"We can talk to each other", taken literally, must be either hopelessly ambiguous (not a statement at all) or true and undecidable.
This is because it requires a tacit conception of truth - 'using the language properly', so to speak, and also of what counts as a language. Both of these must be reasonably reliable if the statement is to be true, but no algorithm written down in the language can demonstrate this reliability.
Also, no algorithm in a 'higher order' language would be translatable, so speculations of this sort are irrelevant (if any sense at all can be attached to them).
The reason the statement is true is not algorithmic: it's falsehood would be unitelligible, a Moorean paradox. If someone insisted on its literal falsehood, we would have to wonder what they meant (certainly not something related to the conventional uses of the words it contains). They would be doing something at the same time as seeming to claim that it was impossible. Either we'd be wrong about what they were doing, or we and they did not share an interpretation of 'impossible'. This is not an algorithmic demonstration because no explanation to such an objector would have any weight - we could never be sure that there was enough mutual understanding to articulate an explanation. We would either find a way of working out what they did mean - would find a way of continuing to talk with them which rendered their objection interpretable - or the conversation would disintegrate.
The tacitly implied predicate 'is true', here, is not grounded in Kripke's sense. But it is still a kind of basis for grounding.
Wednesday, November 20, 2013
Thursday, November 14, 2013
Diagonalisation (?), behaviour, and meaning ...
Does something like this work:
Suppose we were to give a behavioural account to of how to say things in a language - say a list of noises, and what they meant. The list could include not only 'primitive' expressions but also any complexes constructed from them. If we could describe the records in this list, then the list would be enumerable.
Notice that while one side (say the left side) of this list comprises specific physical circumstances (behaviours, or noises), the other side (the right side) is a list of contents, and so can only be identified intentionally.
If we can describe records in the list, then we can describe the contents of each left side of each element. (This means, among other things, that the descriptions of the physical behaviours must also appear as the contents of the intentional side somewhere else in the list, and so have their own describable physical counterparts.)
Everything that can be said could be somewhere in this list, linked up to a way of saying it.
Although the list is formally interminable, however, any actual statement would have to be finite. This is a barrier to the actual list containing the behaviour which counted as a description of itself, since this would require something like infinite repetition of nested representations of the list.
Also, although the list would contain statements about whether some statement was a member of the list, the number of these would be 'smaller' than the number of items in the list - otherwise the only thing the list could contain would be statements about what was in the list.
Since a description of the list would containt a complete statement of what was in the list, this description could not be in the list since there have to be some statements which do not have membership statements in the list.
Suppose we were to give a behavioural account to of how to say things in a language - say a list of noises, and what they meant. The list could include not only 'primitive' expressions but also any complexes constructed from them. If we could describe the records in this list, then the list would be enumerable.
Notice that while one side (say the left side) of this list comprises specific physical circumstances (behaviours, or noises), the other side (the right side) is a list of contents, and so can only be identified intentionally.
If we can describe records in the list, then we can describe the contents of each left side of each element. (This means, among other things, that the descriptions of the physical behaviours must also appear as the contents of the intentional side somewhere else in the list, and so have their own describable physical counterparts.)
Everything that can be said could be somewhere in this list, linked up to a way of saying it.
Although the list is formally interminable, however, any actual statement would have to be finite. This is a barrier to the actual list containing the behaviour which counted as a description of itself, since this would require something like infinite repetition of nested representations of the list.
Also, although the list would contain statements about whether some statement was a member of the list, the number of these would be 'smaller' than the number of items in the list - otherwise the only thing the list could contain would be statements about what was in the list.
Since a description of the list would containt a complete statement of what was in the list, this description could not be in the list since there have to be some statements which do not have membership statements in the list.
Monday, September 09, 2013
Rationality
Rationality is produced in our shared language activity.
The fulcrum of intelligibility is intelligible conversation. Intelligible action is action of which we can give an intelligible account.
Classical economics is mainly grammatical enquiry: how can we use 'choose'?
The fulcrum of intelligibility is intelligible conversation. Intelligible action is action of which we can give an intelligible account.
Classical economics is mainly grammatical enquiry: how can we use 'choose'?
Friday, September 06, 2013
Indirect locutions
I ask "what's for lunch?", and you answer "I'm opening a tin of soup."
Should I tranlsate your answer into this form: "We are having soup for lunch." Or perhaps, even "Soup". Or does this only sound plausible given some theoretical objective?
Why not translate "Soup" into "I'm opening a tin of soup."?
If we say 'context', we're really ducking the question, because this only helps if there is some context in which we can consider the effect of context in general (otherwise we just clamber from one to another). It's hard to think of a better definition of a context-independent enquiry.
Should I tranlsate your answer into this form: "We are having soup for lunch." Or perhaps, even "Soup". Or does this only sound plausible given some theoretical objective?
Why not translate "Soup" into "I'm opening a tin of soup."?
If we say 'context', we're really ducking the question, because this only helps if there is some context in which we can consider the effect of context in general (otherwise we just clamber from one to another). It's hard to think of a better definition of a context-independent enquiry.
What is possible?
Here is a question for metaphysicians:
Are there 'possible worlds' that we cannot imagine?
How would we go about demonstrating that there weren't without begging the question?
If there are, what use is our 'modal intuition'?
Are there 'possible worlds' that we cannot imagine?
How would we go about demonstrating that there weren't without begging the question?
If there are, what use is our 'modal intuition'?
Wednesday, September 04, 2013
Non-Contradiction
Maybe we should think of the rule against contradiction as a translation rule rather than as a speaking rule. It should be a test of a translation schema that it does not render the native speaker as uttering contradictions.
This becomes a 'speaking rule' in the sense that we may say to someone: 'I do not understand you because you seem to be contradicting yourself'. The 'seem to be' is not eliminable: we may have made a translation error. This can never be ruled out on purely formal, or empirical, grounds.
This renders the reductio ad absurdum correctly: it required prior agreement on the issues which generate the contradiction, if it is to be valid. It has this form: I cannot make sense of what you are saying, because however I interpret ('translate' it) it produces a contradiction.
So the RAA is always vulnerable to a 'translation error' defence.
This is fine, though: mathematics depends on agreement about how to speak, and not vice versa.
This becomes a 'speaking rule' in the sense that we may say to someone: 'I do not understand you because you seem to be contradicting yourself'. The 'seem to be' is not eliminable: we may have made a translation error. This can never be ruled out on purely formal, or empirical, grounds.
This renders the reductio ad absurdum correctly: it required prior agreement on the issues which generate the contradiction, if it is to be valid. It has this form: I cannot make sense of what you are saying, because however I interpret ('translate' it) it produces a contradiction.
So the RAA is always vulnerable to a 'translation error' defence.
This is fine, though: mathematics depends on agreement about how to speak, and not vice versa.
Monday, July 15, 2013
Views from inside and outside
We decide what to count as participation in our conversation. We decide what to count as 'language'. So much depends on this decision that it may not feel like a decision, so it's worth explaining what I mean here.
No finite set of specific behaviours, described only as behaviours - i.e. without intentional content - could count as participation in a conversation. Equally, no set of similarly described behaviours could be ruled out as a way of participating in a conversation.
If I hear someone calling me from another room, but investigate to find a recording device, I do no think that it was the recording device that was calling me. If I speculate that, nevertheless, I was being called, and that the recording device was being used do to this, then I must speculate that someone was using it in this way. To imagine that the recording device was calling me, I would need to imagine that it was much more than a recording device.
On the other hand, any distinguishable states of affairs - the presence or absence of a light in a window, a sequence of clicks, whether a clock is set fast or slow, could be used to give a 'signal', and so could be interpreted as having some semantic content. Many things which look 'natural' - the disposition of pebbles on a beach, the entrails of a slaughtered chicken - can, and have been, given semantic content. Sadly, on the other hand, many serious attempts to participate in conversations have been treated as incredible.
We cannot write down a set of rules for what can and cannot be interpreted as a signal. We have lots of rules about the complexity of the signal that can be sent once we describe the possible states of the transmitting and receiving machinery (from Shannon), and we can write down rules for the transmission and receipt of valid signals given these descriptions, but we can say almost nothing about their semantic content.
We could not send a signal to an alien species which explained to them how they should interpret the signal we are sending.
Sometimes it seems almost impossible not to interpret some state of affairs, some 'signal', as having semantic content. A literate person finds it hard not to read the words on an advertising billboard. Perhaps you are finding it equally hard to resist reading what I am writing now. This compulsion can feel almost mechanical, or empirical. If we allow it to guide our search for semantic roots, we will, however, only find more or less complex signalling machinery. We will never be any better off than the aliens.
On the other hand, I could not be explaining all this to you, nor you be trying to understand my explanation, unless you could attribute semantic content to what I am typing here. You must take a certain normative attitude to this string of characters in order to count it as a participation in a conversation, and not as random, or as purely mechanically produced. But you cannot be compelled to do this, which is why I think it's appropriate to speak in terms of making a decision.
The view of the aliens is the outside view - if they can 'see' anything at all it is the complex signalling system. As Davidson might argue, however, it's hard to give sense to 'see' here without making them seem very like us, and so like possible interlocutors. (The 'aliens' metaphor breaks down here - 'alien' is too human a description.)
Our view is the inside view - the view of the participants in a conversation. And this argument is part of that view. It is an exploration of the possibilities it provides, to see which are intelligible. A proposed mechanical/signalling semantic theory would also be one of these possibilities - and so would fail as a fundamental account because such an account would be circular. The rules which described the signalling system would only be rules by virtue of their role in the conversation within which the signalling system theory was being articulated.
We should also feel comfortable about setting aside any other deterministic metaphors here - these, also, can only be constructed within a working conversation, and so cannot be produced as accounts of its semantic content without circularity. It is possible that any 'scientific' account that we can give of the world will turn out to be deterministic, but we cannot project that onto the conditions of possibility of giving such account, since these cannot be fully articulated.
It's worth adding something about the character of a potential interlocutor's 'decision' to participate. Clearly this can't be a 'rational' decision in terms that can be represented within our conversation. 'I have considered the options and decided that it is better for me not to converse with you' is a move in the conversation. If it is regarded as an occasion of exit, then it cannot mean what it might appear to mean if it was a conversational move. It is automatically unintelligible.
It is perhaps better to think in terms of conversations being maintained or breaking down rather than in terms of participants joining or leaving. The edge of the describable world is not on any map.
No finite set of specific behaviours, described only as behaviours - i.e. without intentional content - could count as participation in a conversation. Equally, no set of similarly described behaviours could be ruled out as a way of participating in a conversation.
If I hear someone calling me from another room, but investigate to find a recording device, I do no think that it was the recording device that was calling me. If I speculate that, nevertheless, I was being called, and that the recording device was being used do to this, then I must speculate that someone was using it in this way. To imagine that the recording device was calling me, I would need to imagine that it was much more than a recording device.
On the other hand, any distinguishable states of affairs - the presence or absence of a light in a window, a sequence of clicks, whether a clock is set fast or slow, could be used to give a 'signal', and so could be interpreted as having some semantic content. Many things which look 'natural' - the disposition of pebbles on a beach, the entrails of a slaughtered chicken - can, and have been, given semantic content. Sadly, on the other hand, many serious attempts to participate in conversations have been treated as incredible.
We cannot write down a set of rules for what can and cannot be interpreted as a signal. We have lots of rules about the complexity of the signal that can be sent once we describe the possible states of the transmitting and receiving machinery (from Shannon), and we can write down rules for the transmission and receipt of valid signals given these descriptions, but we can say almost nothing about their semantic content.
We could not send a signal to an alien species which explained to them how they should interpret the signal we are sending.
Sometimes it seems almost impossible not to interpret some state of affairs, some 'signal', as having semantic content. A literate person finds it hard not to read the words on an advertising billboard. Perhaps you are finding it equally hard to resist reading what I am writing now. This compulsion can feel almost mechanical, or empirical. If we allow it to guide our search for semantic roots, we will, however, only find more or less complex signalling machinery. We will never be any better off than the aliens.
On the other hand, I could not be explaining all this to you, nor you be trying to understand my explanation, unless you could attribute semantic content to what I am typing here. You must take a certain normative attitude to this string of characters in order to count it as a participation in a conversation, and not as random, or as purely mechanically produced. But you cannot be compelled to do this, which is why I think it's appropriate to speak in terms of making a decision.
The view of the aliens is the outside view - if they can 'see' anything at all it is the complex signalling system. As Davidson might argue, however, it's hard to give sense to 'see' here without making them seem very like us, and so like possible interlocutors. (The 'aliens' metaphor breaks down here - 'alien' is too human a description.)
Our view is the inside view - the view of the participants in a conversation. And this argument is part of that view. It is an exploration of the possibilities it provides, to see which are intelligible. A proposed mechanical/signalling semantic theory would also be one of these possibilities - and so would fail as a fundamental account because such an account would be circular. The rules which described the signalling system would only be rules by virtue of their role in the conversation within which the signalling system theory was being articulated.
We should also feel comfortable about setting aside any other deterministic metaphors here - these, also, can only be constructed within a working conversation, and so cannot be produced as accounts of its semantic content without circularity. It is possible that any 'scientific' account that we can give of the world will turn out to be deterministic, but we cannot project that onto the conditions of possibility of giving such account, since these cannot be fully articulated.
It's worth adding something about the character of a potential interlocutor's 'decision' to participate. Clearly this can't be a 'rational' decision in terms that can be represented within our conversation. 'I have considered the options and decided that it is better for me not to converse with you' is a move in the conversation. If it is regarded as an occasion of exit, then it cannot mean what it might appear to mean if it was a conversational move. It is automatically unintelligible.
It is perhaps better to think in terms of conversations being maintained or breaking down rather than in terms of participants joining or leaving. The edge of the describable world is not on any map.
Friday, July 05, 2013
Private Languages. Again ... ?
Drawing a few strings together:
We can only give a recursive account of what counts as a language - we point to the language we are using now, as a root, and we show that other things could also count by offering translation schemas (Davidson).
This is not a completely straightforward business.
As we speak, we change the language we are using - any change is possible within the bounds of intelligibility. These bounds, themselves, can partly be described in terms of rules: but not entirely - we have to do a lot of experiment and exploration as well.
If we could articulate all the rules of intelligibility, the question whether our list of rules was intelligible would generate a paradox. We might be tempted to avoid this by expressing rules in a 'meta-language', but this creates another problem. An entirely formal language (one fully defined in terms of specific rules) is subject to an indefinitely large number of interpretations, and it is only by interpreting the language that we give it semantic content. We can only avoid having to choose between paradox and ambiguity by accepting that the rules of intelligibility cannot be completely written down in any language at all.
This is OK, though. Exploring the world and exploring what we can say are closely integrated activities - this is especially clear when we consider our explorations of what we can say about our explorations.
But it does create a problem: if we cannot bound our language by rules, if we cannot fully articulate what we count as our language, then what definite test can we apply to a proposed translation of a potential language into our one?
The answer to this question looks evasive. Although there is a real problem about agreeing a translation schema, it is not an essentially different problem from the kinds of problems we face in agreeing how to talk about other things. If we can agree about anything, and if we can make sufficient sense of the idea of a translation schema that allows for some successful cases, then we can agree about a translation schema.
We can explore, in a partly rule bounded way, what would 'count' as a successful translation of Dolphin into English, just as we can explore, in a partly rule bounded way, what would count as a reasonable explanation for the Aurora Borealis, or for the dishes remaining unwashed.
(We might, after all, learn some things from our attempts translate Dolphin that taught us new ways to speak in English that had a bearing on what we were prepared to count as a successful translation of Dolphin.)
What we cannot do, though, in any language, is say 'Dolphin is a language, but one that we will not ever be able to translate' - we can attach no meaning to 'language' in this statement that would allow us to distinguish language from anything else. We might as well say that stones can speak. (See Ursula le Guin's short story 'The Author of the Acacia Seeds').
So, the first problem with a private language is that either (a) there is a translation schema for it, and it is therefore not, after all, private or (b) it is not a language.
A general problem with an argument of this kind might be that we do not need to explicitly judge that something is a language before we speak it. This is addressed by a similar argument to the one I suggested in Truth Predicates and related posts.
In summary, we have a problem with identifying a candidate L0 as a specific language, since we only have behaviour (or symbol lists or whatever) to go on. No finite set of these can be used to unambiguously attribute an intentional state (such as meaning something) (Kripke).
This doesn't render the idea of a language generally ambiguous, however, unless we are committed to some reductive account of what a language must comprise. Since we know we are speaking to one another now, and since we know (roughly) what we are saying to one another, this doesn't matter. We can construct a recursive account instead.
But we can only explicitly judge that we are speaking to one another (i.e. we can only say so) in a language which contains the equivalent of its own truth predicate. This is because to say 'we speak the same language' is as much as to say 'we speak the same language, and we speak it properly'. Since L0 has no truth predicate (by definition), users of L0 cannot say this.
This means that any identification of L0 as a language will always be provisional and corrigible. There will be no guarantee that if we learn to 'play the L0 game' that we will be speaking a language.
Another way of putting this is that although we might suspend judgment on whether having a language is essentially to do with sharing it (which would beg the question under consideration), it is clear that judging that we have a language requires shared agreement if it is to be intelligible. A truth predicate in a private language would be redundant in exactly the way predicted by Ramsey. A truth predicate in a shared language allows us to explicitly agree, in a restricted sense, what it is that we are sharing. It allows us to ask and answer questions like 'what do you mean by ...?' and 'do you think it is true that ... ?'. Neither of these arise in a private language.
It seems likely, in fact, that all rules about how to speak a private language would strictly be redundant, since they would only report what the speaker already knows in order to speak the language.
Which brings us to what, I think, was Wittgenstein's objection. Even if the rules were stated, the user of a private language could have no way of knowing whether they did apply to the language, since any method of checking this would be no more secure than his confidence that he was using the language correctly in the first place. He would need to be able to judge that 'I am following the rules' didn't break any rules, which he could not securely do.
He could not intelligibly form the judgment 'I am speaking my private language properly'.
We can compare this with the equivalent judgement expressed in a shared language, where either (a) the judgement can reliably attribute an intentional state (of knowing that we are speaking the same language) or (b) there is not, after all, a shared language - we have misunderstood what is being said.
Going back to the translation issue raised at the beginning, however, it seems possible that Wittgenstein took for granted that we would not have difficulty recognising a language. This is implicit in his discussion of the 'slab/block' game near the beginning of PI. As I indicated previously, if any L0 can only be corrigibly identified as a language (unlike a language which contains its own truth predicate), then Wittgenstein cannot establish that the 'slab/block' team are speaking to one another.
As Kripke points out in 'Rules and Private Language', his paradox not only renders the idea of a private language unintelligible, it has catastrophic consequences for identifying anything as a language given the traditional (broadly Tarskian) account of what a language can be. His mistake here is not to recognise that the context of such a judgement will always be from within a working language - one which contains the equivalent of a truth predicate which does not require a reductive account, since the same context provides the root for a satisfactory recursive account.
We can only give a recursive account of what counts as a language - we point to the language we are using now, as a root, and we show that other things could also count by offering translation schemas (Davidson).
This is not a completely straightforward business.
As we speak, we change the language we are using - any change is possible within the bounds of intelligibility. These bounds, themselves, can partly be described in terms of rules: but not entirely - we have to do a lot of experiment and exploration as well.
If we could articulate all the rules of intelligibility, the question whether our list of rules was intelligible would generate a paradox. We might be tempted to avoid this by expressing rules in a 'meta-language', but this creates another problem. An entirely formal language (one fully defined in terms of specific rules) is subject to an indefinitely large number of interpretations, and it is only by interpreting the language that we give it semantic content. We can only avoid having to choose between paradox and ambiguity by accepting that the rules of intelligibility cannot be completely written down in any language at all.
This is OK, though. Exploring the world and exploring what we can say are closely integrated activities - this is especially clear when we consider our explorations of what we can say about our explorations.
But it does create a problem: if we cannot bound our language by rules, if we cannot fully articulate what we count as our language, then what definite test can we apply to a proposed translation of a potential language into our one?
The answer to this question looks evasive. Although there is a real problem about agreeing a translation schema, it is not an essentially different problem from the kinds of problems we face in agreeing how to talk about other things. If we can agree about anything, and if we can make sufficient sense of the idea of a translation schema that allows for some successful cases, then we can agree about a translation schema.
We can explore, in a partly rule bounded way, what would 'count' as a successful translation of Dolphin into English, just as we can explore, in a partly rule bounded way, what would count as a reasonable explanation for the Aurora Borealis, or for the dishes remaining unwashed.
(We might, after all, learn some things from our attempts translate Dolphin that taught us new ways to speak in English that had a bearing on what we were prepared to count as a successful translation of Dolphin.)
What we cannot do, though, in any language, is say 'Dolphin is a language, but one that we will not ever be able to translate' - we can attach no meaning to 'language' in this statement that would allow us to distinguish language from anything else. We might as well say that stones can speak. (See Ursula le Guin's short story 'The Author of the Acacia Seeds').
So, the first problem with a private language is that either (a) there is a translation schema for it, and it is therefore not, after all, private or (b) it is not a language.
A general problem with an argument of this kind might be that we do not need to explicitly judge that something is a language before we speak it. This is addressed by a similar argument to the one I suggested in Truth Predicates and related posts.
In summary, we have a problem with identifying a candidate L0 as a specific language, since we only have behaviour (or symbol lists or whatever) to go on. No finite set of these can be used to unambiguously attribute an intentional state (such as meaning something) (Kripke).
This doesn't render the idea of a language generally ambiguous, however, unless we are committed to some reductive account of what a language must comprise. Since we know we are speaking to one another now, and since we know (roughly) what we are saying to one another, this doesn't matter. We can construct a recursive account instead.
But we can only explicitly judge that we are speaking to one another (i.e. we can only say so) in a language which contains the equivalent of its own truth predicate. This is because to say 'we speak the same language' is as much as to say 'we speak the same language, and we speak it properly'. Since L0 has no truth predicate (by definition), users of L0 cannot say this.
This means that any identification of L0 as a language will always be provisional and corrigible. There will be no guarantee that if we learn to 'play the L0 game' that we will be speaking a language.
Another way of putting this is that although we might suspend judgment on whether having a language is essentially to do with sharing it (which would beg the question under consideration), it is clear that judging that we have a language requires shared agreement if it is to be intelligible. A truth predicate in a private language would be redundant in exactly the way predicted by Ramsey. A truth predicate in a shared language allows us to explicitly agree, in a restricted sense, what it is that we are sharing. It allows us to ask and answer questions like 'what do you mean by ...?' and 'do you think it is true that ... ?'. Neither of these arise in a private language.
It seems likely, in fact, that all rules about how to speak a private language would strictly be redundant, since they would only report what the speaker already knows in order to speak the language.
Which brings us to what, I think, was Wittgenstein's objection. Even if the rules were stated, the user of a private language could have no way of knowing whether they did apply to the language, since any method of checking this would be no more secure than his confidence that he was using the language correctly in the first place. He would need to be able to judge that 'I am following the rules' didn't break any rules, which he could not securely do.
He could not intelligibly form the judgment 'I am speaking my private language properly'.
We can compare this with the equivalent judgement expressed in a shared language, where either (a) the judgement can reliably attribute an intentional state (of knowing that we are speaking the same language) or (b) there is not, after all, a shared language - we have misunderstood what is being said.
Going back to the translation issue raised at the beginning, however, it seems possible that Wittgenstein took for granted that we would not have difficulty recognising a language. This is implicit in his discussion of the 'slab/block' game near the beginning of PI. As I indicated previously, if any L0 can only be corrigibly identified as a language (unlike a language which contains its own truth predicate), then Wittgenstein cannot establish that the 'slab/block' team are speaking to one another.
As Kripke points out in 'Rules and Private Language', his paradox not only renders the idea of a private language unintelligible, it has catastrophic consequences for identifying anything as a language given the traditional (broadly Tarskian) account of what a language can be. His mistake here is not to recognise that the context of such a judgement will always be from within a working language - one which contains the equivalent of a truth predicate which does not require a reductive account, since the same context provides the root for a satisfactory recursive account.
Friday, June 28, 2013
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.
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.
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.
Thursday, June 27, 2013
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).
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).
Wednesday, June 26, 2013
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.
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.
Monday, June 24, 2013
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').
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.
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:
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)
Sunday, June 16, 2013
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.
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.
Sunday, May 05, 2013
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.
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.
Monday, April 22, 2013
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.)
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.)
Friday, April 19, 2013
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.
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.
Monday, March 18, 2013
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.
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.
Monday, February 11, 2013
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.
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.
Subscribe to:
Comments (Atom)