But it is not just generic peace that is to be the umpire of our hearts, but the peace of Christ. Is there something distinctive about the "peace of Christ" that we should consider? It is Christ who said, "Do not think that I have come to bring peace to the earth. I have not come to bring peace but a sword." (Mt 10:34) But it is specifically the peace of Christ not just peace that is to be umpire.
Also, it is Jesus who said to His disciples, "Peace I leave with you; my peace I give to you. Not as the world gives do I give to you. Let not your hearts be troubled, neither let them be afraid." (Jn 14:27) Just what kind of peace is it that Jesus gives us, that can be designated as the peace of Christ as distinct from the peace that the world might give us.
Just making peace, presumably an absence of conflict, untroubled by differences in doctrine, teaching, or faith, our umpire does not appear to do justice to what Paul said here.
What struck me about this is that it is not doctrine, or teachings, or grace, or faith, that should be the "umpire" of our hearts, but "peace." If everyone thought, "How is peace determining what I say or write?" "How does peace determining my response?" "How am I supporting the unity of the one body?" Things might be a bit different.
This appears to me to be an overly simplistic take on the passage, especially when taken in context.
Should we consider this verse, and the conclusion that it is simply peace, rather than doctrine, teachings, grace, or faith, that is to be our umpire, in isolation from the rest of the passage?
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16Let the word of Christ dwell in you richly, teaching and admonishing one another in all wisdom, singing psalms and hymns and spiritual songs, with thankfulness in your hearts to God.
17 And whatever you do, in word or deed, do everything in the name of the Lord Jesus, giving thanks to God the Father through him."
In the very next verse, Paul admonished us to let not only the peace of Christ, but the word of Christ dwell in our hearts, and we are to teach and admonish one another. That would appear to say that we should also teach each other and even correct and admonish each other, which all implies doctrine (which, after all is simply a more formal teaching) is important. Isolating verse 15 from the prior and succeeding verses does not seem a good interpretive strategy.