Commentaries:
Robertson's Word Pictures (NT)
I would fain have kept (eboulomhn katexein). Imperfect middle and present infinitive, "I was wishing to hold back." Again from the standpoint of the arrival of Onesimus.
In thy behalf (uper sou). So "in thy stead," "in place of thee."
He might minister (diakonh). Present active subjunctive (retained after eboulomhn) with ina, purpose continued, "that he might keep on ministering."
Other Robertson's Word Pictures (NT) entries containing Philemon 1:13:
Luke 4:42
Philemon 1:14
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