The following is an excerpt from the book, Slavery and Christianity (Paul’s Letter to Philemon)
by John Robbins (pages 25-26) :
Paul… wrote this letter as a form and model of church discipline. Again, unbeknownst to many commentators, it is Philemon the slave owner, not Onesimus the slave, who is doing something wrong. Paul writes to him and simultaneously to the church in order to correct him. Notice that Paul does not first approach Philemon privately, as churchmen today say is required, based on their inability or unwillingness to understand Matthew 18. The reason for Paul’s publicly correcting Philemon is obvious: The procedure for Matthew 18 is for private sins, not public offenses, and Philemon’s is a public offense. Philemon has not sinned against Paul privately; his actions involve several other people – most obviously Onesimus, but also, the other members of his household, the church that meets in his house, and Paul’s fellow laborers. By approaching Philemon as tactfully and firmly as he does, Paul furnishes an example of how elders should handle cases of public sins through church discipline.