impossibly true

Last night, Rhett asked Dad a question. 

Rhett:  Dad, I have a question.
Seth: Okay.
Rhett:  What is a seven letter word that starts with a P and means "impossible, but true"?
Seth: Umm, I don't know.
Rhett:  You don't know?
Seth:  No.  Why do you need to know?
Rhett: It is for enrichment.  Our teacher tells us a story and then asks us a question about it.  Sometimes the word is in the story but sometimes it is not.
...
Rhett:  So you really don't know what the answer is?
Seth: No son, I really don't.   Maybe you should tell me the story.
Rhett:  Well, the story is about a bird named Paradox. This guy sees this bird that looks like it is filled with water and...
Seth:  Wait, wait, wait.  What is the bird's name?
Rhett:  Paradox.
Seth:  Do you know what paradox means?
Rhett:  No.

Seth gets a dictionary and looks it up.  He reads it to him:  A seemingly contradictory statement that may nonetheless be true. 

Seth:  Don't you think that sounds like your answer?
Rhett: Wait, paradox has 7 letters?!?