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There may be others who remember an averagely diverting series about a gumshoe - if he wasn't a serving police officer - called Petrocelli. (Probably, I could find out, and even buy some DVDs on Amazon for old time's sake, but there's already too much else to watch.)
He made me think (remembering the name caused the thought) of petrochemicals and petroleum, as well as whether it was a plausible Italian surname, and that took me to what Jesus said to Peter:
Much theology wants to describe what happens when Jesus asks Peter three times if he loves Jesus (using different words for the verb 'to love', as C. S. Lewis and others have observed), and to call what Jesus then says to him the 'reinstatement' of Peter. Me, I don't know whether he was reinstated or not (i.e. whether he needed reinstating).
What I do know, as others point out, is the pun that comes out in the Latin version of what was said (presumably from the Vulgate, unless, at this point in the gospel (or is it in Acts?), Jesus utters the words in Latin), which is where we came from with these products and fuels derived from what is under the rock. That, and Jesus, referring to Peter as a foundation (taken as the basis for the authenticity of the Roman Catholic faith*) when he says that on him he will build his church.
I think that it it the word ecclesia that he would have used, from which we, in turn, derive Ecclesiastes and ecclesiastical law, but I really don't know what was meant: not, I suspect, a church as we have it to-day, even if a body of people (rather than a building), and also not, I suspect, the unbroken line of succession that is supposed to go back to Peter (as the basis for the Vatican and what foes with it)...
Funny where thinking about a detective's name takes you!
End-notesAccording to www.ewtn.com/jp2/papal3/holysee.htm, 'The Holy See consists of the Roman Curia and other offices and services which assist the Supreme Pontiff in the Petrine Ministry'.