PAUL draws up a roll of honour and of dishonour of his friends.  Some are only names to us; of some, as we read the Acts of the Apostles as well as the Epistles, we get the occasional revealing glimpse. If we are allowed to use our imagination, we can reconstruct some of the stories. ~Barclay commentary

Beginning with verse 10 we see names named. They are:

Demas [De'mas]
Crescens [Cres'cens]
Titus
Luke
Mark
Tychicus [Ty-chi-cus]
Carpus
Alexander the coppersmith

What you will see in tonight's lesson and those through verse 14 is that they represent a cross-section of what was true in the church then and that same cross-section is still here today.

Now to the other commentaries beginning with the general and going to the specific. First the Matthew Henry Main which covers verses 11 and 12.

Luke however remained with Paul (2 Timothy 4:11-12), and was not this enough? Paul did not think it so; he loved the company of his friends. 2. He speaks respectfully concerning Mark: He is profitable to me for the ministry. It is supposed that this Mark was he about whom Paul and Barnabas had contended, Acts 15:39. Paul would not take him with him to the work, because he had once flinched and drawn back: but now, says he, Take Mark, and bring him with thee. By this it appears that Paul was now reconciled to Mark, and had a better opinion of him than he had had formerly. This teaches us to be of a forgiving spirit; we must not therefore disclaim for ever making use of those that are profitable and useful, though they may have done amiss. ~Matthew Henry Main

Quoted verse
Acts 15:39
And the contention was so sharp between them, that they departed asunder one from the other: and so Barnabas took Mark, and sailed unto Cyprus.

Here is the Matthew Henry Concise which covers verses 9-13

The love of this world, is often the cause of turning back from the truths and ways of Jesus Christ. Paul was guided by Divine inspiration, yet he would have his books. As long as we live, we must still learn. The apostles did not neglect human means, in seeking the necessaries of life, or their own instruction. Let us thank the Divine goodness in having given us so many writings of wise and pious men in all ages; and let us seek that by reading them our profiting may appear to all. ~Matthew Henry Concise

Now this from the Biblical Illustrator:

Only Luke is with me.—
The beloved physician

I. The inducements to remain with Paul.
1. There was the power of friendship. From the earlier references to Demas, we may conclude that he had been associated with the apostle in companionship in trial and labour. Intimacy and affection were motives to stay with him.
2. There was the sense of chivalry. However Demas might be tempted to go, a noble spirit would have said, Not now, when it is a time of comparative loneliness, need, and danger.
3. Interest in the faith. From his former relationship with Paul we must assume knowledge and admiration for the faith. He had seen Christianity, accepted it, and had been privileged to witness its power in the personal piety and devotedness of Paul.

II. The temptations to go.
1. The world’s temptation of Demas was probably not through her seductive glitter of pleasure and pomp, but through her frowns. The apostle was under a cloud. Few seem willing to take him by the hand. Notice how joyously he recognizes the courageous kindness of Onesiphorus [On·e·siph'o·rus] (2 Timothy 1:16-17).
2. Perhaps we may hazard a conjecture respecting the character of Demas. May he not have been one of those whose religious life is just strong enough, or rather weak enough, to live in a religious atmosphere, but utterly unable to live when unsupported by Christian society?
3. The way in which such a character would desert. Not openly, but by degrees. Excuses to omit dangerous duties, and even at the last perhaps only leave Paul on some plausible pretext to go to Thessalonica. The old apostle saw through it: “Having loved this present world.”

III. The contrasted conduct of Luke.
1. While Demas at Thessalonica, Luke at Rome. His helpfulness to Paul. The knowledge of the physician, with its frequently induced sympathetic power and insight. The spiritual refreshment of a brotherly heart. Demas lives the life of him who seeks to save life, but loses it in all its nobility and opportunities of doing kindness. Luke is ready to lose life, but saves its true vitality.

2. For the retrospect of Christendom tells us that Luke in his devotedness has saved his life, while Demas has lost it. The latter is a beacon-warning; the former a guiding light, a name in the Church—loved where Christ is loved, honoured where the apostle is honoured, for constancy, kindliness, and intrepid faith.

Learn therefore that—
1. Chivalry is not strong enough against the world-spirit.
2. A religion which is only dependent on the personal influence of others will prove faulty in the time of trial.
3. Thus only the inner strength supplied by Christ can keep us strong; not Paul, not Apollos, not the wisdom of men, but Christ. For the difference between Luke and Demas was not in outward circumstances. They were equally tried. It is Christ in us which is the hope of glory, a glory the earnest of which is seen in the scorn of earth and the triumph of faith over her frown or her smile. ~Biblical Illustrator

Here is another item from Biblical Illustrator:

[Luke] A faithful friend
A faithful friend will not forsake us in our deepest distress. A faithful friend—and such a one was Luke—loves at all times (Proverbs 17:17). Though Paul be a prisoner and ready to be martyred, yet Luke keeps with him still; though all forsake him, yet he will stick to him. Pot-friendship [incidental friends] will vanish, especially in adversity. Job (Job 6:15) complains of his friends that they had deceived him like a brook; they were not like a river which is fed by a spring and hath a perennity [puh-ren-ity] [continuing, enduring] of flowing, but like a brook which runs in moist times when there is least need of it, but in a drought it fails; like swallows which fly about us in summer, but in winter they leave us and hide themselves in hollow trees or the like. Such vermin abound which run to full barns, but outrun them when empty. Most worship the rising, few the setting sun. ~Biblical Illustrator

Quoted verses:
Proverbs 17:17
A friend loveth at all times, and a brother is born for adversity.

Job 6:15
My brethren have dealt deceitfully as a brook, and as the stream of brooks they pass away.

Now something on Mark from the Jamieson, Fausset, Brown. Mark is referred to in the MacLaren as, "The restored runaway." I stated to you that this list is a cross-section of individuals we see in the history of the Body of Christ. I love this story of Mark.

Take [Mark] — Greek, “take up” on thy journey (Acts 20:13-14). John Mark was probably in, or near, Colosse, as in the Epistle to the Colossians (Colossians 4:10), written two years before this, he is mentioned as about to visit them. Timothy was now absent from Ephesus and somewhere in the interior of Asia Minor; hence he would be sure to fall in with Mark on his journey.

Quoted verses:
Acts 20:13-14
13 And we went before to ship, and sailed unto Assos, there intending to take in Paul: for so had he appointed, minding himself to go afoot.
14 And when he met with us at Assos, we took him in, and came to Mitylene.

Colossians 4:10
Aristarchus [air'is-TAHR-kuhs] my fellowprisoner saluteth you, and Marcus, sister's son to Barnabas, (touching whom ye received commandments: if he come unto you, receive him;)

He is profitable to me for the ministry — Mark had been under a cloud for having forsaken Paul at a critical moment in his missionary tour with Barnabas (Acts 15:37-40; Acts 13:5, Acts 13:13). Timothy had subsequently occupied the same post in relation to Paul as Mark once held. Hence Paul, appropriately here, wipes out the past censure by high praise of Mark and guards against Timothy’s making self-complacent comparisons between himself and Mark, as though he were superior to the latter (compare Philemon 1:24). Demas apostatizes. Mark returns to the right way, and is no longer unprofitable, but is profitable for the Gospel ministry (Philemon 1:11). ~Jamieson, Fausset, Brown

Quoted verses:
Acts 15:37-40
37 And Barnabas determined to take with them John, whose surname was Mark.
38 But Paul thought not good to take him with them, who departed from them from Pamphylia, and went not with them to the work.
39 And the contention was so sharp between them, that they departed asunder one from the other: and so Barnabas took Mark, and sailed unto Cyprus;
40 And Paul chose Silas, and departed, being recommended by the brethren unto the grace of God.

Acts 13:5
And when they were at Salamis, they preached the word of God in the synagogues of the Jews: and they had also John to their minister.

Acts 13:13
Now when Paul and his company loosed from Paphos [PAY-fohs], they came to Perga in Pamphylia [pam-FIL-ee-uh]: and John departing from them returned to Jerusalem.

Philemon 1:24 ...we referenced this verse in our study of verse 10 when we were discussing Demas
Marcus [Mark, the nephew of Barnabas], Aristarchus, Demas, Lucas, my fellowlabourers.

Philemon 1:11
Which in time past was to thee unprofitable, but now profitable to thee and to me:

Note: Demas went from profitable to unprofitable. Mark went from unprofitable to profitable. Clearly this has been the case throughout the history of the Work.

Now to the specific commentaries.

These commentaries are in agreement this time to how the verse is broken down:

1] Only Luke is with me.
2] Take Mark, and bring him with thee.
3] For he is profitable to me for the ministry.

1] Only Luke is with me.

Only Luke is with me - Luke, the author of the gospel which bears his name, and of the Acts of the Apostles. For a considerable part of the ministry of Paul, he was his traveling companion, and we know that he went with him to Rome. ~Barnes Notes

Only Luke is with me - This was Luke the evangelist, and writer of the Acts of the Apostles, who was always much attached to Paul, and it is supposed continued with him even to his martyrdom. ~Adam Clarke

Only Luke is with me - The beloved physician, who wrote the Gospel that bears his name, and "the Acts of the Apostles", and was a constant companion of Paul's in his travels and sufferings: ~John Gill

2] Take Mark, and bring him with thee.

Take Mark and bring him with thee - John Mark, see the notes at Acts 15:37. He was the son of a sister of Barnabas, and had been the traveling companion of Barnabas and Paul. There had been a temporary alienation between Paul and him Acts 15:38; but this passage proves that that had been removed, and that Paul was reconciled to him. ~Barnes Notes

Quoted verses:
Acts 15:37
And Barnabas determined to take with them John, whose surname was Mark.

Acts 15:38
But Paul thought not good to take him with them, who departed from them from Pamphylia [pam-FIL-ee-uh], and went not with them to the work.

Take Mark, and bring him with thee - This was John Mark, the sister’s son of Barnabas, who, after having wavered a little at first, became a steady, zealous, and useful man; his name and conduct have been often before the reader. ~Adam Clarke

Take Mark, and bring him with thee - who might be at Ephesus, or somewhere in Timothy's way as he came to Rome. This seems to be the same with John Mark of Jerusalem, the son of Mary, the sister of Barnabas, and who was with Paul and Barnabas in their travels, and who parted from them at Pamphylia [pam-FIL-ee-uh]; on whose account, and for that reason, there was so great a difference between Paul and Barnabas, as to separate upon it; but now the apostle had entertained a better opinion of him, and was reconciled unto him, and was very desirous of his company and assistance; and which he had, Colossians 4:10 [referenced above]. ~John Gill

3] For he is profitable to me for the ministry.

For he is profitable to me for the ministry - In what way he would be profitable, he does not say; nor is it known why Mark was at that time with Timothy. It may be observed, however, that this is such language as Paul might be expected to use of Mark, after what had occurred, as recorded in Acts15:38 [mentioned above]. He felt that he was now about to die. If he suspected that there was on the part of Mark any lingering apprehension that the great apostle was not entirely reconciled to him, or retained a recollection of what had formerly occurred, nothing would be more natural than that, at this trying time of his life, Paul should summon him to his side, and express toward him the kindest emotions. It would soothe any lingering irritation in the mind of Mark, to receive such a message. ~Barnes Notes

For he is profitable to me for the ministry - Εις διακονιαν· For service; that is, he would be very useful to the apostle, to minister to him in his present close confinement. Some think that the apostle means his preaching the Gospel; but at this time, I should suppose, there was very little, if any, public preaching at Rome. ~Adam Clarke

For he is profitable to me for the ministry - that is, of the Gospel, to assist in preaching it. ~John Gill