How does referential opacity affect statements about what people believe?

In the philosophy of mind, referential opacity describes a linguistic feature of propositional attitudes—such as believing, hoping, or fearing—that complicates how we describe what people think.12

When a statement is referentially opaque, the substitution of co-referential expressions (terms that refer to the same object) within a subordinate "that" clause can change the truth value of the entire sentence. For example, even if it is true that Peter believes that Walter Scott was a Scotsman, it may be false that he believes the author of Waverley was a Scotsman, despite the fact that Walter Scott and the author of Waverley are the same person.1

This phenomenon occurs because propositional attitudes possess intentionality; they are "about" things in a way that captures how an individual associates specific content with an object. Because different intentional contents can be linked to the same real-world entity, referential opacity prevents us from assuming that a person’s beliefs about one description of an object necessarily apply to all other descriptions of that same object.2