What is the meaning of ἡ κοινωνία τῆς πίστεώς σου in Philemon 6? I have seen it rendered fellowship, sharing, communication, et cetera, but I haven't been able to clearly ascertain Paul's meaning—especially its connection to the following phrase, which we might translate that it will be effective to work in you the knowledge of all the good things you have in Christ. I am familiar with John's use of κοινωνία as fellowship or communion between a number of persons, human and divine. That seems to be the sense when Paul uses this word again in verse 17; but how is it best interpreted or translated in this verse?
For all the NT occurances of κοινωνία (and some translations) see here.
When Paul says κοινωνία (“fellowship” or “partnership”) he is using a word taken from the world of business. Think of partners today in a law firm. They share in the responsibility to make the business work, to make money. They share in the risk that it might fail—and if it fails then all will suffer. They share in the success that it brings, and the profits they make. They have a partnership because they all take responsibility and they all work towards a shared goal—not just because they meet together.
So the emphasis here is on the shared nature of the Christian faith, the partnership of the faith. Paul doesn't just want to say "your faith", but he somehow wants to convey the idea that Philemon's faith is the same as Paul's faith—and their shared faith makes them partners in Christ.
The NET Bible translates it well:
Murray Harris in his commentary gives an in-depth consideration of this question. The renderings he offers which seem most plausible to me are:
The option I have listed here as 5 is the one that Harris prefers, and Peter O'Brien as well, among others. Harris cites Romans 15:26; 2 Corinthians 8:4; 9:13; and Hebrews 13:16 to show that κοινωνία can mean charitable contributions or almsgiving. This argument makes some sense to me, since Paul speaks elsewhere of boasting about the generosity of Christians, and because it seems to be a reading which requires less contortion of phrase.