A proud, haughty, or superior manner; arrogance or disdain, especially in the way someone carries themselves or speaks.
From French hauteur, derived from haut meaning 'high.' The metaphorical sense evolved because high social position was expressed through physically elevated bearing and superior attitude.
You see this word pop up in 19th-century novels describing aristocrats—Jane Austen would have loved describing someone's 'hauteur'! It captures that nose-in-the-air snobbery perfectly.
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