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Most of us also believe that things, as a whole, needn't have beenjust as they are. Rather, things might have been different incountless ways, both trivial and profound. History, from the verybeginning, could have unfolded quite other than it did in fact: thematter constituting a distant star might never have organized wellenough to give light; species that survived might just as well havedied off; battles won might have been lost; children born might neverhave been conceived and children never conceived might otherwise havebeen born. In any case, no matter how things had gone they would stillhave been part of a single, maximally inclusive, all-encompassingsituation, a single world. Intuitively, then, the actual world ofwhich Anne's immediate situation is a part is only one among manypossible worlds.
The idea of possible worlds is evocative and appealing. However,possible worlds failed to gain any real traction among philosophersuntil the 1960s when they were invoked to provide the conceptualunderpinnings of some powerful developments in modal logic. Only thendid questions of their nature become a matter of the highestphilosophical importance. Accordingly, Part 1 of this article willprovide an overview of the role of possible worlds in the developmentof modal logic. Part 2 explores three prominent philosophicalapproaches to the nature of possible worlds.[1] Although many of the finer philosophical points of Part 2 dopresuppose the technical background of Part 1, the generalphilosophical landscape laid out in Part 2 can be appreciatedindependently of Part 1.
Call the above basic possible world semantics. Spelling out thetruth conditions for (6) (relative to the intended interpretation ofits language), basic possible world semantics tells us that (6) istrue if and only if
Note that interpreting modal operators as quantifiers over possibleworlds provides a nice theoretical justification for the usualdefinition of the possibility operator in terms of necessity,specifically:
That is, a sentence is possible just in case its negation isn'tnecessary. Since, semantically speaking, the necessity operator isliterally a universal quantifier, the definition correspondsexactly to the definition (7) of the existential quantifier. For, unpacking the right side ofdefinition (10) according to the negation and necessitation clausesabove (and invoking the definitions of truth and truth at a worldsimpliciter), we have:
As noted, the focus of the present article is on the metaphysics ofpossible worlds rather than applications. Of course, the semantics ofmodal languages is itself an application, but one that is of singularimportance, both for historical reasons and because most applicationsare in fact themselves applications of (often extended or modifiedversions of) the semantical apparatus. Two particularly importantexamples are the analysis of intensions and a concomitant explicationof the de re/de dicto distinction.[10]
are said to exhibit modality de dicto (roughly, modality ofthe proposition). Possibleworld semantics provides an illuminating analysis of the keydifference between the two: The truth conditions for both modalitiesinvolve a commitment to possible worlds; however, the truth conditionsfor sentences exhibiting modality de re involve in addition acommitment to the meaningfulness of transworld identity, the thesis that, necessarily, every individual (typically, at anyrate) exists and exemplifies (often very different) properties in manydifferent possible worlds. More specifically, basic possible worldsemantics yields intuitively correct truth values for sentences of thelatter sort by (i) permitting world domains to overlap and (ii)assigning intensions to predicates, thereby, in effect, relativizingpredicate extensions to worlds. In this way, one and the sameindividual can be in the extension of a given predicate at all worldsin which they exist, at some such worlds only, or at none at all. (Forfurther discussion, see the entry on essential vs. accidental properties.)
For sentences like (17) involving only de dicto modalities, Lewis's truth conditionsare similar in form to the truth conditions generated by the modalclauses of basic possible world semantics; specifically, for (17):
Lewis's theory is particularly commendable for its strikingoriginality and ingenuity and for the simple and straightforwardanswers AW1 and AE1 that it provides to our twoquestions QW and QE above. Furthermore, because worldsare (plausibly) defined entirely in nonmodal terms, the truthconditions provided by Lewis's translation scheme themselves appear tobe free of any implicit modality. Hence, unlike many other popularaccounts of possible worlds (notably, the abstractionist accountsdiscussed in the following section), Lewis's promises to provide agenuine analysis of the modal operators.
Possible worlds are then defined as special cases of the type ofentity in question that are in some relevant sense total.Adams (1974), for example, defines possible worlds to be consistentsets of propositions that are total in the sense of containing, forevery proposition p, either p or its negation; Fine(1977), fleshing out ideas of Prior, defines a possible world to be aconsistent proposition w that is total in the sense that, forevery proposition p, w entails either p or itsnegation. For purposes here, however, we will sketch the fundamentalsof the abstractionist view in terms of states of affairs,following the basic features of the account developed by Plantinga(1974, 1976), an account that, in the literature, frequently serves asa particularly trenchant abstractionist counterpoint to Lewis's concretism.[27]
More generally, and a bit more exactly, put: As noted above, thelogical framework of basic possible world semantics is classicalpredicate logic. The logical framework of abstractionism is modalpredicate logic. Hence, if possible world semantics is supplementedwith abstractionist definitions of possible worlds, then the logicalframework of possible world semantics becomes modal predicate logic aswell and, as a consequence, the extensionality of the semantics islost once again. (This point is expressed somewhat more formally inthe supplemental document The Intensionality of Abstractionist Possible World Semantics.) Since, as noted above, the central motivation for possible worldsemantics was to deliver an extensional semantics for modal languages,any motivation for abstractionism as a semantic theory is arguably undermined.[30]
However, it is not entirely clear that this observation constitutes anobjection to abstractionism. For abstractionists can argue that thegoal of their analysis is the converse of the reductionist's goal: Thereductionist wants to understand modality in terms of worlds; theabstractionist, by contrast, wants to understand worlds in terms ofmodality. That is, abstractionists can argue that we begin with aprimitive notion of modality and, typically upon a certain amount ofphilosophical reflection, we subsequently discover an intimateconnection to the notion of a possible world, as revealed in theprinciples Nec and Poss. The analysis that abstractionists provide is designed to make thisconnection explicit, ideally, in such a way that Nec andPoss fall out as theorems of their theory (see, e.g., Plantinga1985 and Menzel and Zalta 2014).
The specter of possibilism first arises with regard tonon-actual possible worlds, which would seem by definition tobe prime examples of mere possibilia. However, we have justseen that the abstractionist can avoid this apparent commitment topossibilism by defining possible worlds to be SOAs of a certain sort.So defined, non-actual worlds, i.e., worlds that fail to obtain, canstill actually exist. Hence, the commitment of basic possible worldsemantics to non-actual worlds does not in itself threaten theactualist's ontological scruples.
However, since no actually existing thing could have been an Exotic,anything that is an Exotic in some possible world cannot be among thethings that exist in the actual world. Thus, the truth conditions thatbasic possible world semantics assigns to some of our intuitive modalbeliefs appear to entail that there are non-actual individuals as wellas non-actual possible worlds. Defining possible worlds as SOAsprovided a way for the actualist to embrace non-actual worlds withoutcompromising her actualism. But how is the actualist to understand theapparent commitment to non-actual individuals in such truthconditions as (25)?
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