The state or quality of having a particular type of head.(noun)
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Use "headedness" in a sentence
"This level-headedness is welcome in a book which deals with collective hot-headedness."
"Bully-headedness is of course a trait that runs in the family."
"The point is, of the many attempts to evaluate and improve police performance the only thing that matches their conceptual wrong-headedness is their cack-handed implementation."