As I think through the dispute I think really what we’re getting at is Peirce’s notion of the Universe of Discourse. The question then becomes what distinguishes or differentiates one universe of discourse from an other? We recognize that there is not just one universe of discourse. For Peirce to denote is to put the sign in relation to the object of common communication. That is, a universe of discourse.
We can of course distinguish two universes such as the universe in which Superman exists and the universe (such as our own) in which he does not. But as soon as we concede this distinguishing universes it seems to me much of what I said follows as a corollary.
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