Begs the question though has a simple, obvious meaning, "it demands [begs] that the question be asked". The only reason that "begs the question" is applied as a translation to petition principii is that beg used to be used in a different way, language has moved on.
If you mean assuming the premise, can't you just say that? Or if you like lording your immense brain over us inferior beings you can use petitio principii and we'll all bow down to your prowess and learnedness and continue to just call it assumption (or presumption, or where appropriate tautology; take your pick).
That said "I could care less" grates with me but I couldn't care less as I know what was intended by the context.
If you mean assuming the premise, can't you just say that? Or if you like lording your immense brain over us inferior beings you can use petitio principii and we'll all bow down to your prowess and learnedness and continue to just call it assumption (or presumption, or where appropriate tautology; take your pick).
That said "I could care less" grates with me but I couldn't care less as I know what was intended by the context.