Philosophy Two-Dimensional Semantics
Cara J. Spencer
  • LAST REVIEWED: 29 June 2011
  • LAST MODIFIED: 29 June 2011
  • DOI: 10.1093/obo/9780195396577-0156


Two-dimensional (2-D) modal logic provides a semantic framework for natural language expressions whose reference systematically varies with context of use, such as indexical pronouns and other expressions that seem to display a similar context sensitivity. Understanding specific uses of such expressions requires both linguistic and nonlinguistic knowledge—knowledge of the meaning of the expression as well as the context in which it is used, and some have argued that the 2-D framework helps distinguish between both sorts of knowledge. The framework has also been brought to bear in debates that turn on how we distinguish knowledge of language from knowledge of the rest of the world, such as the debate over the existence and proper understanding of contingent a priori and necessary a posteriori knowledge and the distinction between internalist and externalist approaches to a variety of philosophical issues (about, for example, belief content). Two-dimensional semantics is less a topic of contemporary philosophical debate than a technical framework for addressing a variety of questions. Philosophical controversies about two-dimensionalism generally concern the assumptions behind its various applications rather than the framework itself, although there are also disagreements about whether the framework illuminates a particular issue. Sometimes those on one side of a debate use the framework, while those on the other side do not. In these cases, this article focuses on work that uses or discusses the 2-D framework explicitly. Different philosophers who use the 2-D framework have also used different terms to refer to the propositions of interest that we can recover from a 2-D matrix. This bibliography will uniformly use R. C. Stalnaker’s terminology: the horizontal proposition associated with an utterance u is the set of worlds w in which u, as uttered in the actual world, is true in w. The diagonal proposition associated with that same utterance is the set of worlds w in which u, as uttered in w, is true in w.

General Overviews

Overviews are of two kinds. Some present the technical framework of multidimensional modal logic, and others consider its application to a particular philosophical issue. Marx and Venema 1997 is in the first category, and it assumes a familiarity with one-dimensional modal logic. Davies and Stoljar 2004 and Gendler and Hawthorne 2002 are introductions to edited collections, and their explanations of the basic 2-D framework and some of its applications will be accessible to anyone with a first course in logic. Chalmers 2006 is a more comprehensive comparison of the interpretations and applications of the framework. Humberstone 2004 explains the development and applications of the framework to problems about modality, and it contains a useful survey of issues outside the problem space of the more strictly philosophical overviews in Davies and Stoljar 2004 and Gendler and Hawthorne 2002.

  • Chalmers, David. “Two-Dimensional Semantics” In Oxford Companion to the Philosophy of Language. Edited by E. Lepore and B. Smith, 574–606. Oxford: Clarendon, 2006.

    A thorough exposition and comparison of interpretations of the 2-D framework and their applications in metaphysics and epistemology, with a focus on the author’s own interpretation and application and a discussion of objections and his replies.

  • Davies, Martin, and Daniel Stoljar. “Introduction.” In Special Issue: The Two Dimensional Framework and Its Applications; Metaphysics, Language, and Mind. Edited by Daniel Stoljar and Martin Davies. Philosophical Studies 118.1–2 (2004): 1–10.

    DOI: 10.1023/B:PHIL.0000019540.28979.7a

    A concise introduction to 2-D modal logic and its use in framing or addressing questions in the philosophy of mind and language and metaphysics and epistemology more generally. It also contains a comprehensive bibliography of classic sources on the 2-D framework and applications.

  • Gendler, T. S., and J. Hawthorne. “Introduction.” In Conceivability and Possibility. Edited by T. S. Gendler and J. Hawthorne, 1–70. New York: Oxford University Press, 2002.

    An excellent introduction to the 2-D framework for philosophers interested in its application to questions about conceivability and possibility. See particularly pp. 39–56.

  • Humberstone, I. Lloyd. “Two-Dimensional Adventures.” In Special Issue: The Two-Dimensional Framework and Its Applications; Metaphysics, Language, and Mind. Edited by Daniel Stoljar and Martin Davies. Philosophical Studies 118.1–2 (2004): 17–65.

    DOI: 10.1023/B:PHIL.0000019542.43440.d1

    Although billed as a retrospective discussion of the author’s own work on the 2-D framework, this paper also includes a wide-ranging explanation of the response to it. It also includes an exhaustive bibliography.

  • Marx, Maarten, and Yde Venema. Multi-Dimensional Modal Logic. Dordrecht, The Netherlands: Kluwer, 1997.

    A comprehensive technical exposition of multidimensional modal systems and their expressive resources that outlines applications to dynamic logic (arrow logic) and temporal logic. This text assumes a general familiarity with modal logic as provided in, for example, Hughes and Cresswell 1996 or Chellas 1980 (both cited under Textbooks).

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