Possible world
Encyclopedia
In philosophy
and logic
, the concept of a possible world is used to express modal claims
. The concept of possible worlds is common in contemporary philosophical discourse and has also been disputed.
's modal realism (see below). There is a close relation between proposition
s 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:
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 implicit traces of the idea in the works of Al-Ghazali
(The Incoherence of the Philosophers
), Averroes
(The Incoherence of the Incoherence
), Fakhr al-Din al-Razi
(Matalib al-'Aliya) and John Duns Scotus. The modern philosophical use of the notion was pioneered by David Lewis
and Saul Kripke
.
and his colleagues. A statement in modal logic that is possible is said to be true in at least one possible world; a statement that is necessary is said to be true in all possible worlds.
s 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
. Many debates in the philosophy of religion
have been reawakened by the use of possible worlds. 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 real, concrete worlds that exist just as unequivocally as our actual world exists, but that 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 that 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.
. 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.
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
and logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...
, the concept of a possible world is used to express modal claims
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
. The concept of possible worlds is common in contemporary philosophical discourse and has also been disputed.
Possibility, necessity, and contingency
Those 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 LewisDavid Kellogg Lewis
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...
's modal realism (see below). There is a close relation between proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
s and possible worlds. We note that every proposition is either true or false at any given possible world; then the modal status
Modal logic
Modal logic is a type of formal logic that extends classical propositional and predicate logic to include operators expressing modality. Modals — words that express modalities — qualify a statement. For example, the statement "John is happy" might be qualified by saying that John is...
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 propositionsTruthTruth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...
are those that are true in the actual world (for example: "Richard NixonRichard NixonRichard Milhous Nixon was the 37th President of the United States, serving from 1969 to 1974. The only president to resign the office, Nixon had previously served as a US representative and senator from California and as the 36th Vice President of the United States from 1953 to 1961 under...
became President in 1969") - False propositions are those that are false in the actual world (for example: "Ronald ReaganRonald ReaganRonald Wilson Reagan was the 40th President of the United States , the 33rd Governor of California and, prior to that, a radio, film and television actor....
became President in 1969") - Possible propositions are those that are true in at least one possible world (for example: "Hubert HumphreyHubert HumphreyHubert Horatio Humphrey, Jr. , served under President Lyndon B. Johnson as the 38th Vice President of the United States. Humphrey twice served as a United States Senator from Minnesota, and served as Democratic Majority Whip. He was a founder of the Minnesota Democratic-Farmer-Labor Party and...
became President in 1969") - Contingent propositions are those that are true in some possible worlds and false in others (for example: "Richard NixonRichard NixonRichard Milhous Nixon was the 37th President of the United States, serving from 1969 to 1974. The only president to resign the office, Nixon had previously served as a US representative and senator from California and as the 36th Vice President of the United States from 1953 to 1961 under...
became President in 1969" is contingently true and "Hubert HumphreyHubert HumphreyHubert Horatio Humphrey, Jr. , served under President Lyndon B. Johnson as the 38th Vice President of the United States. Humphrey twice served as a United States Senator from Minnesota, and served as Democratic Majority Whip. He was a founder of the Minnesota Democratic-Farmer-Labor Party and...
became President in 1969" is contingently false) - Necessarily true propositions (usually simply called necessary propositions) are those that are true in all possible worlds (for example: "2 + 2 = 4"; "all bachelors are unmarried")
- Impossible propositions (or necessarily false propositions) are those that 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
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
, who spoke of possible worlds as ideas in the mind of God
God
God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....
and used the notion to argue that our actually created world must be "the best of all possible worlds
Best of all possible worlds
The phrase "the best of all possible worlds" was coined by the German polymath Gottfried Leibniz in his 1710 work Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal...
". However, scholars have also found implicit traces of the idea in the works of Al-Ghazali
Al-Ghazali
Abu Hāmed Mohammad ibn Mohammad al-Ghazzālī , known as Algazel to the western medieval world, born and died in Tus, in the Khorasan province of Persia was a Persian Muslim theologian, jurist, philosopher, and mystic....
(The Incoherence of the Philosophers
The Incoherence of the Philosophers
The Incoherence of the Philosophers is the title of a landmark 11th century polemic by the Sufi sympathetic Imam Al-Ghazali of the Asharite school of Islamic theology criticizing the Avicennian school of early Islamic philosophy...
), Averroes
Averroes
' , better known just as Ibn Rushd , and in European literature as Averroes , was a Muslim polymath; a master of Aristotelian philosophy, Islamic philosophy, Islamic theology, Maliki law and jurisprudence, logic, psychology, politics, Arabic music theory, and the sciences of medicine, astronomy,...
(The Incoherence of the Incoherence
The Incoherence of the Incoherence
The Incoherence of the Incoherence by Andalusian Muslim polymath and philosopher Ibn Rushd is an important Islamic philosophical treatise, in which the author defends the use of Aristotelian philosophy within Islamic thought.It was written in the style of a dialogue against Al-Ghazali's claims...
), Fakhr al-Din al-Razi
Fakhr al-Din al-Razi
Abu Abdullah Muhammad ibn Umar ibn al-Husayn al-Taymi al-Bakri al-Tabaristani Fakhr al-Din al-Razi , most commonly known as Fakhruddin Razi was a well-known Persian Sunni Muslim theologian and philosopher....
(Matalib al-'Aliya) and John Duns Scotus. The modern philosophical use of the notion was pioneered by David Lewis
David Kellogg Lewis
David Kellogg Lewis was an American philosopher. Lewis taught briefly at UCLA and then at Princeton from 1970 until his death. He is also closely associated with Australia, whose philosophical community he visited almost annually for more than thirty years...
and Saul Kripke
Saul Kripke
Saul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
.
Formal semantics of modal logics
A semantics for modal logic was first introduced in the 1950s work of Saul KripkeSaul Kripke
Saul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
and his colleagues. A statement in modal logic that is possible is said to be true in at least one possible world; a statement that is necessary is said to be true in all possible worlds.
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 conditionalCounterfactual conditional
A counterfactual conditional, subjunctive conditional, or remote conditional, abbreviated , is a conditional statement indicating what would be the case if its antecedent were true...
s in terms of "nearby possible worlds" developed by David Lewis and Robert Stalnaker
Robert Stalnaker
Robert C. Stalnaker is Laurance S. Rockefeller Professor of Philosophy at the Massachusetts Institute of Technology. In 2007, he delivered the John Locke Lectures at Oxford University on the topic of Our Knowledge of the Internal World...
. 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
Zombie argument
The term zombie argument may refer to;*Arguments involving a philosophical zombie, a hypothetical being that is indistinguishable from a normal human being except that it lacks consciousness, qualia or sentience...
, and physicalism
Physicalism
Physicalism is a philosophical position holding that everything which exists is no more extensive than its physical properties; that is, that there are no kinds of things other than physical things...
and supervenience
Supervenience
In philosophy, supervenience is a kind of dependency relationship. For example, mental states might depend on physical brain states. This dependency is typically held to obtain between sets of properties. A classic example is that mental states of pain supervene on 'C-fibers firing'...
in the philosophy of mind
Philosophy of mind
Philosophy of mind is a branch of philosophy that studies the nature of the mind, mental events, mental functions, mental properties, consciousness and their relationship to the physical body, particularly the brain. The mind-body problem, i.e...
. Many debates in the philosophy of religion
Philosophy of religion
Philosophy of religion is a branch of philosophy concerned with questions regarding religion, including the nature and existence of God, the examination of religious experience, analysis of religious language and texts, and the relationship of religion and science...
have been reawakened by the use of possible worlds. Intense debate has also emerged over the ontological
Ontology
Ontology is the philosophical study of the nature of being, existence or reality as such, as well as the basic categories of being and their relations...
status of possible worlds, provoked especially by David Lewis's defense of modal realism
Modal realism
Modal realism is the view, notably propounded by David Kellogg Lewis, that all possible worlds are as real as the actual world. It is based on the following tenets: possible worlds exist; possible worlds are not different in kind from the actual world; possible worlds are irreducible entities; the...
, 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 real, concrete worlds that exist just as unequivocally as our actual world exists, but that 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
Indexicality
In linguistics and in philosophy of language, an indexical behavior or utterance points to some state of affairs. For example, I refers to whoever is speaking; now refers to the time at which that word is uttered; and here refers to the place of utterance...
term, like "now" and "here".) Others, such as Robert Adams and William Lycan
William Lycan
William G. Lycan is a noted American philosopher teaching at the University of North Carolina at Chapel Hill,where he is the William Rand Kenan, Jr. Distinguished Professor. He won the Class of 2001 Outstanding Faculty Award and a Distinguished Teaching Award for Post-Baccalaureate Instruction in...
, 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 that is that way. (Lewis describes their position, and similar positions such as those advocated by Alvin Plantinga
Alvin Plantinga
Alvin Carl Plantinga is an American analytic philosopher and the emeritus John A. O'Brien Professor of Philosophy at the University of Notre Dame. He is known for his work in philosophy of religion, epistemology, metaphysics, and Christian apologetics...
and Peter Forrest
Peter Forrest
Peter James Forrest is a professional Australian cricketer who currently plays for the Queensland Bulls. With a rookie contract in the 2006-07 season, Forrest made his first-class debut for New South Wales against Queensland on 1 March 2007...
, 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
Saul Kripke
Saul Aaron Kripke is an American philosopher and logician. He is a professor emeritus at Princeton and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center...
, in Naming and Necessity
Naming and Necessity
Naming and Necessity is a book by the philosopher Saul Kripke that was first published in 1980 and deals with the debates of proper nouns in the philosophy of language. The book is based on a transcript of three lectures given at Princeton University in 1970...
, 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.
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, fictional universeFictional universe
A fictional universe is a self-consistent fictional setting with elements that differ from the real world. It may also be called an imagined, constructed or fictional realm ....
. 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
Marie-Laure Ryan
Marie-Laure Ryan is a prominent literary scholar and critic. She has written several books and articles on narratology, fiction and cyberculture, and has been awarded several times for her work....
, Lubomir Dolezel
Lubomir Dolezel
Lubomír Doležel is a Czech literary theorist and one of the founders of the so-called fictional worlds theory.- Life, Work, and Academic Career :...
, and Thomas Pavel
Thomas Pavel
Thomas Pavel is a literary theorist, critic, and novelist currently teaching at the University of Chicago.- Biography :...
, 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
Narrative
A narrative is a constructive format that describes a sequence of non-fictional or fictional events. The word derives from the Latin verb narrare, "to recount", and is related to the adjective gnarus, "knowing" or "skilled"...
and thematic concerns.
See also
- Standard translationStandard translationIn modal logic, standard translation is a way of transforming formulas of modal logic into formulas of first-order logic which capture the meaning of the modal formulas. Standard translation is defined inductively on the structure of the formula. In short, atomic formulas are mapped onto unary...
, an embedding of modal logics into first-order logicFirst-order logicFirst-order logic is a formal logical system used in mathematics, philosophy, linguistics, and computer science. It goes by many names, including: first-order predicate calculus, the lower predicate calculus, quantification theory, and predicate logic...
which captures their possible world semantics - n-universesN-universesThe n-universes are a conceptual tool introduced by philosopher Paul Franceschi. They consist of simplified models of universes which are reduced to their essential components, in order to facilitate the associated reasoning...
- Modal fictionalismModal fictionalismModal fictionalism is a term used in philosophy, and more specifically in modal logic, to describe the position that holds that talk of possible worlds is actually false, though adopting such a discourse may be a useful fiction. A contrast to the position of modal fictionalism would be the position...
- FictionalismFictionalismFictionalism is a methodological theory in philosophy that suggests that statements of a certain sort should not be taken to be literally true, but merely as a useful fiction...
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)
External links
- "Possible worlds: what they are good for and what they are" — Alexander Pruss