Paul reminds them that he is not boasting as he tells them about what he has done through Christ.
Paul uses this question to emphasize that they are not bragging about themselves. AT: "We are not beginning to praise ourselves again" (See: rc://en/ta/man/translate/figs-rquestion)
Paul says this to express that the Corinthians already know about Paul and Timothy's good reputation. The question prompts a negative answer. AT: "We certainly do not need letters of recommendation to you or from you, like some people do" (See: rc://en/ta/man/translate/figs-rquestion)
This is a letter that a person writes to introduce and give their approval of someone else.
Paul speaks of the Corinthians as if they are a letter of recommendation. That they have become believers serves to validate Paul's ministry to others. AT: "You yourselves are like our letter of recommendation" (See: rc://en/ta/man/translate/figs-metaphor)
Here the word "hearts" refers to their thoughts and emotions. Possible meanings are 1) Paul and his coworkers are sure about the Corinthians being their letter of recommendation or 2) Paul and his coworkers care very deeply for the Corinthians. (See: rc://en/ta/man/translate/figs-synecdoche).
This can be stated in active form with "Christ" as the implied subject. AT: "which Christ has written on our hearts" (See: rc://en/ta/man/translate/figs-activepassive)
This can be stated in active form. AT: "that all people can know and read" (See: rc://en/ta/man/translate/figs-activepassive)
Paul clarifies that Christ is the one who has written the letter. AT: "you are a letter that Christ has written" (See: rc://en/ta/man/translate/figs-metaphor and rc://en/ta/man/translate/figs-explicit)
"Delivered" here is a metaphor for "brought." This can be stated in active form. AT: "that we brought" (See: rc://en/ta/man/translate/figs-activepassive) (See: rc://en/ta/man/translate/figs-metaphor).
Paul clarifies that the Corinthians are like a spiritual letter, not like a letter that humans write with physical objects.
This can be stated in active form. AT: "It is not a letter that people wrote with ink but a letter that the Spirit of the living God wrote" (See: rc://en/ta/man/translate/figs-activepassive and rc://en/ta/man/translate/figs-ellipsis)
This can be stated in active form. AT: "It is not a letter that people engraved on stone tablets but a letter that the Spirit of the living God wrote on tablets of human hearts" (See: rc://en/ta/man/translate/figs-activepassive and rc://en/ta/man/translate/figs-ellipsis)
Paul speaks of their hearts as if they are flat pieces of stone or clay upon which people engraved letters. (See: rc://en/ta/man/translate/figs-metaphor)