  As its name might suggest, our third approach — combinatorialism — takes possible worlds to be recombinations, or rearrangements, of certain metaphysical simples. Both the nature of simples and the nature of recombination vary from theory to theory. Quine (1968) and Cresswell (1972), for example, suggest taking simples to be space-time points (modeled, perhaps, as triples of real numbers) and worlds themselves to be arbitrary sets of such points, each set thought of intuitively as a way that matter could be distributed throughout space-time. (A world w, so construed, then, is actual just in case a space-time point p is a member of w if and only if p is occupied by matter.) Alternatively, some philosophers define states a world could be in, and possible worlds themselves, simply to be maximally consistent sets of  sentences[37]  in an expressively rich language — “recombinations”, certainly, of the sentences of the language. (Lewis refers to this view as linguistic  ersatzism.[38])  However, the predominant version of combinatorialism finds its origins in Russell's (1918/1919) theory of logical atomism and Wittgenstein's (1921, 1922, 1974) short but enormously influential  Tractatus Logico-Philosophicus. A suggestive paper by Skyrms (1981) spelling out some of the ideas in the Tractatus, in turn, inspired a rich and sophisticated account that is developed and defended in great detail in an important series of books and articles by D. M. Armstrong (1978a, 1978b, 1986a, 1989, 1997, 2004b, 2004c). In this section, we present a somewhat simplified version of combinatorialism that draws primarily upon Armstrong's work. Unless otherwise noted, this is what we shall mean by ‘combinatorialism’ for the remainder. 