Jamieson, Fausset & Brown

It is conjectured that Luke "the beloved physician" (the same as the Evangelist), may have first become connected with Paul in professionally attending on him in the sickness under which he labored in Phrygia and Galatia (in which latter place he was detained by sickness), in the early part of that journey wherein Luke first is found in his company (Act 16:10; compare Note, see on Gal 4:13). Thus the allusion to his medical profession is appropriate in writing to men of Phrygia. Luke ministered to Paul in his last imprisonment (Ti2 4:11). Demas--included among his "fellow laborers" (Plm 1:24), but afterwards a deserter from him through love of this world (Ti2 4:10). He alone has here no honorable or descriptive epithet attached to his name. Perhaps, already, his real character was betraying itself.