Tuesday, February 14, 2006

The Zombic Hunch and the Limits of Thought Experiments

Bring Out Your Dead

Few thought experiments in the philosophy of mind are as popular or famous as the philosopher’s zombie (although John Searle’s Chinese Room probably tops it). These aren’t the cannibalistic, but mercifully slow-walking, corpses of George Romero’s 1978 film Dawn Of The Dead. When philosophers talk about zombies they generally have in mind a being much like me and you in appearance and behaviour — in some instances identical — but lacking any inner mental life, any conscious glow, any feeling of what it is like to experience, say, the scent of a rose or the tang of lemon. But, being behaviourally just like an ordinary human, such a zombie would talk and act just as if they did have conscious experience. Perhaps for all you know me, and everyone other person on the planet, are zombies — it is part of the conception of a zombie that you couldn’t tell by observing our behaviour or by inspecting us physically — that is, the way we act and talk about the world (including our non-existent conscious experience) wouldn’t give our zombiehood away.

Some philosophers have suggested that the possibility, or at least conceivability, of zombies tells us something important about the nature of consciousness and its relation to our physiology, particularly the brain. Others respond that zombies are a confused notion, and have done more harm than good in directing our thoughts about the mind. In the recent book Conversations on Consciousness, Susan Blackmore discusses the possibility and likelihood of zombies with a number of leading philosophers of mind and cognitive scientists, and comparing their accounts can possibly shed some light on what’s going on in the debates.

In discussing zombies with Blackmore, philosopher Ned Block distinguishes between two senses of the philosopher’s zombie, which we might call the ‘functionalist zombie’ and the ‘biological zombie’. I’ll explain both shortly, after a little bit of background on what functionalism is, and the account it gives of the mind (I’ll quote from some good introductory books on the topic that are easily available).

The are many problems in the philosophy of mind, although the problem of consciousness is perhaps currently the most high profile (in the popular mind at least: the past decade has seen a proliferation of popular and semi-popular books on the subject). The are a number of features of mental states we might want to explain: some mental states are caused by states of the world; some mental states cause mental states; some mental states cause other mental states; some mental states are about things in the world; and some kinds of mental states are systematically correlated with certain kinds of brain states (Ravenscroft (2005)).

Functionalism addresses a number of these problems from a perspective that sits well with a materialist conception of the mind, although it is not logically committed to materialism (the idea that everything in the world — mental events and all — have a material, physical basis). In the current climate, in which may if not most philosophers and neuroscientists take the brain to be the material basis of the mind, functionalism has found a welcome home, and has become a major position in the philosophy of mind. However, a wide range of views on the mind–brain relation, and the nature of consciousness, are compatible with materialism, and so functionalism is not the only game in town. However, whatever it’s troubles, functionalism has been an extremely influential approach to the mind, and even its critics take it seriously.

Braddon-Mitchell and Jackson (1996) say “Functionalists take mental states to be the internal causes of behaviour … Mental states are, according to functionalists, internal states within us, but we identify and name them by the effect the world has on them, the effects they have on the world, and the effect they have on the world by causing our behaviour.” Functionalism both helps explain, and derives support from, the fact that mental states can be multiply realised, which means that some states, say pain, can be produced by, or realised in, a number of different physical systems. The possibility of multiple realisation poses problems for theories that identify a given mental state, such as pain, with a certain physical state, such as the firing of C-fibres in the nervous system (although this isn’t neurologically plausible it’s a standard example in the philosophical literature). The claim of the identity theory here is that the firing of C-fibres is identical to being in a state of pain. However, other animals, such as lobsters, seem capable of being in pain states, so an identity theory that identified pain as firing of C-fibres would claim that lobsters must have C-fibres too. But let’s assume that lobsters don’t have C-fibres; they have D-fibres instead. If this is true, then pain can’t merely be the firing of C-fibres. Perhaps we might say that pain is the firing of C- or D-fibres, but then our idea of a mental state is extremely contingent on what we know about nervous systems across the animal kingdom. Functionalism provides an escape from this.

As Ravenscroft (2005) explains, “According to functionalism, C-fiber firing does the same job in me as D-fiber firing does in [lobsters]. On this view, to be in pain is to have an internal state which does a certain job. Which job is that? Very roughly, an internal state does the ‘pain job’ if it is caused by bodily damage and causes us to say ‘ouch’ and rub the sore spot. So according to functionalism, to be in pain is to have an internal state which is activated by bodily damage and which causes us to say ‘ouch’ and rub the sore spot. More generally, according to functionalism, to be in (or have) mental state M is to have an internal state which does the ‘M-job’.” It is important that these functional states have certain causal properties, properties determined by their inputs, how the state responds to the input, its output and its effects on other states of the systems.

Refuting Functionalism?

The idea of multiple realisation is in principle not limited to biological systems as a given functional state can in principle be underpinned by a non-biological machine – a computer, for instance. It has been suggested that a sort of Rube Goldberg device made out of cans, strings and pulleys could, in principle, replicate the functional states of the human brain. An early criticism of the functionalist approach was developed by Block, and is called the China Brain (which inspired the famous Chinese Room). In this thought experiment, everyone in the population of China (assumed to be about a billion, a number much lower, but vaguely in the ball park, of the number of neurons in the human brain) is given a phone. Everyone is also given a set of instructions that say that when a call is received from a given number, or numbers, another call or calls should be made to certain other numbers. In this way, each phone operator is imitating the functional role of an individual neuron.

Now, this is isn’t likely to be set up any time soon, but we can imagine it in principle. So once it was up and running, each phone operator would assume the functional role of a neuron, and collectively they would simulate the functional organisation of the brain. That is, the population would be in the same functional states as a human brain, given the correct inputs and rules of operation. So what if the phone operators were in the same functional state as the brain is when it has a mental state with the content ‘It’s raining’? Would the population of phone operators be in this mental state too? This isn’t about whether individual phone operators would believe that it’s raining, but whether the population of operators are in the functional state of believing that it’s raining – which functionalism is says it is.

It perhaps seems absurd to suppose that the population as a whole is conscious of the belief ‘It’s raining’ in some strange, disembodied state. The existence of a functional state representing the mental belief state ‘It’s raining’ seems insufficient for the conscious awareness of this belief. The problem of consciousness – the first-person perspective on the world, our subjective experience of the world, what it is like to be you, at your computer, as you read this – is indeed a tricky issue for functionalism, as it is for all theories of the mind. But problems in the philosophy of mind are not exhausted by the problem of conscious – in fact, some philosophers, such as Dan Dennett, believe that once the other problems of how the brain/mind works, then the supposed problem of consciousness will disappear. There won’t be an extra ‘something’ to explain when all the other aspects of the mind are explained.

Functionalism fares well in explaining a number of other features of mental states. For instance, it has an explanation of, or at least is compatible with, the following features on mental states that any theory of mind will hopefully address (see Ravenscroft (2005)): some mental states are caused by states of the world; some mental states cause mental states; some mental states cause other mental states; some mental states are about things in the world; and some kinds of mental states are systematically correlated with certain kinds of brain states. It’s not well-suited to explaining the problem of consciousness, as traditionally construed, but does the China Brain thought experiment refute functionalism as an approach to understanding these other aspects of the mind, as it is intended to? It seems perhaps obvious that the China Brain doesn’t have mental states similar in relevant respects to human mental states, but this is an intuition, not an argument, however strong (Braddon-Mitchell and Jackson (1996)).

In any case, Block’s take on the China Brain thought experiment leads him to various conclusions. Block considers functionalism to be insufficient to the task of explaining the phenomenology of mind, and therefore can conceive of a being that is functionally similar to a human, even if physically different from humans, which lacks consciousness. This is a being that is functionally similar to us, like the China Brain was, but which lacks consciousness like the China Brain. This is Block’s notion of what I’ll call a functionalist zombie, and I’ll explore this type of zombie, along with biological zombies, and philosophers’ response to them in the next post.

Zombies And The Philosophers

Ned Block characterises the functionalist zombie as a “person who is functionally like us, but physically so different that this person doesn’t have the physical basis of phenomenology”. He cites the example of a human perhaps made out of silicon chips that were organised to embody functional states identical to those of a human. Block concludes that this being would lack the physical basis of phenomenology, and derives this conclusion from the China Brain thought experiment.

Block also describes a second sort of zombie, what I’m calling a biological zombie:

“The second sort of zombie is a creature that’s physically exactly like us. This is [David] Chalmers’s zombie, so when Chalmers says he believes in the conceivability and therefore the possibility of zombies, he’s talking about that kind of a zombie. My view is that no one who takes the biological basis of consciousness seriously should really believe in that kind of a zombie. I don’t believe in the possibility of that zombie; I believe that the physiology of the human brain determines our phenomenology and so there couldn’t be a creature like that, physically exactly like us, down to every molecule of the brain, just the same but nobody home, no phenomenology. That zombie I don’t believe in, but the functional zombie I do believe in.”

So that’s our starting point: the contrast between functionalist zombies and biological zombies (though this distinction might well be disputed on the grounds that the difference between a functional zombie that behaved intelligently and a creature that behaved in a similarly intelligent fashion but with the boost of consciousness is more imagined than real). Next, here’s how John Searle replies to being asked about zombies by Sue Blackmore, whose reply I’ve included:

“The zombie is really a philosopher’s invention, to imagine a machine or a creature that behaves the same as a person who is conscious but has no consciousness; and I think that makes sense; you can imagine such a thing; I can imagine that you really are a wind up mechanism and that you’re not conscious. It’s a good thought experiment to imagine the differences between ourselves, who have both consciousness and coherent organised behaviour, and the zombie that appears to have the same organised behaviour but does not have any consciousness, has no feelings.”

Blackmore: “Obviously it’s possible to imagine such a zombie, but are you saying that such a zombie could in principle exist?”

Searle: “In principle, sure.”

At first it seems like Searle is just referring to the functionalist conception of a zombie — “a machine or a creature that behaves the same as a person who is conscious but has no consciousness”. But by saying “I can imagine that you are really a wind-up mechanism and that you’re not conscious” he seems to be committing himself to the stronger idea, rejected by Block, of a biological zombie, a creature identical to a human but lacking consciousness. And what could be more identical to Sue Blackmore than the conscious Sue Blackmore? (If he didn’t have this in mind, how could he imagine Blackmore as a zombie, given that she such a zombie would be, in fact, biologically identical to the actual conscious Sue Blackmore? (Of course, we don’t know that Blackmore is really conscious; but Searle is saying that although he thinks that beings of with the kind of biology Blackmore has — humans — are conscious, it’s possible to imagine them as not conscious.) So to take Searle at his word, that he can imagine Blackmore as non-conscious, this strong reading seems fair. The possibility of this biological zombie is often taken to have an important implication: that if we can imagine creatures physically exactly like us, who must definitionally be in identical functional states, then mere functional states are not enough for consciousness. Therefore there is something extra, some special ingredient, that is part of the explanation of consciousness. Blackmore is quick to the chase:

Blackmore: “So as far as you’re concerned, then, there’s something extra; you could have a mechanism that did all this stuff, but it wouldn’t be really like us; it needs something extra, the conscious field or the rational agent or something like that, to make it be like us and have our kind of awareness. Is that what you’re saying?”

Searle: “That’s exactly what I’m saying. I think evolution probably could not have produced such a thing, because evolution produced us. You can imagine evolution producing beings that moved around on wheels instead of on legs; but for all kinds of reasons it’s unlikely that evolution would ever be able to produce that. Similarly, you can imagine evolution producing a well-organised zombie, but it’s unlikely; we just get this much more efficient mechanism if we have consciousness. However, you could, in principle at least, design machinery that could behave as if it were intelligent – that is, could behave in the same way as human beings behave; we’re nowhere near being able to do that, but in principle it’s possible.”

This response muddies the waters a bit in interpreting Searle. He starts by saying that he accepts the conclusion about ‘extra ingredients’ derived from his conception of the zombie thought experiment as discussed Blackmore This suggests that he takes the possibility of biological zombies seriously. This is surprising given the importance Searle places on the brain and its biological functioning in explaining consciousness, which he thinks makes brains conscious, and machines, which don’t have the right arrangement of matter, unconscious.

However, by saying that “I think evolution probably could not have produced such a thing, because evolution produced us”, he seems to suggest something different — at least inadvertently, perhaps. The design process of evolution through natural selection has produced complexly and improbably organised functionally adapted matter — from sub-cellular organelles to organisms — that serves functional ends. Some of this matter is arranged in such a way as to form conscious creatures, like us, and maybe other animals.

I take Searle to believe that the way evolution has operated, and the way it has put physical matter together, entails that consciousness exist. (Not that evolution necessarily entailed the emergence of consciousness, but that given that it put organisms together with our molecular composition, consciousness was inevitable. I say this because Searle believe that the brain in a sense ‘creates’ the mind, that mind is an emergent property of the brain perhaps like wetness is an emergent property of water. Given the molecular structure of water, and the operation of physico-chemical laws, water has the emergent properties associated with being a liquid. In a similar sense, the molecular organisation of the brain (human, at least), operating according to the causal laws of the universe, creates consciousness. Another system made out of different material, say a computer emulating mental processes, would lack consciousness — it hasn’t got the right stuff. This is what I take Searle to mean when he says “I think evolution probably could not have produced such a thing [a mechanism that did all this stuff, but it wouldn’t be really like us], because evolution produced us.”

But then Searle says “you can imagine evolution producing a well-organised zombie, but it’s unlikely; we just get this much more efficient mechanism if we have consciousness. However, you could, in principle at least, design machinery that could behave as if it were intelligent – that is, could behave in the same way as human beings behave; we’re nowhere near being able to that, but in principle it’s possible.” This suggests that Searle now means something else. It seems that he’s now talking about a creature that is not like us molecule for molecule (if it was, it’d be human and conscious). So perhaps Searle means a being potentially quite different from us physically — perhaps a silicon-based life-form, or of just very different biological design — but which was behaviourally similar, one that instantiated the same functional states of a human, but which was a zombie. This, it seems to me, is a rather different claim. On the first reading, it seems that Searle should reject the idea that Blackmore is a zombie, because of his views about the way that consciousness arises from the material composition of the brain. And on the second reading he should reject the possibility too, because he’s supposed to be talking about a functional zombie, which can’t substituted with a biological zombie that Blackmore would have to be if she were any type of zombie! To unpack that a bit, accepting the possibility of a functional zombie doesn’t mean that it’s reasonable to conclude that Blackmore could be a zombie, for if she were to be a zombie she’d have to be a biological zombie, and acceptance of the former doesn’t entail acceptance of the latter.

If this is correct, then the conclusions about the ‘extra ingredient’ needed to explain consciousness don’t follow, and zombies aren’t perhaps so good a thought experiment as Searle thinks.

The next philosopher I want to turn to is David Chalmers, alluded to by Block above and charged with believing in biological zombies. Here’s the relevant dialogue from Conversations On Consciousness (it’s quite long):

Blackmore: “Would you like to explain about zombies?”

Chalmers: “Sure. I think in the actual world, intelligent behaviour and consciousness very likely go together. So when you find a system which is behaving like me and talking like me – it’s probably conscious. But it seems that I could imagine a system which was behaviourally just like me, it walked and talked just like me, it got around its environment, but it didn’t have subjective experience. Everything was dark inside. This would be what philosophers like to call a zombie – a being entirely lacking consciousness.

Now such a being would be tremendously sophisticated. You couldn’t tell the difference from the outside, but there would nobody home inside. Here I am sitting talking to you. All I have access to is your behaviour. Now you seem like a reasonably intelligent human being, you’re saying articulate things that suggest a conscious being inside. But of course, the age-old problem is ‘how do I know?’. It’s at least logically consistent with my evidence that you are a zombie.

Now I don’t think you are, but the very logical possibility of zombies is interesting because then we can raise the question ‘why are we not zombies?’. There could have been a universe of zombies. Think about creating the world. It seems logically within God’s power (and of course the use of ‘God’ here is just a metaphor) to create a world which was physically just like this one with a lot of particles and compelx systems behaving in complex ways, but these were just androids. There was no consciousness at all.

And yet there is consciousness. So that’s been used by some people, including me, to suggest that the existence of consciousness on our world is a further deeper property of the world than its mere physical constitution.”

Chalmers seems to be saying that it’s only something behaviourally like us, not something like us molecule for molecule, that could exist and be lacking in consciousness. When he says “You couldn’t tell the difference from the outside”, he must be interpreted as meaning from a relatively cursory glance of the outside: if outside is taken to mean all types of physical examination and testing, and it’s molecular constitution and physiological operation were found to be identical to that found in humans, then it’d be a human, and we would therefore grant it consciousness (provided we grant the existence of other minds in humans). This gloss is supported by Chalmers’s response to Blackmore’s next question:

Blackmore: “So are you saying that you believe such philosopher’s zombies are possible and the fact that we have consciousness means that we have to add something to the explanation?”

Chalmers: “I think they’re probably not possible in the sense that no such thing could ever exist in this world. I think that even a computer which has really complex intelligent behaviour and functioning would probably be conscious. What is interesting though, is that it doesn’t seem contradictory to suppose, at least in the imagination, that someone, somewhere, in some possible world, could behave like me without consciousness. But our world isn’t like that. So that’s an interesting fact about our world!”

I take Chalmers to be saying that no zombie, in the sense Chalmers intends, could exist in our universe, because of the way it happens to be constructed. But in another possible world, constructed differently, they could. But the possible world Chalmers has in mind cannot be exactly the same as our world – elementary particle for elementary particle, atom for atom, molecule for molecule – as it wouldn’t be an alternative possible world, it’d be our world, which features the very conscious creatures (us) we were trying to imagine didn’t exist!

So Chalmers rejects the possibility of what I called a biological zombie, characterised by Block as “physically exactly like us, down to every molecule of the brain, just the same but nobody home, no phenomenology”. If ‘possible world’ means one that is exactly like our world, then we can ask what it’d mean to imagine such a world containing beings identical to us but without consciousness. It seems akin to saying that you could imagine a world like ours, built from the same elementary particles, fundamental forces and fields, but which didn’t feature mass or electromagnetic radiation or hydrogen. You might be able to say you can imagine such a world, but perhaps your imagination is running away from you there a bit. We might also claim to be able imagine a world identical to this one except that humans can fly by levitation (of course, if it were really identical, we couldn’t, as we don’t); but merely saying this doesn’t then raise interesting questions about why humans, in this world, don’t in fact fly. The mere fact that we think we can imagine this world with something ‘extra’ that enables levitation doesn’t mean that we then have to explain the absence of this ‘extra’ something in this world, or even consider it as a possible ‘extra’ that we could be in possession of. Similarly, the fact that we might — though few do — say that we can imagine identical beings but lacking in conscious, because they lack some mysterious extra ingredient, does not mean that there actually is an ‘extra ingredient’ in our world to explain.

It might be useful here to distinguish between logically possible worlds and nomologically possible worlds, and apply this distinction to the case of zombies. A logical possibility is a state of affairs that doesn’t contradict the laws of logic, and a logically possible world is one the description of which is not self-contradictory. The space of logically possible worlds therefore contains worlds very unlike ours, perhaps where things impossible in our world occur with regularity. A nomological possibility is a possible state of affairs that is consistent with the causal laws of the universe as we know them, and so a nomologically possible world is one that is consistent with the known laws of physics. Under this distinction, levitating humans might be a logical possibility, but they aren’t a nomological possibility. And what does the mere logical possibility of levitation entail for our views about our actual world? Little, in this case. And so why should the logical possibility of zombies be of much relevance to us? The nomological possibility of a zombie would be of interest, but arguing for such a possible being requires a fair bit of work, and is in fact rejected by the philosophers looked at here (with the possible exception of Searle, who seems to drift a bit between the two possibilities, logical and nomological).

Let’s get back to Chalmers. He does not seem to believe in the nomological possibility of what we’ve called a biological zombie, and so Block is wrong to say that this sort of zombie is what Chalmers does in fact believe in. This has implications for what Block claims Chalmers says the implications of zombies are. The sort of zombie Chalmers believes could exist is one that existed in a genuinely alternative possible world, behaved in an intelligent, organised and coherent manner in the pursuit of goals, even reported the possession of conscious experience, but did not have real conscious experience. One, in other words, that had internal functional states that guided intelligent behaviour — Block’s functionalist zombie. Block and Chalmers agree on the nomological possibility of functional zombies and the nomological impossibility of biological zombies. Which prompts Blackmore to ask:

Blackmore: “You say our world isn’t like that. Does this make you a functionalist? Are you saying that, in our world, anything that carries out a certain function must necessarily be conscious?”

Chalmers: “In some very broad sense I am a functionalist. I think that behaviour, and function, and consciousness go together. They are very tightly correlated and associated. But I am not a functionalist in the strong sense of saying that all there is to consciousness is the functioning. So people say that all we have to worry about is functioning and the behaviour and the talking. I think that is just manifestly false because of the direct data of subjective experience. We have correlation of the two without any kind of reduction of one to the other.”

Blackmore: “I want to get this absolutely clear because people talk about your views on zombies a lot. You saying that logically you can conceive of a world in which there would be intelligent-behaving creatures who went around saying like ‘I am conscious’ and ‘I’m experiencing red right now’ and so on, but didn’t have any subjective experience. But you think that in this real world we are in that’s not possible and anything that does these behaviours will necessarily be conscious.”

Chalmers: “That’s exactly right.”

This assent to Blackmore’s presentation of his view reinforces the interpretation of Chalmers’s view that I’ve sketched above. He accepts the nomological possibility of functional zombies, but rejects the nomological possibility of biological zombies.

So far, here’s the tally: Block and Chalmers both accept the nomological possibility of functional zombies, and Searle’s comments suggest that should too, if he’d accept the distinction between functional and biological zombies. Both Block and Chalmers reject the nomological possibility of biological zombies, and therefore reject the conclusions that supposedly follow from their mere conceivability, such as the need to postulate an ‘extra ingredient’ to explain consciousness.

So far one major philosopher has been notable by his absence: Dan Dennett, who doesn’t have much time for considering zombies, driven as it is, he considers, by the ill-founded Zombic Hunch:

“The Zombic hunch is the idea that there could be a being that behaved exactly the way you or I behave, in every regard – it could cry at sad movies, be thrilled by joyous sunsets, enjoy ice cream and the whole thing, and yet not be conscious at all. It would just be a zombie. Now I think that many people are sure that hunch is right, and they don’t know why they’re sure. If you show them the arguments for taking zombies seriously are all flawed, this doesn’t stop them from clinging to the hunch. They’re afraid to let go of it, for fear they’re leaving something deeply important out. And so we get a bifurcation of theorists into those who take the zombic hunch seriously, and those who, like myself, have sort of overcome it. I can feel it, but I just don’t have it anymore.”

I’m not quite sure whether Dennett rejects the nomological possibility of the functional zombie — if it behaved like we did, it’d be conscious like us, perhaps — and I leave that to others to address.

It’s time to summarise. I agree with Dennett that we should let go of the zombic hunch. If you believe in zombies, in the strong, biological, nomological sense, then this should be on the basis of an explicit argument — assent to belief in the possibility of these zombies seems to me more of a conclusion than a starting point for other conclusions to be drawn. As such, asking someone whether they believe in the possibility of zombies (after making sure exactly what you’re talking about!) is a useful diagnostic question in gauging their stance on the mind, but this stance has to be justified by a zombie-independent argument. After all, to avoid circularity you need to provide reasons for concluding that zombies are possible on the basis of your conception of the mind, rather than claiming that zombies are possible, then deriving an account of the mind that explains this possibility — and then using this to explain the possibility of the zombies that motivated your argument!

Notes

Blackmore, S. Conversations on Consciousness (Oxford Univ. Press, 2005).

Braddon-Mitchell, D. & Jackson, F. Philosophy of Mind and Cognition (Blackwell, 1996).

Ravenscroft, I. Philosophy of Mind: A Beginner’s Guide (Oxford, 2005).

3 Comments:

Blogger potentilla said...

I am coming to the conclusion that many of the great philosophical perennials - "consciousness", "free-will", "personal identity", "morals" - are not "real" things, out there, but only approximate labels for ill-defined essentially emotional states arising from our evolutionary history. Perhaps "rationality", too.

6:48 pm GMT  
Anonymous Anonymous said...

You've got Chalmers completely wrong. He believes in the logical (but not nomological) possibility of biological zombies. There could be a universe physically identical to ours, but lacking consciousness. What makes our universe special are the psycho-physical laws of nature which guarantee that every instance of certain brain states leads to certain conscious mental states. This is a law of nature over and above the purely physical laws, however.

Also, I think he would further deny the nomological possibility of functional zombies (cf. "I think that even a computer which has really complex intelligent behaviour and functioning would probably be conscious").

6:47 am GMT  
Blogger Dan Jones said...

Richard, thanks for the comment. I was hoping for people to correct me if I had got some of this wrong, and I'm happy to admit my mistake in this instance (in fact, Chalmers has written to me pointing out much the same). As such, I plan to clarify Chalmers' position and retract my previous characterisation in a new post - and to try to explain what led me astray! No excuse really though, I should've made sure I'd nailed it before posting - but you learn through taking chances and making mistakes, right?

1:50 pm GMT  

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