What I’m noticing was the careful precision with which Peter describes the inspiration of the OT (prophets) in verse 20.
men spoke from God as they were carried along by the Holy Spirit (ESV)
Who caused the prophets to write what they did?
I distinguish two possible senses of cause.
- If we mean “cause” in the sense of “originated the message”, that would be just “God” – a reference to the Father.
- If we mean “cause” in the sense of “superintend the writing process”, that would be “the Holy Spirit”.
So let’s synthesise this. God the Holy Spirit ensured that the prophets wrote the message that God the Father wanted written. In this sense, the prophets wrote what both (indeed, all 3, but that’s not explicit in verse 20) persons of the godhead wanted. But within the Trinity, the Spirit submits to the Father’s wishes.