Three Paradoxes?

I've mentioned three kinds of paradoxes in these posts:

1. Semantic paradoxes (such as the liar)
2. Moorean 'paradoxes'
3. Open-question paradoxes (including Russell's paradox)

I wonder if all share the character of rendering themselves unintelligible if taken 'literally' (i.e. if the words used to utter them are interpreted in the 'usual' way, or canonically). I also wonder if this is interesting or, possibly, trivial: there are lots of ways of making no sense at all.

Semantic paradoxes arise when apparently 'grammatical' (i.e. 'well-formed') statements directly contradict themselves, which is immediately catastrophic. We imagine that 'well-formed' statements should be like formulae in a formal language, and should either be theorems or not - should be definitely true or false. (The scope of the 'formal language' metaphor is problematic, of course.)

A classic example of a liar paradox is:

(A): Sentence (B) is true.
(B): Sentence (A) is false.

Moorean paradoxes are not directly self-contradictory, but directly or indirectly undermine the grounds of their own intelligibility. They are usually constructed from a sentence function which produces true or false statements for most legitimate substitutions but becomes nonsensical (rather than simply false) when a variable is replaced with a first-person indexical.

A classic example of a Moorean paradox is:

"A believes it is raining, but it is not raining."

This is fine when A is replaced by most names or descriptive nouns, but not when it is replaced by a first-person indexical:

"I believe it is raining, but it is not raining."

Open question paradoxes arise from self-referential validity (or intelligibility) dependencies, where some normative concept must (directly or indirectly) include within its scope of adjudiation any account of how it may properly be applied.

A classic example of an open-question paradox is:

(C) "By adhering to theory X, we can reliably distinguish true statements from false statements in all circumstances."

(D) How do we show that (C) is true, without circularity or stipulation?

Open paradoxes unite the Analytic tradition in philosophy because they are generated by all of its main objects of study: goodness, knowledge, meaning, choice, validity etcetera.

Open question paradoxes can be generated in purely syntactical contexts (formal systems) as well as by semantic categories, as Kurt Gödel showed for theorem determination in arithmetic.

(Russell's paradox is an open question paradox because the normative adjudication 'is a member of' is rendered systematically ambiguous for certain cases.)

All of these paradoxes are relevant to enquiries into intelligibility. And they are tied up with the contextuality of language use - a contextuality which philosophers persist in thinking we can somehow 'cancel out', producing words without speakers, assertions without asserters, 'free-standing' statements that are not part of the world they describe ...

We can get some insight into this by considering the simple case of falsehood.

A false statement is the contrary of a statement that is true. We can construct a false statement by appending the 'not' operator to a true statement in whatever way is grammatically appropriate. If 'I am hungry' is true, then 'I am not hungry' is false. If P is true, then ~P is false.

It is easy to demonstrate that if we try to make 'P & ~P' - a statement and its negation - true, then we are committing ourselves to the truth of any random statement Q. This such a powerful logical principle that it can be used to test the consistency of an axiomatic system: to show that they do not lead to contradiction, we need only show that there is some well-formed formula that is not a theorem of the system.

Taken together, these criteria have the consequences that a false statement must 'make sense', but that asserting a false statement does not. Intelligibility and assertability must, in other words, be independent of one another. Trying to make sense of this has led to some bizarre metaphysical speculation (e.g. the 'reality' of 'possible' worlds ...)

Of course, re-engagement with context eliminates this problem: intelligibility and truth also re-engage. The context

 provides truth conditions, which, if necessary, can be explicitly introduced into the discussion. This is what Wittgenstein meant when he talked about 'language going on holiday'. Abstraction can lead us astray: grammar does not confer legitimacy, because we can find ourselves talking nonsense for reasons that we do not have the language to explicate. We think we understand the 'grammar' of a Moorean paradox because we have a picture of what grammatical conformity looks like: rules about how to move the puzzle pieces around, perhaps. But we can only state these rules in a language which we already presume to be intelligible.

Whenever we imagine we can do otherwise, we will find ourselves generating paradoxes that we don't know what to do with. We cannot specify the rules of valid rule generation. We generate rules by experiment, and we are occasionally deceived when we stumble on a rule whose contrary cannot make sense in any intelligible language (and so, also, cannot be the product of a legitimate translation schema for any prospective language).

An essential feature of an experiment is that its outcome can't be predicted (otherwise we wouldn't be undertaking it). When we try to say that a false statement 'makes sense' (even if it can't be seriously asserted), we are stipulating how the experiment must come out - even though we know that falsehood entails complete incongruence.

If we want to say something like 'the truth of X is intelligible, even though X is false', we have to explain what we mean by this. There will always be a contextual ambiguity behind such a statement. 'X is intelligible' and 'X is false' can only be entertained together if they do not share an alethial 'frame' (otherwise we have an ex contradictione explosion ...).

No competent interlocutor would make a paradoxical assertion, of course. There is no context outside philosophical abstraction in which these are intelligible. The fact that we can't write down a set of rules from which this can be deduced should tell us something about our conceptions of philosophical abstraction.

Geometry

'I can make a representation' is not, in any useful sense, a representation. While our 'mapping', 'representing', 'calculating', 'proving' metaphors are harmless - even heuristically powerful - in non-reflexive contexts, they are a barrier to the only kind of 'engagement with reality' that is consistent with the experience and logic of rendering ourselves intelligible.

If we try to 'map' the world of this engagement, we find ourselves, like Kripke, lost in a tangle of wormholes through the infinite dimensions of a Klein bottle world whose geometry varies with our attention. Each corridor is a corridor; each door is a door; each room is a room; but we cannot reliably predict which doors will appear in which corridors, and which rooms they will lead to - all corridors have doors, all doors lead to rooms, but any attempt to map them completely also reorders them in ways we can only partly predict.

We discover that we draw our maps by rearranging the geometry of the landscape. We cannot map our map-making.

But neither can we relinquish it. 'We can relinquish map-making' must, it seems, be a partial map - however ambiguous and qualified. Whether it's one of the parts that changes with our attention, in response to our epistemological needs, may or may not be a question we can address without further rearranging the landscape.

When we ask ourselves questions about fundamental qualifiers like 'changes' and 'stays the same', we experience kaleidoscopic disorientation. Does the meaning of 'stays the same' depend on things staying the same? Does it depend on 'same' meaning the same thing from one occasion of use to another? How would we know?

And yet engaging with this landscape is the only way we can do anything remotely like 'engaging with reality'. We must engage in the map-making activity, while resisting the delusion that this can ever be satisfactorily concluded ...

Motivations and Methods

When we feel a tension between the power of a wordless intuition and the desire to make ourselves intelligible we face our humanity most directly. To some extent, we experience this tension all the time - between our sense of ourselves as language users and the complexities of conversing with others. The difficulty is compounded by the normative, and somewhat ambiguous, boundaries of 'language' and 'conversation'. Whether we count someone as an honest and competent interlocutor, and how much effort we are prepared to put into figuring this out, are normative matters (as is the attribution of 'consciousness' itself - a closely related matter). There is no 'fact' nor any computation that can settle this issue for us. We make experiments, and we decide whether to press on or to give up.

If we decide to treat someone as an interlocutor, we might say this to them, but it would be redundant. If we decide not to, we have, essentially, nothing to say this with. As I've said before in this blog (probably too often): If you can't talk to someone, you can't say so to them.

Returning to wordless intuition and intelligibility:

David Hume observed that we must rely on our senses, even though we cannot demonstrate their reliability. He had a conception of the world and our interactions with it that made this observation seem much less ambiguous than it actually is. For him, our phenomenological space and our capacity to rationally reflect on it (and on other things) were part of the groundwork. It would have been difficult for someone with that particular mindset to see that the role our 'senses' played in our capacity to make ourselves intelligible to one another necessarily gave them just the kind of 'reliable content' that this mutual intelligibility required, and no more. This is the point of Wittgenstein's 'box beetle' thought experiment.

This can be a frightening realisation. The visceral experience of our wordless phenomenological condition reliably driving our capacity to speak, and the related sense that language can give us a transparent view of each other's cognitive and phenomenological spaces - even that our narratives and explanations are 'literally true' in some way that goes beyond 'mutually intelligible' - look essential to sanity.

Until, that is, we try to intelligibly articulate those very conceptions of sanity....

The incongruence we experience when we reflect on the paradoxes and ambiguities this produces might drive us in one of two directions: we might rescue our intuitions at the expense of intelligibility, or we might insist on the reliability of public demonstration, however confused and miserable this made us feel. It goes without saying, almost, that both of these options are, themselves, unintelligible. The first because it cannot be shared (and so becomes a necessarily private conviction - only expressible, if you like, in a 'private language') and the second because it is liturgical - we can only participate in it by recitation and signalling.

The third way is to ground our method in intelligibility experiments - which Hume does, of course, but does not acknowledge. He says, effectively: 'Look - this is what makes sense!', where he might have said 'I think this makes sense - does it make sense to you?'

In a real conversations, of course, the two are equivalent. The intelligibility of an assertion (and of assertions of the 'truth' of assertions) is conditional on the intelligibility of the conversation. Which, in turn, is conditional on the willingness and ability of the participants to engage.

This conditionality can be masked by the apparent independence of a 'text' - can we really be in conversation with David Hume? - and by the apparent 'absolute' or 'necessary' truth of certain logical and mathematical assertions. My present conversation is not with David Hume, however, but with you, about David Hume. Also, as I've pointed out elsewhere in this Blog, some assertions - not just logical and mathematical assertions, but also 'privileged statements' in the sense introduced by Barry Stroud, are impossible to intelligibly deny in any conceivable language. As Donald Davidson might have said,  any translation schema which rendered a 'native' speaker making such a denial would have to be rejected, and if no translation schema can avoid this then what we are dealing with is not a language. Whitman's poetic declaration may be powerful, but it only works with some interpretation ...

The sense of our humanity that I referred to in the first paragraph is most characteristically expressed in our mutual experiments in intelligibility, in our experimental conversations with one another. This is ironically captured in Turing's infamous test of machine intelligence. We cannot construct a machine that exhibits this very recognisable aspect of human intelligence, because we do not know how human beings do this. Large language models can only mimic what has already been said - their coding incorporates semantic rules, it does not enable semantic experiment, and especially not semantic experiment that humans can engage with.

What is more, and Turing knew this when he wrote about machine intelligence, it is also formally impossible to construct such a machine. If we imagine a 'computer'' that could mimic a human linguistic experimenter completely, then we can see that either it, or a 'composite' of them could mimic human conversations and predict their outcomes. Such a composite machine would be running a 'truth algorithm', which it would not be equipped to interrogate (because this would generate an open question paradox). Another way of putting this is that we cannot imagine such a machine, because we cannot validate its mechanisms (and so cannot be sure that our 'imagining' is correct), or, perhaps, that if we 'found' such a machine we would not be able to correctly determine its function. Either possibility renders the proposal unintelligible.

So it's humanity all the way down ...

A Summary

The world is permitting us to have the conversation we are having now. Within this conversation, we can say things about the world (for instance, that it is permitting us to have this conversation). Some of these things we say about the world are, literally, undeniable.

Any statement which renders conversation impossible whenever we attempt to take it seriously must be at least false. The contraries of some of these statements must be true in any intelligible language - they are Barry Stroud's 'privileged statements'. (This circumstance also elucidates puzzles like 'Moore's paradox'.) The intelligibility of our present conversation is the fulcrum on which our capacity to talk about the world turns.

We cannot intelligibly deny that we are having a conversation, because if we are not having a conversation then we can't explicitly 'deny' anything at all. You might imagine that any of us could 'deny' it privately - as a thought, rather than as a statement in a shared conversation. This 'denial' would have to either (a) be 'non-linguistic' or (b) be articulated in some 'private language' which cannot in principle be used for public conversation.

It's worth reminding ourselves here of the role of interpretation, and of how we attribute intentional states. If  you tell me you believe something, and I acknowledge you as an honest and competent interlocutor, then I must accept your statement as irrevocable evidence of your intentional state with respect to that belief. To do otherwise is to doubt your honesty or competence - to doubt the quality of your participation in our conversation. In other circumstances, we can only attribute beliefs to one another hypothetically and corrigibly - perhaps on the basis of behaviour, or on other 'indirect' evidence. It is therefore impossible to unequivocally attribute the belief that conversation is impossible, since it can never be articulated within a conversation. This means that alternative interpretations of the evidence are always intelligible.

At the very least, we can do without being able to attribute such a belief. If we also want to do without 'private languages', then we must.

In general, to have an intelligible thought is to have a thought that can, in principle, be shared in a conversation. We have many 'unintelligible thoughts' - in the sense of more-or-less conscious mental processes - which seem, subjectively, to viscerally drive our capacity to converse in certain ways.  This is why we imagine that our 'inner experience of the world' must be a validating ground of what we say. This subjective 'ground' is not directly shared with our interlocutors, however, so we can neither point to it as evidence nor fully explain its role in driving our 'linguistic behaviour'. As Hume observes, we may be compelled by it but we cannot validate our compulsion. This is, if you like, what it 'feels' like to be a language user, what it feels like to be able to converse. We cannot use it to justify what we say.

One implication of the intelligibility of our conversation is that many statements beyond the ones within this conversation must also be intelligible. To deny this would make our present conversation unintelligible. 'Only what we are saying now makes sense' cannot make sense - at the very least because it denies the sense of any further discussion of what counts as sense-making. The individual parts of our conversations 'work' only as elements in networks of other experiments with sense-making. Quine and Davidson (among others) thought something like this, but made a mistake about how it came about.

The nodes in these networks are linguistic moves, and the links are meaning rules and truth conditions (or conditions of legitimate use).  We discover them through linguistic experiment, through exploring what we find intelligible. Some experiments lead to the collapse of any possibility of network construction - sometimes directly and sometimes very indirectly indeed.

We cannot construct a 'complete and final' model of this network, as this would generate an open question paradox. 'This is a complete and final description of the way we use language' can only be made sense of as a node in the network it claims to validate. On the other hand, 'we cannot explore any aspect of this network' cannot be a node in any intelligible semantic network.

There is no 'explanation' of how we come to have conversations that can validate the having of conversations. All explanations take place within conversations - our ability to converse validates our explanations, not vice versa. Within specific contexts, and sometimes in the context of the possibility of conversation in general, some explanations turn out to be the only ones that are intelligible.

With respect to the general validity of our scientific conversations, we can say that they are at least 'permitted' - that the world allows us to talk about it in the way that we do. What we find, though, is that 'We can talk as though X is true' and 'X is true', taken unconditionally, share the same truth conditions. On some accounts, this would imply that they 'mean' the same thing, although some metaphysical thinkers might find this objectionable - especially, perhaps, theologians.

(I am reminded, again, of Robert Winston's response to Richard Dawkins' question about how a 'man of science' like himself can believe in God: "I'm going to give you a very Jewish answer: it depends on what you mean by ''God'.")

And that's more or less it. The solution to a problem first posed by the Greeks ...

The Primacy of the 1st and 2nd Person Perspective, the Roots of Validation

Hume's observation that we cannot demonstrate the reliability of our sensory inputs, but must, nevertheless, build our knowledge of the world from them stands at the focus of the modern analytic tradition in epistemology. How this observation is made and interpreted, how it 'works' within a community of language users, has had some attention. It deserves much more: We can only share Hume's skepticism if we have a shared understanding of what it is that he is skeptical about.

Almost the whole of philosophy (and empirical science) has oriented itself towards validating third-person narratives - validating that something 'is the case' as though this could be demonstrated independently of whether the statement of that something (or its contrary) is intelligible within our conversation (literally, the conversation between you and me). That this is an error is what we should have learned from Moore's paradox. It is the deep truth that Barry Stroud passed by when he dismissed the epistemological relevance of 'privileged statements'.

There is no such thing as pure third-person validation. A third-person conversation can only count as a conversation if you and I can agree on this. Our agreement about Hume - our confidence in our shared capacity to consider him - is epistemologically prior to anything he might have said.

It is, of course, difficult to imagine how our present conversation might remain intelligible to us if we disagreed very profoundly about certain historical facts, but that does not make the facts the grounds for the intelligibility - it makes our experiments with intelligibility the grounds for what we count (at the limit what we must count) as facts.

However counter-intuitive this might seem, it is - to paraphrase Sherlock Holmes - the only hypothesis which must survive a considered skeptical assault. While we might share doubts about Hume, we cannot intelligibly share doubts about our doubts about Hume without wondering whether we are, in fact, having an intelligible conversation about doubt. Or perhaps about anything.

Metaphysics studies what must be true for our conversations to be intelligible, without considering that intelligibility must be a test of metaphysics, and not vice versa. And intelligibility is not a 'third-person' attribute. We can always articulate a radical skepticism about the intelligibility of a conversation between third parties, but we cannot intelligibly articulate a similar skepticism about the conversation you and I are presently having.

More on Metaphysics ...

A way of talking that we are comfortable with can feel like it has metaphysical roots. Each member of a language community might (silently) refer to 'different' metaphysical roots of this kind, but still be able to sustain conversations with each other (this is an extension of the 'box-beetle' parable).

When we describe these roots, of course, we may find that we disagree. A characteristic of these descriptions (when nothing more nefarious is at stake) is that however different the metaphysical inspirations are, they cannot be distinguished on the basis of 'truth-conditions'. If they could, then some would not survive. Or the community would fragment - members would become unintelligible to one another. Truth conditions, after all, must also be intelligible.

Machines ...

 A machine is not just an object - or even a set of 'processes' (as in a computer program). For it to be a machine it must, in addition to this, be accompanied by a promise. For human-made machines the promise is from the constructor: 'I promise this will fulfil its function'. For 'natural' machines the promise is from the theoriser - the person articulating the hypothesis that the object is a machine - and it is a promise that this person knows how the machine works; knows what its 'function' is.

The 'stability' of machines is therefore a projection of our belief in semantic stability. We can only make promises if we know what we are saying, and we can only know what we are saying if, to some minimal extent, words mean the 'same' from one occasion of use to another.

This is one of the reasons why the 'fact' that we can construct machines and the fact that we can talk about the world are really the same fact.

Most machines are, of course, a bit 'unreliable'. Their accompanying promises are not always fulfilled. We can only make adjudications about this in a working language. (Collapsing bridges - which appear in many 'reality' diatribes - can only be identified through this kind of adjudication.)

What this means is that semantic stability underpins the identification and appraisal of 'machines'. Which, in turn, means that no 'mechanistic' account can be given of semantic stability.

(We should know this, of course, from the Goodman/Kripke paradox.)

We certainly can't intelligibly articulate a speculation that semantic stability is some kind of 'illusion' either ... nor even the related speculation that we might wonder about this privately.

So much, by the way, for mechanistic determinism. Which seems like a fairly trivial corollary, under the circumstances ...

Stroud again ...

Barry Stroud's exact error is that he thought a wedge could be driven between 'X is true' and 'We can in all respects converse as though X were true'. He missed the real force of Wittgenstein's 'beetle' argument.

'X is true', in other words, literally means that we can, in all respects, converse as though X were true. No sense can be attached to it otherwise.

We might imagine that a 'thought' can be true, or a 'proposition' can be true, independent of language. But this is exactly to imagine that the contents of my box must be the 'same' as the contents of your box for our discourse to be meaningful. In fact, issues of 'sameness', and even the concept of 'sameness' itself can only arise within a functioning discourse.

'Sameness' is, fundamentally, a semantic concept. When we say 'we can only speak to one another because there are some things in the world that are the same as one another', we are arguing that sameness 'in the world' can be deduced from our ability to converse.

Our ability to converse is the fulcrum - not some fact about the world. If there is a 'verificationist principle' at work here, it is the possibility of verification itself - the possibility of producing an intelligible account of anything at all.

Our private phenomenological space is, to a relevant extent, radically unshareable. When we make it the locus for intentional states, we do no more than claim that we can talk to one another. When we attribute intentional states to those with whom we cannot converse (our pets, for instance) we are no more than saying 'if they could talk, they would talk this way'.

I can only ask a philosophical question in a functioning conversation. The idea of a philosophical question about whether it is possible to have a functioning conversation is unintelligible. We would need a 'private' language in which to ask such a question, and such a language would only be intelligible if it could, in principle, be shared.

Bomb Disposal Revisited

In a 2007 post entitled "Meaning and Transmission", I (slightly) explored an example of good-faith falsehood. In a draft of a paper on Business Ethics that I put together a while later, I found a better development of the example:

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A claim, or a belief, that a conversational move is honest cannot be sustained if it is also recognised by interlocutors that the move has consequences which are inconsistent with the possibility of the conversation.  This follows from the characterisation given elsewhere in this blog – the method of recursion cannot produce inconsistent results; the language game must remain playable.  This has the consequence that any honest move must be consistent with the indefinite extension of the conversation (in principle) on the basis of any general rules, or attributed intentional states, implied by the move.

In order to explore this, I am going to outline a strong apparent counter-example, and then explain why it fails.  In the course of this, some more detailed aspects of the approach will become clear.

Imagine that A is a bomb-disposal expert, and that she is advising B how to disarm a bomb.  A is safe from the effects of making a wrong decision, but B will be blown up if he cuts the wrong wire.  B, with two wires left to cut – a red one and a blue one – asks A which one to cut first.  Both know that the wrong choice will be fatal to B.  A knows that the red wire should be cut first.

Now add the following circumstance:  B completely believes that A wants him dead, and wishes to exploit the current situation to that effect.  A knows that B believes this, but B does not know that A knows this.  A does not want B dead.

The obvious consequence of this is that if A is to save B’s life, she must tell him to cut the wrong wire – because whichever wire she tells him to cut, he will cut the other.

The interesting issues here are:

1. A, clearly, should not tell B the truth about which wire to cut first, if she wants to save his life..

2. We have no grounds for thinking that killing B is a good thing to do.  At least for A and for B, it is not a good thing to do.

3. By telling B to cut the blue wire, A confirms B’s suspicion that she is trying to kill him, and – presumably – does substantial damage to the possibility that B might regard A as an honest interlocutor.

In the absence of complicated and unlikely presuppositions, I think we would want to regard A’s participation in this conversation (‘Cut the blue wire’) as honest engagement.  However, it is both untruthful and fatal to the conversation (though not, happily, to B).

Why is this not a counter-example?

The answer is that it only works as a counter-example if something like the interpretation we have given to the circumstances is correct.  However, the grounds we have for thinking that it is correct are very peculiar.  If we try to imagine this situation without the explanatory gloss given to A’s intentional state – her knowledge, desires, and beliefs – B’s interpretation of the situation would have seemed the most likely.  In this circumstance, we have no behavioural, or indeed any public, evidence that A is trying to save B’s life – indeed, quite the contrary.

We can only come to know unambiguously what A’s intentional state is through having a conversation with A, with the presumption of honest (and now truthful) engagement that this requires.  We can be misled by the authorial access of a narrator here – it is only because we (improbably, and without explanation) ‘know the whole story’ that the counter-example seems to make sense.  Once we have spoken to A, it is no longer a counter-example, but a perfectly intelligible (and true) account given in A’s conversation with us.  In order to complete this, we would surmise that if B knew the ‘whole story’, and was an interlocutor in the shared conversation, B would share our interpretation – or if there was conflict, it would have to be resolved for the conversation to continue.

It can be difficult to untangle the various complications of self-reference, authorial access, behavioural implication, and conversational competence that this kind of example illustrates.  It’s worth setting some of these out in a summary:

4. Authorial access:  I have produced this counter-example in a conversation with you (the reader), and provided no account of how I came to know A’s intentions.  If I failed to provide this account when queried, the quality of my participation in this conversation would be in doubt.  Given the circumstances, a reliable account would need to refer to a conversation I had with A that was contiguous with the one I’m having with you.  Any other evidence would have to include this, at least indirectly – e.g. if a third party told me of A’s intentions, based on A’s account to them.

5. Behaviour:  An interpretation of A’s behaviour, in the absence of some conversation with A, would be unlikely to include the possibility that it was well intentioned.  It could not exclude it either, but there are great many things it could not exclude (the Kripke/Goodman paradox, again).

6. Competence and honesty:  If, in some conversation I had with A, A had lied to me about her intentions (e.g. to cover up her attempt to kill B), then A would not have been an honest participant in that conversation, and so its status as a conversation would be degraded.  This either (a) could be discovered through further conversational experiment or (b) is not an intelligible possibility.

7. Self-reference:  While we might think we can intelligibly theorise about a circumstance where honest participation necessarily produced an ultimate conversational disaster, we can only do this by presuming that, at least for us, this disaster has not occurred.  The tragedy of A and B can only be narrated if someone can narrate; its details (which include their intentional states) are only credible if they have participated in some part of the extended conversation in which this narration takes place.

On being the value of a bound variable ...

A difficulty with theological dogma (whether about god or about 'reality') is its insistence on metaphysical literality. Dogmatic truth cannot just be 'a way of speaking', however carefully we qualify that phrase. 

There is an important sense in which science can be comfortable with  'We can talk as though X is true' and 'X is true' being methodologically indistinguishable, when understood in the most unrestricted way. Dogma cannot.

This has some odd consequences. One is that religious 'truth' trumps intelligibility - so that we end up with 'mysteries' like the Catholic trinity. Another, related to this, is that it must be possible to distinguish meaning from truth-value - since specifying a theory of truth ('X is true iff Y') implies a methodological test (in the broadest sense of a 'specific way of finding out') that at least implies a difference in meaning, even if meaning can't be entirely reduced to methodology. 'God exists' and 'we can talk, in the most unrestricted way, as though God exists' must mean different things, even though the methods used to test the truth of the first are exactly the same as the methods used to test the truth of the second.

One place that we could look for such a difference might be in subjective experience which, as David Hume observed, commands conviction without providing arguments. No methodological test can be specified. Willard Quine went with this in the end, by more or less stipulating that sensory input just was the basis of scientific proof - a perspective as dogmatic as any credo.

From a psychological perspective, the experience of conviction without awareness has its place in what is called 'procedural knowledge' - we can know how to do something without being able to explain how to do it or even being able to properly articulate our knowledge; frequently without even being able to give a very satisfactory account of how we came by this knowledge. Facility with language depends upon extensive procedural knowledge - most people have far more semantic and grammatical knowledge than they can articulate or give an account of. The 'obviousness' of how to talk, to most language users, makes the link between the inner world of 'experience' and the shared world we describe to one another. Our congruent public narrative convinces us of the congruence of our sensory apparatus. Without any 'argument' ...

If we attempt to construct a more public test based on this ('let me show you and you will agree with me'), we render important truths vulnerable to empathic failure unless we are ready to resort to accusations of bad faith. If say that I do not see your god from the best perspective you can construct, then either your test has failed or I am a liar.

'We agree about how to talk', however, must be true, to some minimal extent, before we can put together narratives about 'procedural knowledge', or ask questions about 'reality', or construct advantageous perspectives. This is a matter of intelligibility rather than visceral conviction (although it may be this as well) and so doesn't solve the 'really' problem in the kind of way that would relieve any felt metaphysical anxiety. If the existence of God could be derived from the possibility of intelligible speech, the 'as if' problem would go away, but would make the existence of God a consequence of our ability to talk to one another. I'm not sure how satisfactory this would be to a dogmatic believer.

The same thing applies to the relationship between the experience of being here and the value of the noun 'I'. While solipsism may be grammatically unintelligible, the 'fact' that we directly experience only one 'sensorium', and the 'fact' of our limited ability to share it, point in the other direction - which means no more nor less than that the 'unshareable' parts are outside the scope of intelligible discourse. The experience of 'I' and our knowledge of 'God' seem to belong in the same sensory wilderness.

It is much harder to dispense with 'I' than with 'God' in first-person conversations of course. And substituting 'God' into sentence functions doesn't generate Moorean paradoxes. Which, I suppose, is a kind of demonstration of agnosticism without relativism. "I don't need 'God'" makes sense, but "I don't need 'I'" doesn't.

A person as viscerally convinced of the existence of God as they are of the existence of the objects in the room they are in may find it difficult to hold a conversation with someone who does not share one or the other of these convictions. Whether it is a 'matter of fact' that the objects, or God, are 'really' in the room will not be relevant to their difficulty. If the difficulty is insurmountable, it won't even be clear what they might mean by a 'matter of fact'.

When Richard Dawkins asked Robert Winston, a practising Jew, how he, a 'man of science' could believe in God, Winston said "I'm going to give you a very Jewish answer: It depends on what you mean by 'God'".

He understood some important aspects of the relationship between methodology and meaning. As he might.