Albert Barnes Commentary Acts 18:15

"but if they are questions about words and names and your own law, look to it yourselves; I am not minded to be a judge of these matters." — Acts 18:15 (ASV)

Of words. A dispute about words; for such he would regard all their controversies about religion to be.

And names. He had probably heard something of the nature of the controversy and understood it to be a dispute about names; that is, whether Jesus was to be called the Messiah or not. To him this would appear as a matter pertaining to the Jews alone, and to be ranked with their other disputes arising from the difference of sect and name.

Of your law. A question respecting the proper interpretation of the law, or the rites and ceremonies it commanded. The Jews had many such disputes, and Gallio did not regard them as coming under his cognizance as a magistrate.

Look you to it. Judge this among yourselves; settle the difficulty as you can. Compare John 18:31.

For I will be no judge of such matters. I do not regard such questions as pertaining to my office, or deem myself called on to settle them.

The phrase "words and names" may be understood in connection with "Doctrines." For look you to it, compare John 18:31; Acts 23:29; and Acts 22:11, 19.