Kirkegaard On The Sentence Theory Of Truth-Bearers

[UPDATE: Emil responds here. I'll just note that by "noneism" I mean the position usually called "Meinongianism," which is simply the view that some objects have the property of non-existence. The term was coined, I think, by Richard Routley in "Exploring Meinong's Jungle," and also used by Graham Priest to describe his version of the thesis. I guess I probably just should have said "Meingongianism." The only reason I didn't was that I wanted to make clear that I was talking about the general claim, not Meingong's specific version of it.]

Emil Kirkegaard has been posting about truth-bearer theory over at Clear Language, Clear Mind. In this post, he mentions dialetheism.

He's been arguing for a theory according to which propositions are the primary bearers of truth. In the post in quest, he objects to sentence theory on the basis of ambiguity, suggesting (if I'm understanding his argument correctly) that since sentences can be ambiguous, if they are the primary bearers of truth, truth itself must be ambiguous and we have to give up on classical logic.

Here's his example:

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Consider the sentence:

S. It is logically possible that I exist and that I do not exist.

Is (S) true or false? I can’t tell because it is ambiguous. If you don’t see how it is ambiguous try deciding whether the predicate “It is logically possible” applies to only “I exist” or to both “I exist” and to “I do not exist”. Which is it? Logic helps us see the difference. We may formalize the two interpretations like this:

1. ◊Ei∧◊¬Ei
2. ◊(Ei∧¬Ei)

(Where “Ex” means x exists, “i” means I.)

We can translate these into english-ish:

1*. It is logically possible that I exist and it is logically possible that I do not exist.

2*. It is logically possible that (I exist and that I do not exist).

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His line of thought seems to be that if this is just an ambiguity about which proposition the sentence expresses, and propositions are the things that are ultimately true or false, then what we could call the "Classical Principle" (Bivalence + Monaletheism) still holds--"every proposition is either true or false, but not both." If, on the other hand, the sentence itself is what's true or false, the "Classical Principle" formulated for sentences--"every sentence is either true or false, but not both" doesn't seem to hold. He speculates that perhaps we could say that S is both true and false, or that it's neither true nor false. Either way, the Classical Principle (and, given some basic assumptions about the relationship between falsehood and negation, etc.) classical logic itself, seems to be out the window.

I've got some further thoughts about this, but this post is going to be a bit hurried, so I'll just stick with making three quick points about this example. None of these really touch on the central issue--are sentences the bearers of truth?--but I'd be happy to get in to that in the comments if anyone's interested. Meanwhile, here's what I've got:

(1) The indexical phrasing might make things a bit confusing in this specific case. On one level, it's surely contingent that Ben Burgis exists, but one might argue that it's logically impossible that any instance of "I exist" tokened by anyone could ever be false. What one thinks about what to ultimately make of this might depend on what one thinks about the widely alleged essentialness of indexical claims--if "I exist" really *means* Ben Burgis exists, that's one thing, but given that I could forget that I'm Ben Burgis but still be quite sure that I exist, there are tricky issues at play here.

(2) Another complicating factor about the example is that existence is being treated as a predicate, which seems to assume "noneism," the view that there are objects that have some properties (like being referred to) but which don't exist. Anyone who agrees with Quine's claim in "On What There Is?" that the answer to the question of ontology ("what exists?") is "everything" would, while agreeing that it's possible for there to be no object that Ben-Burgisizes, strong object to ◊¬Ei.

(3) Where "I exist" is interpreted as "Ben Burgis exists," and we're assuming noneism, the "both" option seems very strange. After all, the "false" part comes from the alleged logical impossibility of my both existing and not existing, and anyone who thought that "both" is a conceptual possibility (i.e. who was a dialetheist) would pretty much by definition think that it was at least *logically* possible for me to both exist and not exist, even if as a matter of fact this never happens. Or maybe not...any dialetheists out there with specific reasons for thinking that contradictions about *existence* are logically impossible?