Possible world

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In philosophy and logic, the concept of possible worlds is used to express modal claims. In philosophy, the term "modality" covers such notions as "possibility", "necessity", and "contingency". Talk of possible worlds is very widespread in contemporary philosophical discourse (especially in the English-speaking world), though much about them is disputed.

Contents 1 Possibility, necessity, and contingency 2 Formal semantics of modal logics 3 From modal logic to philosophical tool 4 Comparison with the many-worlds interpretation 5 Possible-world theory in literary studies 6 See also 7 External links 8 Further reading

[edit] Possibility, necessity, and contingency

Some theorists who use the concept of possible worlds consider the actual world to be one of the many possible worlds. For each distinct way the world could have been, there is said to be a distinct possible world; the actual world is the one we in fact live in. Among such theorists there is disagreement about the nature of possible worlds; their precise ontological status is disputed, and especially the difference, if any, in ontological status between the actual world and all the other possible worlds. One position on these matters is set forth in David Lewis's modal realism (see below). There is a close relation between propositions and possible worlds. We note that every proposition is either true or false at any given possible world; then the modal status of a proposition is understood in terms of the worlds in which it is true and worlds in which it is false. The following are among the assertions we may now usefully make:

• True propositions are those which are true in the actual world (for example: "Richard Nixon became President in 1969")
• False propositions are those which are false in the actual world (for example: "Ronald Reagan became President in 1969")
• Possible propositions are those which are true in at least one possible world (for example: "Hubert Humphrey became President in 1969")
• Contingent propositions are those which are true in some possible worlds and false in others (for example: "Richard Nixon became President in 1969" is contingently true and "Hubert Humphrey became President in 1969" is contingently false)
• Necessary propositions are those which are true in all possible worlds (for example: "2 + 2 = 4"; "all bachelors are unmarried")
• Impossible propositions (or necessarily false propositions) are those which are true in no possible world (for example: "Melissa and Toby are taller than each other at the same time")

The idea of possible worlds is most commonly attributed to Gottfried Leibniz, who spoke of possible worlds as ideas in the mind of God and used the notion to argue that our actually created world must be "the best of all possible worlds". However, scholars have also found traces of the idea in the writings of Lucretius (De Rerum Natura, Book 2, ll. 1023–89), Averroes,^{[citation needed]} and John Duns Scotus.^{[citation needed]} The modern philosophical use of the notion was pioneered by David Lewis and Saul Kripke.

[edit] Formal semantics of modal logics

Further information: Modal logic

A systematic theory derived from possible worlds semantics was first introduced in the 1950s work of Saul Kripke and his colleagues. To put things in a way similar to the way suggested above, possible worlds are used to provide a semantics for claims about possibility and necessity: a statement in modal logic that is possible is said to be true at at least one possible world (noting that logicians prefer to say at, not in, a possible world); a statement that is necessary is said to be true at all possible worlds, and a statement that is true is one that is at least true at this world (the actual world). (Note that by these definitions all necessary statements are also counted among the possible statements, and of course among the true statements.)

The term "possible worlds semantics" is often used as a synonym for Kripke semantics, but this is widely regarded as a mistake: Kripke semantics can be used to analyse modes other than alethic modes (that is, it can be used in logics concerned not with truth per se; for example, in deontic logic, which is the logic of obligation and permission); and Kripke semantics does not presuppose modal realism, which the language of possible worlds arguably presupposes.

[edit] From modal logic to philosophical tool

From this groundwork, the theory of possible worlds became a central part of many philosophical developments, from the 1960s onwards – including, most famously, the analysis of counterfactual conditionals in terms of "nearby possible worlds" developed by David Lewis and Robert Stalnaker. On this analysis, when we discuss what would have happened if some set of conditions were the case, the truth of our claims is determined by what is true at the nearest possible world (or the set of nearest possible worlds) where the conditions obtain. (A possible world W₁ is said to be near to another possible world W₂ in respect of R to the degree that the same things happen in W₁ and W₂ in respect of R; the more different what happens in two possible worlds in a certain respect, the "further" they are from one another in that respect.) Consider this conditional sentence: "If George W. Bush hadn't become president of the U.S. in 2001, Al Gore would have." The sentence would be taken to express a claim that could be reformulated as follows: "In all nearest worlds to our actual world (nearest in relevant respects) where George W. Bush didn't become president of the U.S. in 2001, Al Gore became president of the U.S. then instead." And on this interpretation of the sentence, if there is some nearest world to the actual world (nearest in relevant respects) where George W. Bush didn't become president but Al Gore didn't either, then the claim expressed by this counterfactual would be false.

Today, possible worlds play a central role in many debates in philosophy, including especially debates over the Zombie Argument, and physicalism and supervenience in the philosophy of mind. Intense debate has also emerged over the ontological status of possible worlds, provoked especially by David Lewis's defense of modal realism, the doctrine that talk about "possible worlds" is best explained in terms of innumerable, really existing worlds beyond the one we live in. The fundamental question here is: given that modal logic works, and that some possible-worlds semantics for modal logic is correct, what has to be true of the world, and just what are these possible worlds that we range over in our interpretation of modal statements? Lewis argued that what we range over are nothing more nor less than real, concrete worlds that exist just as unequivocally as our actual world exists, but which are distinguished from the actual world simply by standing in no spatial, temporal, or causal relations with the actual world. (On Lewis's account, the only "special" property that the actual world has is a relational one: that we are in it. This doctrine is called "the indexicality of actuality": "actual" is a merely indexical term, like "now" and "here".) Others, such as Robert Adams and William Lycan, reject Lewis's picture as metaphysically extravagant, and suggest in its place an interpretation of possible worlds as consistent, maximally complete sets of descriptions of or propositions about the world, so that a "possible world" is conceived of as a complete description of a way the world could be – rather than a world which is that way. (Lewis describes their position, and similar positions such as those advocated by Alvin Plantinga and Peter Forrest, as "ersatz modal realism", arguing that such theories try to get the benefits of possible worlds semantics for modal logic "on the cheap", but that they ultimately fail to provide an adequate explanation.) Saul Kripke, in Naming and Necessity, took explicit issue with Lewis's use of possible worlds semantics, and defended a stipulative account of possible worlds as purely formal (logical) entities rather than either really existent worlds or as some set of propositions or descriptions.

[edit] Comparison with the many-worlds interpretation

The concept of possible worlds has sometimes been compared with the many-worlds interpretation of quantum mechanics; indeed, they are sometimes erroneously conflated. The many-worlds interpretation is an attempt to provide an interpretation of nondeterministic processes (such as measurement) without positing the so-called collapse of the wavefunction, while the possible-worlds theory is an attempt to provide an interpretation (in the sense of a more or less formal semantics) for modal claims. In the many-worlds interpretation of quantum mechanics, the collapse of the wavefunction is interpreted by introducing a quantum superposition of states of a possibly infinite number of identical "parallel universes", all of which exist "actually", according to some proponents. The many-worlds interpretation is silent on those questions of modality that possible-world theories address.

Major differences between the two notions, aside from their origins and purposes, include:

• The states of quantum-theoretical worlds are entangled quantum mechanically while entanglement for possible worlds may be meaningless;
• according to a widely held orthodoxy among philosophers, there are possible worlds that are logically but not physically possible, but quantum-theoretical worlds are all physically possible.

Given that both possible-world theories and quantum many-world theories are philosophically contentious, it is not surprising that the precise relations between the two are also contentious.

[edit] Possible-world theory in literary studies

Possible worlds theory in literary studies uses concepts from possible-world logic and applies them to worlds that are created by fictional texts. In particular, possible-world theory provides a useful vocabulary and conceptual framework with which to describe such worlds. However, a literary world is a specific type of possible world, quite distinct from the possible worlds in logic. This is because a literary text houses its own system of modality, consisting of actual worlds (actual events) and possible worlds (possible events). Thus, a literary universe is granted autonomy in much the same way as the actual universe.

Literary critics, such as Marie-Laure Ryan, Lubomir Dolezel, and Thomas Pavel, have used possible-worlds theory to address notions of literary truth, the nature of fictionality, and the relationship between fictional worlds and reality. Taxonomies of fictional possibilities have also been proposed where the likelihood of a fictional world is assessed. Possible-world theory is also used within narratology to divide a specific text into its constituent worlds, possible and actual. In this approach, the modal structure of the fictional text is analysed in relation to its narrative and thematic concerns.

[edit] See also

• Alternative history
• Alternate history (fiction)
• Counterpart theory
• Impossible world
• Mental space
• Modal logic
• Multiverse (science)
• Problem of the future's contingents
• Two dimensionalism

[edit] External links

• "Possible worlds: what they are good for and what they are" — Alexander Pruss

[edit] Further reading

• D.M. Armstrong, A World of States of Affairs (1997. Cambridge: Cambridge University Press) ISBN 0-521-58948-7
• John Divers, Possible Worlds (2002. London: Routledge) ISBN 0-415-15556-8
• Paul Herrick, The Many Worlds of Logic (1999. Oxford: Oxford University Press) Chapters 23 and 24. ISBN 978-0-19-515503-7
• David Lewis, On the Plurality of Worlds (1986. Oxford & New York: Basil Blackwell) ISBN 0-631-13994-X
• Michael J. Loux [ed.] The Possible and the Actual (1979. Ithaca & London: Cornell University Press) ISBN 0-8014-9178-9
• G.W. Leibniz, Theodicy (2001. Wipf & Stock Publishers) ISBN 978-0875484372
• Brian Skyrms "Possible Worlds, Physics and Metaphysics" (1976. Philosophical Studies 30)