Finer most nearly means:

better

Explanation

Finer is (comparative of `fine'') greater in quality or excellence; "a finer wine"; "a finer musician".

Better is (comparative of `good'') superior to another (of the same class or set or kind) in excellence or quality or desirability or suitability; more highly skilled than another; "You''re a better man than I am, Gunga Din"; "a better coat"; "a better type of car".

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