Paul is calling them to a knowledge of the faith and an upright life. Once they have recognized the authority of the apostle and his worth in God’s sight, they will start to be concerned about themselves.
"But I hope that ye shall know that we are not reprobate." What followed naturally was to have said, "but if ye have become reprobate, yet we have not." He doth not, however, say so, for fear of wounding them, but he hints it in an obscure manner, without either making the assertion thus, "ye are reprobate," or proceeding by question and saying, "But if ye are reprobate," but leaving out even this way of putting it by question, he indicates it obscurely by adding, "But I hope that ye shall know that we are not reprobate."
Here also again, great is the threat, great the alarm. "For since ye desire," he says, "in this way, by your own punishment to receive the proof, we shall have no difficulty in giving you that demonstration." But he does not indeed so express himself, but with more weight and threatening. "But I hope that ye shall know that we are not reprobate." "For ye ought indeed," he saith, "to have known even without this what we are, and that we have Christ speaking and working in us; but since ye desire to receive the proof of it by deeds also, ye shall know that we are not reprobate."
[AD 384] Ambrosiaster on 2 Corinthians 13:6