Do most of the OPC congregations hold strictly to public church discipline or rebuke?
I would say yes to the above with some qualification.
Judicial discipline is required in churches where members are guilty of serious doctrinal divergence from the Bible or serious violations of the Law of God. "Judicial Discipline" is the process by which we deal with such offenses against God's Truth and His Law.
If offenses are private in nature (that is, between but a very few persons), trials may be held privately, and if there is genuine repentance, publicity may be avoided. However, apart from such sensitive exceptions, most discipline matters, though administered by the elders of the church (including ministers), are open to the membership.
As for "rebuke," that is one of the degrees of judicial censure. The order of censure is as follows in ascending order: Admonition, Rebuke, Suspension (from either office or the Lord's Supper), and Excommunication.
All censures can be lifted when demonstrable repentance is forthcoming. Some offenses which are for petty sins such as we all are subject to commit do not require formal discipline. And judicial discipline doesn't happen every day or every year in the average OPC. Yet a church which does not exercise discipline in matters serious is subject to eventual decay and even extinction as a true church of Jesus Christ.
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