Meta Ontology

In sections 1 through 5, I develop in detail what I call the standardtheory of worlds and propositions, and I discuss a number of purportedobjections. The theory consists of five theses. The first two theses,presented in section 1, assert that the propositions form a Booleanalgebra with respect to implication, and that the algebra is complete,respectively. In section 2, I introduce the notion of logical space:it is a field of sets that represents the propositional structure andwhose space consists of all and only the worlds. The next three theses,presented in sections 3, 4, and 5, respectively, guarantee the existenceof logical space, and further constrain its structure. The third thesisasserts that the set of propositions true at any world is maximalconsistent; the fourth thesis that any two worlds are separated by aproposition; the fifth thesis that only one proposition is false atevery world. In sections 6 through 10, I turn to the problem of reduction. In sections 6 and 7, I show how the standard theory can be used to supporteither a reduction of worlds to propositions or a reduction ofpropositions to worlds. A number of proposition-based theories aredeveloped in section 6, and compared with Adams's world-story theory. Aworld-based theory is developed in section?, and Stalnaker's account ofthe matter is discussed. Before passing judgment on the proposition basedand world-based theories, I ask in sections 8 and 9 whether bothworlds and propositions might be reduced to something else. Insection 8, I consider reductions to linguistic entities; in section 9,reductions to unfounded sets. After rejecting the possibility ofeliminating both worlds and propositions, I return in section 10 to thepossibility of eliminating one in favor of the other. I conclude,somewhat tentatively, that neither worlds nor propositions should bereduced one to the other, that both worlds and propositions should betaken as basic to our ontology.