In this post, I’ll enumerate a few more reasons why I believe that when Paul states that Philemon and Onesimus are adelphoi en sarki that he does not mean that they are both human beings.
Third, Paul notes that Philemon’s and Onesimus’s sharing “brotherhood in the flesh” is a relationship that goes beyond what Onesimus and Paul share. In some way, that is, Philemon and Onesimus are adelphoi en sarki in a way that Paul and Onesimus are not. Paul states that Onesimus is “a beloved brother, exceedingly to me, but how much more to you, both in the flesh and in the Lord.”
If Paul meant to note that Philemon and Onesimus share a common humanity, this would make little or no sense. All humans share in a common humanity. But if Philemon and Onesimus are adelphoi en sarki with this phrase meaning “actual brothers in the flesh,” then Paul’s words make good sense here. Onesimus would clearly be dearer and more beloved as a brother to Philemon than to Paul.
Fourth, Paul might have used other expressions if he were going to insist on the common humanity of Philemon and Onesimus. In Acts 10, Luke narrates the meeting between Peter and Cornelius, who falls on his face upon meeting Peter. Peter lifts him up and says, “I also am a man” (v. 26). I’ve already mentioned Seneca’s 47th letter, in which he claims that all humans “sprang from the same stock, [are] smiled upon by the same skies, and [are] on equal terms with [those who are free], each breathing, living, and dying.” Further, all humans “spring from the gods” equally. While other examples could be cited it is unlikely that if Paul meant to note their common humanity that he would assert that Philemon and Onesimus are adelphoi en sarki—“brothers in the flesh.”
Finally, if Paul really wanted to communicate that these two were blood brothers, what other expression could he have possibly used other than adelphoi en sarki? That they are “brothers in the flesh” is simply the plainest and most straightforward way of understanding this expression, even though it then functions as a serious thorn in the flesh for the majority view of the scenario lying behind Paul’s letter.
For tomorrow, a few alternative scenarios that can account for Paul’s language in v. 16.
Faith Improvised 
chappymartin
In the Epistle to the Trallians Ignatius uses a very similar expression -“both in the flesh and in the spirit”. Ignatius was “refreshed in every respect” (Chapter XII)in both these ways. Of course this phrase modifies the verb “refreshed”, but it is very possible that there is a verbal meaning in saying “brother” in Philemon. In other words “acting as a brother both w/physical things like food and provisions as well as encouragement via the Spirit.”
Also it is not clear that it is only Philemon who can relate to Onesimus on that level of “flesh and spirit”. It is simply that Onesimus would be more involved in Philemon’s life because he was his slave.
So we could paraphrase verse 16 like this – “no longer as a slave but more than a slave, a close brother, like he was especially to me, but of course he would be like that to you even more so, both with everyday physical necessities and encouragement via the Spirit, because of him being your slave”
timgombis
It seems to me that this suggestion stretches the language too far from the natural sense.
If you heard someone say, “this man is my brother,” would you take him to mean something like, “this man is an encouragement to me?” Would his words not mean that the two people involved are actually brothers?
Looking more closely at the words Paul uses, I’m not sure how else they can be used.
chappymartin
Dr. Gombis,
By showing that quote from Ignatius I was able to show that natural sense of SARX can also entail “that which is external”. So I found your comment odd.
timgombis
It seems to me that Ignatius’ comment that he is refreshed “in the flesh and in the spirit” means that in both realms he is refreshed. But Paul doesn’t mention in vv. 15-16 of Philemon anything about being refreshed (he does say this earlier, actually). He mentions being “beloved brothers” in these two realms. It just seems the most natural meaning of “being a beloved brother in the flesh and in the Lord” to take it as being actual brothers and being fellow Christians. A verbal notion seems beyond the natural sense of Paul’s words here, at least to me.
Andrew
Paul was a Benjaminite. Do we know Philemon’s tribe?
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Joel Badal
I agree with you! Tim. I think the minority view needs more attention. The brother to brother or en sarke is important to note. Good reflection here. I raised your posts in one of my preaching courses and students were shocked of the possible different interpretation.
Blessings brother. Joel Badal, jbadal@crossroads.edu