According to Wikipedia, "any definition that attempts to set out the essence of"

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According to Wikipedia, "any definition that attempts to set out the essence of" a concept "specifies the necessary and sufficient conditions for a thing being a member of" the set corresponding to that concept. Ok. But I wonder if it wouldn't be great if, for some more difficult concepts, we could at least specify some sufficient conditions in a way that we would pick most things that are members a the corresponding set. For instance, wouldn't it be a nice philosophical progress if we could get a "definition" (?) of beauty that would cover most beautiful things and no non-beautiful thing? I mean a definition that is not circular, of course.