About this topic
Summary Possible worlds semantics is a general approach to theories of meaning, on which meanings (or, more precisely, semantic values) are assigned to sentences in terms of the truth-values they take across all possible worlds. The intuition is that the meaning of a sentence specifies how the world would have to be for that sentence to be true (or false). This is typically made precise by identifying the semantic value of a sentence with its possible-worlds intension, a function from possible worlds to truth-values. When those values are just true and false (and are mutually exclusive), possible worlds intensions are equivalent to sets of possible worlds (the worlds at which the sentence is question is true). The approach can be generalised by treating semantic values for sub-sentential items (such as nouns and verbs) as functions from possible worlds to other entities (such as particulars, properties and relations). ‘Possible worlds semantics’ is also used in a narrower sense, to refer to formal Kripke semantics for modal (and other) logics. 
Key works Carnap 1947 and Wittgenstein 1922 are important precursors to possible worlds semantics. Kripke developed the formal semantics for modal logic in Kripke 1959, 1963 and for intuitionistic logic in Kripke 1963. Key works applying possible worlds semantics to natural language include Cresswell 1973Lewis 1970, Montague 1973Kratzer 1977Lewis 1986 and Lewis 1973Hintikka 1962, 1967 develops formal possible worlds semantics and applies it to epistemic concepts.
Introductions Heim & Kratzer 1998 is a very comprehensive (although difficult) introduction to possible worlds semantics and its application to natural language. Lewis 1970 is a much shorter overview. Girle 2003 and Girle 2000 are introductory textbooks on formal possible worlds semantics in modal logic. Cresswell & Hughes 1996 is a classic textbook in modal logic. Sider 2010 includes a good presentation of quantified first-order logic.
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  1. The Lesson of Kaplan's Paradox About Possible World Semantics.C. Anthony Anderson - 2009 - In Joseph Almog & Paolo Leonardi (eds.), The Philosophy of David Kaplan. Oxford University Press. pp. 85.
  2. 'First-Order Modal Logic', to Appear in V. Hendricks & SA Pedersen, Eds.,'40 Years of Possible Worlds', Special Issue Of.H. Arlo-Costa - forthcoming - Studia Logica.
  3. Representing Counterparts.Andrew Bacon - 2014 - Australasian Journal of Logic 11 (2):90-113.
    This paper presents and motivates a counterpart theoretic semantics for quantifi ed modal logic based on a fleshed out account of Lewis's notion of a `possibility.' According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. A semantics for quanti ed modal logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory, (...)
  4. Property Identities and Modal Arguments.Derek Nelson Ball - 2011 - Philosophers' Imprint 11.
    Physicalists about the mind are committed to claims about property identities. Following Kripke's well-known discussion, modal arguments have emerged as major threats to such claims. This paper argues that modal arguments can be resisted by adopting a counterpart theoretic account of modal claims, and in particular modal claims involving properties. Thus physicalists have a powerful motive to adopt non-Kripkean accounts of the metaphysics of modality and the semantics of modal expressions.
  5. The Interpretation of Necessity and the Necessity of Interpretation.Roberta Ballarin - 2004 - Journal of Philosophy 101 (12):609-638.
    Much has happened in modal logic since 1947. In particular, in regard to the problem of interpreting such logics. In that fateful year Quine published his seminal paper “The Problem of Interpreting Modal Logic” from which this work takes inspiration. Since then a certain kind of model theory – universally referred to as “possible worlds semantics” – has come to dominate both advanced research and introductory textbooks. Many would say that the problem of interpreting modal logic has been resolved. In (...)
  6. Can Counterfactuals Really Be About Possible Worlds?Stephen Barker - 2011 - Noûs 45 (3):557-576.
    The standard view about counterfactuals is that a counterfactual (A > C) is true if and only if the A-worlds most similar to the actual world @ are C-worlds. I argue that the worlds conception of counterfactuals is wrong. I assume that counterfactuals have non-trivial truth-values under physical determinism. I show that the possible-worlds approach cannot explain many embeddings of the form (P > (Q > R)), which intuitively are perfectly assertable, and which must be true if the contingent falsity (...)
  7. Nature Without Abandoning Kripke–Putnam Semantics1.Helen Beebee - 2013 - In Stephen Mumford & Matthew Tugby (eds.), Metaphysics and Science. Oxford University Press. pp. 141.
  8. Branching Versus Divergent Possible Worlds.Jiri Benovsky - 2005 - Kriterion - Journal of Philosophy 19 (1):12-20.
    David Lewis' modal counterpart theory falls prey to the famous Saul Kripke's objection, and this is mostly due to his 'static' ontology (divergence) of possible worlds. This paper examines a genuinely realist but different, branching ontology of possible worlds and a new definition of the counterpart relation, which attempts to provide us with a better account of de re modality, and to meet satisfactorily Kripke's claim, while being also ontologically more 'parsimonious'.
  9. Possible Worlds Semantics: A Research Program That Cannot Fail?Johan Benthem - 1984 - Studia Logica 43 (4):379 - 393.
    Providing a possible worlds semantics for a logic involves choosing a class of possible worlds models, and setting up a truth definition connecting formulas of the logic with statements about these models. This scheme is so flexible that a danger arises: perhaps, any (reasonable) logic whatsoever can be modelled in this way. Thus, the enterprise would lose its essential tension. Fortunately, it may be shown that the so-called incompleteness-examples from modal logic resist possible worlds modelling, even in the above wider (...)
  10. A Modality Called ‘Negation’.Francesco Berto - 2015 - Mind 124 (495):761-793.
    I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the following (...)
  11. Impossible Worlds.Francesco Berto - 2013 - Stanford Encyclopedia of Philosophy (2013).
    It is a venerable slogan due to David Hume, and inherited by the empiricist tradition, that the impossible cannot be believed, or even conceived. In Positivismus und Realismus, Moritz Schlick claimed that, while the merely practically impossible is still conceivable, the logically impossible, such as an explicit inconsistency, is simply unthinkable. -/- An opposite philosophical tradition, however, maintains that inconsistencies and logical impossibilities are thinkable, and sometimes believable, too. In the Science of Logic, Hegel already complained against “one of the (...)
  12. Negation on the Australian Plan.Franz Berto & Greg Restall - forthcoming - Journal of Philosophical Logic.
    We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...)
  13. Non-Locality and Possible Worlds. A Counterfactual Perspective on Quantum Entanglement.Tomasz Bigaj - 2006 - Ontos Verlag.
    This book uses the formal semantics of counterfactual conditionals to analyze the problem of non-locality in quantum mechanics. Counterfactual conditionals enter the analysis of quantum entangled systems in that they enable us to precisely formulate the locality condition that purports to exclude the existence of causal interactions between spatially separated parts of a system. They also make it possible to speak consistently about alternative measuring settings, and to explicate what is meant by quantum property attributions. The book develops the possible-world (...)
  14. Believing in Semantics.John C. Bigelow - 1978 - Linguistics and Philosophy 2 (1):101--144.
    This paper concerns the semantics of belief-sentences. I pass over ontologically lavish theories which appeal to impossible worlds, or other points of reference which contain more than possible worlds. I then refute ontologically stingy, quotational theories. My own theory employs the techniques of possible worlds semantics to elaborate a Fregean analysis of belief-sentences. In a belief-sentence, the embedded clause does not have its usual reference, but refers rather to its own semantic structure. I show how this theory can accommodate quantification (...)
  15. Possible Worlds Foundations for Probability.John C. Bigelow - 1976 - Journal of Philosophical Logic 5 (3):299--320.
  16. Impossible Worlds and Logical Omniscience: An Impossibility Result.Jens Christian Bjerring - 2013 - Synthese 190 (13):2505-2524.
    In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that (...)
  17. Pictures, Perspective and Possibility.Ben Blumson - 2010 - Philosophical Studies 149 (2):135 - 151.
    This paper argues for a possible worlds theory of the content of pictures, with three complications: depictive content is centred, two-dimensional and structured. The paper argues that this theory supports a strong analogy between depictive and other kinds of representation and the platitude that depiction is mediated by resemblance.
  18. The Logic of Hope: A Defence of the Hopeful.Einar Duenger Bohn - 2018 - Religious Studies 54 (1):107-116.
  19. Possible Worlds: An Introduction to Logic and its Philosophy.Raymond Bradley - 1979 - Blackwell.
    object an item which does not have a position in space and time but which exists. (Philosophers have nominated such things as numbers, sets, and propositions to this category. The need to posit such entities has been discussed and disputed for at least 2400 years.).
  20. Partial Worlds and Paradox.Elke Brendel - 1993 - Erkenntnis 39 (2):191 - 208.
    Since universal language systems are confronted with serious paradoxical consequences, a semantic approach is developed in whichpartial worlds form the ontological basis. This approach shares withsituation semantics the basic idea that statements always refer to certain partial worlds, and it agrees with the extensional and model-theoretic character ofpossible worlds semantics. Within the framework of the partial worlds conception a satisfactory solution to theLiar paradox can be formulated. In particular, one advantage of this approach over those theories that are based on (...)
  21. On Context Shifters and Compositionality in Natural Languages.Adrian Briciu - 2018 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 25 (1):2-20.
    My modest aim in this paper is to prove certain relations between some type of hyper-intensional operators, namely context shifting operators, and compositionality in natural languages. Various authors (e.g. von Fintel & Matthewson 2008; Stalnaker 2014) have argued that context-shifting operators are incompatible with compositionality. In fact, some of them understand Kaplan’s (1989) famous ban on context-shifting operators as a constraint on compositionality. Others, (e.g. Rabern 2013) take contextshifting operators to be compatible with compositionality but, unfortunately, do not provide a (...)
  22. David Lewis: On the Plurality of Worlds.Phillip Bricker - 2006 - In John Shand (ed.), Central Works of Philosophy, Vol. 5: The Twentieth Century: Quine and After. Acumen Publishing.
    David Lewis's book 'On the Plurality of Worlds' mounts an extended defense of the thesis of modal realism, that the world we inhabit the entire cosmos of which we are a part is but one of a vast plurality of worlds, or cosmoi, all causally and spatiotemporally isolated from one another. The purpose of this article is to provide an accessible summary of the main positions and arguments in Lewis's book.
  23. The Language of Reasons and 'Ought'.Aaron Bronfman & J. L. Dowell - forthcoming - In Daniel Star (ed.), Oxford Handbook of Reasons.
  24. Contextualism About Deontic Conditionals.Aaron Bronfman & Janice Dowell, J. L. - manuscript
  25. "The Metaphysics of Modality" by Graeme Forbes. [REVIEW]Mark A. Brown - 1990 - Philosophy and Phenomenological Research 50 (3):615.
  26. Meaning and Necessity.V. C. C. - 1957 - Review of Metaphysics 10 (3):536-536.
  27. Quantified Hintikka-Style Epistemic Logic.Lauri Carlson - 1988 - Synthese 74 (2):223 - 262.
    This paper contains a formal treatment of the system of quantified epistemic logic sketched in Appendix II of Carlson (1983). Section 1 defines the syntax and recapitulates the model set rules and principles of the Appendix system. Section 2 defines a possible worlds semantics for this system, and shows that the Appendix system is complete with respect to this semantics. Section 3 extends the system by an explicit truth operatorT it is true that and considers quantification over nonexistent individuals. Section (...)
  28. Meaning and Necessity.Rudolf Carnap - 1947 - University of Chicago Press.
    "This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence.
  29. Essentialism and Individuation in Modal Logic.Troy Thomas Catterson - 2003 - Dissertation, Boston University
    This dissertation addresses the problem of trans-world identity in possible worlds semantics, and argues that essentialism does not provide a satisfactory solution to it. If one takes possible worlds semantics seriously as a viable elucidation of the logic of the metaphysical modalities, one must also take a realistic stance toward possible worlds. But then, contrary to Kripke, Plantinga, Van Inwagen, and others, there is a problem with trans-world identity; the real problem being, not the problem of identifying individuals across possible (...)
  30. Modal Sequents.Claudio Cerrato - 1996 - In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer Academic Publishers. pp. 141--166.
  31. The Necessity of Being.Joseph Chiari - 1973 - New York: Gordian Press.
  32. The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic.Charles S. Chihara - 1998 - Oxford University Press.
    A powerful challenge to some highly influential theories, this book offers a thorough critical exposition of modal realism, the philosophical doctrine that many possible worlds exist of which our own universe is just one. Chihara challenges this claim and offers a new argument for modality without worlds.
  33. Metanormative Theory and the Meaning of Deontic Modals.Matthew Chrisman - 2016 - In Nate Charlow & Matthew Chrisman (eds.), Deontic Modality. New York: Oxford University Press. pp. 395-424.
    Philosophical debate about the meaning of normative terms has long been pulled in two directions by the apparently competing ideas: (i) ‘ought’s do not describe what is actually the case but rather prescribe possible action, thought, or feeling, (ii) all declarative sentences deserve the same general semantic treatment, e.g. in terms of compositionally specified truth conditions. In this paper, I pursue resolution of this tension by rehearsing the case for a relatively standard truth-conditionalist semantics for ‘ought’ conceived as a necessity (...)
  34. On the Meaning of 'Ought'.Matthew Chrisman - 2012 - In Russ Shafer-Landau (ed.), Oxford Studies in Metaethics, vol. 7. Oxford University Press. pp. 304.
    Discussions about the meaning of the word “ought” are pulled in two apparently competing directions. First, in ethical theory this word is used in the paradigmatic statement of ethical principles and conclusions about what some agent is obligated to do. This leads some ethical theorists to claim that the word “ought” describes a real relation, roughly, of being obligated to (realism) or expresses some non-cognitive attitude toward agents acting in certain ways (expressivism). Second, in theoretical linguistics this word is classified (...)
  35. Master in Logic and Metaphysics.Rodrigo Cid - 2013 - Fundamento: Revista de Pesquisa Em Filosofia 6:79-87.
    My main purpose in this article is to present an argument for the idea that necessity qua truth in all possible worlds, without other qualifications, leads us to contradiction. If we do not want to accept the contradiction, we will face a dilemma: or accepting that everything we take as contingent is in fact necessary, or accepting that we cannot translate some sentences – at least the indexed to worlds sentences – to the possible worlds vocabulary. We have an intuition (...)
  36. Minimising Existence: Or How to Stop Worrying and Love the Barcan Formulae.Nicola Ciprotti - 2006 - Annali Del Dipartimento di Filosofia 12:215-238.
    The paper is intended to provide a full-scale defence of the infamous Barcan Formulae. Not only do I put forth some arguments, both semantic and metaphysical, against recent criticism; I also take pains at supplying some rationale in favour of the formal semantics underlying the Formulae, namely Possibilist quantification. Such a task is carried out through an argument for Compositional Nihilism, according to which nothing but mereological simples ever exists, and consequently through an informal sketch of the metaphysics of possible (...)
  37. Meredith, Prior, and the History of Possible Worlds Semantics.B. Jack Copeland - 2006 - Synthese 150 (3):373-397.
    This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.
  38. The Genesis of Possible Worlds Semantics.B. Jack Copeland - 2002 - Journal of Philosophical Logic 31 (2):99-137.
    This article traces the development of possible worlds semantics through the work of: Wittgenstein, 1913-1921; Feys, 1924; McKinsey, 1945; Carnap, 1945-1947; McKinsey, Tarski and Jónsson, 1947-1952; von Wright, 1951; Becker, 1952; Prior, 1953-1954; Montague, 1955; Meredith and Prior, 1956; Geach, 1960; Smiley, 1955-1957; Kanger, 1957; Hintikka, 1957; Guillaume, 1958; Binkley, 1958; Bayart, 1958-1959; Drake, 1959-1961; Kripke, 1958-1965.
  39. Modality, Quantification, and Many Vlach-Operators.Fabrice Correia - 2007 - Journal of Philosophical Logic 36 (4):473-488.
    Consider two standard quantified modal languages A and P whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of A are actualist while those of P are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive-i.e., so that for each sentence (...)
  40. Around the Tree: Semantic and Metaphysical Issues Concerning Branching and the Open Future.Fabrice Correia & Andrea Iacona (eds.) - 2013 - Springer.
    Over the past few years, the tree model of time has been widely employed to deal with issues concerning the semantics of tensed discourse. The thought that has motivated its adoption is that the most plausible way to make sense of indeterminism is to conceive of future possibilities as branches that depart from a common trunk, constituted by the past and the present. However, the thought still needs to be further articulated and defended, and several important questions remain open, such (...)
  41. Modalities and Multimodalities.Alexandre Costa-Leite - 2013 - Manuscrito 36 (1):191-195.
  42. The Worlds of Possibility: Modal Realism and the Semantics of Modal Logic. [REVIEW]M. J. Cresswell - 2003 - International Studies in Philosophy 35 (4):194-195.
  43. Semantical Essays Possible Worlds and Their Rivals.M. J. Cresswell - 1988
  44. From Modal Discourse to Possible Worlds.Maxwell J. Cresswell - 2006 - Studia Logica 82 (3):307-327.
    The possible-worlds semantics for modality says that a sentence is possibly true if it is true in some possible world. Given classical prepositional logic, one can easily prove that every consistent set of propositions can be embedded in a ‘maximal consistent set’, which in a sense represents a possible world. However the construction depends on the fact that standard modal logics are finitary, and it seems false that an infinite collection of sets of sentences each finite subset of which is (...)
  45. Embedded Counterfactuals and Possible Worlds Semantics.Charles B. Cross - 2016 - Philosophical Studies 173 (3):665-673.
    Stephen Barker argues that a possible worlds semantics for the counterfactual conditional of the sort proposed by Stalnaker and Lewis cannot accommodate certain examples in which determinism is true and a counterfactual Q > R is false, but where, for some P, the compound counterfactual P > (Q > R) is true. I argue that the completeness theorem for Lewis’s system VC of counterfactual logic shows that Stalnaker–Lewis semantics does accommodate Barker’s example, and I argue that its doing so should (...)
  46. From Worlds to Probabilities: A Probabilistic Semantics for Modal Logic.Charles B. Cross - 1993 - Journal of Philosophical Logic 22 (2):169 - 192.
    I give a probabilistic semantics for modal logic in which modal operators function as quantifiers over Popper functions in probabilistic model sets, thereby generalizing Kripke's semantics for modal logic.
  47. Literary Semantics and Possible Worlds = Literatursemantik Und Mögliche Welten.Károly Csúri - 1980 - Auctoritate Et Consilio Cathedrae Comparationis Litterarum Universarum Universitatis Szegediensis de Attila József Nominatae Edita.
  48. Possible Worlds and a Theory of Meaning for Modal Language.Barbara Davidson & Robert Pargetter - 1980 - Australasian Journal of Philosophy 58 (4):388 – 394.
  49. Possible Worlds for Modal Primitivists.Louis deRosset - 2014 - Journal of Philosophical Logic 43 (1):109-131.
    Among the most remarkable developments in metaphysics since the 1950’s is the explosion of philosophical interest in possible worlds. This paper proposes an explanation of what possible worlds are, and argues that this proposal, the interpreted models conception, should be attractive to anyone who thinks that modal facts are primitive, and so not to be explained in terms of some non-modal notion of “possible world.” I articulate three constraints on any acceptable primitivist explanation of the nature of possible worlds, and (...)
  50. Logic for Contigent Beings.Harry Deutsch - 1994 - Journal of Philosophical Research 19:273-329.
    One of the logical problems with which Arthur Prior struggled is the problem of finding, in Prior’s own phrase, a “logic for contingent beings.” The difficulty is that from minimal modal principles and classical quantification theory, it appears to follow immediately that every possible object is a necessary existent. The historical development of quantified modal logic (QML) can be viewed as a series of attempts---due variously to Kripke, Prior, Montague, and the fee-logicians---to solve this problem. In this paper, I review (...)
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