The quality or state of being angelical; the condition of having angel-like characteristics.
From 'angelical' plus the suffix '-ness' (forming abstract nouns from adjectives), a common pattern in English like 'kindness', 'happiness', 'darkness'.
English loves stacking suffixes—'angelical' is 'angel' + '-ical', and 'angelicalness' is 'angelical' + '-ness'—this layering lets us create increasingly abstract concepts from concrete root words.
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