For you will not abandon my soul to Sheol,
or let your holy one see corruption (Ps 16:10).
I'd like to comment on this verse:
i) Peter cites this passage as a prooftext for the Resurrection of Christ. Many people construe it along the same lines as the incorruptible body of favored saints in Catholic piety. However, I seriously doubt that's what's in view:
ii) On that interpretation, David implies that if you discovered his tomb centuries later, you'd find his body intact. But surely David's concern is not what happens to his body when he dies, but what happens to David when he dies. What fate awaits David on his deathbed? If David passed into oblivion at the moment of death, but his body survived incorrupt, how would that be any comfort to David or his readers? So I think that misses the point.
iii) Moreover, that's reinforced by the synonymous parallelism, where the second clause is roughly equivalent to the first clause: "You will not abandon my soul to Sheol (or the grave)." The passage concerns the afterlife.
Normally, dead people stay dead. They don't return from the grave. As a result, their body decays.
iv) And that's what lends force to Peter's argument. At the time he spoke, David had been dead for about a thousand years. He was long gone. He didn't return from the grave.
Moreover, even if (ex hypothesi) the ghost of David appeared to some people, Jews believed in ghosts, so a Davidic apparition wouldn't be extraordinary. Hence, the passage demands something different. Something stronger. A personal resurrection.
v) So how can this be about David? It can't. It must be about someone else. It must be Messianic.
And there's a link between David and the Davidic messiah. Among other things, the messiah is David's heir. So he inherits the promises made to David.
vi) A stock objection to Peter's interpretation is that his argument turns on a particular word, and his argument only works in the LXX. The Hebrew word means "pit," not "decay".
However, scholars like Waltke, Reinke, and Vaccari, have argued that the Hebrew word sahat has two meanings: "pit" or "decay". Cf. NIDOTTE, 4:1113; B. Waltke & J. Houston, The Psalms as Christian Worship: Hearing the Voices of the Psalmist and of the Church in Response (Eerdmans, 2010), 323-24n76.
Furthermore, the meaning is context-dependent. As Waltke explains: with verbs of motion such as "descent" it means "pit"; with verbs of sense such as "see" it means "decay." B. Waltke, "Why I have Kept the Faith," I (Still) Believe: Leading Bible Scholars Share Their Stories of Faith and Scholarship (Zondervan 2015), 241.
Since the verb in Ps 16:10 is a verb for sight, that selects for "decay" rather than "pit".
vii) At best, Peter only knew a smattering of Hebrew. (And Luke knew no Hebrew.) His argument turns on the precise nuance of a Hebrew word. And, as it turns out, that's exactly right.
viii) An unbeliever might deny that the Psalm is actually Davidic. But even if we grant that denial for the sake of argument, it makes no substantive difference. Whoever the Psalmist was, when he died, he didn't return from the grave. So it can't refer to the Psalmist.
ix) An unbeliever might claim the Psalmist was wrong. At the time of writing, he was still alive. But his hope was misplaced.
But if the Psalmist was obviously wrong, why did Jews include it is the Psalter? Unless they thought it referred to someone other than the Psalmist.