Truth Predicates - further on Kripke etc.

Perhaps this is a clearer exposition:

Consider two cases:

(A) The traditional case -

This is the 'hierarchy of languages' case, in which each successive meta-language in the hierarchy can be used to articulate a theory of truth for the language below.  At the bottom, we must have a language - L0 - which has no truth predicate.

The problem is that we then only have behavioural grounds for regarding L0 as a language.  This is because we cannot agree with speakers of L0 that we know how to speak their language.  Such an agreement embodies an agreement about how to tell the truth in L0, and L0 does not have the resources to do this.

Unfortunately, this means that we cannot unambiguously identify L0 as a language, because this would require drawing an unambigous conclusion about the intentional states of its speakers - about the rules they were following.  Kripke himself has shown the incoherence of this.

We don't, strictly, have definite grounds for attributing any intentional states at all to the speakers - any regularities we may have identified in a finite set of observations may be accidental.

It is, however, possible that the only interpretation of the behaviour of the 'speakers' of L0 that we can practically manage (that is computable for us) is one which attributes intentional states to them.  We still have a problem about which intentional states to attribute.

So - being sure that L0 is a language, and being sure whether we can correctly translate it, are both out of reach.

Davidson and Quine have also made this observation in a different context, in discussions on translation and the indispensability of a 'Principle of Charity' for the reduction of ambiguity.

(B) The 'natural language' case -

Consider this statement:

(B1) 'I never know how to tell the truth in the language I am speaking'.

If it is true that I do not know how to tell the truth in the language that I am speaking, then B1 cannot be a statement to this effect, since I don't know how to make these statements.

B1 can, however, be false - and must be false, in fact, in any intelligible language game.  This gives us:

(B2) 'I sometimes know how to tell the truth in the language I am speaking'

This must be true.  It also must be a case of my successful truth-telling (included in the scope of the 'sometimes').

Now think about:

(B3) 'We both know how to speak this language.'

This must have the consequence that we would (to some minimal extent) share judgements about the truth and falsehoods of assertions in our shared language.  So we can both make B2 type statements, and we would agree about the application of the truth predicate in B2.  We must, obviously, agree that B3 is true.

If we are learning a language from native speakers who do not share our 'meta-language', then we might test our success by checking with the native speakers that they agree with us about statements like B3, made in the object language.

If they learned our meta-language, we would expect them to agree with us about truth attribution in the meta-language, including the truth value attributed to the translation of B3 (and, to some extent, to the elements of our translation schema).

Notice that in this case, we cannot be in doubt about the intentional states of the speakers without also being in doubt about whether we have correctly made statement B3.

If we are not speaking the same language (if we have made a gross, but not yet obvious, mistake about how to speak the language), then we do not know how to say we are both speaking the same language in that language.


So, unlike case (1), we can unambiguously attribute intentional states, and we can unambiguously identify the language, in judgements we share with other speakers of the language.

What is the point of this?

Well, there is this apparent antinomy:

According to the traditional approach, we cannot tolerate a truth predicate in the language to which it applies without generating liar type paradoxes.

But it is clear from the 'natural language' approach that we can only unambiguously identify something as a language if it contains its own truth predicate.  This is because we need to be able to share explicit judgements within the language or, at least, with speakers of the language about whether we are speaking it correctly.

This has deep consequences for the kind of thing we can regard as a theory of truth.  The traditional approach assumes that a theory of truth is reductive - that the truth predicate for a language can be rendered in terms of, say, set theory, but only in the meta-language.

A natural language theory of truth - and I am arguing that this is the only approach which avoids the Kripkean ambiguity catastrophe - must be recursive.  We do not at any point dispense with the truth predicate, but we find cases where it can only be attributed in one way without generating incoherence (as in  B1), and build outwards from there.

This does not generate a catastrophe in any way which can be rendered intelligible (as I have argued elsewhere in this blog).

I think this approach also has the useful outcome of neutralising liar type paradoxes.  I'm less sure about this, but I think it would be harder to construct a catastrophic liar example within a recursive account.

We can still say, of course, things like 'This statement is not true' - but we only show ourselves to be confused about how to speak here.  There is no underling classification of the kind which generates the liar because there is no reductive theory about whose reliability we can ask intelligible questions.

Cognitive Benchmarking, Kripke, Kahneman, and 'bias'

A difficulty for cognitive psychologists is establishing a standard for correct (non-biased) cognition.  Why do we count some cognitive outcomes as right and others as wrong?

Behaviourally, we might use cognitive bias to explain behaviour inconsistent with a known objective.  We need to be sure, here, that we have correctly identified the objective, correctly described the behaviour, and correctly understood the actors perception of the relationship - and none of these judgements can be made unambiguously on purely empirical grounds (Kripke).

Also, how do we know that our assessment of a judgement as 'unbiased' is not, itself, biased?

The answer, of course, is to do with quality of argument - an unbiased judgement is one which is consistent with a certain linguistic computation, which preserves intelligibility.  While it is possible to wonder whether our activity reflects a cognitive bias, it isn't possible to speculate, within a conversation, that the grounds of the conversation generate nonsense - this would make the speculation itself nonsense as well.

In the case of a (potential) interlocutor, we may have to choose between attributing cognitive bias or withdrawing interlocutor status - between saying 'your choice doesn't make sense' and finding that what they appear to say doesn't make sense.

Kripke inverted. A transfinite approach to a theory of truth ...

Reading Kripke's proposal that there must be meta-language/object-language congruence at some indefinitely distant point in an indefintely dimensioned space of linguistic hierarchies, I wondered:  why not start from there, then?  (If we count backwards from infinity, it is zero that is out of reach ...)

Also, I have remarked before in this blog that the top of the meta-linguistic hierarchy must always be whatever language we are speaking now:  this conversation, in other words.

So:

In the conventional picture, a language can only be a meta-language if includes a T predicate that can be interpreted as a truth predicate for some 'object' language.  Only the bottom level object language can do without one.  We may be confused by the fact that we call this thing a 'truth' predicate, of course, since all it does is make a distinction between certain classes of statements in the object language.  The meta-language may also be used to articulate a theory of truth for the object language if it says how this distinction is made - although the theory may only comprise comprehensive lists of statements in each class.

The reason that the theory cannot be articulated within the object language is that it fails to ground 'liar' statements - Tarski regarded this as catastrophic, as he thought the liar must be interpreted as both true and false.  Since the T predicate can only be interpreted as a truth predicate if it avoids contradiction (among other things?), it must render at least two discrete classes of statements in the object language.  (As a minimum, one which can be interpreted as containing 'true' statements, and the other as containing 'false' ones).  Not all statements in the object language (formally) need to belong to one of the classes.

If the T predicate was part of the object language, we could construct these two statements:

(1)  'Statement (1) belongs in class B' and
(2)  'Statement (2) belongs in class A'

If membership of class A is interpreted as 'being True' then (1) generates a liar paradox, if B, then (2) is a liar.  The other statement of the pair, in each case, is normatively self-referential in a similar way to the liar, but does not generate an immediate contradiction.  (There are lots of variations on this representation - I can't guarantee that this one isn't flawed.)

The meta-linguistic solution is to make statements like (1) and (2) only available in a higher order language, and not in the 'object' language.  A meta-language, then is defined as a language which contains a truth predicate for some object language.

A question related to Kripke's project is whether there is a meta-language which must contain its own truth-predicate.  He seems to be saying that while this is ruled out in a simple 'enumerable' hierarchy of meta-languages, the need to be able to talk about the whole hierarchy indicates that the full set of meta-languages is not enumerable.  He suggests that (a) this creates some special problems which are not easy to address, but also that (b) it creates a space for a language with the property of being able to contain its own truth predicate.  (I may not have this completely right?)

It isn't clear how we get to this language, however, if we take the traditional starting point of an object language with no truth predicate.

What I suggest is that this is a mistake - and in fact that it is incoherent.  There is no unambiguous case of a language without a truth predicate:

If we are considering some behaviour (taken very generally) as a candidate for linguistic behaviour, then Davidson argues (correctly, I think) that we can only draw a positive conclusion if we can come up with a truth-preserving translation schema for the behaviour.  If we cannot produce such a schema for a pattern of behaviour, we do not have grounds for regarding the behaviour as a language at all.

On the other hand having such a proposed schema does not guarantee that we are dealing with a language.  Davidson shows that some Principle of Charity is needed to get started here, and, in addition, the Kripke/Goodman paradox renders all intentional interpretations of behaviour provisional.

The only thing that can ‘guarantee’ such a judgement is sharing it with a speaker of the object language.  In this case, failure to correctly interpret their behaviour is also, directly, failure to share their judgement.  This may not sound very reassuring, but it puts our shared judgment with speakers of the object language on the same footing as our shared judgements of each other as speakers of the meta-language.  We cannot say, within a shared conversation, that it is possible that we are radically failing to understand one another - this is a speculation which renders its own (apparent) articulation unintelligible.

The judgment that we are speaking a language properly (with one another) must include a judgement that we share a theory of truth (though not necessarily one we can articulate).  If we don’t generally know how to tell the truth, then we don’t know how to speak the language.  If we want to explicitly make these kinds of judgements, then we need the equivalent of a truth predicate for the language we are using (even if this is tacitly embedded in the statement that we are spreaking the language properly).

Asking someone whether you are speaking their language properly includes asking them whether you know how to tell the truth in it.  It is not possible to unambiguously identify behaviour as linguistic without this shared agreement, therefore it is not possible to unambiguously identify a language as a language unless it contains a truth predicate.

So, no unambiguous case of an L0.

(Interestingly, this renders the 'slab block' game from PI ambiguous in the relevant way.  We cannot know that the participants are talking to one another.)

When we converse with one another, we may explicitly negotiate specific articulated theories and facts, but we also – both explicitly and tacitly – negotiate the application of the truth predicate for our shared language.  If we have no truth predicate, we don't have a way of explicitly agreeing that we have a shared language.  Whether we also want to say that we negotiate the ‘theory of truth’ for this language depends on whether we think of this as fully articulable (in which case the answer is no) or only partly  (which allows the answer to be yes).

So, I think of this as inverting Kripke because my starting point is the necessity of a self-applicable truth predicate in any language within which a reliable judgement about linguistic status can be made.  This is, a fortiori, any language that can be used for philosophical discussion.

Our judgements about truth telling - our applications of the predicate - must generally be reliable in this language if we are not to be generally talking nonsense (which is ruled out by the incoherence of 'we are generally talking nonsense'.)

Finally, we can only unambiguously identify behaviour as language use if we can share this judgment with the users of the language.  We can't form this judgement on the basis of behaviour alone.  This means that the idea of a language without a truth predicate is actually more incoherent than the idea of one which contains its own truth predicate (so long as we don't conclude that the theory of truth for this language is fully articulable).

Rules and Contradictions

If we are following a (complex) rule which leads us to a contradiction after some series of exercises in which it seems to work, then there must be another rule which avoids the contradiction but works for the successful cases. We might also revise our expectations about the successful cases, of course, but assuming that we can't do this for all successful cases, the conclusion still stands.

Does an argument like this make sense? Yes, but only so long as we hold on to some successful cases. We can't (intelligibly) deny them all (since a denial would depend on some successful rule following).

Does this mean that there are some reliable rules 'in the world' - even if we haven't discovered them yet?

Perhaps, in the sense that this may be a methodologically harmless way of talking - but no, if it is construed as an argument for a metaphysical position.  There are two reasons for this:

(1) For Kripkean/Goodmanesque reasons we know that there will be an indefinite number of potential rules which we might 'discover' here.  A rule which avoids present anomalies and preserves predictive power may produce future anomalies.  Even one which doesn't may not be a unique alternative.  It seems absurd to say that some indefinite set of potential rules is 'really there' in the world.

(2) We are arguing from the a priori (because undeniable) possibility of talk to the necessity of undiscovered rules.  If our talk breaks down, then statements like 'there are undiscovered rules' will also evaporate.

Intuitions ...

See: Essential Metaphysics?

There's no reason why the intuitions which support first order speech should come out as 'true' when articulated in higher order conversations - in fact, this expectation can be very misleading. There is no harm in mathematicians being platonists, but if they want to explore meta-mathematical issues which turn on exactly this intuition, they will get into trouble, because it will turn out to be false (or even unintelligible).

(The reason it will be false is that it is a metaphysical or ontological issue, and these change their character - especially whether they should be taken 'literally' or 'seriously' - in a way which depends on the level of enquiry.)

The trouble is that the way things seem to 'go wrong' here is very disturbing, because some of the intuitions in question appear to underpin the very capacities which can then be turned on them to show their incoherence. Also, first level performance can be damaged by too much higher level enquiry. If you're trying to solve differential equations, you don't want to be distracted by ontological uncertainties about their subject matter. Worse, the internal heuristic models and images we conjure with often seem to be essential to solving the problem.

This is another version of the phenomenological mistake (see 'Thoughts on thoughts').

Experiment and experience

If we try to explain how the world constrains what we can believe, and what we can say, we must describe enough of this constraining world to render the method of constraint intelligibly unequivocal.

A sensory empiricist epistemology cannot be hand-waving, or metaphorical. We can't just point to a few appealing parables and say 'all the rest is like this, even if we cannot give a proper account of it'. It needs to be a theory, not a 'foundation myth'.

Can a 'good enough' account of this kind be given, without encountering open question problems?

Can we give an account of the relationship between language and the world without begging the question whether the foundations of such an account can be independent of its reliability? It doesn't sound likely, for the very general reason that we have to give an account of the 'way the world is' (with respect to the way it modifies our knowledge) which is independent of our account of how we find out the way the world is, since that is the account we're trying to construct ...

We do, of course, give reliable accounts of the world. We also find out about the world by doing experiments. But before an experiment becomes an experiment we must, already, have agreed about what its outcomes might be and what their relevance is.

The Liar

If you have a definite method for working out the meaning of an expression, and the method is explained in the language of the expression you want to decode, then the method is self-referential.  Also, it is self-referential in a specific way:  its scope of adjudication, its normative range, includes any accounts that can be given of itself.

This makes it ambiguous, since it cannot reliably decode itself.

If I have a 'method X' for determing the meaning of any statement S, then I can say:
C:  "Method X, applied to 'S', produces meaning M"

I can ask of a method X whether it is correct, complete, and consistent.

I will set correct aside for the moment, since that question seems to imply the availablity of a 'super-method', when we have already specified X as this method.

With respect to completeness, we seem to be balked by the ambiguity problem.  When we apply X to C we get an indefinite regress, because we must apply X to 'X' (as an element of C).  We have to know what 'X' means before we can apply method X.

But if we are balked by ambiguity in this instance, then we should also be balked by the following case:

R(i):  "I know what 'R(i)' means"

This doesn't, on the face of it, look ambiguous - but any method of disambiguating it will get caught in the loop of disambiguating 'R(i)'.

(The case of R(ia) "I do not know what 'R(1a)' means" shifts the puzzle from 'R(1a)' 'I do not know', suggesting a link between traditional semantic paradoxes and so called 'Moorean' paradoxes.)
 
Similarly:

R(ii) "No definite method can disambiguate the meaning of 'R(ii)'"

R(ii) seems unambiguous.  If it is true, then its unambiguity cannot be attributed to any method of disambiguation.  If it is false, then some definite method can disambiguate it - but then any such method must get caught in the loop of disambiguating 'R(ii)'.

Coming back briefly to the correctness of any proposed disambiguation method:  The absence of such a method cannot, of course, be grounds for believing that we do not, in general, know what we mean when we speak.  Otherwise we wouldn't know what we meant when we tried to articulate such a position.

Demonstrating either the meaningfullness or the meaninglessness of the 'Liar' paradox would require a theory of meaning (to ground the demonstration).

However, the more catastrophic consequences of the 'Liar' depend exactly upon the presumption that meaning can be attributed methodically.  So we seem to have a dilemma - either it is catastrophic, or it cannot be shown to be meaningful or meaningless.

(Kripke believes he has a kind of solution to this problem?  It is arcane, and depends upon further fundamentals which - although they may also be fundamentals of mathematics - do not have a special claim in this context.  A hinge in a space of infinite dimensions can still only be mapped from 'outside' that space, though it must be located 'within' it.  Being able to find something and knowing where it is may seem to amount to the same thing, until one wants to construct a formal account of informal methods.  A map is not a list of methods.  [Is Kripke's use of Cantor a solution for Kripke or a problem for Cantor?])
 
Perhaps we can set the paradox aside as a curiosity arising from our partial and incomplete attempts to fully systematise meaning and truth.

We can even deal with it pragmatically, or contextually, if we like - particulary since there is no context in which it arises outside of quotation marks.  Even in philosophical conversation.

Here are some options:

• It is meaningless.
• It is meaningful, but its meaning cannot be calculated.
• It is meaningful, but neither true nor false. (Kripke?)
• It is meaningful, but both true and false. (Other desperate souls)
• It signposts a boundary to algorithmic meaning production which is more restrictive than the boundary of meaningfullness generally (Sensible people)

We will never calculate a Gödel number, and we will never use the liar outside of quotes, so perhaps its a matter of taste.  Although I hope not.

A distinction of 'as if' circumstances

Here is a case:

TPO: "We can talk about the world as though it contains physical objects."

TPO is clearly true - we do talk about the world this way.  But we want to say something a little bit more:  that this talk is true, or correct.  We say that for this to be true, the world must contain physical objects.  And, of course, the problem with that is to say "The world must contain physical objects" is no more than to talk as though it does.

Suppose we construct some metaphysical or naturalistic theory to get around this - let us say that either (a) the fundamental structure of the words includes physical objects or (b) our talk is somehow the consequence of the existence of physical objects.  All theories of this type will either (i) be further "as if" talk already incorporating and referring to physical objects, or (ii) "as if" talk incorporating and referring to processes and structures which are equally difficult to render epistemologically explanatory.

The only way forward, then, is to forget the "physical objects" bit and focus on the "talk".  The fact that we can talk is not a different kind of fact from the fact that there are physical objects in the world, except that we can't question it.  To question it, we need to be able to talk.

We cannot, either, be 'silently skeptical' in any intelligible way - it is impossible to construct grounds for attributing such a skepticism to anyone, or for denying it of them.  It has only a formal possibility - and it is a possibility which is consistent with any facts or denials of facts whatsoever.  It is a possibility which has no consequences - it neither allows anything nor excludes anything.  It is, from certain perspectives, difficult to know what a statement of such a possibility could mean.

Let's compare TPO with TSP:

TSP: "We can talk as though star signs predicted personality traits."  This is the scary possbility that epsitemological realists want to deal with.

Clearly, some people do talk as though star signs predicted personality traits - they say things like "Star signs predict personality traits".  Why doesn't this count as the same kind of 'as if ' as the one we find in TPO?

The answer here is not to do with any metaphysical or naturalistic circumstance.  It is because we can only rescue "Star signs predict personality traits" by radically adjusting the meaning of 'predict'.  It is very clear that object language talk produces predictions in a very different sense from the sense used by astrologists.  Or, if 'predict' must be held stable, then 'personality traits' will have to go - we have to accept very different ways of attributing these from the ways adopted by psychologists, or even by reasonably astute lay observers.  We cannot work out the rules governing this conversation well enough to know how to continue it beyond repetition of the core liturgy.

Can we make 'physical object' talk fall apart in a similar way?  No.  There are clearly contexts (e.g. metaphysics ...) where this talk becomes very peculiar, but this is an extreme test.  There are no contexts in which astrological predictions of personality traits can be incorporated reliably into a productive and meaningful conversation.  We might play with the words in instrumental or aethetic contexts, but we cannot play the language game of scientific theory.  They do not bound a conversation in a creative, sense-making way.  If we insist on taking their truth 'literaly', their meanings, and so even the possiblity of 'literality', disappear.

Russell's Paradox and Open Question Arguments

This is probably very obvious to people who think about this more than I do.

Gödel's proofs show that any attempt to reduce mathematics to logic would generate a kind of open question argument, because any method of demonstrating the validity of a theory in the relevant logic would have an arithmetical isomorph.

Russell's paradox shows the impossibility of reducing mathematics to the most unrestricted kind of set theory (Frege's project), because the naïve concept of 'set' which it employs is inconsistent.  There are sets whose intensional definitions generate ambiguous extensions.

There are similarities between the open question paradoxes and the class paradoxes, and the attempts to address them have a lot in common with one another.  Stipulation, hierarchy, and concrete construction rules figure in both.

Russell's paradox is generated because we assume that our concept of a set is consistent.  But we can only prove this by having a method of distinguishing sets - and this method, if it had an arithmetical isomorph, would depend upon the undefined notion of a set on which some logics of arithmetic depend.  Also, if we could construct a logic of arithmetic without the concept of a set, then Russell's paradox - and indeed the whole of set theory - would no longer be important.  Gödel has shown, however, that no other approach to logification can avoid replacing sets with some other paradoxical fundamental.

The 'open question' in set theory is:  'What is a set?'.   In other words:  'What kinds of things are included in the set of sets?'

We can't answer this question without circularity (and so Russell's paradox) or stipulation (various type theories, ZF set theory etc.).  We can answer it recursively if we can show that some (necessarily 'open') concept of a set or class is grammatically necessary (in the Wittgensteinian sense - i.e. necessary if we are to talk at all).

Stipulative definitions are always incomplete, because we can't render the language of the stipulation entirely unambiguous.  A stipulative definition which it would be unintelligble to query is a recursive definition.

Person Centred Counselling

We are, fundamentally, language users.  Language users share certain heuristics, certain 'internal models' that express themselves in ways of talking.  I imagine these in terms of (a) what people say about them (b) how they feel to them and (c) what 'mechanism' undelies them (which the speaker may only be partly aware of).  This is not a technical description - it's meant to reflect something like our explanations, our phenomenological condition, and something else - our neurology or subconscious or something similar.


Changing the models and changing the way we talk happen together.  While there may be causal interactions these can in either direction, and sometimes trying to impose a causal account is just misleading.

What is clear is that exploring new ways of talking feels like discovering new models, and discovering new models leads to different ways of talking.  We also learn by talking - to others, and, derivatively, to ourselves.  Our language provides us with 'internal' computational tools as well as with a medium of communication.

But talking is not free - it is action as well as expression;  we do, as well as say, when we talk.  This is most obvious in commercial exchanges, but can be seen in interpersonal interactions as well.  We can't discuss relationship problems with a partner without changing the relationship, and the problems.  And talking to ourselves - setting aside the very limited case of linguistic computation, or 'mental arithmetic' - has severe limitations.  It raises private language issues, for one thing.  But it also just doesn't work - we need an interlocutors perspective to get us out of rat-runs, to see the things we cannot see.

A counselling context should allow experiments with new models and ways of talking in a safe environment.  We can think of the Rogerian core conditions - positive regard, empathy, and congruence - in conversational terms:  I want to talk to you; I am going to understand you; I am going to make sense.  (Or at least I'm going to try very hard, and it's not going to be your fault if I fail.)

Language and The World

The ontology of our world is a reflection of our 'grammar', in the sense that grammatical rules are taken to include mathematics.  This is why we are tempted to 'explain' one in terms of the other, but our sense of 'explanation' breaks down here.  We explain by talking, and we cannot somehow drag the unarticulated world into our discourse.  Similarly, whatever our visceral phenomenological convictions, we cannot show each other how they make our conversatoin intelligible - we can only do this by engaging in the conversation.

And we cannot 'explain' both at once - either in terms of some other 'substrate' (which would be a silly mistake, simply deferring the confusion), or by playing with what we mean by 'explanation'.  We cannot explain the grounds of our explanations, however we conceive these;  and if we remove the open question difficulty from the concept of explanation, it is no longer explanation - it no longer has the appropriate normative scope.

This  is, again, reminiscent of what happens with all these normative meta-hierarchies - they leave no place for a language which we can use to describe the hierarchy.  This language must either be at the 'top' of the hierarchy - so rendering the hierarchy redundant - or it must be incoherent, and so not a language.  This is just Russell's paradox and the incompleteness/inconsistency proofs in another guise.

But it is only within this world that we can intelligibly raise sceptical questions, and so questions of this kind about the existence of the world are unintelligible.  We can bootstrap from the incoherence of certain scepticisms - e.g. about the existence of the world which enables the asking of sceptical questions.

This is not comforting either for traditional epistemology or for the naive realism of some practising scientists.  Private phenomenological anxieties come out as a kind of inarticulable madness, and the practical success of naive realism only shows that it is a successful heuristic.

Falsehood and nonsense

A disagreement in a shared game can only be a misunderstanding.  It may not be resolved, and the game may have some limitations as a result, but a claim that it cannot be resolved is unintelligible in the game.

You and I cannot agree on the meaning of a statement and disagree about it's truth unless we misunderstand each other.  While the meaning of a statement may comprise more than it's 'truth conditions', shared meaning implies at least shared agreement about what would make a statement true.

If we cannot agree on the meaning of a statement, we don't know what we are disagreeing about when one asserts and the other denies.

Persistent local disagreement can infect the whole game, so that we cannot understand what anything each other 'says' means.  If you insist the the world is round, and I that it is flat, our attempts to resolve this will disrupt what we mean by 'the world' and 'flat' and every other token we try to use in the 'conversation' of resolution - which will eventually break down and we will see that we weren't having a conversation at all, even one in which we can agree about our mutual incoherence.

Maybe fear of enquiry is a fear of this terminal incoherence.  A limited game may seem better than no game at all.

Certainty

Certainty, as an intentional state, must be attributed to interlocutors whose participation in the conversation includes "I am certain that ...".  It may be provisionally attributed, with the relevant Kripkean caveats, to other things and people to which/whom we find it practically necessary to attribute intentional states.

A completely private state of certainty is as unintelligible as a completely private conception of the meaning of "I am certain".  So, therefore, must a completely private state of being certain and correct be unintelligible.

This might be quite a disturbing idea to anyone drawn to philosophy as a cure for paranoid anxieties about the reliability of their interlocutors.

It is also catastrophic for any program of constructing epistemological fundamentals from private experiences.

However, it does allow a perspective on some of what is involved in actually being certain and correct:  Someone who says something correct, but is not certain about it, cannot fully understand what it is that they have said.  If I said "I believe it is the case that ~(p&~p), but I'm not sure", then I could not be said to understand the law of non-contradiction.

Primes

What is 'natural' about the 'natural numbers'?  Without some primitive (and, so, poorly defined) conception of 'sequence', we cannot generate them.

We could just as well regard the primes as 'prim-ative' and define an operator for their combination into complexes.  ('Multiplication').

Would these primes appear in a 'natural' sequence if there was nothing peculiar about our conception of sequence?  Maybe we're trying to make it do the wrong thing.

The combination of sequence and primes gives us the 'no largest prime' proof, and sequence generates unlimited quantities and unlimited complexities in a counter-intuitive way.  We know these cannot exist in any articulable world.  To say that they exist in the word 'prior' to articulation is to say something about this world, to partly articulate it ... and to say, about it, that it cannot be completely articulated.  'There will always be things we don't know'.  Is that all?  Or will there always be important things that we don't know?

I don't want to know the position, mass, and velocity of every molecule; but I do want to know whether my bath water is too hot.

And another thing ...

Here is, perhaps, a better way of wording the argument:

Remember that we are introducing this possibility - that someone may believe that it is not possible to talk - into our present converstaion.  To do this, we need to be able articulate this attribution coherently.

If I say "Mary knows how to talk but doesn't believe that it works", I am either saying something false, or showing that I don't understand what 'talk' means.

The only properly complete answer to "What does 'talk' mean'?" is recursive, and the root is ostensive:  it is what we are doing now, in having this conversation, in writing and reading this post.  And we are doing this successfully (on the whole), or we are not doing it at all.

Since I would be saying of Mary (in the example) that she does not understand this - that she does not accept that we are talking now - I am also saying that she does not mean by 'talk' what we mean by 'talk'; and so that my statement about her does not mean what it initially appears to mean.

It is, in fact, another Moorean 'paradox'.

Some other things we can't not believe in ...

Of course there are others that are peculiar, and almost certainly related.

Could we say, for instance, that someone understood basic arithmetic if they also believed that it didn't work?  This is a tricky one.

They would need to give us an explanation with made arithmetic sense.

If they said, for instance, "I can see how adding up works for the examples you have shown me, but I don't think you can extrapolate from these cases to all possible cases"; we would know they were making a mistake of some kind.

On the other hand, Gödel's proofs are, exactly, proofs that arithmetic does not work in the way that many Arithmeticians previously thought.  Certain basic expectations cannot be extended to the set of all possible numbers.

No-one, however, would draw the conclusion from Gödel's argument that there must be something fundamentally wrong with arithmetical computation - or, for instance, with the fundamental theorem (unique factoring into primes).

We're just changing out a bit of structure here, not rebuilding the boat.  Even if the change makes some aspects of the navigation appear more mysterious than they did before...

Why we can't believe it is not possible to talk ...

What does 'talk' mean in 'We can talk to one another?'

It means our participation in the functioning language game we are presently engaged in (with all its relevant contiguities), within which we are interlocutors.  And it only means this - there isn't some further way of defining what we mean by 'talk'.  No other account can be complete or unambiguous (for Kripkean reasons).

This means that a belief that we cannot talk is internally incoherent - it is a belief that the functioning language game in which we are engaged is not a functioning language game.

It is not just that we cannot reliably attribute this believe, we cannot coherently attribute it.

Proving rules

There is a saying that 'the exception proves the rule'.  I used to find this very puzzling when I was young.

It means (I think) that an exception which honours the purpose of the rule helps us to understand how to follow it 'properly'.

In a Dworkinesque example, the rule 'do not walk on the grass' is made intelligible by the exception of the gardener's behaviour.  Because the gardener can walk on the grass, we understand the rule as having the purpose of preserving the lawn, and this helps us to follow it:  it makes it more intelligible even though (apparently) less universal - less mechanical.

If we want to construct a machine, however, we do not need intelligible rules, we need reliable rules.  We need to be able to use the rules to predict the behaviour of the machine.  Production line manufacturing, particularly in it's earliest manifestations, increased control and predictability, as well as efficiency (although efficiency dominated the PR).  A human production line worker is expected to behave in a machine-like way.

I expect that the tacit negotiations of just how machine-like would reflect important aspects of the power structures of particular institutions.

A  syntactical, mathematical, or 'physical' rule can look machine-like.  It operates over a restricted domain, and has explicit outcomes for all the possibilities within that domain.  It is 'embedded' in the description of the domain.  When we explain 'mass', we also explain 'acceleration' and 'force'.  We can write down some equations which exhaust these concepts and their interactions.

There are appropriate and inappropriate ways of applying this 'formalism' to the 'real world', of course, and the rules for doing this have to be intelligible rather than computationally reliable.

Compositional meanings, again.

Does a sentence have meaning?

Davidson seems to dispense with word meanings, but retain sentence meanings.  This is OK, if you think (as he does?) of words as affecting sentence meaning through composition rules, but not having meanings on their own.  But if we distinguish 'having a meaning' from 'having a role in generating meaning', we need to have some kind of criteria for doing this.

Clearly, for Davidson, the sentence/fact relationship won't work for this, because he accepts the relevance of the slingshot argument.

So why do sentences have meaning?  We have to be careful here:  if sentences only have meaning as individual elements in a playable language game, then they may be no better off than words or other sub-sentential elements.

But we can't think of the game as a whole as having 'a meaning'.  We can think of it as being meaningful.

Matrix questions and intelligibility

If the question 'Are we living in a matrix?' can be taken seriously, it cannot also be a question which it is only possible to ask in the matrix world.

If we think of the matrix world as a kind of deception, and that we are deceived that we are asking a question - including a question about whether we live in a matrix world - then we are not asking a question.  If we are 'really' asking a question, then it is a question which makes sense in the 'real' world and so is not, itself, a product of the matrix.

If we can ask the question, some part of us is cognitively independent of the matrix.

Verifiability ...

After hearing David Chalmers talking about The Matrix in Aberdeen:

This is probably not novel, but the verification theory of meaning had at least one thing to be said for it:  that a statement which cannot in principle be verified or falsified is meaningless.  The difference between the film matrix and the philosophical matrix (the brain in the vat) is that in the film Neo escapes from the matrix.  There is a narrative of discovery.

It's when we think we might live in a matrix from which we cannot escape, that we are thinking nonsense.  We are wondering, then, whether Neo 'really did' escape, or whether he only passed into another illusion - another manifestation of the 'real' matrix.

Without the narrative of escape - the possibility of making a test, at least in principle - the metaphysical speculation becomes meaningless.  With the possibility of a test, the 'metaphysical' speculation stops being metaphysical.  Perhaps we'd better not say it becomes 'scientific', as other tests might be appropriate.

There are some special cases - logical rules, for instance - where the alternative to their truth is that all statements become meaningless.  This prevents certain kinds of (experimental) speculation about alternatives to them, but still allows this argument for their truth to be made.  And in real cases where a potential interlocutor cannot be interpreted in a way which is consistent with their conforming to these rules, exactly their status as an interlocutor is called into question.

When we speak meaningfully, we are not claiming to have a fully worked out verification scheme in mind - far less a methodologically privileged one along the lines of the Logical Positivists' - but we also can't claim that no verification scheme could ever be available.  This claim is catastrophic for meaningfulness.

And, of course, both skeptics and religious believers do make this kind of claim:  the first that nothing can be proved and the others that certain things can never be disproved.

Open Questions

Open question paradoxes arise from questions that have this structure:

"What intelligible account can we give of the reliability of our intelligible accounts?"

What sensible story can we tell about how to tell sensible stories?

Formal systems within which questions with this character can be raised will be incomplete or inconsistent.  Even if we try to ask the question in a very disguised way - for instance by looking for a foundation for mathematics in set theory - our trick will be found out.

It cannot be sensible, or even intelligible, to say that we cannot give sensible or intelligible accounts - because our 'serious' statements must be accompanied by a tacit claim that they are, themselves, sensible and intelligible.  The claim that we cannot give intelligible account is either unintelligible or false.

So (a) we must be able to give intelligible accounts and (b) we cannot give a 'complete' account of why they are intelligible.

We can, however, found our accounts of the intelligibility of some statements on the intelligibility of others - even down to the intelligibility of logical axia, to the extent that these can be shown to be intelligible as a consequence of the necessity of intelligibility itself.

So that's OK, then.

However intolerable our private epistemic anxieties, we cannot intelligibly aritculate them.

Obvious arrangements

I have four socks which comprise two pairs.

Two of the socks have red toes, and two have green toes.

I bought these socks in a yacht chandlers.

Chinese Rooms, Translation, and Semantic Chaos

If I wanted to talk to you, and we spoke different languages, I might employ a translator - someone who spoke both your language and mine.

Translation software, of variable reliability, is also available.  We might look forward to this improving.

Suppose software existed which reliably translated your language into mine, and mine into yours.  Why would either of us, then, learn the other's language?  In fact, why would anyone learn both languages?

If no-one learned both languages, how would the software be maintained?  We could explore misunderstandings by discussing them with one another via the software ... which is approximately how we maintain our monoglot exchanges?

We feel as though we can ignore the problems this creates for settling the meanings of monoglot exchanges, because we do (a priori) manage to mean some definite things by what we say.  We always have the starting point of the present exchange that we are engaged in.

Would we be able to ignore these problems in a much more machine mediated system?  What about a world where every communication depended on mechanical mediation, where everyone needed a translation machine in order to speak at all?

It's not just a matter of hearing unfamiliar languages being translated here, but of having to treat what is going on as a language entirely on the evidence of the translation device.  And by 'what is going on' we can only mean 'whatever the device is translating' - which may be nothing we can independently discern ...

What could we say, in this environment, about the objects of the translation software?  There doesn't seem to be a coherent sense in which we could claim that it was preserving some kind of semantic content, since there would be no independent community of interlocutors to regulate this.  There would be no linguistic community that did not depend on the translation devices.

Phenomenology, again...

Hume, expressing a central Enlightenment norm, warns us against projecting our normative needs onto an indifferent reality.

Neither this thought, nor any other, can be articulated without observing the norms which make conversation possible; but these, themselves, can only be partly articulated, and provide only slight phenomenological comfort - so Hume's injunction has been practically reliable.  The moral certainties he was tilting at were misleading in proportion to the comfort they pretended to provide.

But we are left with (1) the necessity of conversational norms to philosophical theory and (2) the visceral intuitions to which we, as competent language users, are subject.  The possibility of articulating anything at all rules out certain skeptical positions, and we only respond to, rather than understand, the mechanism which drives our articulations.  We know we can talk, and we see the world as talkers see it.

Our phenomenological state, beyond supporting our conversations, fuels much wordless anxiety and confusion.  Perhaps we can take a perverse comfort from not being obliged to be able to account for every twinge.

Emergence?

If the biosphere is to include intentional creatures, then the problem of stating its boundary conditions is not to do with complexity or emergence, but is a consequence of our being part of the biosphere.

To be able to state boundary conditions is to be in a certain intentional state, and any statement of biosphere boundary conditions would, inter alia, be a statement of the boundary conditions for being in intentional states, and so of the boundary conditions for being in that one in particular.  This means that these boundary conditions would have to define what it was to be in an intentional state, and what it was to be in the intentional state of being able to state boundary conditions.  It would be a boundary condition and also define what a boundary condition was.

This can't work, of course, because such a boundary condition would be computationally incomplete, or self-referential.  We couldn't state the boundary condition without first stating a boundary condition for stating boundary conditions, and so on ...

Again, we have to give our fundamental accounts in terms which include 'primitive' intentional states which cannot be defined away.

Methods, Family Resemblances, and Rules of Reference

'Object Oriented Programming' is a structured programming approach adopted by software designers, and which is supported in fairly disciplined (although somewhat varying) ways by certain programming environments (e.g. Java, C++, Visual Basic, and others).

In these contexts, an 'object' can be thought of as a collection of data items, and a set of methods for accessing and manipulating them.  Each object has its own private set of data, and that data can only be accessed by calling on one of its methods - and not, for instance, through a public structure of variables or constants.

The power of this structure is that once an object, or rather an object 'class' - a type of object - has been constructed and tested, it can be relied upon in a large number of different contexts.  Because its methods and data are 'private' to it, their operations will not be interfered with in unexpected ways by other processes in the system, because the disciplines of the environment, or the structure of the software, prevent this.

What I want to say a little bit more about here is the concept of a 'method' borrowed from this environment.

Imagine (as in a classical example given in other expositions) that your objects are simulacra of vehicles in, say, a traffic network simulation.  Each of these vehicles will have methods associated with the kinds of things that vehicles do - we may want to feed them instructions about speeding up, slowing down, turning, stopping etc.  In interactions between them (collisions, collision avoidance etc.) we will want to define the ways that they will behave and calculate the outcomes.

For some instructions, the vehicles will react in different ways.  For instance, the instruction 'open the throttle 10%' initiates a method, with an argument, to a vehicle simulacrum.  The 'open the throttle' method of each vehicle type will tell it how to respond, and that response will be mediated by, and will alter, its internal data states.  A lorry, for example, will accelerate more slowly than a sports car.  A vehicle that already has its throttle fully open will not change its behaviour.  A vehicle with its engine switched off will not change its behaviour.  Some vehicles in certain icy conditions might lose adhesion.

Once we have constructed the classes of objects required (different types of vehicle) and instances of the classes (actual vehicles, with initial data states) the fact that all objects from certain classes have an 'open the throttle' method, simplifies the simulation.  We can, for instance, see what happens if everyone on the M6 between 7:30 and 8:30 in the morning were to open their throttles by 5%.

The relevance of this example is in the fact that there is no disciplinary or structural reason why methods with the same name should execute in commensurate ways over objects.  There is no reason why the method 'open the throttle' in some object classes would not produce bizarre behaviour (driving off into a field, deleting itself from the programme, sending a recording of  'Yankee Doodle' to the sound card ...).

Clearly the programme will be much easier to understand if different objects executed similar sounding methods in commensurate ways, but what counts as 'commensurate' for this purpose will be a feature of the programmer or of the reader and user, not of the objects or methods.  If these interlocutors find the ways that different object classes executed homonymal methods commensurate, then they are commensurate.

We might give a 'family resemblance' (after Wittgenstein) account of why a group of methods seemed commensurate.  This kind of semi-descriptive account can give the extension of a class, but at the expense of rendering membership decisions, themselves, in terms of methods which vary with the objects subject to the decision.  In other words, 'family resemblance' accounts really tell us no more about the way that methods are commensurate than the fact that they share a name does, since they, themselves, may depend upon a set of methods which we can only show to be commensurate by referring to some further family resemblance a little higher up the hierarchy of accounts.

Object oriented programming, then, has done something very odd.  In pursuit of reliability and predictability, it has created a place for natural language categories that it is hard to give a formal account of.  It has done this by allowing these to be coded in a variety of different ways, depending upon the objects they are to be applied to.  It has placed the decisions about how to organise these in an intelligible way in the hands of the programmers and users, so that this intelligibility is an aspect of the playability of the language game in which they are interlocutors, and not of structural features of the methods themselves.

It is sometimes useful to keep this model in mind when considering some of the 'hinges' of intelligibillity in general - hinges upon which anything that counts as a language must turn.

An example might be made, here, of reference and naming.  It's clear (although perhaps a more formal argument to this effect should be constructed) that it is necessary to be able to refer and to name in order to be able to speak at all.  Powerful instances of this suggest themselves - in particular the case of referring to interlocutors, but also cases of referring to and identifying the great range of  'objects' which are projected from nominal grammatical forms.  'Me', 'my pig', 'pig' and 'Piggy' (the name of my pig) all seem to need 'content'.

In the empiricist tradition, some of these contents have been sought in the world, and so the 'reference' relationship has seemed to have a special epistemological and linguistic significance.

If we think, instead, of 'reference' and 'naming' as being essential grammatical or semantic categories requiring contextual methods (as throttle manipulations might be to a traffic simulation), we can see that all this requires is that thes methods are adequately defined for the objects they are relevant to, and that this 'adequacy' is no more than that they are intelligible for, i.e. usable by, interlocutors.

It may still make sense to ask how reference works, or how naming works, but the answer to this question will be provided by an examination of the way the related methods are implemented with respect to specific linguistic 'objects', or computational contexts.  Any commonality would be provided by the grammatical and conversational needs, not by relationships between the methods (except in so far as these shed light on the conversational needs they might be meeting).

It is not surprising, perhaps, that specific 'methods' of naming (e.g. causal chain accounts) can seem very compelling in specific contexts.  References to actual historical figures must, after all, guarantee some narrative of this kind - so that where the narrative fails, the reference fails also.  References to fictional figures must, however, work in some quite different way, with different associated failures.  And there can be many differences of detail between methods - is Gilgamesh a fictional character in just the same way as are Zeus, or Mrs. Bennet, for instance?

Similarly, we can be tempted into a misleading simple mindedness about whether a proper name can function as a description - cases can vary, so long as the consequences of variation don't threaten local intelligibility.  We don't need to give a further account of how intelligibility in general is maintained, as this is guaranteed by our ability to request and give accounts.

This kind of mistake is a consequence of expecting some epistemological or metaphysical significance of a grammatical category, simply on the grounds that it 'works':  we think that because it works there must be a unifying underlying mechanism, when in fact grammatical necessity generates the requirement for mechanisms, for methods, which then may vary between classes of object/contexts.

A general demonstration that such methods must fail would be a demonstration that we could not render ourselves intelligible in a language which required reference, but this is not the same as demontrating that there must be some general method (however complex or conjunctive its definition).  It does have the consequence that we must be able to produce a method when one is needed, but that is a much weaker conclusion, and unlikely to have much fundamental significance.

An aim of the object oriented approach, after all, is computational robustness, not formal elegance.  The discovery that a method implementation is incoherent only affects the class of objects which incorporate that implementation.  Other classes sharing a 'commensurate' method (one which does something similar for those classes, and has a similar name) may not be affected at all.

References, and so referential failures, are accomplished in a variety of ways in order to achieve a grammatical object.  These 'methods' are defined in the contexts for which they are constructed, and exist to bring these contexts within the scope of a particular grammatical category.  It makes no more sense to ask how naming really works, outside of these contexts and this category, than it does to ask what 'open the throttle' really means outside the scope of the traffic simulator and the conversation of the programmers (and ourselves).

We can be confused by the grammatical necessity of reference within any language in which we might want to interrogate our theories and concepts (including the concept of reference) into thinking that we have found a special link between language and the world.  What we should see, instead, is the necessity of constructing links of this kind in some way or another in order to bring the world within the scope of our articulated interrogations.  (And this may be done tacitly, as well as explicitly.)

Obviously, an account of any one of these links cannot, itself, depend upon the link being accounted for; nor can a comprehensive dictionary of these accounts depend upon any subset of them for its intelligibility.  This means that the grammatical concept of reference, the only one that is 'necessary', cannot be accounted for in terms of the methods, even though it is only the methods which do the 'work' we require to be done, by setting out definite computational or narrative approaches to fulfilling the grammatical requirement.

Our story about the relationship between language and the world is not essentially different from other stories in language about the world.  It can't depend upon its own account of its possibility or integrity.

Intentionality, Function and Description

I don't think Dennett ever realy tells us how a bag of molecules can take an intentional stance, but his hierarchy has some appeal.

I offer the following version:

Physical
System (signalling)
System (function)
Intentional
Reflexive

And, as before, while we must attribute intentionality to an interlocutor, we may attribute otherwise if it 'works' (though always fallibly, from Kripke).

What I hadn't thought about properly until a talk with BT on Monday, is that there are circumstances where we must practically, as opposed to 'logically' (or to avoid undermining our own intelligibility), attribute intentionality (and function).  This is where lower level descriptions are just too complex.

Higher level biological systems are a good example:  a physical description of them woud be hopelessly complicated, and only a functional description is tractable.

With some computer systems, it is possible (depending upon the level selected) that even a system level descriptions would be too complex.  And it looks like brains might be like this too ....

These are still different reasons from the ones we have for treating interlocutors as intentional.  What I'm wondering, though, is whether there is some relationship here that I'm missing.

One of the reasons I'm wondering is that there isn't such a big difference between treating a system as law bound and treating it as functional.  Maybe.

And if we cannot maintain intelligibility without attributing intentionality on practical grounds, what then?

Indispensible Indexicals

(Maybe this is just more on Moore's Paradox ...)

Traditional approaches to formalising natural language have tended to treat indexicals as a kind of short-hand: as though they can always be substituted with non-contextual names or descriptions without changing the sense of the embedding expression.

I'm not sure whether this presumption has ever been thoroughly examined.  What would a language without indexicals look like?  If we always referred to ourselves by name, or by description, for instances ...

There would be an important epistemological difficulty, arising from the point I have made in earlier posts about Kripke's rule following argument:  While 'Mary is talking to John' is a corrigible intentional description of their behaviour, 'I am talking to you' is not.


Only the first and second person have this character - 'They are having a conversation' is subject to behavioural justification in a way in which 'We are having a conversation', or 'I am talking to you' are not.  We can probably alwasy replace 'they' with a context free name or description, but not so 'I' or 'you'.

If this is correct, then not only are the first and second person indexicals not dispensable, but their role is epistemologically fundamental.

Knowing the answer. Happy New Year.

If we could look into the future to see the answers to our questions, we would hear people uttering sublime truths without understanding.  They will even live their lives by them, and build and use machines which depend upon them.

But they will not have arrived at them via our questions, and, because they 'know' the answers, they will not understand our confusion.

We might live among them for a while thinking this, and then begin to wonder whether we had understood their language at all, or simply stumbled into a jungle of misleading homonymy.

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.