[NB: This post is a bit of a rant, and doesn't really come to an end or conclusion. It's just me thinking by writing, which is one of the most profitable ways I know to work my thoughts out. So, read on. But don't think I'm making conclusions or judgements; my thoughts could completely change. In other words, this is fluid, not static. RWB]
Here are some things about αλλα that I've noticed as I've worked through the 638 NT instances (a few times).
When considering an instance of αλλα, know that most of the time (approx. 85% of the time in the NT), a relationship with a negator of some sort is involved.
Instead of just making the oh-to-common mental note associating αλλα with the English gloss "but" and moving on, look around for the negative to determine what two things are in relationship with each other via αλλα.
Here's what I'm presently calling the "αλλα Funnel":
1: Look for a negator. This will be some form of ου or μη, most likely; or some other word like ουδεις, μηδεις, ουκετι, μηκετι, etc.) Again, around 85% of NT instances of αλλα involve a negator. You need to find it. Note the very small proportion of items that have negators on both sides of the αλλα (3 instances; e.g. 1Co 4.4).
2: First, look up (to the left). Over 75% of αλλα in NT have the negator preceding.
3: Still looking? Okay, look down (to the right). About 10% of αλλα in the NT have a negator following. In this case, the negator is usually ου or ουκ, and it usually follows the αλλα directly.
4: Still looking? Well, there are 15% or so instances of αλλα in the NT that do not seem to involve a negator. This is the minority case, so look again (up and down) to be sure.
5: Still looking? Then stop looking and assume there is no negator. At this point, you need to isolate the two items in relationship with each other through the αλλα. This is usually brain-dead easy; sometimes, though, it is a pain (Gal 4.8-9? 1Co 15.35?). Note that there are some instances where αλλα doesn't seem to be responding to an explicit statement. My working hypothesis at present is that αλλα must be a response (contrast, correction, clarification, expansion, what-have-you) to something; and when nothing is explicit the response must be to something implicit in the context. Examine the context and try to figure it out if the connection isn't readily apparent.
Now you're at the bottom of the funnel. The easy part is done, the hard work begins.
αλλα is typically described as a "strong adversative" and, to define "strong", most grammars say it is "stronger than δε". That isn't too helpful. That's like saying "bold" is stronger than "confident". So read the whole context of the statement (or statements) in question that uses αλλα as a hinge to compare. Read the larger context. What is happening with the two phrases/clauses that αλλα stands between? What is the point of the comparison of those two items? Is it replacement/correction? Is it enhancement or expansion? Don't cop out and just say it means "but"; get your mind out of the word-level jumble and think about the relationship between the phrases/clauses and what the point of the author could be in placing these items in juxtaposition with each other, using αλλα as a guide to that author's intent. He's left clues with αλλα, use (or non-use) of negators, and the items he's comparing.
On Lexicons and αλλα
This could actually be a whole additional post, but it won't be. In short, I've read most lexicon definitions of αλλα, and they are all uniformly unhelpful. They seem to jump from lexicography to syntax quickly, sorting "senses" by differing syntactic contexts that αλλα appears in. Cataloguing of instances by syntactic context does not make a helpful lexicon article.
I'm largely convinced that one of the reasons that αλλα is typically classed as an "adversative" is simply because in most of its instances it stands between two clauses/phrases, one negative and one non-negative. In this case, it is the clauses/phrases that are adversary, not αλλα. Then, if no negator is present, αλλα is said to be, perhaps, correlative or contrastive or continuative something like that.
[[This brings up a side rant: Morphologies of the Greek New Testament that provide senses/classifications to conjunctions (e.g. GRAMCORD, "conjunction, coordinating, adversative") are also relatively unhelpful if you're really interested in what the conjunction is up to. Why do I say this? Get yourself a few different morphologies that do this, and you'll see that everyone has different ideas in this area. Compare GRAMCORD to Friberg's morphology. You'll see that many do seem to be the same on first glance, but that's because most morphologies classify most instances of αλλα the same exact way. GRAMCORD has 97.6% of αλλα classified as "conjunction, coordinating, adversative"; Friberg has more variation with 86.5% as "conjunction, superordinating (hyperordinating)". (Full disclosure: The Logos Morphology has even more variation, but it also has more categories) Am I saying they should all be consistent? No; I don't subscribe to a 'concordant' method of morphological classification. I'm just saying there is a lot of variation so it brings into question the classification schemes themselves.]]
So what does αλλα do? What does it indicate? I'm still working on that.
My hope is to have some flash of insight and arrive at a grand unification theory. But I think a large part of the problem is that traditional methodology seems bound to try to answer the question, "how do I translate it?" (hence all sorts of categories and memorization of short glosses) when, in order to actually understand what the author is communicating, we really should be asking the question, "what does it mean?" or, perhaps, "how does it all go together?".
In the context of examining a discourse to better understand "what does it mean?", we need to examine how different parts of the discourse relate to each other. One way that discourse parts relate to each other is though use of conjunctions. So when the author/writer uses αλλα with two items in juxtaposition to each other, what is that author communicating? Are there semantic or grammatical connections between the two juxtaposed items and the rest of the discourse?
My guess is that that, chances are, αλλα means the same thing no matter what context it appears in. Instead, it's how the juxtaposed items relate to each other through αλλα that variation in understanding arises.
Update (2008-03-16): Responding to a few of the comments, I can only emphasize the word 'rant' in regards to αλλα and morphologies and lexicography/lexicons (not to mention grammars). If you compare the labelling of senses/types of αλλα across morphologies, you'll soon find that opinions differ, particularly as you get outside of the easy-to-understand instances (usually in some sort of negative context) and into the 'long tail' of instances. And that's fine; my rant is more my response to the difficulty of the problem than complete dissatisfaction with existing lexicons/morphologies. I guess my issue with the αλλα article in BDAG (and elsewhere) is that by their structure and breakdown they seem more geared toward telling me what to think about specific instances of αλλα than in sewing all that discussion up at the end and giving some thoughts on αλλα in general. It's more of a catalogue of instances than a discussion of the word.
To respond specifically to Mike about BDAG: I suppose one thing I'd like to see in BDAG is after the separation of discussion of αλλα in particular contexts, some discussion of how even in these differing contexts αλλα is functioning similarly. I realize the first sentence of the definition speaks of this somewhat, but something tying the whole thing in general would be nice.
To respond to Ken about adversative as a label: I don't have such a list, and I don't really have a problem with 'adversative' as a word to describe how αλλα functions. I do think that αλλα can be 'adversative' when no negator is present in either clause/phrase of the structure in question. What gives me pause would be to say of any instance of αλλα that it is an 'adversative αλλα'. No, it's αλλα. The context may be adversative, and αλλα is likely the hinge joining two adversarial or contradictory things; but that doesn't mean that αλλα is adversative. Anyway, that's my own issue with labelling things that I need to get over; not necessarily an issue with morphological classifications.