John Calvin Commentary Colossians 4:14

"Luke, the beloved physician, and Demas salute you." — Colossians 4:14 (ASV)

Luke saluteth you. I do not agree with those who understand this to be Luke the Evangelist, for I believe that he was too well known to need such a designation, and he would have been distinguished by a more magnificent commendation. He would, undoubtedly, have called him his fellow worker, or at least his companion and sharer in his struggles. I rather conjecture that he was absent at that time, and that it is another person of the same name who is called a physician, to distinguish him from the other. Demas, whom he mentions, is undoubtedly the person about whom he complains — that he later deserted him (2 Timothy 4:10).

When he speaks of the Church in Nymphas's house, let us remember that, in the example of one household, a rule is laid down for what all Christian households should be — that they should be so many little Churches. Therefore, let everyone know that this responsibility is placed on him: to train up his household in the fear of the Lord, to keep it under holy discipline, and, finally, to form in it the likeness of a Church.