  The intuitionist conception of goodness may be regarded as mysterious because it is alleged to be unanalysable or indefinable. But that wouldn’t pick up on the non-natural nature that intuitionists claim moral properties have. This objection would apply to any notion that philosophers claim is primitive in the sense that no informative definition in other terms can be offered, be it the notion of explanation, knowledge, or pain. It expresses rather a certain philosophical disappointment that a definition can’t be offered. It is often said that “One person’s primitive is another person’s mystery”, but this supposed sense of mystery attaches to the unanalysability claim rather than the non-naturalness claim.