmetic is ... at least from a natural language point of view?

Is Goodman's paradox self-referential?

And, of course, I'm writing this post because I've suddently realised that it is, in a rather subtle way:

'Grue' is a colour predicate, and therefore has the 'logical grammar' of a colour word. However, if we attempt to describe a world where objects have grue-type qualities, it is exactly the possibility of colour language that we undermine.

To get to the 'observed vs. unobserved' version of the paradox, we are asked to speculate on the possibility that colours change when we look at them. This possibility could be entirely unobjectionable - we could say, for instance, that our experience of colour requires an interaction between light waves and our visual system, so it's unintelligible to speak of the 'colour' of an unobserved object. On the other hand, it could refer to a colour concept which has no 'use' (in the Wittgensteinian sense) - which depends upon the possibility of assertions which have truth conditions which cannot, in principle, be tested for. We would have no occasion to choose 'grue' over 'green', or vice versa, in our descriptions - these words would be functionally synonymous. In other words, this version of the 'paradox' either has reasonable consequences or no practical consequences. To argue that it has conceptual consequences is to require too much of colour concepts - it is to require, among other things, that they must be 'complete' in Waisman's sense. Almost no empirically based concepts have this quality.

In the 'after time t' version, we generate an indefinitely large number of paradoxical colours - at least one for every possible time t, and many more if we ring a few permutations (why restrict ourselves to temporal boundaries? and why only one?). If we needed to eliminate all the possibilities these represent before being able to reliably attribute colour qualities, we would have no colour language - we could never get it going.

In other words, although 'grue' behaves (grammatically) like a colour, it can only be constructed by requiring too much of our colour concepts or by undermining the possibility of colour concepts altogether. It is self-referential, because it is constructed from an existing grammar - and incoherent, because it does this in a way which questions the possibility of that grammar.

We can know that we need not consider grue-type possibilities from the usability of our colour language, and if that language breaks down then so does the possibility of constructing gruenesses.

'True for us'

I'm sure I've said this before, but I was pressed very specifically on this question in a recent discussion and I think the answer is worth putting succinctly:

Can't we only say that "We can talk" is true for us, rather than in general?

If a statement must be true in any language game that we can play, then 'true for us' is 'true in general'. This is because 'true for us' suggests 'false for someone else' - someone playing a game we cannot play presumably. The trouble with this is that if it's a game we cannot play, then it's a game we can't translate - so we we don't know whether we're dealing with a language at all. This is obviously Davidson's line, and I think he's right. Also from Davidson, we can see that a translation hypothesis which rendered the belief system of the subjects being translated absurd or false would (principle of charity) be rejected. (If we did not reject translation hypotheses of this kind, we would have no grounds for rejecting any translation hypotheses - if we allow that people talk nonsense, we can allow them to 'say' anything at all.) Since 'we can talk' must be true for us, a translation hypothesis rendering a 'foreign' expression as 'we cannot talk' would have to be rejected.

If it isn't 'true for us' then we can't intelligibly hypothesise that it is true for someone else.

Hinges again ...

Rather than dwelling on the 'madnesss' of querying hinges, it seems much more natural to say that while they may not be propositions in the (sub-) game which they enable, they can be propositions in a game which interrogates the playability of the game that they enable.

This points, of course, at the questions which I think are important - to do with the hinges of any possible language game and the (fundamental) unintelligibility of asking whether we can talk - whether we can ask questions. Whether it is possible to do philosophy is not a philosophical question.

Meaning, metalanguage, and internal/external criteria

Putnam's 'twin world' example only works, I think, if we allow ourselves to articulate the possibility of seriously confused interlocutors - a possibility that cannot be articulated within any conversation they are having with each other. It's a language/meta-language confusion.

We can talk about the twin worlds, and their confused (?) inhabitants, but they cannot - without resolving the ambiguity his example depends on. In order for them to talk to one another, the water/twater issue would have to be resolved.

We can't hypothesise that we may, in some systematic way, be making water/twater mistakes, or be subject to water/twater ambiguities - we might as well hypothesise that we are confused about our hypotheses.

The conversation we are having now is always at the top of whatever meta-hierarchy is coherently conceivable. We can hypothesise about the confusions of users of lower level languages, but we can't extrapolate upwards from these hypotheses. And: interpretations which render the native confused are always corrigible (Kripke again ...). We can only (and we must) make incorrigible mutual attributions of intention in a shared conversation.

Davidson's idea that we must always be interpreting each other also has to be considered in this light: we do not have an internal conversation within which we make 'interpretive judgements' about what an external interlocutor means. We are able to make correct judgements about this, but these judgements can only be considered when they are expressed - when statements of them form part of the conversation. At this stage, the 'internal' becomes just whatever it was - whatever private precursor or accompaniment we happened to have.

If we imagine this 'internal' separated from the external statement, what is it that we are imagining? Just our own beetles. Not irrelevant, but not an 'internal representation' either.

Whatever is going on 'inside my head' (whatever beetle scratches there ...) it only gets out, it only becomes available to philosophical theory, as the intentional component of my participation in this conversation. And by that stage, all the important bridges have been crossed. It has become my 'beetle', and not [my beetle].

In this context, as well, the question of 'first person authority' becomes an issue of linguistic competence - the 'capacity' to correctly report on (or otherwise reflect) our intentional states when we speak. We attribute this 'authority' when we attribute interlocutor status - "You have no idea what you really think" is, here, more or less equivalent to "You do not know how to speak". This is not, of course, a playable move - it can't be part of a shared conversation.

Recursive roots

Here is a (wildly) speculative consequence of what I'm saying:

There's a relationship between inductive mathematical proofs and recursion - recursive functions can have their values determined by a definite finite algorithm, and by demonstrating that a function is recursive we are demonstrating that such an algorithm exists (whether or not it is practicable).

Inductive proofs depend upon the induction axiom in formalisations of arithmetic. By showing that zero has a certain property, and that the successor of any number with this property must also have it, we show that all numbers have it. This is an axiom of arithmetic (and it needs to be formaly stated in a way which avoids talk of 'properties'). The 'numerical' root of induction - zero - is also defined axiomatically as the cardinality of the empty set. Many proofs for the whole of arithmetic must depend upon this inductive principle, and its stipulated root.

It is this formalised arithmetic - which establishes induction and zero as axiomatic - which can represent axiomatic systems and theorem generation in general and so its own axiomatisation a` la Gödel.

If I have the right picture of a natural language, then the recursive roots of empricial demonstration will comprise the statements which must be true for the language - and so for argument - to be possible. These roots are not arbitrary, though, since they appear directly as statements about the possibility of language and argument (which cannot be rendered 'formally' - i.e. stripped of semantic content).

Could we write down a specification for a 'naturalised' arithmetic which took the possibility of arithmetic and of computation as its recursive roots, rather than a specific set of (semi-arbitrary?) generative rules?

Some might say: but these rules just are arithmetic. No conception of arithmetic is possible without them.

Maybe this is a place where we are deceived by our intuitions. Can we ask questions like 'Is arithmetic fundamentally about counting, about succession?' or 'Is arithmetic fundamentally about computation, about argument?'. And we have reasons for thinking a certain kind of computation (algorithmic, recursive) goes along with the possibiltiy of counting, of enumeration.

Suppose, however, that we started with a different number: not the cardinality of the empty set, but the Gödel representation of the statement that there is some statement x such that x is a theorem of arithmetic. On the face of it, this does not require completeness, but it does require consistency (since otherwise ~x would also be a theorem). This number must exist in any arithmetic (I think?), and must allow the generation of other numbers (or it wouldn't be arithmetic?) in a way similar to the way zero and succession work in Peano arithmetic.

The value of x (and so also its representation) is a function of the axiomatic system and rules selected, and the coding system used to Gödelise them (as Chaitin's Omega number is a function of the actual structure of the machine it describes). This is true of the theorems of arithmetic generally, of course, but these depend upon a definition of zero that is not open to further interpretation, that 'has no semantic content'.

(Maybe we should think of the value, representation, and 'meaning' of zero as being generated by the rules and coding system as well. But zero is also a word in our natural langauge...)

Anyhow: If there is some number which is the code for a statement that there is some theorem of arithmetic (in the syntax of the axiomatisation that is being encoded), then is that number (or its isomorphs in differently coded and axiomatised, but 'semantically equivalent' systems ... can this make any sense?) a candidate for a general recursive root for a 'natural' arithmetic?

Could its 'existence' be more 'necessary' than the unique cardinality of the empty set?

Another Summary

We need to take the 'language game' metaphor completely seriously - even to the point of thinking about linguistic exchanges in terms of game theory.  Except that the moves we are analysing are irreducibly semantic, and one of the objects of the game is to maintain the game - to maintain the semantic underpinnings of the possibility of describing any game, including formal mathematical games.

Necessary Paradoxes

We experiment with how to talk - we find out what works.  Sometimes we can write down rules from our experiments, that can be used to predict what will work and what will not.  Some of these rules will be provisional, and some will be derived (and so hypothetical on their derivations).  All these rules tell us what will be true.  Some (provisional and hypothetical) rules are just statements like 'P is true'.  Some of these rules seem to be hypothetical only on the possibility that there are any rules like this at all - the possibility of intelligibility, of language itself - but there will always be an interpretive (a semantic) step in any demonstration of this.  To those who accept this step - we might call them those to whom we can speak - the rules which can be demonstrated in this way will seem to be absolutely true.

We need 'is true' to talk about all these kinds of rules.  We cannot ('in principle') write down all the rules - we never reach the end of experiment.

'Semantically closed' languages must be 'empirically' open.  It is the paradoxes that give us science.

Prediction, Theories of Truth

I was trying to explain this argument to someone a few days ago, when we both suddenly saw the problem with it:

In outline, it is the argument that a comprehensive 'predicting machine' would have to incorporate a theory of truth for the language of any people whose behaviour it was going to predict, and so it's workings would be incomprehensible - unintelligible - to them.  It would have to be a 'black box'.

The problem is this:

The machine could predict behaviour - physical movements etc. - without intentional content.  In fact, if it was a machine which conformed to the traditional deterministic metaphors, it would be restricted to doing only this.  Someone examining the output of the machine might interpret it as having content - 'I know what these sounds mean', or 'I know what is described here - it is a person who is thinking this'.  But this interpretation would be made now - in the conversation of the interpreter.  It would not be a necessary component of the raw output.

If the output were to have semantic content, the predictor could not be just a mechanical device.  A semantic predictor would need to produce interpreted output, in the language of the user.  It is this kind of predictor - an 'oracular' predictor - which would need to incorporate a theory of truth for the language of its subjects, but a predictor of this kind could not be rendered in rule based terms - because it could not be a 'machine'.  It would have to be capable of normative judgements.  A prediction such as 'Mary will fall in love with John, and will tell him' could be fulfilled in a number of physically quite distinct ways.  The oracular predictor would need to know what our interpretive decisions would be in order to reliably make such a statement.

A computer which renders its outputs in a natural language can look like an oracular predictor, but examining its internal processes partly undermines this illusion.  We would see how it 'appeared' to speak, and what the nature of our 'conversation' with it was.  Whether, in some future, people might continue to attribute interlocutor status to objects such as this will be a matter for them.

What may bring them closer to this attribution would be a 'mechanical' understanding of how biological human beings speak - and this is some way away.  It is likely that the models will be so complex that few will understand any part of them, and no-one will understand them fully.

In this kind of world the metaphor of universal determinism will seem absurd - it will seem to be based on an astonishingly naïve conception of 'science' as something that could be grasped or managed by individual human beings.  The world will seem to be made up of 'black boxes' ... maybe not such an unfamiliar world after all.

Semanitc Rules

A minimum condition for a linguistic move to be meaningful is that it must commit it's user to some other moves.

A 'use' theory of meaningfulness, and maybe of meaning, could be constructed in terms of 'meaning committments' - i.e. the further moves that must be accepted as 'legitimate' in order for a move under consideration to be meaningful.  It may be that an explication of the further moves is also an explication of the meaning, and the fact that this could never be exhaustive wouldn't matter because only some further moves would be relevant to any particular context.

There would be irreducibly semantic aspects of the further moves - meanings can only depend on other meanings.

When we describe a a 'move' in this game, the description will always refer to some semantic elements.  So, therefore, will the rules of the game - which must rule some moves in and others out.  (The rules of logic are not exempt here - see Logic and Interpretation).

In any case, the apparent clarity of any rule depends upon it's being embedded in an 'unproblematic' semantic framework.

Where does this go?

Logic and Interpretation

Here are two compound expressions:

~(P&~P)

    P&~P

Conventionally, the first is a tautology and the second a contradiction.  However, we might introduce a 'rule of interpretation' here:

When an expression appears on the left of an ampersand, it means the contrary of what it would mean if it appeared on the right.

Applying this rule, we make the first expression a contradiction, and the second a tautology.

Since it is always possible to distinguish expressions that are sentences, and to distinguish whether they are on one side of an ampersand or the other, it seem likely that this rule would not render the notation inconsistent.  By putting '~( ... )' round all sentential expressions on one side of an ampersand we could 'encode' and 'decode' our normal propositional logic.

If this was a rule that a reader might mistakenly apply when doing logical calculations, we would have to warn against it.  On the other hand, such a warning would sound mad to a reader who had never thought of such a rule.  It would say 'Remember to treat an expression on one side of the ampersand as meaning the same thing as when it appears on the other side'.  But this, of course, is another rule of interpretation, just like the first one.

Neither rule is more fundamental than the other.  Each resolves an ambiguity which, if we did not see it, would not need resolving.

Not only is it absurd to consider ourselves to be applying a myriad of interpretational rules in order to eliminate unimagined ambiguities, it is also incoherent.  In order to say 'I am applying rule X', we need to articulate rule X, and so also interpret it.  Not only would every rule, itself, require interpretation; but there would be rules whose correct interpretation would depend upon their own application.

Constructive Semantics

We can be confused by the fact that breaking some rules (e.g. non-contradiction) destroys semantic content.  We can't conclude from this that there is a set of rules which, if followed, guarantees semantic content.

In fact, the OQ argument would suggest otherwise - because we would need to know what these rules meant.

A constructive semantics could be quite rough and ready, and contain many unresolved ambiguities, and still do the work that is required of it (i.e. make semantic determination tractable).  What would also be required would be a method for resolving the ambiguities and cleaning up any loose ends that became problems, and this method could be (I think would need to be) experimental.

What we can't tell, however, is whether there are some things that we resolve by experiment that could be worked out from some set of rules that we are (unknowingly?) following.  For this to make sense, the rules would have to be discoverable - but the OQ problem doesn't rule this out.  It just rules out the discovery of a complete set of rules.

Some Intentional Facts

That I know how to do arithmetic is a fact about the world.

Does this make either epistemology or mathematics empirical?

We test whether I know by making experiments.  Does the verb 'to know' mean something beyond the quality of these tests?

Yes, but this is because we don't understand what an 'experiment' is - specifically, we don't understand that whether an experiment has taken place, and what it's outcomes are, depend upon semantic considerations that cannot be eliminated, cannot be exchanged for something which looks more mechanical.