This is inspired somewhat by some (somewhat maddening) comments at Metaphysical Mayhem and some (extremely enlightening) conversations with John Hawthorne.

Back in the day there was this old problem about how we could make sense of propositions like (1).

(1) The King of France does not exist.

Very roughly, the worry (or at least a worry) was that if this is to really express a proposition then the denoting term in it must denote something, and if it denotes something that something is probably at the very least King of France, whence we get the unwanted conclusion that either (1) does not express a proposition or France is a monarchy. Just as roughly, Russell solved this problem by noting that the (putatively) denoting term is a quantifier, not a proper name, and quantifiers can make contributions to propositions without actually denoting anything. So far, so good. The problem comes with (2), (3) and similar sentences.

(2) Leopold Bloom does not exist.
(3) “Ern Malley”:http://www.ernmalley.com/ does not exist.

I’m inclined to think that both of these claims are false, but then I have a very expansionary ontology. I certainly think it’s an open ontological possibility that they express true propositions. But now we can run the same problem. Back in the day some people offered the same solution as Russell did. Names, they said, were disguised descriptions, so it’s possible that they can make meaningful contributions to propositions without actually denoting. Nowadays orthodoxy is that that’s wrong, and names are directly referential.

I want to revive a version of the quantificational view. But I don’t want to say that names are descriptions. Names, I’ll assume, are normally directly referential. I claim (completely unoriginally) that this is consistent with the (well-motivated) view that in some contexts they are syntactically quantificational. I also claim (I think a little more originally, though I make no promises here) that being in front of the predicate _exists_ or a modification of this is one of those contexts. This all gets a bit complicated, so it’s mostly going below the fold.

_Type-Raising_
Few philosophers talk about sentences like (4), but I think they should.

(4) Leopold Bloom and several of his friends liked drinking wine.

I haven’t done a survey, but I bet a disturbing number of philosophers think the analysis of (4) is something like (67).

(67) Leopold Bloom liked drinking wine and several of his friends liked drinking wine.

Now (67) may or may not be truth-conditionally equivalent to (4), but it certainly isn’t the correct analysis of it. In (4) the _and_ connects two subject-terms, in (67) it connects two sub-sentences. The standard Montagovian analysis of this takes the difference here seriously, and says that in (4) we have a compound subject.

This leads to a small technical problem. ‘And’ normally only joins terms of the same syntactic type. And ‘Leopold Bloom’ is of type e (i.e. an entity), while ‘several of his friends’ is of type (e/t)/t (i.e. a function from functions from entities to truth values to truth values). It looks like we should have a type mismatch in (4). The standard solution is that in (4) ‘Leopold Bloom’ _type-shifts_ into something of type (e/t)/t. That is, it type-shifts into the type that is normal for quantifiers.

My principal claims here are two.

* When a name type-shifts so it is of type (e/t)/t, what it contributes to the proposition the sentence expresses is not an individual but, as the syntax suggests, a second order function (i.e. a function from functions from individuals to truth values to truth values.) or a class or in general something other than the (alleged) denotata of the name.
* In a sentence of the form _NN exists_, the name _NN_ type-shifts so it is of type (e/t)/t.

These claims would have the nice result that (2) and (3) can express propositions, even true propositions, even if Leopold Bloom and/or Ern Malley do not exist. There are two other reasons to like this move.

_Scope Variation_
Intuitively, (2) is true in some contexts and false in others. When we are talking about the inhabitants of the concrete, material world, (2) sounds true. When we are talking about which fictional characters really exist, and which are merely the products of confused students’ imaginations, (2) sounds false. Peter van Inwagen has made this point in several places, but he puts it down to ambiguity/contextual variation in the meaning of ‘exists’. I think van Inwagen is right about the data, wrong about the explanation.

Very roughly (and I need to find something more careful here because I think there’s counterexamples to what follows) _exists_ is always a function from things like quantifiers (i.e. things of type (e/t)/t)) to truth-values, a function that returns _true_ if the domain of said quantifier is non-empty, and _false_ if it is. (The worry is about sentences like _Every unicorn exists_. I’m not yet sure how to deal with them.)

The scope of a quantifier can be determined by context. Just which bottles are being quantified over in _Every bottle is in the corner_ is a matter of context. Similarly, just which Leopold Blooms are being quantified over in _Leopold Bloom exists_ is, I say, a matter of context. In some contexts it includes Joyce’s famous protaganist, and the sentence is true, in others it does not, and the sentence is false. I think this is the simplest explanation to date of the intuitive contextual variation of sentences like (2).

_What Can’t_ Exist
The following is entirely due to John Hawthorne. (Except for errors of transcription and the like.)

If _exists_ was a normal predicate you’d expect to be able to get a well-formed sentence out of putting it after any referring term. (This isn’t a universal principle, but it’s hard to see how anything of the form _R exists_ could be ill-formed because it contains a category error or anything of the kind.) But this isn’t what we find. In each of the following, the (b) sentence is ill-formed.

(5) a. Here is where the pilgrims landed.
b. *Here exists.
c. Plymouth Rock exists.

(6) a. Three is the smallest prime.
b. *Three exists.
c. The number three exists.

(7) a. Red is my favourite colour.
b. ??Red exists.
c. The colour red exists.

This data cries out for explanation. I (or at least John) have a partial explanation. _Exists_ is of the type ((e/t)/t)/t, and the subjects in the (b) sentences cannot type-shift to be of type (e/t)/t. There is independent evidence for this claim, in that the terms above cannot conjoin easily with quantifiers.

(8) a. ??Here and many other places in New England are popular with tourists.
b. Plymouth Rock and many other places in New England are popular with tourists.

(9) a. ??Three and many other numbers are in Plato’s heaven.
b. The number three and many other numbers are in Plato’s heaven.

(10) a. ?Red and two other colours are on the Australian flag.
b. The colour red and two other colours are on the Australian flag.

The data here are not rock-solid, though I think the case of ‘here’ is fairly strong. And I don’t have a theory about what unifies the category of words listed here. But I do think that a unified explanation of the phenomena is in order, and the hypothesis that _exists_ requires its subject to type-shift offers the hope of such an explanation. Note that we don’t need to make _any_ metaphysical assumptions in order to run this argument. This is a purely syntactic argument that we don’t need to postulate denotata for a name _NN_ in order for the sentence _NN exists_ to express a proposition.

_Conclusion (for now)_
There is a lot of literature on type-shifting, and on when an expression can be properly regarded as a quantifier rather than a directly referring expression. Before I do anything more with this idea I’ll have to, er, read that literature and see if it knocks my little proposal out of the water. And I’ll have to check for originality. But compared to the treatments I know about that are on the table for (2) and (3), I think this one has a lot of virtue.