We could easily think of integrity ("righteously" in NKJV) strictly in terms of law and pursue it no further. But when we see how this word is translated elsewhere, we add a dimension that helps us better understand how we should act toward our fellowman.
In Luke 23:41 and I Thessalonians 2:10, the same word is rendered "justly," meaning right, proper, or fair. This is the adverbial form of the Greek dikaios, meaning "to be conformed to that which is right," which Plato said is inseparably bound to the word translated "sober" above. A person who is dikaios neither selfishly nor forgetfully transgresses the bounds of what is right. He gives everyone his due.
To Christianity, this translates into "my duty is my right." This concept branches out into areas of life like civility, consideration, concern, and respect and has little or nothing to do with what we normally consider as "law." I Corinthians 13:4-7 is a clear example of such instruction.
The grace of God obligates us to these duties in our relationships with others. To conform to them fulfills what Paul means by living with integrity in Titus 2:12. It encompasses keeping the commandments, of course, but it also involves such virtues as probity, honesty, goodness, irreproachability, fairness, nobility, and being just and sensitive to another's needs, including giving correction in kindness and mercy (Galatians 6:1-2).
John W. Ritenbaugh
Five Teachings of Grace