In This Article Expand or collapse the "in this article" section Impossible Worlds

  • Introduction
  • General Overviews
  • From Possible Worlds to Impossible Worlds
  • World Structure
  • Impossible Worlds and the Reduction of Modality

Philosophy Impossible Worlds
Ira Kiourti
  • LAST REVIEWED: 27 March 2019
  • LAST MODIFIED: 27 March 2019
  • DOI: 10.1093/obo/9780195396577-0188


Impossible worlds constitute an increasingly popular yet controversial topic in logic and metaphysics. The term “impossible worlds” parallels the term “possible worlds” and commonly refers to setups, situations, or totalities (“worlds”) that are inconsistent, incomplete, non-classical, or non-normal in possible-world semantics and metaphysics. These may verify a proposition and its negation, be silent as to the truth value of a proposition, or somehow fail to conform to the (classical) laws of logic. Some authors object to the term “impossible world,” preferring to talk of nonstandard worlds or partial situations instead. While the term “impossible world” is sometimes used to refer to a world that is inaccessible from another relative to some specified accessibility relation, impossible worlds are often conceived of as absolutely impossible in a broadly logical, conceptual, or metaphysical sense. As in the case of possible worlds, modern talk of impossible worlds originates with semantic interpretations of modal and non-classical logics, yet the potential applicability of these worlds to logical, metaphysical, and semantic philosophical puzzles has allowed them to permeate the wider philosophical arena. Arguments for impossible worlds often parallel those for possible worlds (see From Possible Worlds to Impossible Worlds) and focus largely on the proposed applications for such worlds (see Applications). As with possible worlds, there are various metaphysical conceptions of impossible worlds (see the Metaphysics of Impossible Worlds), and objections to such worlds are often theory specific (see Objections to Applications and Objections to Impossible Worlds). This article focuses on modern work on impossible worlds and its critics.

General Overviews

Because the topic of impossible worlds is still relatively new, there are few general overviews. Berto and Jago 2018 is a notable exception, with particular emphasis on the logical and semantic developments around impossible worlds, up to and including the most-recent debates. It also contains a rich bibliography on the topic. Nolan 2013 is another useful overview, making a good case as to why one would want to venture into impossible worlds. Priest 1997a, a special edition of the Notre Dame Journal of Formal Logic devoted to impossible worlds, constitutes a central case for impossible worlds, with a collection of key papers on the topic. Priest 1997b is an informative introduction to that collection. Priest 2008 is a clear, accessible introduction to non-classical logics and their accompanying semantics of possible and impossible worlds, and Beall and Van Fraassen 2003 offers nonspecialists a basic grounding in modal and many-valued logics. Both works place developments in their historical and philosophical contexts. Girle 2003 is a general introduction to possible worlds, with a chapter dedicated to impossible worlds. Berto 2006, notable as an Italian work, investigates paraconsistent logics and discusses impossible-world semantics for such logics. Krakauer 2018 is an entry dedicated to impossible worlds in PhilPapers, a growing resource of publications with active links to online material.

  • Beall, J. C., and Bas C. Van Fraassen. Possibilities and Paradox: An Introduction to Modal and Many-Valued Logic. Oxford: Oxford University Press, 2003.

    Offers a basic grounding in philosophical logic, with emphasis on modal and many-valued systems, as background for early-21st-century philosophical debates. Presents motivations for impossible worlds.

  • Berto, Francesco. Teorie dell’assurdo: I rivali del principio di non-contraddizione. Rome: Carocci, 2006.

    An investigation (in Italian) of the law of non-contradiction and paraconsistent logics. Chapters on non-adjunctive and relevant logics include impossible-world semantics for such logics and discuss an interpretation of impossible worlds as information states, which may be locally inconsistent or incomplete.

  • Berto, Francesco, and Mark Jago. “Impossible Worlds.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford University, 2018.

    Good introduction to the topic, covering all key areas and placing impossible worlds in historical context, with particular emphasis on formal developments. Regularly updated. Has a good bibliography.

  • Girle, Rod. Possible Worlds. Chesham, UK: Acumen, 2003.

    Focuses on existence, quantification, and impossibility. Discusses impossible worlds in the context of epistemic possibility; free, paraconsistent, and relevant logics; and the analysis of possibility as truth at a world. A chapter is devoted to impossible worlds.

  • Krakauer, Barak, ed. “Impossible Worlds.” In PhilPapers. London, Canada: PhilPapers Foundation, 2018.

    DOI: 10.1007/s11098-012-9998-0

    PhilPapers is a growing resource for philosophy papers, including on impossible worlds, regularly updated.

  • Nolan, Daniel P. “Impossible Worlds.” Philosophy Compass 8.4 (2013): 360–372.

    DOI: 10.1111/phc3.12027

    Good overview of motivations and applications for impossible worlds. Contains helpful examples of impossible reasoning and impossible fictions. Draws parallels between possible and impossible worlds.

  • Priest, Graham G., ed. Special Issue: Impossible Worlds. Notre Dame Journal of Formal Logic 38.4 (1997a).

    A special issue on impossible worlds, including works cited in this entry. A concentrated effort at making sense of impossible worlds and showcasing applications. Available online.

  • Priest, Graham G. “Editor’s Introduction.” In Special Issue: Impossible Worlds. Notre Dame Journal of Formal Logic 38.4 (1997b): 481–487.

    DOI: 10.1305/ndjfl/1039540765

    A clear introduction to impossible worlds, with signposts for articles in the collection. Also contains a short reply to Stalnaker 1996 (cited under Objections to the Coherence of Impossible Worlds). Available online.

  • Priest, Graham G. An Introduction to Non-classical Logic: From If to Is. 2d ed. Cambridge, UK: Cambridge University Press, 2008.

    DOI: 10.1017/CBO9780511801174

    Clear introduction to non-classical logics couched in possible-world semantics. Links logical developments to philosophical debates, including that on impossible worlds. First edition published in 2001.

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