To entreat or implore earnestly; to pray or plead to someone to reconsider.
From Latin exorare, composed of ex- (out) and orare (to pray, speak). The verb entered English in the 16th century with the sense of praying someone out of a position or decision through persistent pleading.
Latin had separate words for different kinds of speaking—orare was specifically about prayer and formal pleading, which is why we get words like 'oration' and 'orator' from the same root. Medieval monks used forms of this word when describing prayers that might change God's mind!
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