v1-4: Paul's third visit, and his second letter. He had repeated his warnings; some had sinned, and not repented, "I will not spare"; he would bring proper discipline. He felt obliged to speak firmly where they had persisted in their sins.

The false apostles had claimed to speak in Christ's name. Paul was thus challenged to respond. His response would be with a powerful rebuke. The power of God would be manifested in rebuke and discipline. There is a suggestion that there would be some sign of God's power, as part of the rebuke for sins. There is also some indication that the false apostles failed to rebuke open sins, and failed to expose hidden sins.

v5-6: The test of faith, that Jesus Christ is in you. Paul is looking for clear evidence of faith. Paul is willing to apply the same test to himself, and those he was working with. His clear expectation was that they would be found in Christ. The alternative was "that we have failed the test", or been disqualified, or reprobate (AV), see Is 1.22. The Gk word signifies dross or slag that rises to the top of a metal furnace when it is heated, and is discarded as useless.

v7: Paul's prayer for them was simple, that you do no evil. This is consistent with the previous verses. Ultimately this is more important than whether they accepted Paul's apostleship, "though we may seem to have failed"; they may reject Paul's leadership role, but they must not reject the Lord.

v8: The truth of God will be vindicated, and our lives and ministry must be submitted to it.

'Nothing of significance, nothing of consequence, nothing of importance, nothing that is lasting, nothing that matters can truly be accomplished which is "against the truth." (Dave Breese, Seven Men Who Rule the World from the Grave')

v9: Desire for maturity in them, which is produced by obedience and faith. The word "perfection" means fit, or suitable; mature ordered lives. Paul continues the prayer in v11.

v10: Paul had no wish to be firm or harsh with the Corinthians. His hoped that his firm letter would produce the required repentance before he arrived.

v11: Again, our aim should be perfection, as in v9. Paul had spoken the words of God; the Corinthians now had to respond.

v12-13: Paul's rebukes are not inconsistent with his love; he still prays for them, and genuinely wishes God's blessing upon them.

v14: Paul closes with a further prayer, asking for the Triune God to bring great blessing upon them.