Update: the current consensus appears to be "habent papem." Can anyone confirm that? (I got a C in my one semester of Latin, and cattitude isn't home to ask.)
Well, the elementary Latin dictionary has nothing for "papa", only "papai" meaning "how strange!" and "pappas," a tutor, both of which are glossed first with Greek equivalents.
That may be, but I wouldn't trust a classical Latin dictionary with church Latin any more than I'd use a Shakespearean concordance to make sense of rap lyrics.
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Re: pontificem habent
From:
Re: pontificem habent