Figure Analysis
Paul's letter to Philemon is addressed to Philemon (duh), but it also pretty heavily concerns his runaway slave, Onesimus. Hey, it's his freedom hanging in the balance, so we'll forgive Onesimus for making sure Paul crossed his T's and dotted his I's.
All about Phil
Paul starts out by addressing Philemon, who's a pretty model Christian:
I always thank my God because I hear of your love for all the saints and your faith toward the Lord Jesus. I pray that the sharing of your faith may become effective when you perceive all the good that we may do for Christ. I have indeed received much joy and encouragement from your love, because the hearts of the saints have been refreshed through you, my brother. (Philemon 1:4-7)
Paul also implies that he personally converted Philemon to Christianity (Philemon 1:19), so they're obviously old friends. This Philemon sounds like a good dude.
Well…maybe not. See, in addition to being an awesome Christian, Philemon also owned slaves. One of those slaves was named Onesimus.
The One and Only Onesimus
It's clear that Onesimus is a slave owned by Philemon. Onesimus meets up with Paul in prison and, after talking to Paul, decides to convert to Christianity. Paul calls Onesimus "my child" and "my own heart" (Philemon 1:10, 12), so apparently they've gotten pretty tight behind bars.
Onesimus even has an interesting slave name: it means "profitable" or "useful". That means Paul is looking to pack in the puns when he says, "Formerly he was useless to you, but now he is indeed useful both to you and to me" (Philemon 1:11). Basically, Paul means that, now that Onesimus is a Christian, he's actually earned his name by being useful to God.
But there's one big question still: why exactly is Onesimus with Paul in prison? Most scholars think he's a runaway slave (source, 1146) but some folks have questioned this. Why would a slave run away to a prison? Maybe Onesimus has actually been sent by Philemon to help Paul out while he was in prison (source, 1233). In the course of serving Paul, Onesimus was converted.
But then why does Paul need to encourage Philemon to "welcome" Onesimus back? Would Philemon be mad that Onesimus accepted Jesus? And why would Paul offer cover for Onesimus "if he has wronged [Philemon] in any way, or owes [him] anything" (Philemon 1:18)? Something's fishy.
Master and Slave in Christ
In any case, it's clear from the letter that Paul is really interested in one question: how should Philemon and Onesimus relate to each other now that they're both "in Christ"? Back in Galatians, Paul said, "there is no longer slave or free" (Galatians 3:28)…but did he mean that literally?
It seems he did. Paul doesn't expressly come out and say it, but he strongly hints that Philemon and Onesimus can't go back to the same master/slave relationship:
Perhaps this is the reason he was separated from you for a while, so that you might have him back forever, no longer as a slave but more than a slave—a beloved brother—especially to me but how much more to you, both in the flesh and in the Lord. (Philemon 1:15-16)
Paul envisions a Christian community where masters and slaves are now as close as family. He encourages Philemon to "welcome [Onesimus] as you would welcome me" (Philemon 1:17). Philemon should see Onesimus as his equal, not his inferior (source, 1146).
So how did this all work out? No one knows. Since we don't know where and when this letter was written, we can't be sure how things panned out for Paul. Did Philemon ever "prepare a guest room" for Paul? And, most importantly, did Philemon let his brother in Christ go?
We've got our fingers crossed on that last one.