David spoke about the resurrection of Christ, but it doesn’t necessarily mean that he understood the fuller meaning of what he was saying about himself. When God speaks through his prophets (i.e., Isaiah 7:14), there is a deeper meaning intended by God which isn’t intended by the human author (sensus plenior). When Luke wrote his gospel, he didn’t intend to say that Mary was immaculately conceived without the stain of original sin (1:28), but this is the deeper meaning intended by God.
This is what the Hebrew Bible reads: כִּי, לֹא-תַעֲזֹב נַפְשִׁי לִשְׁאוֹל; לֹא-תִתֵּן חֲסִידְךָ, לִרְאוֹת שָׁחַת.
*For Thou wilt not abandon my soul to the nether-world; neither wilt Thou suffer Thy godly one to see the *pit. - Psalm 16:10
In ancient Jewish belief in David’s time, the pit was the place in Hades/Sheol where wicked people go. It’s synonymous with the Christian concept of Hell. So what David intends to say about himself isn’t that God will not allow his body or that of the Messiah to decay in the grave. Verse 10 is part of a wider passage (vv.7-11), and so it should be read within the context of this passage. It’s primary fulfillment concerns David, who is speaking about himself in his relationship with God. The secondary fulfillment concerns Christ and is the underlying deeper meaning intended by God through the voice of his prophet. Peter is telling the crowd just that: There is a deeper meaning to what the Jews have understood David to mean which is fully realized in Christ.
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