Monday, March 16, 2009

metalinguistic predicates vs. object language operators

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.


jrshipley said...

Risking a suggestion too obvious: Quine's "Three Grades of Modal Involvement". Then I'd look at articles citing that.

cotnoir said...

It might be worth noting the following: with an object truth predicate that is "transparent" (in the sense that a sentence A and Tr`A' are completely intersubstitutible in any non-opaque sentential context) the distinction between predicate and operator is unimportant. One can always use the truth predicate to go back and forth.

Of course, the logic of such a truth predicate will have to be wildly non-classical -- see Field's "Saving Truth from Paradox" and Beall's "Spandrels of Truth" for systems which have such a predicate.