The quality or state of being able to be fined or refined into a finer state.
Compound of 'fineable' plus '-ness,' a suffix that turns adjectives into abstract nouns. This layered suffix construction ('fine-able-ness') shows English's method of building meaning through accumulated morphemes.
English builds words like Lego—stack enough suffixes and you can describe nearly any quality, which is why 'fineableness' is instantly understandable even though you've probably never encountered it before.
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