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2010-10-27
Vagueness and context
I'm currently a postgraduate studying philosophy of mind. I have studied logic, but only at undergraduate level, and it was over 30 years ago. So I apologise for the probable naivety of this question.
I'm going to take the liberty of quoting from Melvin Bragg's email newsletter about a radio programme on logic hosted by him, broadcast yesterday on the UK station BBC Radio 4. In a post-programme discussion between the participants,

A C Grayling, usually more slicingly exact than a Gillette razor, defended vagueness in the following terms: if he rushed into a bedroom at two o’clock in the morning and shouted “Fire!” this could open a wide range of possibilities for any logical person.  Was he talking about a candle being lit downstairs?  Was he talking about something that had happened in another place?  But we mere mortals would be vague enough to understand that the house was ablaze and rush out.  Something to be said for vagueness then. (Melvyn Bragg's In Our Time Newsletter - Logic - 21/10/2010)

This seems very wrong to me. Given the context, the shouted word "Fire!" seems really quite precise. And if context is entirely ignored, then any human communication whatsoever is vague to the point of utter meaninglessness. What this illustration demonstrates is not the power of vagueness, but that of context.

But then AC Grayling is quite a "big name". Or maybe Melvin got it wrong. If not, what am I missing? What's the relationship between vagueness and context?

(Link to the programme on BBC iPlayer.)

2010-11-01
Vagueness and context
You're right, it's much more about context than vagueness. It sounds like Grayling was celebrating the power of context in enabling us to convey a great deal of information with few words (though in this case the tone and manner of delivery would also be a key factor). On the other hand, there is a link to vagueness in a broad sense of that word--probably too broad for most philosophers these days 'Fire' on its own can mean many things. In that sense it is' vague'. Context and other factors help to disambiguate it. In fact, 'vague' is here being used as more-or-less synonymous with 'ambiguous'. In recent philosophical logic, however, 'vagueness' means something much more specific. It is exemplified by a word like 'red'. Some objects are clearly red. Others are clearly not red. A third category consists of objects that are borderline--a kind of orangy redness that is hard to classify one way or the other. Furthermore, there is no precise boundary between the things that are clearly red and the things that are borderline, or between the things that are borderline and the things that are clearly not red. Many terms exemplify this sort of pattern--in fact our language is full of them. (To take another example consider: exactly how many hairs does a person have to have to be able to escape being 'bald'? There appears to be no precise answer.)

2010-11-01
Vagueness and context
If I got it right, Grayling's example is issued to stand for a "sample" of vagueness and you claim it's basically a matter of context. 
Now, even if the example proved wrong (since "Fire!" could easily convey both the intention and the reference of his message, hence its precision), it doesn't mean that "context" would become all that matters when dealing with vagueness, if anything. Ok, perhaps Grayling's instance is not illustrative. But it doesn't mean that in any circumstance the power of context is a touchstone. If I were to teach an Indian my language, would s/he claim some words are vague? If yes, would it be a matter of context? It depends on the meaninf of "context", which brings us back to vagueness.

2010-11-01
Vagueness and context
I think Grayling was using the word "vagueness" a bit loosely (if not downright incorrectly), at least as far as philosophical terminology is concerned. Not vagueness, but ambiguity is the property exhibited by this utterance of "fire!" - it could mean many things, but, as you say, context makes clear what it does mean.
The utterance would exhibit vagueness, on the other hand, if the [implied] claim that "there is a fire" lacked precisely specifiable truth conditions, resulting in the possibility of borderline cases -- of 'almost-fires' or 'maybe-fires'! -- in which it failed to take a determinate binary truth value.

So the distinction, on my understanding (I'm just finishing an undergrad. philosophy of logic course, but am relying on memory and haven't bothered to consult my sources for this post) is as follows: ambiguity = meaning dependent on context, while vagueness = no precisely specifiable truth conditions.

Incidentally, I don't know if Grayling actually used the phrase "any logical person", but, if so, extra demerits for that; I am aware that words have quite distinct colloquial and technical senses, but, still, the employment of the term for the study of deductive entailment to denote a caricatured cold-blooded Vulcan-style rationality really annoys me! :-p