1 Timothy 5:20

τοὺς ἁμαρτάνοντας. Those found sinning, sc. the presbyters, with whose discipline the whole section is taken up. So also ἐνώπιον πάντων does not mean that the whole congregation is to be assembled when a presbyter receives rebuke, but that the sentence shall be delivered in the presence of all his co-presbyters. The case is quite different from such a case as that contemplated in Matthew 18:15; for Timothy will act, not as a private individual, but as the representative of the Church and the official guardian of its discipline.

ἵνα καὶ οἱ λοιποὶ φόβον ἔχωσιν, that the rest also (sc. the other presbyters) may have fear; cp. Deuteronomy 13:11. The sentence is delivered in public for the sake of those who hear it.