However, unlike possible world semantics, predicates are not to be thought of as having different extensions at different worlds. Rather, for Lewis, each n-place predicate has a single extension that can contain n-tuples of objects across many different worlds — intuitively, all of the objects that have the property or n-tuples of objects that stand in the relation expressed by the predicate across all possible worlds. Such a move is not feasible in basic possible world semantics, which is designed for a metaphysics in which one and the same individual can exemplify a given property in some worlds in which they exist but not others. Hence, a typical predicate will be true of an individual with respect to some worlds and false of it with respect to others.

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However, unlike possible world semantics, predicates are not to be thought of as having different extensions at different worlds. Rather, for Lewis, each n-place predicate has a single extension that can contain n-tuples of objects across many different worlds — intuitively, all of the objects that have the property or n-tuples of objects that stand in the relation expressed by the predicate across all possible worlds. Such a move is not feasible in basic possible world semantics, which is designed for a metaphysics in which one and the same individual can exemplify a given property in some worlds in which they exist but not others.

Hence, a typical predicate will be true of an individual with respect to some worlds and false of it with respect to others. Hence, 19 might appear to be exactly the concretist truth condition for the denial of the right conjunct of 16 , i. In fact, Lewis whole-heartedly accepts that things have accidental properties and, indeed, would accept that 16 is robustly true. His explanation involves one of the most interesting and provocative elements of his theory: the doctrine of counterparts.

Roughly, an object y in a world w2 is a counterpart of an object x in w1 if y resembles x and nothing else in w2 resembles x more than y. A typical other-worldly counterpart of Algol, for example, might resemble her very closely up to some point in her history — a point, say, after which she continued to live out her life as a stray instead of being brought home by our kindly dog-lover John. Hence, sentences making de re assertions about what Algol might have done or what she could or could not have been are unpacked, semantically, as sentences about her counterparts in other possible worlds.

The Analysis of Intensions. As in basic possible world semantics, intensional entities in general can be defined in terms of the basic ontology of the theory independent of the linguistic roles they can play as the intensions of predicates. A property is any set of individuals. Note that propositions are thus simply properties of worlds on these definitions. To the extent that these notions are free of modality, Lewis has arguably reduced modal notions to non-modal.

The chief question Lewis faces in this regard is whether there are enough worlds to do the job. From this it would follow that the worlds required by the concretist truth condition for any intuitive modal truth exist. Toward this end, Lewis initially considers the evocative principle: Ways Absolutely every way that a world could be is a way that some world is.

Since, in particular, a world satisfying 20 seems quite obviously to be a way a world could be, by Ways such a world exists. But there is a fatal flaw here: Lewis himself , 84 identifies ways that a world could be with worlds themselves. So understood, Ways collapses into the triviality that every world is identical to some world. The principle has two aspects. Given that individuals are worldbound, however, the principle is expressed more rigorously and more generally in terms of other-worldly duplicates: R1 For any finite or infinite number of objects a1, a2, To express this a bit more rigorously, say that objects a1, a2, Worlds that satisfy the concretist truth conditions for workaday possibilities like 16 are easily conceived as consisting of duplicates of relevant parts of the actual world — suitably organized to retain their actual properties, or not, as needed.

Hence, the existence of such worlds does indeed appear to follow from the existence of the actual world by recombination. Worlds containing talking donkeys, exotic species resulting from a wholly different evolutionary history, worlds with silicon-based life forms, and so on present a bigger challenge to the view. Nonetheless, it is not entirely implausible to think such worlds exist given suitable duplication and reorganization of microphysical objects.

Hence, there is no obvious reason why he cannot respond to charges of incompleteness by saying that it is simply a presupposition of his theory that logical space has no gaps, that there are always enough worlds to satisfy the concretist truth condition for any intuitive modal truth. Their role, therefore, is to give us insight into the richness and diversity of set theoretic space, not a complete mechanism for proving which particular sets do or do not exist.

However, Lewis argues that no other theory explains so much so economically. The theoretical benefits are worth it. We can now imagine, as in our example, further detail being successively added to that description to yield more complex ways things could be: Anne working at her desk in her office; music being in the background; her husband being on the phone in the next room; her neighbor mowing the lawn next door; and so on.

Thus, for example, that things could be in the simple state described above might be spelled out in one of the following ways: The proposition that Anne is in her office and at her desk is possibly true. Possible worlds are then defined as special cases of the type of entity in question that are in some relevant sense total. Adams , for example, defines possible worlds to be consistent sets of propositions that are total in the sense of containing, for every proposition p, either p or its negation; Fine , fleshing out ideas of Prior, defines a possible world to be a consistent proposition w that is total in the sense that, for every proposition p, w entails either p or its negation.

Just as some propositions are true and others are not, some SOAs are actual and others are not. It is simply to say that it is not, in fact, a condition, or state, that the concrete world is actually in.

So, henceforth, to express that an SOA is actual we will usually say that it obtains. An SOA is said to be possible necessary, impossible insofar as it is possible necessary, impossible that it obtain.

Note also that, for the abstractionist, as for the concretist, the actual world is no different in kind from any other possible world; all possible worlds exist, and in precisely the same sense as the actual world. The actual world is simply the total possible SOA that, in fact, obtains. And non-actual worlds are simply those total possible SOAs that do not. What of existence in such worlds? Clearly, because SOAs are abstract, individuals cannot exist in abstractionist worlds in anything like the same literal, mereological sense.

Unlike concretism, then, abstractionism does not entail that individuals are worldbound; there is no inconsistency whatever in the idea that many distinct worlds can include the existence of one and the same individual. Indeed, typically, abstractionists are staunchly committed to transworld identity and hold that most any given individual exists in many possible worlds and, moreover, that contingent individuals, at least, can exemplify very different properties from world to world.

Abstractionists, therefore, have no need to appeal to counterparts to understand de re modalities and can therefore accept the truth conditions for such modalities given by basic possible world semantics spelled out, of course, in terms of their definitions AW2 and AE2. In particular, they can take the standard possible world truth condition for, e.

The reason for this is clear: abstract possible worlds are defined in irreducibly modal terms — a possible world is an SOA that among other things possibly obtains; or a set of propositions such that it is possible that all of its members are true; or a property that is possibly exemplified; and so on. If we now unpack the modal operators in 22 using the corresponding truth conditional clauses of standard possible world semantics, the result will contain further world quantifiers.

More generally, and a bit more exactly, put: As noted above, the logical framework of basic possible world semantics is classical predicate logic. The logical framework of abstractionism is modal predicate logic. Hence, if possible world semantics is supplemented with abstractionist definitions of possible worlds, then the logical framework of possible world semantics becomes modal predicate logic as well and, as a consequence, the extensionality of the semantics is lost once again.

This point is expressed somewhat more formally in the supplemental document The Intensionality of Abstractionist Possible World Semantics. Since, as noted above, the central motivation for possible world semantics was to deliver an extensional semantics for modal languages, any motivation for abstractionism as a semantic theory is arguably undermined. That is, abstractionists can argue that we begin with a primitive notion of modality and, typically upon a certain amount of philosophical reflection, we subsequently discover an intimate connection to the notion of a possible world, as revealed in the principles Nec and Poss.

The analysis that abstractionists provide is designed to make this connection explicit, ideally, in such a way that Nec and Poss fall out as theorems of their theory see, e. Hand in glove with the irreducible nature of modality is the nature of intensional entities. Abstractionists, by contrast, define worlds in terms of intensional entities.

This divergence in their choice of ontological primitives reflects, not only their differing stances toward modality, but also an important methodological difference with regard to metaphysical inquiry.

Within a given theory, any entities that can play those roles fruitfully for the purposes at hand are justifiably identified with those notions — regardless of how well they comport with pre-theoretic intuitions. By contrast, at least some abstractionists — Plantinga perhaps most notably — believe that we have intuitive, pre-theoretic knowledge of intensional entities that precludes their being identified with set theoretic constructions of any sort.

For abstractionists, however, actuality is a special property that distinguishes exactly one possible world from all others — the actual world is the only world that happens to obtain; it is the one and only way things could be that is the way things as a whole, in fact, are.

However, for most abstractionists, the distinctiveness of the actual world does not lie simply in its actuality but in its ontological comprehensiveness: the actual world encompasses all that there is. In a word: most abstractionists are actualists.

Actualism is the thesis that everything that there is, everything that has being in any sense, is actual. In terms of possible worlds: Everything that exists in any world exists in the actual world. However, although possibilism and abstractionism are entirely compatible — Zalta , for example, embraces both positions — abstractionists tend to be actualists. The reason for this is clear: Basic possible world semantics appears to be committed to possibilism and abstractionism promises a way of avoiding that commitment.

The specter of possibilism first arises with regard to non-actual possible worlds, which would seem by definition to be prime examples of mere possibilia. However, we have just seen that the abstractionist can avoid this apparent commitment to possibilism by defining possible worlds to be SOAs of a certain sort.

So defined, non-actual worlds, i. However, the specter of possibilism is not so easily exorcised. For non-actual worlds are not the only, or even the most compelling, examples of mere possibilia that seem to emerge out of basic possible world semantics.

For instance, it is quite reasonable to think that evolution could have taken a very different course or, if you like, that God could have made very different creative choices and that there could have been individuals — call them Exotics — that are biologically very different from all actually existing individuals; so different, in fact, that no actually existing thing could possibly have been an Exotic.

However, since no actually existing thing could have been an Exotic, anything that is an Exotic in some possible world cannot be among the things that exist in the actual world.

Thus, the truth conditions that basic possible world semantics assigns to some of our intuitive modal beliefs appear to entail that there are non-actual individuals as well as non-actual possible worlds.

Defining possible worlds as SOAs provided a way for the actualist to embrace non-actual worlds without compromising her actualism. But how is the actualist to understand the apparent commitment to non-actual individuals in such truth conditions as 25? Answers that have been given to this question represent a rather deep divide between actualist abstractionists.

Trace actualists come in two varieties: new actualists and haecceitists. New actualists like Linsky and Zalta and Williamson , , argue that, in fact, all individuals are actually existing, necessary beings but not all of them are necessarily concrete.

Some concrete individuals — those traditionally mis- categorized as contingent beings — are only contingently concrete. Likewise, some non-concrete individuals — those, like possible Exotics, traditionally mis- categorized as contingently non-actual mere possibilia — are only contingently non-concrete.

Notably, the domain d w of a world w is understood not as the set of things that exist in w — for all individuals exist in all worlds — but the set of things that are concrete in w. On the other hand, haecceitists like Plantinga introduce special properties — haecceities — to similar ends.

The haecceity of an individual a is the property of being that very individual, the property being a. A property is a haecceity, then, just in case it is possible that it is the haecceity of some individual. More importantly, for haecceitists, haecceities are necessary beings.

More generally and more carefully put: Necessarily, for any individual a, i a has a haecceity h and ii necessarily, h exists. Like the new actualists, then, the metaphysics of the haecceitists enables them to systematically reinterpret possible world semantics in such a way that the truth conditions of modal discourse are expressed solely in term of actually existing entities of some sort rather than actual and non-actual individuals.

So reinterpreted, the truth condition for 23 is: There is a possible world w and a haecceity h that is i exemplified in w and ii coexemplified with the property being an Exotic in w.

Hence, unlike trace actualism, there are no such vestiges in the actual world of objects that are not actual but only could have been. The logical consequences for no-trace actualists, however, appear to be severe; at the least they cannot provide a standard compositional semantics for modal languages, according to which roughly the meaning of a sentence is determined by its logical form and the meanings of its semantically significant constituents.

A number of important objections have been voiced in regard to abstractionism. Some of these are addressed in the document Problems with Abstractionism.



Maushicage Classical, Early, and Medieval Poetry and Poets: Hence, they argue, there are innumerably many possible worlds other than our own, which exist just as much as ours does. Possible worlds are mere descriptions of ways this world workds actual one might have been, and nothing else. This page was last edited on 12 Octoberat Added to PP index Total downloads 10, of 2, Recent downloads 6 months 24 18, of 2, How can I increase my downloads? But, again, we will not pursue this question here. Towards a Proper Treatment of Quantification in English. Print Save Cite Email Share. Philosophical Studies 2: History of Western Philosophy.


Possible Worlds

Hence, under E! That is, for an actualist, it is a theorem of SQML that it is necessary that everything necessarily exists, that anything that there could have been already exists necessarily. It follows that it is not even possible for there to be contingent beings, contrary to very strong, ordinary modal intuitions. For to say that an object is contingent is to say that it either could exist but in fact does not, or that it does exist but in fact might not.


Example[ edit ] Consider the statement " Sherlock Holmes exists. This contingency is usually described by the statement "there is a possible world in which Sherlock Holmes exists". The possibilist argues that apparent existential claims such as this that "there are" possible worlds of various sorts ought to be taken more or less at face value: as stating the existence of two or more worlds, only one of which at the most can be the actual one. Hence, they argue, there are innumerably many possible worlds other than our own, which exist just as much as ours does.

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