I think a puzzle for Davidson's approach is that we couldn't work out how to speak a language from a truth theory for the language on its own. Since a truth theory for a language only allows us to distinguish true from false sentences of the language, it can only teach us what to assert and what to deny. It is hard to see how context can get in here.
I don't mean just the kind of context that disambiguates indexicals, or gives sense to 'occasion sentences', but also the conversational context, the context that makes a certain utterance 'appropriate'.
Is there an important difference, here, between having a theory of truth for L and having a list of all the true sentences of L? Isn't a theory of truth (as envisioned by Tarski and Davidson) just a way of generating such a list, or determining whether an arbitrary sentence is a member of it?
How would we make a transition from having such a list, or such a test, to being able to speak L? We may not be able to give a full account of meaning in terms of use, but we can't give an account that denies its relevance. If we don't know how to use an expression, we don't know what it means.
We can be confused by the fact that we might learn to speak French from a theory of truth for French written down in English, but we would oly be able to do this if we can, as well, transfer certain principles of appropriate use from the English context onto the French expressions that we have learned.
Even if these principles were, themselves, articulated in both English and in French, they would not be part of the hypothesised theory of truth for French.
Friday, December 30, 2011
Friday, December 23, 2011
A priori tautologies
On second thoughts, logically a priori statements are slightly interesting, because the rules that they ultimately depend on are only intelligible within practices which, themselves, are at least partly 'hinged' upon non-tautological a priori statements.
It is not possible to articulate a logic without a language to articulate the logic in, and the possibility of this language, if it is considered by its speakers, must be the subject of an a priori judgment.
The necessity of logical laws follows from the a priori possibility of the language in which they are entertained.
It is not possible to articulate a logic without a language to articulate the logic in, and the possibility of this language, if it is considered by its speakers, must be the subject of an a priori judgment.
The necessity of logical laws follows from the a priori possibility of the language in which they are entertained.
Distinctive definition of 'A Priori' ... tidying up
An 'a priori' statement is one which, though not a logical theorem, cannot be false in any playable language game. Whether we call logical theora a priori is a matter of taste, but they are certainly not interestingly a priori.
Among necessary falsehoods, we can recognise hypotheses about the impossibility of language in general, claims which are Moorean 'paradoxical' etc.
There is room for us to argue about whether some particular statement is a priori or not - for "Neurath's Boat" type reasons, and because there is an open question bar to a general theory here. Whether some statements are a priori may be a matter of linguistic experiment - of 'doing philosophy', perhaps.
Among necessary falsehoods, we can recognise hypotheses about the impossibility of language in general, claims which are Moorean 'paradoxical' etc.
There is room for us to argue about whether some particular statement is a priori or not - for "Neurath's Boat" type reasons, and because there is an open question bar to a general theory here. Whether some statements are a priori may be a matter of linguistic experiment - of 'doing philosophy', perhaps.
Thursday, December 01, 2011
Composition
Clearly, some 'concepts' are, at least partly, compositional.
We can't conclude from this that:
(a) we can recognise compositionality from particular structural features, or
(b) that the meaning of a composed 'concept' is exhausted by an account of its composition
This is partly because we can't sideline idiomatic uses. 'Brown suit' has a content which cannot be discovered from 'brown' and 'suit', because to wear a brown suit means something different than to wear a grey suit. Or a pink suit.
It is possible that compositionality (ugh) is not even that important - that it sort of helps us along, but more as a kind of mnemonic than because we need it.
'But' the grammarians say 'how do you account for our indefinite capacity to construe meaning from a finite set of components?'.
The answer is in two parts: what is the evidence that we have this indefinite capacity? It doesn't exist, because an indefinite capacity can't be demonstrated. It can only be a potential account - and an unlikely one, given our finite condition.
The second part is that even if we settle on requiring a rule-based account of human 'language' behaviour, this need not be a grammatical account. A finite computational engine can produce speech-like behaviour from non-grammatical components - e.g. a list of sentences linked to a list of appropriate reponses. Even were such an engine to do a little humanish parsing, this need not be its only method.
Dyslexic people sometimes have difficulty discriminating individual words - since they don't have the resource of a reliable capacity to decode or concoct written sentences, they are more dependent on phonetic elements. For instance, they are more likely to think that common complex expressions - 'Just now', 'Good day', 'How are you' - are single words.
Most of us, even if not dyslexic, can remember similar errors from childhood. I remember hearing 'Here we go round the' (... Mulberry bush) as 'Helligo rounda'. The fact that it didn't have any clear meaning didn't especially distinguish it within my limited experience, and even adult literate reflection can't make a lot of relevant sense out of the first line of this nursery rhyme.
(Mulberries don't grow on bushes, for one thing.)
The compositionality argument has two parts:
(1) There are cases where we can deduce the meaning of an expression from grammatical rules and the 'meanings' of its parts (word meanings, in particular).
(2) We need some story about how we can decode expressions we haven't heard before.
But this is pretty ramshackle. As above, (1) is rarely possible in a completely satisfactory way. And (2) ignores lots of other resources we might draw on - particularly context, including any preceding linguistic exchange.
After all, that's how we start 'decoding' in the first place ...
We can't conclude from this that:
(a) we can recognise compositionality from particular structural features, or
(b) that the meaning of a composed 'concept' is exhausted by an account of its composition
This is partly because we can't sideline idiomatic uses. 'Brown suit' has a content which cannot be discovered from 'brown' and 'suit', because to wear a brown suit means something different than to wear a grey suit. Or a pink suit.
It is possible that compositionality (ugh) is not even that important - that it sort of helps us along, but more as a kind of mnemonic than because we need it.
'But' the grammarians say 'how do you account for our indefinite capacity to construe meaning from a finite set of components?'.
The answer is in two parts: what is the evidence that we have this indefinite capacity? It doesn't exist, because an indefinite capacity can't be demonstrated. It can only be a potential account - and an unlikely one, given our finite condition.
The second part is that even if we settle on requiring a rule-based account of human 'language' behaviour, this need not be a grammatical account. A finite computational engine can produce speech-like behaviour from non-grammatical components - e.g. a list of sentences linked to a list of appropriate reponses. Even were such an engine to do a little humanish parsing, this need not be its only method.
Dyslexic people sometimes have difficulty discriminating individual words - since they don't have the resource of a reliable capacity to decode or concoct written sentences, they are more dependent on phonetic elements. For instance, they are more likely to think that common complex expressions - 'Just now', 'Good day', 'How are you' - are single words.
Most of us, even if not dyslexic, can remember similar errors from childhood. I remember hearing 'Here we go round the' (... Mulberry bush) as 'Helligo rounda'. The fact that it didn't have any clear meaning didn't especially distinguish it within my limited experience, and even adult literate reflection can't make a lot of relevant sense out of the first line of this nursery rhyme.
(Mulberries don't grow on bushes, for one thing.)
The compositionality argument has two parts:
(1) There are cases where we can deduce the meaning of an expression from grammatical rules and the 'meanings' of its parts (word meanings, in particular).
(2) We need some story about how we can decode expressions we haven't heard before.
But this is pretty ramshackle. As above, (1) is rarely possible in a completely satisfactory way. And (2) ignores lots of other resources we might draw on - particularly context, including any preceding linguistic exchange.
After all, that's how we start 'decoding' in the first place ...
Friday, November 25, 2011
Turing cognitivism
The halting problem has a structural similarity to the Goodman/Kripke paradox insofar as the fact that the machine has not yet halted cannot count as evidence that it will not halt.
Also, the demonstration that a human mind is like a general cognitive engine - a Turing machine - would have to include a demonstration that it was following the rules of such a machine, and Kripke has shown that this demonstration cannot be conclusively constructed.
So, curiously, it seems that if my mind is like a Turing machine, there is no finite way in which I could demonstrate this. It would not be a computable issue.
The proposal that the mind is a kind of Turing machine can only ever be a kind of assumption of cognitive science - a 'false heuristic'? - and not part of a deductive cognitive theory.
Also, the demonstration that a human mind is like a general cognitive engine - a Turing machine - would have to include a demonstration that it was following the rules of such a machine, and Kripke has shown that this demonstration cannot be conclusively constructed.
So, curiously, it seems that if my mind is like a Turing machine, there is no finite way in which I could demonstrate this. It would not be a computable issue.
The proposal that the mind is a kind of Turing machine can only ever be a kind of assumption of cognitive science - a 'false heuristic'? - and not part of a deductive cognitive theory.
Wednesday, November 23, 2011
'Meaning is Use'
We could confuse two views:
(1) If we know how to use a word, then we know it's meaning.
(2) We give the meaning of a word by giving an account of its use.
The first seems unexceptionable.
The second is much more problematic. To give an account, we are already depending upon some un-articulated meaning/uses. Why should some of these be more 'obvious' than others? Why, apart from a specific context of enquiry (a specific question, or specific ignorance) should some be based on others?
Also, we do not learn use meanings from such definitions - although these may aid us in some specific circumstances. We learn them through practice, through experiments with use.
Also, approach (2) is confusing with respect to meaningfulness in general - knowing how to talk preceeds knowing that a certain articulated use of a word is correct. It's perfectly easy to imagine a restricted language game in which the meaning relation didn't exist - in which no accounts of meanings were ever given. As with the 'slab, brick' game, we might construct a theory of the meanings of the words in such a language. But giving a type (2) theory in terms of uses rather than representations does not avoid the difficulty that Wittgenstein used this game to illustrate: we cannot say that the users of the game share our theory of their meanings.
If we play chess with someone who cannot speak, can we say that they are following the rules of chess? Kripke would say: only provisionally, and they might be following any number of other sets of rules which produced congruent behaviour in the games we had actually played with them. Wittgenstein might say that they were not following rules, but just playing chess. And that we might be wrong about that.
When we make a (1) type judgement - that we know how to use a certain word - we are exposed to Kripke's scepticism about what we might mean by it unless we make it in a shared conversation which 'works'. To ask whether this shared conversation might rest upon unrecognised Kripkean ambiguities is to ask whether it is, in fact, a shared conversation - a question which cannot arise within it. When I say 'I know how to talk to you - I know what we mean by what we say', I am not saying something than can be refuted (shown to be false) by some behavioural evidence because a consequence of my being wrong would not be that I had said something false, but that I had not said anything meaningful - and so not anything at all.
So 'meaning is use' turns out to be a warning, not a theory - and, in particular, a warning against the semantic role of type (2) articulations.
(1) If we know how to use a word, then we know it's meaning.
(2) We give the meaning of a word by giving an account of its use.
The first seems unexceptionable.
The second is much more problematic. To give an account, we are already depending upon some un-articulated meaning/uses. Why should some of these be more 'obvious' than others? Why, apart from a specific context of enquiry (a specific question, or specific ignorance) should some be based on others?
Also, we do not learn use meanings from such definitions - although these may aid us in some specific circumstances. We learn them through practice, through experiments with use.
Also, approach (2) is confusing with respect to meaningfulness in general - knowing how to talk preceeds knowing that a certain articulated use of a word is correct. It's perfectly easy to imagine a restricted language game in which the meaning relation didn't exist - in which no accounts of meanings were ever given. As with the 'slab, brick' game, we might construct a theory of the meanings of the words in such a language. But giving a type (2) theory in terms of uses rather than representations does not avoid the difficulty that Wittgenstein used this game to illustrate: we cannot say that the users of the game share our theory of their meanings.
If we play chess with someone who cannot speak, can we say that they are following the rules of chess? Kripke would say: only provisionally, and they might be following any number of other sets of rules which produced congruent behaviour in the games we had actually played with them. Wittgenstein might say that they were not following rules, but just playing chess. And that we might be wrong about that.
When we make a (1) type judgement - that we know how to use a certain word - we are exposed to Kripke's scepticism about what we might mean by it unless we make it in a shared conversation which 'works'. To ask whether this shared conversation might rest upon unrecognised Kripkean ambiguities is to ask whether it is, in fact, a shared conversation - a question which cannot arise within it. When I say 'I know how to talk to you - I know what we mean by what we say', I am not saying something than can be refuted (shown to be false) by some behavioural evidence because a consequence of my being wrong would not be that I had said something false, but that I had not said anything meaningful - and so not anything at all.
So 'meaning is use' turns out to be a warning, not a theory - and, in particular, a warning against the semantic role of type (2) articulations.
Monday, November 14, 2011
Why should we expect unexamined heuristics to be false?
Here are some reasons why they might be:
(1)
Given Nature's indifference between functioning heuristics, and the likelihood that the ratio of successful false heuristics to successful true ones is likely ot be high, the probability that an unexamined heuristic is false must be high.
(2)
There is a sense in which all all language users share a specific false heuristic: that they somehow live in the same world, and that this is why their shared language makes sense. In fact, they only think they live in the same world because their shared language makes sense. It is only in a shared language game that this question can arise, and it is only because the shared language game works that we can sustain the illusion of some pre-linguistic shared world.
(3)
Why would we articulate a tacit heuristic? In normal conversation, this would only happen if a difficulty had arisen: if interlocutors discovered that just pointing to a practice did not resolve a dissonance. In this case, the interlocutors have discovered that they are unintelligible to one another, and need to modify the game to recover.
Except in the case of a simple grammatical or computational error, this process would have to result in at least some interlocutors abandoning heuristics as they articulated them.
(4)
The work of interrogating a heuristic falls outside the discipline the heuristic underpins - settling issues of its truth or falsehood is unlikly to be relevant to the discipline. It might shed light on whether the discipline as a whole made sense, but this is not an issue routinely raised by practitioners, who can point to their own successful (?) practices in support of their intelligibility and who can therefore relegate heuristic 'housekeeping' to philosophers. Their (reasonable) presumption might be that practically inconsequential inconsistencies in the underlying heuristics must be addressable.
An efficient intellectual division of labour would lead to disciplinary heuristics being simplified, since more generally defensible underpinnings would incorporate complexities which were practically irrelevant.
(1)
Given Nature's indifference between functioning heuristics, and the likelihood that the ratio of successful false heuristics to successful true ones is likely ot be high, the probability that an unexamined heuristic is false must be high.
(2)
There is a sense in which all all language users share a specific false heuristic: that they somehow live in the same world, and that this is why their shared language makes sense. In fact, they only think they live in the same world because their shared language makes sense. It is only in a shared language game that this question can arise, and it is only because the shared language game works that we can sustain the illusion of some pre-linguistic shared world.
(3)
Why would we articulate a tacit heuristic? In normal conversation, this would only happen if a difficulty had arisen: if interlocutors discovered that just pointing to a practice did not resolve a dissonance. In this case, the interlocutors have discovered that they are unintelligible to one another, and need to modify the game to recover.
Except in the case of a simple grammatical or computational error, this process would have to result in at least some interlocutors abandoning heuristics as they articulated them.
(4)
The work of interrogating a heuristic falls outside the discipline the heuristic underpins - settling issues of its truth or falsehood is unlikly to be relevant to the discipline. It might shed light on whether the discipline as a whole made sense, but this is not an issue routinely raised by practitioners, who can point to their own successful (?) practices in support of their intelligibility and who can therefore relegate heuristic 'housekeeping' to philosophers. Their (reasonable) presumption might be that practically inconsequential inconsistencies in the underlying heuristics must be addressable.
An efficient intellectual division of labour would lead to disciplinary heuristics being simplified, since more generally defensible underpinnings would incorporate complexities which were practically irrelevant.
Wednesday, November 09, 2011
Pointing to Practices
While we can 'point' to practices which underpin our thought and talk, we should be careful about how we use this in our explanations. In empirical or anthropological explanations, this pointing is possibly helpful and probably harmless.
If we are looking for a justification for the kind of thinking and talking we are doing, then this pointing may not be helpful.
We can be deceived by something here: often we do point to an unquestioned practice in order to 'justify' something, in ordinary talk. I think this is often just to remind an interlocutor of a shared committment, however, so it really only counts as a hypothetical justification: "Remember that X implies Y" is OK if someone has temporarily forgotten the relevance of X and its status as a fundamental. So the form of the argument is: if we are having the conversation I think we are then you must see that Y is unavoidable.
But, of course, it may exactly be X or its relevance that are in play; and there may exactly be confusion over the nature of the conversation. Regress beckons ...
Some might argue, from here, that we should review what we mean by 'justify', to bring it more into line with pointing at shared committments. This move is exposed to an open question objection unless the shared commitments are unavoidable - if they must be shared by anyone having what could count as 'a conversation' at all. In this case, confusion stops the conversation; we have no tools for exploring or explaining it.
If we are looking for a justification for the kind of thinking and talking we are doing, then this pointing may not be helpful.
We can be deceived by something here: often we do point to an unquestioned practice in order to 'justify' something, in ordinary talk. I think this is often just to remind an interlocutor of a shared committment, however, so it really only counts as a hypothetical justification: "Remember that X implies Y" is OK if someone has temporarily forgotten the relevance of X and its status as a fundamental. So the form of the argument is: if we are having the conversation I think we are then you must see that Y is unavoidable.
But, of course, it may exactly be X or its relevance that are in play; and there may exactly be confusion over the nature of the conversation. Regress beckons ...
Some might argue, from here, that we should review what we mean by 'justify', to bring it more into line with pointing at shared committments. This move is exposed to an open question objection unless the shared commitments are unavoidable - if they must be shared by anyone having what could count as 'a conversation' at all. In this case, confusion stops the conversation; we have no tools for exploring or explaining it.
Tuesday, October 04, 2011
Moral certainty
If I was subjectively certain about something, and was unable to see how I might be wrong, would I have a proof? We would suppose not, although this is the context of Cartesian anxiety.
What if no-one else could see how I might be wrong either? Even after considerable discussion and investigation?
At some point, out investigations would convince us that we could only be wrong if we had made some general mistake about the possibility of demonstration - about how to talk intelligibly about the object of my certainty. Might this also be a mistaken conclusion?
This kind of structure of doubt applies to groups as well as to individuals, but it has a limit. If we can pose the question, and make no more assumptions in our proof than those that are required to make the posing of the question possible, then we have a different kind of demonstration - it's structure is 'we know the answer if we can ask the question'. (Some obvious questions - 'can we ask questions?' - can be answered very directly this way.)
Can we have a hypothetical attitude to our participation in a conversation? We obviously can't express this within the conversation ("I'm not sure whether we are actually able to talk to each other") because we would be saying that we didn't know what the meaning of this sentence token was. If we were, we could not seriously express the doubt (or we'd by lying if we pretended to - another way to end the conversation ...)
We obviously can't 'privately' ask a question that we can't ask publicly. This would require a private language. We can be 'mad' - we can fail to engage in conversations in a humanly recognisable way. Or we can appear to talk nonsense to any potential interlocutor.
No one could say of our madness: 'they suffer from Cartesian anxiety', except provisionally, and perhaps poetically. The only positive demonstration of such a thing would be our articulation of it, which would prove it false.
What if no-one else could see how I might be wrong either? Even after considerable discussion and investigation?
At some point, out investigations would convince us that we could only be wrong if we had made some general mistake about the possibility of demonstration - about how to talk intelligibly about the object of my certainty. Might this also be a mistaken conclusion?
This kind of structure of doubt applies to groups as well as to individuals, but it has a limit. If we can pose the question, and make no more assumptions in our proof than those that are required to make the posing of the question possible, then we have a different kind of demonstration - it's structure is 'we know the answer if we can ask the question'. (Some obvious questions - 'can we ask questions?' - can be answered very directly this way.)
Can we have a hypothetical attitude to our participation in a conversation? We obviously can't express this within the conversation ("I'm not sure whether we are actually able to talk to each other") because we would be saying that we didn't know what the meaning of this sentence token was. If we were, we could not seriously express the doubt (or we'd by lying if we pretended to - another way to end the conversation ...)
We obviously can't 'privately' ask a question that we can't ask publicly. This would require a private language. We can be 'mad' - we can fail to engage in conversations in a humanly recognisable way. Or we can appear to talk nonsense to any potential interlocutor.
No one could say of our madness: 'they suffer from Cartesian anxiety', except provisionally, and perhaps poetically. The only positive demonstration of such a thing would be our articulation of it, which would prove it false.
Wednesday, August 24, 2011
Signal Content
If we ask what a signal (or the state of a machine) 'means', we are attributing an intentional state to the machine, to the originator of the signal.
If we examine how an actual example of a homeostatic mechanism behaves, we do not find intentional states - just physical circumstances. We cannot (Kripke) 'decode' a thermostat (i.e. an actual physical device) unequivocally in terms of temperature maintenance.
We might talk about 'correct' and 'incorrect' signals, without attributing intentionality to the machine or the signal, but we would still have to make this judgement in terms of the overall function of the machine - and therefore in terms of the intentions of its creator or designer.
We can say 'at this point, line 4 should go high'. If it does not, then this is a malfunction - either a mechanical failure, a design failure, or a poor mechanical implementation of a design. (Are these all different?).
If we say 'line 4 high indicates that the lift door is open', and we find line 4 high when the door is shut, can we say that line 4 gave an 'untrue' signal? We can say the signal was incorrect. If we say that the machine says the lift door is open when it is shut, then we can say the machine lied, or was mistaken, but this goes along with attributing intention - we make a normative choice here about the status of the machine; we treat it as an interlocutor.
If we examine how an actual example of a homeostatic mechanism behaves, we do not find intentional states - just physical circumstances. We cannot (Kripke) 'decode' a thermostat (i.e. an actual physical device) unequivocally in terms of temperature maintenance.
We might talk about 'correct' and 'incorrect' signals, without attributing intentionality to the machine or the signal, but we would still have to make this judgement in terms of the overall function of the machine - and therefore in terms of the intentions of its creator or designer.
We can say 'at this point, line 4 should go high'. If it does not, then this is a malfunction - either a mechanical failure, a design failure, or a poor mechanical implementation of a design. (Are these all different?).
If we say 'line 4 high indicates that the lift door is open', and we find line 4 high when the door is shut, can we say that line 4 gave an 'untrue' signal? We can say the signal was incorrect. If we say that the machine says the lift door is open when it is shut, then we can say the machine lied, or was mistaken, but this goes along with attributing intention - we make a normative choice here about the status of the machine; we treat it as an interlocutor.
Friday, June 24, 2011
Articulating tacit rules
Attributing conformity with a tacit rule to a non-interlocutor is always corrigible (Kripke). Articulating a tacit rule we 'discover' we have been following changes if from being tacit - and also changes the way we talk.
Imagining that before we articulated the rule we must, indeed, have been following it is to make exactly the corrigible attribution we might make to a non-interlocutor. When we move from tacit to articulated, we also move from corrigible to incorrigible.
Can we say that we moved from less clear to more clear meanings?
Imagining that before we articulated the rule we must, indeed, have been following it is to make exactly the corrigible attribution we might make to a non-interlocutor. When we move from tacit to articulated, we also move from corrigible to incorrigible.
Can we say that we moved from less clear to more clear meanings?
Monday, June 13, 2011
Evolution
Nature is indifferent between a successful heuristic and a true theory; but we cannot be, or our justification for saying so could be that this comprised part of a successful heuristic.
It is incoherent - for instance - to try to support our belief that the future will, in some way, be like the past by saying that it is a component of a successful heuristic. "It's been OK so far" isn't a ground for complacency just because we've got away with it up until now ...
It is incoherent - for instance - to try to support our belief that the future will, in some way, be like the past by saying that it is a component of a successful heuristic. "It's been OK so far" isn't a ground for complacency just because we've got away with it up until now ...
Saturday, April 23, 2011
Truth telling and its effects ...
Telling the truth is not free. Some can afford it better than others.
Our reflections on the price we are prepared to pay cannot be articulated in the language game in which the moves under consideration are to be made.
They might be articulated in another context - perhaps a privileged context, such as an academic discussion. Such a discussion will have a different price list.
It is only when there is no context in which we can render ourselves intelligible that we are finally damned; that we become completely incoherent, and unable even to say so.
Our reflections on the price we are prepared to pay cannot be articulated in the language game in which the moves under consideration are to be made.
They might be articulated in another context - perhaps a privileged context, such as an academic discussion. Such a discussion will have a different price list.
It is only when there is no context in which we can render ourselves intelligible that we are finally damned; that we become completely incoherent, and unable even to say so.
Wednesday, April 20, 2011
Patterns
Children are often given mathematical puzzles that involve working out how to continue a sequence of numbers. Wittgenstein focuses on this kind of situation when discussing rules and mathematics.
There can, of course, be no 'right' answer to how to continue any finite sequence, since there will be an infinte number of potential rules that its generation might instantiate. Given this, it is odd that children are - generally explicitly, and always implicitly - told that there is a 'right' answer. Valid, but peculiar, rules will be rejected (e.g. suggesting that the sequence '2, 4, 6 ...' instantiates listing even numbers in the odd hundreds and odd ones in the even hundreds).
This is an essential part of teaching mathematics - this weeding of peculiar rules. In fact, a sound intuition about which rules would be peculiar is a component of 'mathemtical ability'.
A child that is being given this mathematical training is getting two signals from the teacher with each exercise: one is the list of numbers, and the other is a reassurance that there isn't something 'tricky' going on - that this list really is a sort of message, a hint that some simple and obvious solution is the 'correct' one.
We handle numbers using manageable rules - which comprise a subset of the formally possible rules. All the mathematical 'observations' made by humanity so far comprise a finite set, and so could instantiate an infinitely large number of mutually incoherent sets of rules. We have selected from these the humanly manageable ones which appear to be coherent.
We have no way - we could have no way - of demonstrating that the set we have selected is the only possible one. Such a demonstration would depend upon a set of rules which would have to have mathematical meanings.
If we had two sets of rules which were internally consistent (and so were consistent with all our 'observations') but inconsistent with each other, we could only choose between them on the basis of an observation we had not previously made - but the generation of mathematical 'observations' is a rule-driven business ...
Maybe we cannot state a complete set of rules, because we modify their meanings as we do mathematics - because doing mathematics is partly a matter of resolving rule ambiguities.
And that's apart from any open question issues which would arise.
There can, of course, be no 'right' answer to how to continue any finite sequence, since there will be an infinte number of potential rules that its generation might instantiate. Given this, it is odd that children are - generally explicitly, and always implicitly - told that there is a 'right' answer. Valid, but peculiar, rules will be rejected (e.g. suggesting that the sequence '2, 4, 6 ...' instantiates listing even numbers in the odd hundreds and odd ones in the even hundreds).
This is an essential part of teaching mathematics - this weeding of peculiar rules. In fact, a sound intuition about which rules would be peculiar is a component of 'mathemtical ability'.
A child that is being given this mathematical training is getting two signals from the teacher with each exercise: one is the list of numbers, and the other is a reassurance that there isn't something 'tricky' going on - that this list really is a sort of message, a hint that some simple and obvious solution is the 'correct' one.
We handle numbers using manageable rules - which comprise a subset of the formally possible rules. All the mathematical 'observations' made by humanity so far comprise a finite set, and so could instantiate an infinitely large number of mutually incoherent sets of rules. We have selected from these the humanly manageable ones which appear to be coherent.
We have no way - we could have no way - of demonstrating that the set we have selected is the only possible one. Such a demonstration would depend upon a set of rules which would have to have mathematical meanings.
If we had two sets of rules which were internally consistent (and so were consistent with all our 'observations') but inconsistent with each other, we could only choose between them on the basis of an observation we had not previously made - but the generation of mathematical 'observations' is a rule-driven business ...
Maybe we cannot state a complete set of rules, because we modify their meanings as we do mathematics - because doing mathematics is partly a matter of resolving rule ambiguities.
And that's apart from any open question issues which would arise.
Monday, April 18, 2011
Private Languages
Maybe this is the Private Language Argument:
Suppose I told you 'I have a private language, which I can use when I am thinking things to myself'. You might ask 'What do you say to yourself, in your private language?'
I could answer in two ways:
(1) I could give you a translation, in our shared public language, of what I say to myself.
(2) I could say that my private language was not translatable into a public language.
I could not, of course, simply give you a 'raw' private utterance, with or without a translation. This would be to render the private language public.
(1) Is what we presently have. If I tell you what I am thinking, I am doing as much as this - but this does not demonstrate that I have a private language: It only demonstrates that I can use our public one.
(If we could conclude from our use of a public language that we 'must' have some private 'language of thought', then what would we have to conclude from our use of this private language? That we must have an even more private language of proto-thought? What kind of explanation could this possibly provide?)
If I want to demonstrate the possibility of a private language by an argument produced in our public language, I would need to have a way of pointing at the private language in a way which showed (a) that it was a language and (b) that it was not a public language. But I can't point to it if it's private, and I can only show that it's a language if it can be spoken.
With respect to (2), the idea of a language which is in principle untranslatable is (obviously) incoherent for Davidsonian reasons. How could we know it was a language?
Suppose I told you 'I have a private language, which I can use when I am thinking things to myself'. You might ask 'What do you say to yourself, in your private language?'
I could answer in two ways:
(1) I could give you a translation, in our shared public language, of what I say to myself.
(2) I could say that my private language was not translatable into a public language.
I could not, of course, simply give you a 'raw' private utterance, with or without a translation. This would be to render the private language public.
(1) Is what we presently have. If I tell you what I am thinking, I am doing as much as this - but this does not demonstrate that I have a private language: It only demonstrates that I can use our public one.
(If we could conclude from our use of a public language that we 'must' have some private 'language of thought', then what would we have to conclude from our use of this private language? That we must have an even more private language of proto-thought? What kind of explanation could this possibly provide?)
If I want to demonstrate the possibility of a private language by an argument produced in our public language, I would need to have a way of pointing at the private language in a way which showed (a) that it was a language and (b) that it was not a public language. But I can't point to it if it's private, and I can only show that it's a language if it can be spoken.
With respect to (2), the idea of a language which is in principle untranslatable is (obviously) incoherent for Davidsonian reasons. How could we know it was a language?
Monday, March 21, 2011
Evolved Function
There are two ways of describing an evolutionary process, just as there are two ways of describing a computational proces: (a) from an intentional perspective and (b) from a mechanical perpsective. It is mistake to think that when we understand one we understand the other; and it is a bad mistake to think we can reduce the intentional to the mechanical.
It is possible that we may be able to 'reduce' the mechnical to the intentional, in the sense that we cannot understand rule following (and so mechanism) except in terms of a system falling under the scope of some intentional concept.
We can only render the evolution of function (an intentional category) intelligible by referring to higher functions. If longer legs aid survival by allowing higher escape speeds, we 'explain' longer legs in terms of the function of speed ,whose relevance is the function of escape, whose relevance is the function of survival. If we didn't understand what survival was, or why it was 'desirable', this explanation would have no force.
We could tell a different - much more complex - story about about the macrobiology of evolution, involving reproductive chemistry, the coding options available within DNA sequencing, genotype/phenotype relationships, protein folding and structure, environmental factors etc. We can't, at present, tell enough of this story to be able to completely describe many large scale functional behaviours in terms of detailed mechanisms. Even when we can do this, however, we will not be able to 'render' function as mechanism except by stipulation. And this would expose our accounts of function to mechanical failure - just as if we tried to define a logical operator in terms of what a particular electronic digital component did.
In my last post I said we should think of machines as elements in a conversation between their designers and users. When we discover a 'natural machine' we don't recognise the normative aspects of attributing function, and so we arrive at the argument from design.
And maybe this is lucky - especially if it is our visceral normative attributions which prevent us, on the whole, from seeing each other as machines. Excessive intentional attribution is probably less dangerous to us than deficient intentional attribution. From a functional point of view.
It is possible that we may be able to 'reduce' the mechnical to the intentional, in the sense that we cannot understand rule following (and so mechanism) except in terms of a system falling under the scope of some intentional concept.
We can only render the evolution of function (an intentional category) intelligible by referring to higher functions. If longer legs aid survival by allowing higher escape speeds, we 'explain' longer legs in terms of the function of speed ,whose relevance is the function of escape, whose relevance is the function of survival. If we didn't understand what survival was, or why it was 'desirable', this explanation would have no force.
We could tell a different - much more complex - story about about the macrobiology of evolution, involving reproductive chemistry, the coding options available within DNA sequencing, genotype/phenotype relationships, protein folding and structure, environmental factors etc. We can't, at present, tell enough of this story to be able to completely describe many large scale functional behaviours in terms of detailed mechanisms. Even when we can do this, however, we will not be able to 'render' function as mechanism except by stipulation. And this would expose our accounts of function to mechanical failure - just as if we tried to define a logical operator in terms of what a particular electronic digital component did.
In my last post I said we should think of machines as elements in a conversation between their designers and users. When we discover a 'natural machine' we don't recognise the normative aspects of attributing function, and so we arrive at the argument from design.
And maybe this is lucky - especially if it is our visceral normative attributions which prevent us, on the whole, from seeing each other as machines. Excessive intentional attribution is probably less dangerous to us than deficient intentional attribution. From a functional point of view.
Saturday, March 19, 2011
Talking Machines
We should think of a machine as part of a conversation between its creators and its users. It's like the mechanial parts of our talking activity - the noises, the physiology, the writing technology. They might break down, they might take different forms, but their character is given by their intentional content.
A machine's character is also given by the intentions of its creators, and the 'sharing' or 'communicating' these with its users. It is not given my any physical description.
This applies most clearly to 'ideal' machines, such as Turing machines.
A real computer is part of a complex conversation between 'programmers' and 'users' - or, more correctly, between different classes of users.
The 'limitations' of these machines can only be given, in any intelligible way, in terms of the 'limitations' of intentional ascriptions - of 'rule following'. If we say that there must be some rule which underpins the possibility of intentionality, we are making a mistake.
A machine's character is also given by the intentions of its creators, and the 'sharing' or 'communicating' these with its users. It is not given my any physical description.
This applies most clearly to 'ideal' machines, such as Turing machines.
A real computer is part of a complex conversation between 'programmers' and 'users' - or, more correctly, between different classes of users.
The 'limitations' of these machines can only be given, in any intelligible way, in terms of the 'limitations' of intentional ascriptions - of 'rule following'. If we say that there must be some rule which underpins the possibility of intentionality, we are making a mistake.
Friday, March 11, 2011
OQ Arguments, and Crispin Wright's 'dilemma'
For any potential source of knowledge (the reliability of our senses, religious inspiration, scientific method), we cannot both (a) have it as an empirical fundamental and (b) show it to be reliable. These two are mutually exclusive, because any demonstration that our knowledge of (b) is reliable has to be based on some other fundamental.
We also cannot say 'this must be accepted without demonstration' because we have to explain the 'must'.
We also cannot say 'this must be accepted without demonstration' because we have to explain the 'must'.
Thursday, February 24, 2011
The Scope of a Rule
To speak, we must (a) attribute rule following and (b) attribute belief in natural laws (the 'rules' which the world follows).
Some of these rules have an indefinte scope. This can make it sound as though their scope precedes and exceeds the scope of language - of what we can talk about. We can only imagine such a thing by considering the possibility of a world that we cannot (in principle) talk about, but which, nevertheless, follows the rules. Whatever the value of this as a metaphysical speculation, we can't test it.
A specific case is the rules we presume to underpin the possibility of language itself. We imagine that logical and mathatical laws have a wider scope than simply guiding how we speak. This belief is associated with the kinds of things we say about them - among which are statements like 'these laws have indefinite scope'. Such a statement is true with respect to any testable case, since such a case must be articulable. Also, to qualify it would suggest that there was some articulable case in which they did not hold.
But its generality and lack of qualification do not need to extend to 'things we cannot talk about'. And there can be no rule that defines the boundary between what we can talk about and what we cannot.
When we explore this boundary, we generate paradoxes. This does not mean that the exploration is invalid or absurd. It means we must be careful about the conclusions we draw from these explorations - and about what we mean when we talk about them.
All the objects in the metaphysical world beyond the reach of speculation are paradoxical.
Conclusions drawn from the indefinite scope of our rules of intelligibility will also be paradoxical, since they depend upon speculations about these objects.
Meaning sneaks into the incompleteness and inconsistency proofs at the level of the rules themselves.
Some of these rules have an indefinte scope. This can make it sound as though their scope precedes and exceeds the scope of language - of what we can talk about. We can only imagine such a thing by considering the possibility of a world that we cannot (in principle) talk about, but which, nevertheless, follows the rules. Whatever the value of this as a metaphysical speculation, we can't test it.
A specific case is the rules we presume to underpin the possibility of language itself. We imagine that logical and mathatical laws have a wider scope than simply guiding how we speak. This belief is associated with the kinds of things we say about them - among which are statements like 'these laws have indefinite scope'. Such a statement is true with respect to any testable case, since such a case must be articulable. Also, to qualify it would suggest that there was some articulable case in which they did not hold.
But its generality and lack of qualification do not need to extend to 'things we cannot talk about'. And there can be no rule that defines the boundary between what we can talk about and what we cannot.
When we explore this boundary, we generate paradoxes. This does not mean that the exploration is invalid or absurd. It means we must be careful about the conclusions we draw from these explorations - and about what we mean when we talk about them.
All the objects in the metaphysical world beyond the reach of speculation are paradoxical.
Conclusions drawn from the indefinite scope of our rules of intelligibility will also be paradoxical, since they depend upon speculations about these objects.
Meaning sneaks into the incompleteness and inconsistency proofs at the level of the rules themselves.
Saturday, February 19, 2011
Worlds without people ...
Suppose we imagine a world - perhaps this world at a different time - without any people in it, so that 'there is no language in that world' is true. What are our grounds for saying that this, or that anything at all, is true in this 'non-linguistic' world? Only that you and I, now, can agree about it - and can agree about what any such world would be like.
We cannot say that there might be some other world, that we cannot imagine or agree about, and yet that there is some definite thing that must be true about it. What kind of thing could a truth that no-one could ever agree about be?
We cannot say that there might be some other world, that we cannot imagine or agree about, and yet that there is some definite thing that must be true about it. What kind of thing could a truth that no-one could ever agree about be?
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