Dissertation, Princeton University (
1983)
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Abstract
In sections 1 through 5, I develop in detail what I call the standard
theory of worlds and propositions, and I discuss a number of purported
objections. The theory consists of five theses. The first two theses,
presented in section 1, assert that the propositions form a Boolean
algebra 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 and
whose space consists of all and only the worlds. The next three theses,
presented in sections 3, 4, and 5, respectively, guarantee the existence
of logical space, and further constrain its structure. The third thesis
asserts that the set of propositions true at any world is maximal
consistent; the fourth thesis that any two worlds are separated by a
proposition; the fifth thesis that only one proposition is false at
every 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 support
either a reduction of worlds to propositions or a reduction of
propositions to worlds. A number of proposition-based theories are
developed in section 6, and compared with Adams's world-story theory. A
world-based theory is developed in section?, and Stalnaker's account of
the matter is discussed. Before passing judgment on the proposition based
and world-based theories, I ask in sections 8 and 9 whether both
worlds and propositions might be reduced to something else. In
section 8, I consider reductions to linguistic entities; in section 9,
reductions to unfounded sets. After rejecting the possibility of
eliminating both worlds and propositions, I return in section 10 to the
possibility of eliminating one in favor of the other. I conclude,
somewhat tentatively, that neither worlds nor propositions should be
reduced one to the other, that both worlds and propositions should be
taken as basic to our ontology.