Rather than choosing between the sparse and abundant conceptions, the very promoters of this distinction have opted in different ways for a dualism of properties, according to which there are properties of both kinds. Lewis endorses abundant properties as reduced to sets of possibilia, and sparse properties either viewed as universals, and corresponding to some of the abundant properties (1983), or as themselves sets of possibilia (1986b: 60). Bealer (1982) proposes a systematic account wherein