For example, Luke tells us in Acts 14:21-23 that after they had proclaimed the good news to that city and had made many disciples, they returned to Lystra, then on to Iconium and Antioch. 22 There they strengthened the souls of the disciples and encouraged them to continue in the faith, saying, “It is through many persecutions that we must enter the kingdom of God.” 23 And after they had appointed elders for them in each church, with prayer and fasting they entrusted them to the Lord in whom they had come to believe.
Is this Luke projecting backwards, or noting what actually happened? For various reasons, including 1 Thessa 5, this is an adequate summary of Paul's modus operandi regarding the appointment of leaders. I also concur with Charles Barrett, Acts 1-14, pg. 687 who notes that “This was, no doubt, a kind of ordination, in that it gave some Christians a special kind of responsibility and service; cf. 6:6; 13:1-3; 20:17, 28.” Which brings us back to our text in Philippians 1. Does this refer to a position or function? And more importantly, can we separate these two ideas in the 1st century? The dictum, you are what you do, raises several questions at this point. O’Brien, Philippians, pg. 48, comments that:
It has been suggested that these titles are to be understood in a functional rather than an official sense, that is, describing an activity rather than an office (cf. Rom 12:8; Gal. 6:6; 1 Thess. 5:12). Here, however, he has in view particular members of the congregation who are specifically described and known by these two titles; otherwise the additions seem to be meaningless.
Dunn, Beginning From Jerusalem, pg. 1017-1018 cautiously notes that:
we learn that there were two groups of office-bearers, or probably more accurately, two leadership roles which had already emerged in Philippi – ‘overseers (episkopoi) and deacons (diakonoi)’ (1:1). It will hardly be coincidental that these become the titles for regular offices or roles in the churches of the next generation. Whether the structures of church organisation which we see in 1 Timothy 3 and Titus 1 were already emerging in Philippi, it is not possible to determine now. Certainly some leadership and administrative functions must be attributed to the episkopoi and diakonoi of Philippi. But how well defined or (alternatively) amorphous or embryonic these functions were some twelve years after the church began, and to what extent the use of these titles indicates a drawing on religious or secular precedents, we cannot tell.
This group was known in the capacity that they served for Paul takes it for granted that the Philippians will know who he is talking about when he greets this group(s). Paul did appoint leaders in newly founded/established communities of faith, and whatever specific functions or tasks these elders and deacons (or elders who serve, depending on how you translate it) they were distinct enough for Paul to offer them specific greetings, because they served specific/special functions.