You are exactly right. The natural language version is ambiguous. c.f.: "Aunt May believes that Santa Claus fights crime." Philosophers actually argue about

You are exactly right. The natural language version is ambiguous. c.f.: "Aunt May believes that Santa Claus fights crime." Philosophers actually argue about things like this, not so much for Santa Claus fighting crime, but whether e.g. "Santa Claus has a beard" is true or false.