Ben makes three somewhat related points. I have comments only for the two first.
The first point
Here’s what he had to say:
(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.
I certainly did not try to get into problems by using indexicals (such as pronouns). It seems that I can avoid this issue by simply choosing another example (more about this in the second comment) or avoiding indexicals at all. I suppose I could just change it to:
S. It is logically possible that Emil Kirkegaard exists and that Emil Kirkegaard does not exist.1
(Though as for the problems with being wrong about “I exist” (the proposition!), see this discussion over at Philosophyforum.com. There is something curious about the phrase “cannot be wrong” when applied to truth bearers. It is not clear how to properly understand it. I made two quick analyses of the concept in this essay.)
The second point
Ben’s second point:
(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.
I do not believe in “noneism” (never heard of it). I only write it like that because it is simpler and not confusing in most cases. Here are two other ways to formalize the same sentence (original (S)):
(Where “Ux” is some unique description of me. I will just translate it to “is Emil Kirkegaard”, alternatively it could be “fits the unique description of Emil Kirkegaard”.)
So, in predicate logic english-ish:
1*. It is logically possible that there exists at least one person such that that person is Emil Kirkegaard and it is logically possible that it is not the case that there exists at least one person such that that person is Emil Kirkegaard.
2*. It logically possible that (there exists at least one person such that that person is Emil Kirkegaard and that it is not the case that there exists at least one person such that that person is Emil Kirkegaard).
The sheer length of this is why I usually use ‘simplified predication’ when formalizing.
The sentence may have been more ambiguous than I originally thought. How about this interpretation?:2
3. 1. ◊(∃x)(Ux)∧¬(∃x)(Ux)
3*. It is logically possible that there exists at least one person such that that person is Emil Kirkegaard and it is not the case that there exists at least one person such that that person is Emil Kirkegaard.
That’s just applying the predicate “it is logically possible” to the first part and not the second.
1Philosophers have some weird history for using their own names in examples. I shall follow their example. Just for kicks.
2Is there any convention about what to do when both asking a question and mentioning things that require a colon (:)?