I am interested in the distinction between metalinguistic predicates (sentential predicates) and object language operators (or sentential functors). This distinction seems to be very important for topics like (i) the Kripkean necessary aposteriori & contingent apriori, (ii) various implementations of two-dimensional semantics (especially metalinguistic versions?), (iii) issues surrounding context-dependence and monstrous operators, and probably many more things.
But I don't have much to say about it because I don't fully understand the distinction and how exactly metalinguistic predicates work (how are they treated in the formal system?) So this is just a plea for help. Where is this distinction discussed? Where are metalinguistic predicates discussed? I can't seem to find anything but perhaps I am searching for the wrong thing.
The distinction I have in mind is illustrated below:
(1) It is F that S.
(2) `S' is F.
(1a) It is necessary that two is prime.
(2a) `Two is prime' is necessary.
(1b) It is true that I am hungry.
(2b) `I am hungry' is true.
(1c) It is believed by John that Cicero is Tully.
(2c) `Cicero is Tully' is believed by John.
(1d) It is a priori that bachelors are unmarried.
(2d) `Bachelors are unmarried' is a priori.
(1e) It is true at 2:00am that its raining now.
(2e) `Its raining now' is true at 2:00am.
Any help would be greatly appreciated.