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.

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.

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'.

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.

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?

Barry Stroud

It may be a contingent matter that there was no language at the time of the dinosaurs, but only we can say so. We cannot imagine the truth of some state of affairs separately from the possibility of expressing it except by imagining a conception of it that cannot be translated into our conception. If I think 'at the time of the dinosaurs, there was no language' I am imagining being transported to that time and having no-one to talk to. What else could I be imagining? That some invisible, even non-existent, person was similarly transported ...

The dinosaurs could not know that it was true that they had no language.

If I say to you 'There was no language at the time of the dinosaurs', what non-linguistic 'fact' about the time of the dinosaurs are we expressing that makes that time different from what we would say of it in any case? We say a lot of things about dinosaurs, but we don't say 'and there was no language then'. What would this add if we did? We don't wonder whether they could talk to one another, and so go to find an expert who can tell us.

And it is not whether there was language at the time of the dinosaurs that is important, it's that we can, now, talk about the dinosaurs. This is no different from talking about anything else - including things that happen now, contemporaries of our linguistic abilities.

If I say something about the time of the dinosaurs, I am not concerned about whether what I say was true then, but with whether it is true now: and the only conception I can give to whether it was true then is whether I would say now that it was true then ....

What is it, exactly, that was true then except what we agree about now? And If we don' t have that agreement, how do we identify the thing we might have agreed about?

Private Language Questions

This is the real power of the Private Language Argument:

The question 'Is it possible to ask questions?' can have only one answer if it is a question. We might imagine, however, that it is something we could wonder about, non-linguistically. It would be like wondering whether it was possible to talk.

What would this 'wondering' be like?

It could be like privately articulating the question 'Is it possible to ask questions?' We could wonder whether any previous public questioning and answering we had done had really 'worked' - whether it had comprised real questions and answers. It's hard to separate this question from the question whether we had really been speaking at all in the past - whether we had understood what anything we thought we were saying meant. This is incomprehensible, but it has a specific incomprehensibility here: we could not know what we were 'privately' doing by asking ourselves 'Is it possible to ask questions?' as this private act depends upon the validity of the public practice of speaking - which we wish to query, or about which we have become sceptical.

What the PL argument says is that there cannot be some private language in which we could comprehensibly articulate these queries - e.g. about the possibility of asking questions or about whether it was really possible to talk to people.

The PLA can be reformulated in Davidsonian terms:

If some private language were to count as a language, we would have to be able to interpret it, or translate it, into the public language in which we are conducting our enquiry. I think this is what Wittgenstein meant by saying that otherwise we would not know what rules we were following or whether we were following them correctly.

If we can only render the concept of a rule intelligible in terms of intentionality (which I've argued for earlier), and we can only reliably attribute intentional states to interlocutors (from Kripke's paradox), then this result is what we would expect.

Another perspective on this: how would my (or your) having a thought in our private language be represented, and how would our thought be attributed to us, in the public language of our enquiry? If I say of someone that they have articulated the possibility that it might rain in their private language, then I might as well be saying of them that they thought it would rain.

I could say of someone 'she thinks in Polish', and imagine her thinking the Polish sentence for 'I think it will rain'. I can imagine her inventing a language which can be translated into our language, and using that language to say something that would translate as 'I think it will rain'. I cannot imagine her thinking it will rain, but somehow representing this in a language I cannot translate. Such a language might as well be random - have no rules, but just mean whatever she took for the moment it to mean. She might think it would rain, attach this thought to a noise, a colour, an unpleasant memory, her confusion about linear programming algorithms, and any of these would do. Anything at all could 'stand for' her thought that it would rain, and so anything could be 'translated' into our language of enquiry as 'I think it will rain', and different things could be translated so at different times. There could be no rules in this translation schema, and so it could not even be reliably applied from one occasion to another.

If we translated:

'X, on occasion Y translates from our language of enquiry into "It will rain" in Sophie's private language'

into Sophie's private language, we could not know whether our translation was correct.

And if we could not know whether our translation into Sophie's language was correct, we could not know whether the translation of any such statement back into our language of enquiry was correct, and so we could not know what anything in Sophie's 'language' meant.

Linguistic Rules and Bush Tracks

It's a mistake to think that because we can discern linguistic rules a language user must, in some sense, know what these rules are. This is like saying a train knows where the track is.

A language user may have a quite restricted kind of linguistic competence, and still be able to function - and to appear to function well.

Imagine someone who knew, say three thousand sentences and was competent in selecting the occasions on which to produce them. It might take considerable study to be sure that this was a case of rote learned responses, rather than what we might think of as full linguistic competence.

What is more important, though, is that these rote learned sentences would sound as though they had been constructed according to grammatical rule - whereas in fact they had just been memorised.

This isn't to say that there may be no such thing as grammatical rules, or other linguistic rules. It is to say that these rules are a tool of the linguistic student, not of the speaker. We should know this from the opening examples from the Investigations - the builders. The rules appear when we analyse, interpret, or translate the builders linguistic behaviour. We do not have grounds for saying that the builders are intentionally following these rules of grammar that we have discovered.

Grammatical rules are rules of linguistic behaviour, not of meaning or truth. We discover them as we discover 'laws of nature', and so these discoveries are subject to the same Goodmanesque or Kripkean uncertainties.

Hume, Is->Ought, Open Questions ...

Hume's paragraph on deriving ought from is suppresses the methodological rule by which he selects 'is' statements.

This rule is, of course, normative - and so Hume cannot allow it to be deduced from factual statements. It can, however, be induced - as his method for selecting facts.

This leaves him with a dilemma if asked to respond to an explicit statement of the rule: He can either (a) deny the validity of the rule (which undermines his is-ought insight) or he can (b) accept it as implied by his fact selection process, if not by the 'facts' that he selects. In the second case, the selection method must either include or imply the rule 'no value statement can be a fact', rendering the argument circular.

If the rule depends on the fact selection process, it doesn't depend on the facts. Does this leave the argument intact (though weakened by circularity)? The scope of Hume's 'facts' is narrow: arguably only the direct evidence on which natural science depends. Most 'social facts' include value statements or value commitments, from which 'oughts' can be deduced (as in Searle's argument).

Rules and Arithmetic

Maybe the exact statement which (indirectly) generates the contradiction is:

"The rules have greater scope than what we can describe"

which must come out as:

"The rules have greater scope than the language which gives them sense".

Rule based proofs

Suppose we have a set of rules for constructing proofs for a system, and the rules could (in principle) be used to construct a proof of the validity of the system. And suppose that we have a proof-computational analogue of validity, as Gödel has. But we add one more thing: the system we are working with is a 'language', and our concept of a rule is grounded in the intelligibility of this language - so that we give an account of 'rule' in terms of some actual rules, and we we give an account of these recursively (or transcendentally) as I've indicated elsewhere in this blog. (We show that the failure of one of these to be a rule would be inconsistent with the intelligibility of the language.)

Would we then be trying to ground the intelligility of the language (it's capacity to test validity) in the intelligibility of the language (upon which the rules of demonstration ultimately rest)? And, if we were, why would this circularity produce a contradiction, rather than just be vacuous or invalid?

Maybe because these are the only two options - vacuous circularity or inconsistency. Although that's a bit vague and long-range.

Arithmetic is a good subject for this kind of investigation because of its capacity to model an indefinite range of rules and representations. It's because it can do this that it generates the incompleteness and inconsistency theorems.



The cycle I'm thinking of looks something like this:



(1) It is possible to state a rule, because we couldn't speak otherwise - it is a consequence of intelligibility

(2) Some of the rules we must be able to state are rules of logic and of arithmetic

(3) We can use these rules to specify a general theory of validity

(4) A demonstration of validity is, essentially, a demonstration of intelligibilty...

What happens as we go around this circle?

Maybe we discover that either (a) we stop meaning anything (we execute the recitations of a machine) or (b) the meanings change as we iterate.

(a) would be a result of being able to give a complete behavioural account of what was going on (which we could only do in a 'meta-language'). Once we've done this, we can't constrain the meaning of the behaviour we have described.

(b) means the rules change as well. To change the meaning of a rule is to change its consequences - what can be deduced from its truth. This means that we don't get a 'closed' system of proofs.

(This is all consistent with (i) the current conversation being the top of the meta-linguistic hierarchy and (ii) unspecifiable constraints on meaning, allowing developmental change - especially as we change meta-linguistic perspective.)

How could we say that the 'meanings' of the rules (Peano plus logic?)that Gödel employed changed?

Or is it the meaning of 'validity' which changes?

His computations might be 'meta-computations', since he - in some sense - demonstrates that they are 'in principle' executable, but does not execute them.

This is like saying that a rule we use applies outside of any possible scope of use. That it is 'universal', where this includes things we can't talk about as well as things we can.

Counting

It's easy to imagine a counting system which functions for some particular set of circumstances, but doesn't work 'in general' (e.g. the 'one, two, many' system occasionally attributed to some 'primitive' people by anthropologists).

Does this mean that we can ask the question whether our counting system might be like this, and that we might discover (in some future) that it didn't really work in some particular, presently unimaginable (undescribable) circumstance?

The best answer to this question would show that the question could only be asked if our counting system did not suffer from this defect. This would avoid the problems associated with giving a general account of counting (Peano/Gödel), or with 'defining' counting in terms of the system we presently use.

Gödel's method, which shows that Peano's calculus can be represented arithmetically, suggests a route to an answer: if our question can be represented arithmetically, and would only make sense if this was the case, then we might regard it as answered.

There are loads of bear traps, though - 'making sense' being an obvious one. But if we think of 'making sense' in terms of practical interpretation (the playability of the game), then there is still a possibility of a transcendental demonstration.

Would we be saying that only a person who counts the way we do could understand the question the way we do? Along with a Davidsonian attitude to conceptual schemes, this might work (so long as we avoid trivial solutions, e.g. that part of the understanding included a certain kind of generalisability of our counting method).

We would need to avoid any tacit reference to an 'ideal' counting system - one which is at the top of some abstract hierarchy in which, say, arabic numerals are above roman or greek numbering systems; or in which 'more' abstract rank above 'less' abstract systems.

(I think I can only deal with (a) games which are playable, and (b) potential games which are not - and there is no final method for discriminating between these. But, of course, the playability of a game, e.g. a question asking game, can have general consequences.)

Gödel's proofs depend upon demonstrations of indescribable worlds - no 'practical' arithmetic would encounter his numbers. There are many things we might think we could do with numbers (e.g. rank them, perform certain algebraic operations on them) which are not possible with Gödel's examples. They aren't quite as minimally articulated as we might think a 'number which is indescribable' would be - we have some elements of their descriptions.

(Some objections to Cantor's proofs arose from their consequence that there were indescribable numbers?)

Is it OK to say that we can't ask any questions of an indescribable collection? Does it matter if it only contains numbers? Can we make this restriction, given the representational power of numbers?

Perhaps the possibility of speculation depends upon arithmetic being constrained in a way which (a) cannot be fully articulated, and (b) avoids Gödel's consequences.

We can allow such a constraint as (a) because it is the kind of constraint implied by the possibility of a theory of truth for our language. There must be some constraint, but we cannot fully articulate it.

If we wonder how we can talk, do we also wonder whether ... ?

If I wonder whether it is possible to talk, it cannot be because I'm wondering whether 'it is possible to talk' is true.

I must be wondering in some other way - some way which requires interpretation. I must be in a potentially ambigous intentional state, whereas if I say that I wonder what day it is I cannot - by accident, for instance - be wondering something else.

If I say 'I wonder whether it is possible to talk?' you might be puzzled: I can't be believe we can't talk without rendering my statement uninterpretable. If my statment means anything, then I can't be seriously wondering.

Some other rules we can't follow ...

If we can only give an account of rule following in terms of intentionality, then we need to be able to associate a particular rule with an intentional state. Lets say that the 'rule of addition' is what someone is following when we agree with them that they are adding.

We can render a number as a rule by representing it as 'the number that ... ' etc. In order to be a proper example of a number we need to be able to do certain things with it - e.g. determine whether another (arbitrary) number is greater or smaller than it, determine the outcomes of using it in certain arithmetical contexts etc.

It seems likely that the paradoxical numbers pointed to by Cantor, Borel, Gödel and Chaitin aren't fully numerical in this sense. There are arithmetical operations we can't do on them. (Are they like 'incomplete concepts'?).

A number like this can't be fully represented in terms of intentionaly tractable rules, and if we can only avoid Kripkean chaos by rendering rules in terms of intentional states - attributable to interlocutors in a (necessarily playable) language game - then these numbers begin to soften in the mist, as the idea of an 'intentionaly intractable' rule begins to look analytically incoherent.

Maybe Gödel's paradoxes only arise when we assume that we can construct these rules. He has put together a set of rules that defines validity for the system within which they are (presumably) validly constructed. Maybe we can only imagine doing this if we can imagine a rule that is independent of an intentional state - that is prior to, rather than depending upon, the possibility of attributing such a state.

To be able to do computations based on Peano's axioms and the relevant logical transformations is to be able to unambiguously follow certain rules (i.e. is to be able to avoid Kripke's chaos). We cannot show that we have avoided ambiguity by applying some further rules which, mysteriously, avoid Kripke's problem ...

We have to be careful of specifying rules which we cannot fully state, and which cannot (therefore) be defined in terms of an attributable intentional state. We should be careful of saying 'there is some rule such that following it would have the consequence X'; and, of course, of saying 'there is some number such that ...', particularly when we know this rule, or this number cannot be stated. This is the case when a rule is meta-specified as the rule which must be followed in order to validly state rules (and to attribute rule following).

Language

Imagine a hierarchy:

(1) Mechanincal, natural.

At this level, we describe everything in terms of physical interactions. It is a world without semantic content.

There will appear to be only one way of describing the world mechanically, and we might think of this as 'reality'.

(2) Signalling

At this level, we divide the world into systems and sub-systems. These have formal characteristics which might be instantiated in a number of different physical ways. Each unit is attached to one or more other units by a 'channel' which has a 'band width'. The bandwidth is the number of different signals the channel can carry. Channels are asynchronous - they carry signals in one direction only. For synchronous signalling, we need more than one channel (even if both might be implemeted using the same physical substrate).

To be a channel, at least one possible signal must be 'useful'. By this, I mean something like: we can specifiy the conditions under which it would be sent, and what effect it has on its recipient.

The formal characteristics of the system as the rules that describe the behaviour of the units and the structure of the signals.

There will always be more than one way of dividing up level 1 in this way - it will be a matter of taste or convenience whether we describe some things in terms as internal structure of individual units or in terms of sets of interacting sub-units.

(3) Semantic

At this level, we give the signals and the behaviours 'meanings'. These are always provisional (Kripke). Perhaps we might say that the a meaning interpretation is a 'model' of the system, but perhaps this would be confusing.

In any case, this is the level at this we introduce intentional content. We can say 'Unit A has told Unit B that the temperature has reached 0 degrees', or 'Unit A has instructed Unit B to switch on the heater'.

(4) Validity attributing

A signal can be interpreted as an adjudication on the correctness or incorrectness of (a) a semantic interpretation or (b) its intentional content. Things get pretty wobbly at this stage. What is really going on here?

Particularly difficult issues arise if we interpret a signal as adjudicating on the correctness of our interpretation of it.

Is this a model people use? It looks like it to me. It can be partly 'unpacked' in some cases, and this contributes to the illusion.

But the whole thing is an 'interpretation' ...

Talking about semantic content

Does this make sense:

Giving semantic content is like giving a dictionary definition. If you already know how to speak the language, it gives you a way of extending your ability at the margins.

Its similarity to rendering formal syntax is misleading: of course we can write down some rules - this is not a useful model, though, because of the OQ arguments. We can only write down some rules if we can already write down something.

And dictionary definitions are only really useful if we also have some tacit 'hooks'. If we have only synonyms, then the only argument for replacing the synonym with the defined word will be convenience - we can say something more quickly, or in a less clumsy way.

We have to be able to show as well as tell.

We might, like the ordinary language philosophers and the linguists, articulate the way we talk. As we do this, we change the way we talk - words have their meanings 'tidied up', and so changed. Sometimes they are changed in more dramatic ways, that we take time to articualte (as scientific terms change meaning - space, mass, distance).

Discovering how we talk, how we can talk, and what the world is like are not three different enterprises.

What's wrong with the picture theory of language is what's wrong with semantic content, and also what's wrong the 'languages of thought'. This isn't to say that these models, these metaphors, have no empirical value - they may be important heuristics for certain kinds of studies. They just can't answer any interesting epistemological or ontological questions.

Chomsky, Davidson, & learning ...

This may be a caricature.

Once I learn to ride a bicycle, I can ride it through many landscapes. Once I can sing in tune, I can sing many tunes. There may be rules about following maps or reading music, but not about riding bicycles or singing in tune.

We can analyse map-reading metalinguistically. We can generate isomorphs of the map, or of a musical score. These things require us to be able to talk about them, agree about them, in certain ways. We can't do the same for the 'methods' of singing in tune or bicycle riding, both of which are needed for music and bicycle navigation.

While there are some rules of grammar and syntax, and some rules of meaning there are also just some things that we find that we agree about in practice - that just don't give us enough trouble for us to reflect on them. When we try to reflect on them ('how does reference work?') we find ourselves in a Wittgensteinian predicament. Some aspects of these things seem too obvious to remark on and yet too obscure to explain.

A language may well need generative meaning rules, but this is not all it needs. There must also be things we do not yet know that we will agree about - things we might call 'discoveries' when we encounter them. Discovering that we agree about something may look like new knowledge about the world or about ourselves. In many cases, it may be a matter of taste which - it may come down to metaphysical prejudice.

We can do something like following rules that we can not write down - we know this from the open question arguments. We also know that we learn to speak, and that we can learn to do things without being able to articulate the rules which govern them.

Where does this leave Davidson's argument for a constructive account of meaning? At least we know that if we tried to pursue his programme, the meanings of things we said about meaning would change ...

Constructivist meaning

Suppose we had a set of Davidsonian meaning rules. Could the sentences constructed using these rules be arbitrarily long, or complex? We could not set a limit based on cognitive capacity, because this cannot be represented within the rules. How could we write down a limit that wasn't arbitrary?

Would we otherwise be committed to saying, for some 'long' sentences, that they had a meaning but it was not practical to work out what it was?

We might say that a complex computer programme, represented in a high-level language, has a 'meaning' in this way. As soon as we begin to summarise or analyse the code - in terms of it's functions, or into different functional 'blocks' - we are hostage to interpretive ambiguities.

Is this also true about a large piece of language? A book, or this blog?

Does the whole book have a 'meaning' which could be analysed in terms of a Davidsonian theory?

Interpretation

We can imagine a language without the tools to reflect on its own activity - one which functions, but which cannot be used to formulate validity rules or make intelligible attributions of truthfulness.

I think that there are commercial exchanges which take place in a languages like this. We shouldn't insist on interpreting them in terms their use of tokens we also use - they will certainly sound like nonsense if we do this. This is how we should undertstand Moore's paradox - as challenging the conventional meanings of the tokens it employs. Finding that a translation schema for an unknown language produced Moorean statements in critical contexts would invalidate the schema.

We can also imagine a language which does have the relevant capacities - a language in which it begins to be possible to do philosophy.

And we can imagine a language in which it is possible to speculate about how to interpret other languages - or other things as languages.

In our language, a comprehensive validation is one which shows that the falshood of a statement is inconsistent with the possibility of using the language. A comprehensive validation of an interpretation, then, would be a demonstration that the falsehood of the interpretation was inconsistent with the possibility using the language.

We know, from Kripke, that interpretations are always provisional. This doesn't mean that some specific interpretation cannot be ruled out, though. Can we imagine that someone who is quad/adding is actually playing chess? And if we cannot, is this a logical or a cognitive limitation? Is such an interpretation incoherent or just impossibly complex to apply?

Formally, the second seems more likely, but it isn't easy to work out what this means.

In any case, we don't need to worry about that - the interpretive judgements we are making are those that can be made intelligibly within the game we are presently playing.

Is there a problem with giving an account of what it is that we are interpreting, before we interpret it? Imagine a space with a dimension for every freedom of the human body, which could be used to describe any position that we might adopt. A function in this space could describe a movement. What would the function, or functions, associated with 'he waved goodbye' look like? How would we (a) distinguish them from others and (b) recognise them from the mathematics? This is like Wittgenstein on smiles which are only a millimetre too wide ...

We are good at finding the things in the world that we need to be able to recognise in order to be able to talk about it. We know this because we are able to talk about it. It is not a consequence of this that we must be able to say how this knowledge is acquired - contra Davidson. That something is possible is not the same as that it is explicable, or we would be able to explain the possibility of explanation, which is incoherent.

Models

A model provides a grammar and a vocabulary. When it 'works' we think there is some additional similarity, some isomorphism, which underlies this. All there is is a judgement - and we cannot speculate on whether such judgements are, in general, reliable.