The SEP article on indexicals mentions a lot of the seemingly logical complications that arise in connection with them. Indexicals are also comparable to variables and hence objects of schematism, so again there seems to be a "logical" quality to them. The way Korsgaard and Darwall (for the latter, see his The Second-Person Standpoint) talk about the "personal perspectives" sounds like a discussion about some obscure alternative in a theory of logic.
More specifically, suppose that semantic reference is related to extensions of intensions and then quantification, all bundled up as a theory of existence-talk. Self-reference exists, and this seems like self-quantification, then, or so a circularly founded elementhood-like relation. Etc. and so forth and so on; so would it be possible to conceive of a "first-person logic" with a fundamental sentence of self-reference I ∈ I, i.e., "I am an element of myself"? Or things along that line, anyway. Is the difference between first=, second-, and third-person perspectives a logical difference, a cognitive/epistemic difference, a mathematical difference, something else, all of the above...?