Which witch is which? Exotic objects and intentional identity

This paper is about intentional identity, the phenomenon of intentional attitudes (beliefs, desires, etc.) having a common focus. I present an argument against an approach to explaining intentional identity, defended by Nathan Salmon, Terence Parsons and others, that involves positing exotic objects (e.g. mythical objects, merely possible objects or non-existent objects). For example, those who adopt this sort of view say that when two astronomers had beliefs about Vulcan, their attitudes had a common focus because there is an exotic (abstract, non-existent or merely possible) object that both of their beliefs were about. I argue that countenancing these exotic objects does not help us explain intentional identity.