Matthew Poole and continuators on Colossians 4:14

14 Luke the beloved physician , and Demas greet you .

Whether this Luke was the same with him that penned the Gospel and the Acts, because the Apostle here gives him no higher a commendation, some doubt? But others, and the most, conclude that as Matthew from a publican, became an Apostle, and others from fishers of fishes, fishers of men, so Luke from a Physician of the body, became a Physician of Souls, and that this was the very person who was Paul's perpetual and individual compantion in his Travels, 2 Tim. 4.11. Philem. 24. considering from his style he was an excellent Graecian (very fit for a Physician) and made use of proper medical terms, Act. 15.39. & 17.16. and here the Apostle calls him beloved as he had done Tychicus, v. 7. and elsewhere his fellow labourer who onely of those that were not Prisoners stuck to him, 2 Tim. 4.11. some think it to be Luke whose praises are celebrated in the Gospel or Evangelical Churches, 2 Cor. 8.18. the others would have that to be Barnabas, or some other; his practising of Physick was no more inconsistent with being an Evangelist than Paul's Tent-making with being an Apostle, 2 Thess. 3.8.

He adds a third in this Salutation from others, and that is Demas who hitherto did persevere, and that as one of his fellow labourers, Philem. 24. Though it should seem afterwards when the persecution grew hotter, he did for some worldly respect, leave Paul, and depart unto Thessalonica, 2 Tim. 4.10.