Indeed, but the issue here is not whether Peter Parker is identical with Spider-Man, but whether two beliefs are the same. The conventional way of looking at it

Indeed, but the issue here is not whether Peter Parker is identical with Spider-Man, but whether two beliefs are the same. The conventional way of looking at it is that talking about what people believe or feel, rather than how the world is (putting aside the complication that this is a fictional character!) creates an "intensional context", in which the substitutability of one name or noun phrase for another is not a given, even if they designate the same thing. For materialists, it is not difficult to see that the brain of Aunt May believing only "Spider-Man fights crime" would be in a different state than if she also believed "Peter Parker fights crime", as going from the former to the latter would require some physical change.