When looking into the use of αλλα, one needs to (at least to some degree) consider the difference between αλλα and δε. Grammarians have hopelessly associated the two together. The conjunction δε is usually described as having "adversative" qualities, though it can also be "continuative" or even "transitional". The primary description of αλλα seems to be that it, as an adversative, is "stronger than δε" (though sometimes it is "transitional" too, they say). So αλλα is the "strong adversative" while δε is the "weak adversative". Or something like that.
And that description is somewhat helpful, but it leaves a lot to be desired. All these different functions/descriptions are based, it seems, on context of usage. When looking at the problem from a discourse level, however, these contextual descriptions don't really help, particularly when the basic recommendation for translation is to just use the English "but" for both cases. That may be accurate translation, but it doesn't really help us understand what is going on in the Greek and what function these two conjunctions have.
What are "strong" and "weak" adversatives? It seems the strong adversative is normally a corrective (and normally a negative particle or adverb is involved); the weak is normally a development of argument of some sort. Here's Hermas, Visions 3.1.9, in Holmes' 2nd edition, first in Greek then in English. This excerpt has two instances of αλλα; we're only interested in the second one for purposes of this blog post. <CP ...> marks the "counterpoint", typically the first phrase/clause that αλλα responds to; <P ... > marks the "point", typically the salient bit of the whole comparison.
(9) <CP θέλοντος οὖν μου καθίσαι εἰς τὰ δεξιὰ μέρη οὐκ εἴασέν με,> ἀλλʼ <P ἐννεύει μοι τῇ χειρὶ ἵνα εἰς τὰ ἀριστερὰ μέρη καθίσω>.
διαλογιζομένου μου οὖν καὶ λυπουμένου
ὅτι οὐκ εἴασέν με εἰς τὰ δεξιὰ μέρη καθίσαι, λέγει μοι·
Λυπῇ, Ἑρμᾶ;
ὁ εἰς τὰ δεξιὰ μέρη τόπος ἄλλων ἐστίν,
τῶν ἤδη εὐαρεστηκότων τῷ θεῷ
καὶ παθόντων εἵνεκα τοῦ ὀνόματος·
<CP σοὶ> δὲ <CP πολλὰ λείπει ἵνα μετʼ αὐτῶν καθίσῃς>·
ἀλλʼ <P ὡς ἐμμένεις τῇ ἁπλότητί σου,
μεῖνον,
καὶ καθιῇ μετʼ αὐτῶν,>
καὶ ὅσοι ἐὰν ἐργάσωνται τὰ ἐκείνων ἔργα
καὶ ὑπενέγκωσιν ἃ καὶ ἐκεῖνοι ὑπήνεγκαν.
Holmes, M. W. (1999). The Apostolic Fathers : Greek texts and English translations (Updated ed.) (346). Grand Rapids, Mich.: Baker Books.
(9) <CP Then when I wanted to sit down on the right side, she would not let me,> but <P indicated to me with her hand that I should sit on the left side>.
Then as I thought about this and was sad
because she would not permit me
to sit on the right side,
she said to me,
“Are you sad, Hermas?
The place on the right side is for others,
who have already pleased God
and have suffered for the sake of the Name.
But [δε] <CP you fall far short of sitting with them.>
But [αλλα]
<P persevere in your sincerity,
as you are now doing,
and you will sit with them,>
as will all who do what they have done
and endure what they have endured.”
Holmes, M. W. (1999). The Apostolic Fathers : Greek texts and English translations (Updated ed.) (347). Grand Rapids, Mich.: Baker Books.
Can you get the sense of the difference between δε and αλλα? Heckert summarizes δε as a "marker of development". In this case, δε is a further development of the preceding statement describing the meaning of the right side. The right side is for others; Hermas has fallen short of the status the others have achieved. The status of the right side and reason for Hermas' exclusion is more clear with the δε statement. This instance of δε would probably normally be classed as a "continuative" or "copulative"; in this instance it represents a further development of the state of those on the right side. In short, those on the right have "already pleased God", Hermas hasn't done this yet, therefore he is not worthy.
After explaining the right side, and why Hermas can't sit there, the good lady offers him some hope. This is the counterpoint, the foil the αλλα statement ends up responding to. Αλλα sits in the middle. Heckert calls αλλα a "marker of contrast". Here, the contrast is between Hermas' falling short of those on the right side, and what Hermas can do to achieve right-side worthiness. In the CP, Hermas can't sit with those on the right side as he is unworthy of them. But in the P, the good lady offers Hermas hope! He can sit with them if he keeps up what he has started.
This gets to what has been cookin' in my thinking concerning the use of αλλα, from the discourse level. I've looked at a lot of instances of αλλα (approaching 1000!) in both the NT and the Apostolic Fathers. When αλλα is used, as Heckert maintains, there is contrast involved. But I also think that when αλλα is used, it is the statement that happens after the αλλα that is being made prominent. That is, in this case, the important bit isn't that Hermas can't sit on the right side. The important bit is that, if he does the right stuff, Hermas will be able to sit on the right side among the honored of God, those who have suffered for the sake of the Name.
In other words, I'm beginning to come to the conclusion that αλλα does involve contrast, as Heckert maintains. With αλλα, there always seems to be a pair of things, whether the comparison/contrast is in the same phrase, in the same clause, in the same sentence, in the same paragraph, or whether the αλλα appears to be contrasting previous content at the discourse level or even contrasting an underlying idea floating in the contextual ether. The αλλα makes the contrast explicit and the content following the αλλα is the more salient bit. It is the reason for the contrast, it is the important piece of the puzzle that keeps the discourse going.
At least, that's where I'm at now. These things may change.