Shared ground
Paul treats “letters of commendation” as a normal social tool in his world, but not the right measure of his credibility with Corinth (v.1). Instead, he points to the Corinthians themselves as the evidence: they are his “letter,” tied to him by deep personal concern (“written in our hearts”) and visible to outsiders (“known and read by all,” v.2).
Paul also redirects attention away from himself. The Corinthians are ultimately “a letter of Christ,” with Paul and his coworkers serving as the channel through which that letter was delivered (v.3). The “writing” that matters is God’s Spirit producing real, internal change (“on hearts”), contrasted with external writing (“ink”) and “stone tablets” (v.3; compare Exodus 31:18).
Where interpretation differs (only where needed)
One question is what “written in our hearts” mainly emphasizes (v.2). Some read it mostly as Paul’s affection and personal investment in them (they are “in his heart”). Others think it mainly points to the Corinthians’ inner transformation (the message “written in their hearts”), with “our hearts” functioning as a close relational way of speaking about the shared community.
Another question is the scope of “known and read by all” (v.2). Some understand it as the local public in Corinth—neighbors, visitors, and critics who can observe the community. Others take it more broadly as the wider reputation of the church and Paul’s work beyond Corinth.
Why the disagreement exists
Paul mixes metaphors and relationships: the Corinthians are “our letter,” yet also “a letter of Christ,” and the writing is both internal (“hearts”) and publicly legible (“read by all”). Because the language is compressed, readers weigh different parts of the imagery (Paul’s relationship, the Corinthians’ change, public perception) differently.
What this passage clearly contributes
Explicitly, the text claims Paul does not accept credential papers as the basis for his legitimacy with Corinth (v.1). It also claims the Corinthians’ lived reality is a public “letter” that functions as evidence of his ministry (v.2). Finally, it grounds that evidence in Christ’s ownership and the Spirit’s work rather than Paul’s self-promotion: Christ is the source, Paul is the servant-agent, and the Spirit is the one who “writes” on human hearts (v.3).