The quality or state of being amicable; the capacity or tendency to be friendly and peaceful in dealings or disputes.
From 'amicable' plus the suffix '-ness' (from Old English, denoting a state or quality). This is an alternate form of 'amicability,' using the Germanic suffix '-ness' rather than the Romance suffix '-ity.'
English often has two ways to express the same quality—'amicableness' uses native Germanic roots while 'amicability' uses Romance roots—and speakers use whichever sounds more natural in context, even though they mean the same thing.
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