Burkitt:

11 For the grace of God that brings salvation hath appeared to all men, 12 Teaching us, that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world.

As if the apostle had said. Let all sorts of men, servants and masters, children and parents, old and young, discharge their duties faithfully to God and one another; for the grace of God,  discovered in the gospel, has appeared to all men, teaching them to deny all doctrines and practices which are ungodly, and all worldly lusts of sensuality, and that we should live soberly, with respect to ourselves, righteously and charitably towards our neighbor, and holily towards
God, in this present world.

Note here, 1. A choice and excellent description of the gospel; it is the grace of God, that is, the doctrine of God’s free grace and gratuitous favor declared in Christ to poor sinners.

Note, 2. The joyful message which the gospel brings, and that is, salvation: the gospel makes a gracious tender of salvation, and that universally, to lost and undone sinners.

Note, 3. The clear light and evidence that it doth hold forth this message in and by; it has appeared or shined forth like the day-star, or the rising sun.

Note, 4. The extent of its glorious beams, how far they reach, to all indefinitely. The grace of God bringing salvation has appeared unto all men; that is, it is tendered to all without restriction or limitation.

1. As to nations, Jew or Gentile.

2. As to persons, rich or poor, bond or free;

3. Without restriction, as to the number and greatness of their sins;

4. Without restriction, in reference to the degree of their graces.

Note, 5. The great lesson which the gospel leaches, negative and positive;

1. Negative, To deny ungodliness and worldly lusts; where, by ungodliness, understand all sins committed against the first table; by worldly lusts, all sins committed against the second table; called worldly lusts, because the object of them is worldly things, and because they are the lusts of worldly men.

2. Positive, to live,

1. Soberly: he begins with our duty to ourselves, then to our neighbor, and last of all to God, and so proceeds from the easier to the harder duties: and observe the connection, soberly, and righteously, and godlily, not disjunctively; as if to live soberly, righteously, or in pretence godlily, were sufficient. A sobriety in speech, in  behavior, in apparel, in eating and drinking, in recreations, and in the enjoyment of lawful satisfactions.

2. Righteously, exercising justice and charity towards our neighbor: he that is uncharitable, is unjust and unrighteous, and the unrighteous shall no more enter into the kingdom of God, than the unholy : and all a person’s pretences to godliness are but hypocrisy, without righteousness toward our neighbor.

3. Godlily; godliness as an internal and external part ; the internal and inward part of godliness consists in a right knowledge of him, in a fervent love unto him, in an entire trust and confidence in him, in an holy fear to offend him, in subjecting our wills entirely to him, in holy longings for the fruition and enjoyment of him. The external and outward part of godliness consists in adoration and bodily worship; this is due to God from us; he was the Creator of the body as well as of the soul, the Redeemer of the body as well as of the soul, and will glorify the body as well as the soul ; therefore we are to glorify God with our bodies, and with our spirits, which are the Lord’s.

Note, 6. The time when, and the place where, this lesson is to be learnt, in this present world. Here is the place, and now is the time when this duty of living soberly, righteously, and godlily in this present world, is to be performed by us. Learn, That a sober, righteous, and godly life, in this present world, is absolutely necessary in order to our obtaining the happiness and glory of the world to come. Inference: if so, what a cheat doth that man put upon his soul, who trusts to a death-bed repentance? Be it never so sincere, how can it be said to be a living soberly, righteously, and godlily, in this world, when just stepping into eternity?

William Burkitt, Expository Notes With Practical Observations on the New Testament (Philadelphia: Published by Thomas Wardle, 1835), 2:568. [Some spelling modernized; italics original; some reformatting; and underlining mine.]