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A possible world is a complete and consistent way the world is or could have been. They are widely used as a formal device in
logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...

logic
,
philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questio ...

philosophy
, and
linguistics Linguistics is the scientific study of language, meaning that it is a comprehensive, systematic, objective, and precise study of language. Linguistics encompasses the analysis of every aspect of language, as well as the methods for studying ...

linguistics
in order to provide a semantics for intensional and
modal logic Modal logic is a collection of s originally developed and still widely used to represent statements about . The basic (1-place) modal operators are most often interpreted "□" for "Necessarily" and "◇" for "Possibly". In a , each can be expr ...
. Their
metaphysical Metaphysics is the branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and ...

metaphysical
status has been a subject of controversy in
philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questio ...

philosophy
, with modal realists such as
David LewisDavid or Dave Lewis may refer to: Academics *A. David Lewis (born 1977), American comic writer and scholar of religion and literature *David Lewis (academic) (born 1960), English scholar of development *David Lewis (lawyer) ( – 1584), Welsh ...
arguing that they are literally existing alternate realities, and others such as
Robert Stalnaker Robert C. Stalnaker (born 22 January 1940) is an American philosopher who is Laurence S. Rockefeller Professor of philosophy at the Massachusetts Institute of Technology. He is a Fellow of the American Academy of Arts and Sciences and a Corres ...
arguing that they are not.


Logic

Possible worlds are one of the foundational concepts in modal and
intensional logic Intensional logic is an approach to predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and ...
s. Formulas in these logics are used to represent statements about what ''might'' be true, what ''should'' be true, what one ''believes'' to be true and so forth. To give these statements a formal interpretation, logicians use structures containing possible worlds. For instance, in the
relational semantics Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joy ...
for classical propositional modal logic, the formula \Diamond P (read as "possibly P") is actually true if and only if P is true at some world which is ''accessible'' from the actual world. Possible worlds play a central role in the work of both linguists and philosophers working in formal semantics. Contemporary formal semantics is couched in formal systems rooted in
Montague grammar__notoc__ Montague grammar is an approach to natural language semantics Semantics (from grc, wikt:σημαντικός, σημαντικός ''sēmantikós'', "significant") is the study of meaning, reference, or truth. The term can be used to ...
, which is itself built on
Richard Montague Richard Merritt Montague (September 20, 1930 – March 7, 1971) was an American mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such t ...
's
intensional logic Intensional logic is an approach to predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and ...
. Contemporary research in semantics typically uses possible worlds as formal tools without committing to a particular theory of their metaphysical status. The term ''possible world'' is retained even by those who attach no metaphysical significance to them.


Argument from ways

Possible worlds are often regarded with suspicion, which is why their proponents have struggled to find arguments in their favor. An often-cited argument is called the ''argument from ways''. It defines possible worlds as "ways how things could have been" and relies for its premises and inferences on assumptions from
natural language In neuropsychology Neuropsychology is a branch of psychology. It is concerned with how a person's cognition and behavior are related to the brain and the rest of the nervous system. Professionals in this branch of psychology often focus on ...
, for example: :(1)
Hillary Clinton Hillary Diane Rodham Clinton ( Rodham; born October 26, 1947) is an American politician, diplomat, lawyer, writer, and public speaker who served as the from 2009 to 2013, as a from from 2001 to 2009, and as from 1993 to 2001 as the wife ...

Hillary Clinton
could have won the
2016 US election The 2016 United States elections were held on Tuesday, November 8, 2016. Republican nominee Donald Trump Donald John Trump (born June 14, 1946) is an American media personality and businessman who served as the 45th president of the ...
. :(2) So there are other ways how things could have been. :(3) Possible worlds are ways how things could have been. :(4) So there are other possible worlds. The central step of this argument happens at ''(2)'' where the plausible ''(1)'' is interpreted in a way that involves quantification over "ways". Many philosophers, following
Willard Van Orman Quine Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician Logic (from Greek: grc, λογική, label=none, lit=possessed of reason Reason is the capacity of ...
, hold that quantification entails
ontological commitmentAn ontological commitment of a language is one or more objects postulated to exist by that language. The 'existence' referred to need not be 'real', but exist only in a universe of discourse. As an example, legal systems use vocabulary referring to ...
s, in this case, a commitment to the existence of possible worlds. Quine himself restricted his method to scientific theories, but others have applied it also to natural language, for example, Amie L. Thomasson in her ''easy'' approach to ontology. The strength of the ''argument from ways'' depends on these assumptions and may be challenged by casting doubt on the quantifier-method of ontology or on the reliability of natural language as a guide to ontology.


Philosophical issues and applications


Metaphysics

The
ontological Ontology is the branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Ph ...

ontological
status of possible worlds has provoked intense debate.
David LewisDavid or Dave Lewis may refer to: Academics *A. David Lewis (born 1977), American comic writer and scholar of religion and literature *David Lewis (academic) (born 1960), English scholar of development *David Lewis (lawyer) ( – 1584), Welsh ...
famously advocated for a position known as
modal realism Modal realism is the view propounded by David Kellogg Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on the following tenets: possible worlds exist; pos ...
, which holds that possible worlds are real, concrete places which exist in the exact same sense that the actual world exists. On Lewis's account, the actual world is special only in that we live there. This doctrine is called ''the indexicality of actuality'' since it can be understood as claiming that the term "actual" is an
indexical In semiotics, linguistics, anthropology and philosophy of language, indexicality is the phenomenon of a ''sign'' pointing to (or ''indexing'') some object in the context (language use), context in which it occurs. A sign that signifies indexically i ...
, like "now" and "here". Lewis gave a variety of arguments for this position. He argued that just as the reality of atoms is demonstrated by their explanatory power in physics, so too are possible worlds justified by their explanatory power in philosophy. He also argued that possible worlds must be real because they are simply "ways things could have been" and nobody doubts that such things exist. Finally, he argued that they could not be reduced to more "ontologically respectable" entities such as maximally consistent sets of propositions without rendering theories of modality circular. (He referred to these theories as "ersatz modal realism" which try to get the benefits of possible worlds semantics "on the cheap".) Modal realism is controversial. W.V. Quine rejected it as "metaphysically extravagant". Stalnaker responded to Lewis's arguments by pointing out that a way things could have been is not itself a world, but rather a property that such a world can have. Since properties can exist without them applying to any existing objects, there's no reason to conclude that other worlds like ours exist. Another of Stalnaker's arguments attacks Lewis's ''indexicality theory of actuality''. Stalnaker argues that even if the English word "actual" is an indexical, that doesn't mean that other worlds exist. For comparison, one can use the indexical "I" without believing that other people actually exist. Some philosophers instead endorse the view of possible worlds as maximally consistent sets of propositions or descriptions, while others such as
Saul Kripke Saul Aaron Kripke (; born November 13, 1940) is an American philosopher and logician in the analytic tradition. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Pr ...

Saul Kripke
treat them as purely ''formal'' (i.e. mathematical) devices.


Explicating necessity and possibility

At least since Aristotle, philosophers have been greatly concerned with the logical statuses of propositions, e.g. necessity, contingency, and impossibility. In the twentieth century, possible worlds have been used to explicate these notions. In modal logic, a proposition is understood in terms of the ''worlds in which it is true'' and ''worlds in which it is false''. Thus, equivalences like the following have been proposed: * ''
True propositions
True propositions
'' are those that are ''true in the actual world'' (for example: "
Richard Nixon Richard Milhous Nixon (January 9, 1913April 22, 1994) was the 37th president of the United States The president of the United States (POTUS) is the and of the . The president directs the of the and is the of the . The power o ...

Richard Nixon
became president in 1969"). * '' False propositions'' are those that are ''false in the actual world'' (for example: "
Ronald Reagan Ronald Wilson Reagan ( ; February 6, 1911June 5, 2004) was an American politician who served as the 40th president of the United States The president of the United States (POTUS) is the and of the . The president directs the of ...

Ronald Reagan
became president in 1969"). * '' Possible propositions'' are those that are ''true in at least one possible world'' (for example: "
Hubert Humphrey Hubert Horatio Humphrey Jr. (May 27, 1911 – January 13, 1978) was an American pharmacist and politician who served as the 38th vice president of the United States The vice president of the United States (VPOTUS) is the second-highest offi ...
became president in 1969"). (Humphrey did run for president in 1968, and thus could have been elected.) This includes propositions which are necessarily true, in the sense below. * ''
Impossible propositions
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"). * '' Necessarily true propositions'' (often simply called ''necessary propositions'') are those that are ''true in all possible worlds'' (for example: "2 + 2 = 4"; "all bachelors are unmarried"). * ''
Contingent propositions In philosophy and logic, contingency is the status of propositions that are neither true under every possible interpretation (logic), valuation (i.e. tautology (logic), tautologies) nor false under every possible valuation (i.e. contradictions). A c ...
'' are those that are ''true in some possible worlds and false in others'' (for example: "
Richard Nixon Richard Milhous Nixon (January 9, 1913April 22, 1994) was the 37th president of the United States The president of the United States (POTUS) is the and of the . The president directs the of the and is the of the . The power o ...

Richard Nixon
became president in 1969" is ''contingently true'' and "
Hubert Humphrey Hubert Horatio Humphrey Jr. (May 27, 1911 – January 13, 1978) was an American pharmacist and politician who served as the 38th vice president of the United States The vice president of the United States (VPOTUS) is the second-highest offi ...
became president in 1969" is ''contingently false'').


Other uses

Possible worlds play a central role in many other debates in philosophy. These include debates about the Zombie Argument, and
physicalism In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical reality Reality is the sum or aggregate of all that is ...
and
supervenience In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, lang ...
in the
philosophy of mind Philosophy of mind is a branch of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, a ...

philosophy of mind
. Many debates in the
philosophy of religion Philosophy of religion is "the philosophical examination of the central themes and concepts involved in religious traditions". Philosophical discussions on such topics date from ancient times, and appear in the earliest known s concerning philo ...
have been reawakened by the use of possible worlds.


History of the concept

The idea of possible worlds is most commonly attributed to
Gottfried Leibniz Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the " 1666–1676" section. ( – 14 November 1716) was a German polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, " ...

Gottfried Leibniz
, who spoke of possible worlds as ideas in the mind of
God In monotheistic Monotheism is the belief A belief is an attitude Attitude may refer to: Philosophy and psychology * Attitude (psychology) In psychology Psychology is the science of mind and behavior. Psychology includes the ...

God
and used the notion to argue that our actually created world must be "the
best of all possible worlds The phrase "the best of all possible worlds" (french: le meilleur des mondes possibles; german: Die beste aller möglichen Welten) was coined by the German people, German polymath Gottfried Leibniz in his 1710 work ''Théodicée, Essais de Théod ...
".
Arthur Schopenhauer Arthur Schopenhauer (; ; 22 February 1788 – 21 September 1860) was a German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citize ...
argued that on the contrary our world must be the worst of all possible worlds, because if it were only a little worse it could not continue to exist. Scholars have found implicit earlier traces of the idea of possible worlds in the works of
René Descartes René Descartes ( or ; ; Latinized Latinisation or Latinization can refer to: * Latinisation of names, the practice of rendering a non-Latin name in a Latin style * Latinisation in the Soviet Union, the campaign in the USSR during the 1920s ...

René Descartes
,"Nor could we doubt that, if God had created many worlds, they would not be as true in all of them as in this one. Thus those who could examine sufficiently the consequences of these truths and of our rules, could be able to discover effects by their causes, and, to explain myself in the language of the schools, they could have a priori demonstrations of everything that could be produced in this new world." -The World, Chapter VII a major influence on Leibniz,
Al-Ghazali Al-Ghazali (, ; full name or , ; Latinized Algazelus or Algazel; – 19 December 1111) was a Persian Persian may refer to: * People and things from Iran, historically called ''Persia'' in the English language ** Persians, Persian people, the ...

Al-Ghazali
(''
The Incoherence of the Philosophers ''The Incoherence of the Philosophers'' (تهافت الفلاسفة ''Tahāfut al-Falāsifaʰ'' in Arabic language, Arabic) is the title of a landmark 11th-century work by the Persian theologian Al-Ghazali and a student of the Ash'ari, Asharite s ...
''),
Averroes Ibn Rushd ( ar, ; full name Image:FML names-2.png, 300px, First/given, middle and last/family/surname with John Fitzgerald Kennedy as example. This shows a structure typical for the Anglosphere, among others. Other cultures use other struc ...

Averroes
('' The Incoherence of the Incoherence''),
Fakhr al-Din al-Razi Fakhr al-Dīn al-Rāzī or Fakhruddin Razi ( fa, فخر الدين رازي) (26 January 1150 - 29 March 1210) often known by the sobriquet Sultan of the theologians, was a Persian polymath, Islamic scholar and a pioneer of inductive logic. He w ...
(''Matalib al-'Aliya'') and
John Duns Scotus John Duns ( – 8 November 1308), commonly called Duns Scotus ( ; ; "Duns the Scot"), was a Scottish Catholic priest and Franciscan friar The Franciscans are a group of related Mendicant orders, mendicant Christianity, Christian Cath ...

John Duns Scotus
. The modern philosophical use of the notion was pioneered by
David LewisDavid or Dave Lewis may refer to: Academics *A. David Lewis (born 1977), American comic writer and scholar of religion and literature *David Lewis (academic) (born 1960), English scholar of development *David Lewis (lawyer) ( – 1584), Welsh ...
and
Saul Kripke Saul Aaron Kripke (; born November 13, 1940) is an American philosopher and logician in the analytic tradition. He is a Distinguished Professor of Philosophy at the Graduate Center of the City University of New York and emeritus professor at Pr ...

Saul Kripke
.


See also

* Standard translation, an embedding of modal logics into
first-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal system A formal system is an used for inferring theorems from axioms according to a set of rules. These rul ...
which captures their possible world semantics * N-universes *
Modal fictionalism Modal fictionalism is a term used in philosophy, and more specifically in the metaphysics of Modal logic, modality, to describe the position that holds that modality can be analysed in terms of a fiction about possible worlds. The theory comes in tw ...
*
Fictionalism Fictionalism is the view in philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philos ...
* Impossible world *
Modal realism Modal realism is the view propounded by David Kellogg Lewis that all possible worlds are real in the same way as is the actual world: they are "of a kind with this world of ours." It is based on the following tenets: possible worlds exist; pos ...
* Extended modal realism * Alternate history *
Molinism Molinism, named after 16th-century Spanish Jesuit The Society of Jesus (SJ; la, Societas Iesu) is a religious order of the Catholic Church The Catholic Church, often referred to as the Roman Catholic Church, is the List of Christ ...


References


Further reading

*D.M. Armstrong, ''A World of States of Affairs'' (1997. Cambridge: Cambridge University Press) *John Divers, ''Possible Worlds'' (2002. London: Routledge) *Paul Herrick, ''The Many Worlds of Logic'' (1999. Oxford: Oxford University Press) Chapters 23 and 24. *David Lewis, ''
On the Plurality of Worlds ''On the Plurality of Worlds'' (1986) is a book by the philosopher A philosopher is someone who practices philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The c ...
'' (1986. Oxford & New York: Basil Blackwell) *Michael J. Loux d.''The Possible and the Actual'' (1979. Ithaca & London: Cornell University Press) *G.W. Leibniz, ''Theodicy'' (2001. Wipf & Stock Publishers) *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. * * {{DEFAULTSORT:Possible World Possibility Modal logic Semantics Linguistics Concepts in logic Conceptual modelling Interpretation (philosophy) Possible worlds