In a way that shows willingness to accept different ideas, beliefs, and perspectives without prejudice.
From 'broadminded' (broad + minded, meaning having a wide-ranging intellectual capacity) + '-ly' adverbial suffix. This became popular in English during the 19th century as a counterpoint to 'narrowminded.'
The metaphor of 'broad mind' versus 'narrow mind' shows how deeply we think of thought patterns as having literal width—even neuroscience uses concepts like 'cognitive flexibility,' which echoes the same spatial metaphor.
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