Commentaries:
Jamieson, Fausset, and Brown
In order to depict his desertion, he informs Timothy that Erastus, one of his usual companions (Acts 19:22, possibly the same Erastus as in Romans 16:23, though how he could leave his official duties for missionary journeys is not clear), stayed behind at Corinth, his native place, or usual residence, of which city he was "chamberlain," or city steward and treasurer (Romans 16:23); and Trophimus he left behind at Miletus sick. (On his former history, see on Acts 20:4; Acts 21:29). This verse is irreconcilable with the imprisonment from which he writes being the first: for he did not pass by Corinth or Miletus on his way to Rome when about to be imprisoned for the first time. As Miletus was near Ephesus, there is a presumption that Timothy was not at Ephesus when Paul wrote, or he would not need to inform Timothy of Trophimus lying sick in his immediate neighborhood. However, Trophimus may not have been still at Miletus at the time when Paul wrote, though he had left him there on his way to Rome. Prisca and Aquila were most likely to be at Ephesus (II Timothy 4:19), and he desires Timothy to salute them: so also Onesiphorus' household (II Timothy 1:18). Paul had not the power of healing at will (Acts 19:12), but as the Lord allowed him.
Other Jamieson, Fausset, and Brown entries containing 2 Timothy 4:20:
Acts 20:4-5
Romans 16:23
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