The quality or state of being set aside, aside, or removed from the main consideration; the characteristic of being incidental or peripheral.
From 'aside' + '-ness' (forming nouns expressing a state or quality). The suffix '-ness' has been used since Old English to create abstract nouns from adjectives and adverbial phrases.
Creating '-ness' nouns is one of English's favorite tricks, and this word captures something genuinely useful: the idea that some things have a special 'quality of being aside.' It's the kind of word that seems obvious once you read it but is rarely needed.
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