 To believe is to take something to be the case or regard it as true (see the entry on  belief).  When one says something like “the liar believes that his pants are on fire”, one attributes to the subject (the liar) an attitude (belief) towards a proposition (his pants are on fire). Likewise, when one says something like “the liar imagines that his pants are on fire”, one attributes to the subject (the liar) an attitude (imagination) towards a proposition (his pants are on fire). The similarities and differences between the belief attribution and the imagination attribution point to similarities and differences between imagining and believing. 