Author’s Introduction (Full text, footnotes omitted)
- While many are impressed with the utility of possible worlds in linguistics and philosophy, few can accept the modal1 realism of David Lewis, who regards possible worlds as sui generis entities of a kind with the concrete world we inhabit.
- Not all uses of possible worlds require exotic ontology. Consider, for instance, the use of Kripke models to establish formal results in modal logic2. These models contain sets often regarded for heuristic reasons as sets of “possible worlds”. But the “worlds” in these sets can be anything at all; they can be numbers, or people, or fish. The set of worlds, together with the accessibility relation and the rest of the model, is used as a purely formal structure. One can even go beyond establishing results about formal systems and apply Kripke models to English, as Charles Chihara has recently argued. Chihara shows, for instance, how to use Kripke models (plus primitive modal3 notions) to give an account of validity for English modal4 sentences. In other cases worlds are not really needed at all. It is often vivid to give a counterexample thus: “There is a possible world in which P. Since your theory implies that in all worlds, not-P, your theory is wrong.” But the counterexample could just as easily be given using modal5 operators: “Possibly, P. Since your theory implies that it is necessary that not-P, your theory is wrong.”
- Unfortunately for those who yearn for desert landscapes, many interesting applications require more ontological seriousness. In "Chalmers (David) - The Conscious Mind: In Search of a Fundamental Theory", David Chalmers uses worlds to (among other things) set up his two-dimensional modal6 framework. In defining the primary intension of ‘water’ as a function that assigns to any (centered) world, w, the class of things that would count as water in w when w is “considered as actual”, Chalmers is not thinking of the set of worlds as a purely mathematical structure. He means to refer to a particular function defined on a space of genuine possible worlds. Or consider Lewis’s formulation of materialism as the claim that no two possible worlds lacking “alien natural properties” differ without differing physically. This is no claim about the formal structure of Kripke models; it is a claim about a particular class of worlds, the class of worlds that lack alien natural properties.
- Other examples abound. Linguists and philosophers of language utilize set-theoretic constructions out of possible worlds and individuals as semantic values. Philosophers use possible worlds to define probability functions, properties and propositions. Worlds are used to state theories, make claims, formulate supervenience7 theses and illuminate distinctions. Worlds may be used to give the truth conditions for ordinary quantification over possibilities, for example “there are at least five ways to win this chess match”. The journals and books published in the last forty years contain hundreds of uses of possible worlds, few of which could be reconstructed as purely formal uses of Kripke models or as Chihara-style applications. Moreover, these invocations of possible worlds talk usually go far beyond using possible worlds language as a kind of vivid shorthand for sentences containing modal8 operators: it is well-known that a language employing quantification over possible worlds and individuals has more expressive power than the language of modal9 predicate logic.
- Possible worlds semantics and metaphysics appear to require genuine worlds. And yet, who can believe Lewis’s modal10 realism? Like many, I turn to reduction. An adequate reduction of talk of possibilia — worlds and their inhabitants — must be materially adequate, but must not appeal to objectionable entities (like Lewisian worlds). Given such a reduction, the contemporary possible-worlds theorist’s tools may be freely used with a clear ontological conscience.
- A good starting point is what Lewis calls “linguistic ersatzism”, which identifies possible worlds with maximal consistent sets of sentences. But linguistic ersatzism faces an apparently devastating problem, the problem of descriptive power. The solution to this problem will lead to an unfamiliar but attractive theory.
- Because of my own views (which I will not defend here), the theory to be developed will assume world-bound individuals and counterpart theory. But the theory can be developed under other assumptions.
- Section I describes the problem of descriptive power for linguistic ersatzism. Section II introduces the theory to be defended and describes its solution to the problem of descriptive power. Section III then gives an extensive formal development of the theory. Section IV replies to objections, and section V compares the theory with modal11 fictionalism12.
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