 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 qualities are the coarse-grained properties that “provide the world with its causal and phenomenal order” (1982: 183) and concepts are the fine-grained properties that can function as meanings and as constituents of mental contents. He admits a stock of simple properties, which are both qualities and concepts (1982: 186), wherefrom complex qualities and complex concepts are differently constructed: on the one hand, by thought-building operations, which give rise to fine-grained qualities; on the other hand, by condition-building operations, which give rise to coarse-grained qualities. Orilia (1999) has followed Bealer’s lead in also endorsing both coarse-grained qualities and fine-grained concepts, without however identifying simple concepts and simple qualities. In Orilia’s account concepts are never identical to qualities, but may correspond to them; in particular, the identity statements of intertheoretic reductions should be taken to express the fact that two different concepts correspond to the same quality. Despite its advantages in dealing with a disparate range of phenomena, dualism has not gained any explicit consensus. Its implicit presence may however be widespread. For example, Putnam’s (1970: §1) distinction between predicates and physical properties, and Armstrong’s above-mentioned recognition of second-class properties may be seen as forms of dualism.