Philosophy Two-Dimensional Semantics
by
Cara J. Spencer
  • LAST REVIEWED: 08 October 2015
  • LAST MODIFIED: 29 June 2011
  • DOI: 10.1093/obo/9780195396577-0156

Introduction

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.

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    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.

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    • 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.0000019540.28979.7aSave Citation »Export Citation »E-mail Citation »

      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.

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      • 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.

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        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.

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        • 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.d1Save Citation »Export Citation »E-mail Citation »

          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.

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

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            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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            Textbooks

            The only textbook treatments of two-dimensional (2-D) modal logic are in modal logic textbooks. Hughes and Cresswell 1996 and Chellas 1980 are standard introductions that could be used as textbooks for a first course in modal logic. For some philosophical purposes, these treatments tend to be simultaneously too much information (because they consider issues that are not relevant for many philosophical applications) and not enough information (as they have little if anything to say about 2-D systems). Sider 2010 offers a happy medium, introducing enough about modal logic and its 2-D variant to explain its various applications while leaving out some aspects of the full presentation that are less relevant for the applications. Some of the applications of the 2-D framework in semantics work in tandem with, or presuppose an understanding of, core applications of modal logic in semantics, and these are described in Partee, et al. 1990. There are no textbook treatments of the philosophical applications of the 2-D framework, so those seeking an introduction should look to General Overviews. Some of the original primary source material presupposes little specialized background and offers an excellent introduction to the problems. See in particular R. C. Stalnaker’s article “Assertion” (Stalnaker 1978), D. Kaplan’s article “Demonstratives” (Kaplan 1989), and David K. Lewis’s article “Index, Context, and Content” (Lewis 1981) in Context Sensitivity in Natural Language Semantics. See S. Kripke’s Naming and Necessity (Kripke 1980 in Precursors to the Debate) and David Chalmers’s The Conscious Mind (Chalmers 1996 in Mental Content and Consciousness).

            • Chellas, B. Modal Logic: An Introduction. Cambridge, UK: Cambridge University Press, 1980.

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              A standard text in modal logic, with exercises.

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              • Hughes, G. E., and M. J. Cresswell. A New Introduction to Modal Logic. London: Routledge, 1996.

                DOI: 10.4324/9780203290644Save Citation »Export Citation »E-mail Citation »

                An update of a standard textbook for a first course in modal logic, with exercises.

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                • Partee, B. H., A. G. B. ter Meulen, and R. E. Hall. Mathematical Methods in Linguistics. Dordrecht, The Netherlands: Kluwer, 1990.

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                  Chapter 15 covers applications of modal logic to address several problems that pertain to background applications of the 2-D framework in linguistics.

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                  • Sider, T. Logic for Philosophy. New York: Oxford University Press, 2010.

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                    Aimed at graduate students in philosophy and assuming a first course in formal logic, this book lays out the more advanced logic that students will need to read contemporary philosophy. It includes chapters on propositional modal logic and its 2-D variant plus exercises.

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                    Anthologies

                    Although there have been many papers published on the two-dimensional (2-D) framework and its applications, there are only two collections specifically on the subject. Of the two, Garcia-Carpintero and Macià 2006 is more wide-ranging, covering defenses and criticisms of some familiar applications of the framework and some more speculative applications to problems in pragmatics, ethics, and consciousness. Stoljar and Davies 2004 is more narrowly focused on uses of the 2-D framework to characterize necessity and a priority, and it includes a particularly helpful and concise introduction to the issues by the editors. There is some overlap between the two volumes—the contributions by G. Evans, Martin Davies, and R. C. Stalnaker are the same, and the David Chalmers contribution in Stoljar and Davies 2004 is an abridged version of the one in Garcia-Carpintero and Macià 2006. Gendler and Hawthorne 2002 collects new work on conceivability and possibility, some of which considers the application of the 2-D framework in that problem space. Stalnaker 1999 and Stalnaker 2003 contain Stalnaker’s papers on the application of the framework to problems in pragmatics and semantics (in the former) and the interpretation of the framework and its limits (in the latter). The introductory essays in both volumes include explanations of the basic 2-D framework. Preyer and Peter 2007 collects new papers on context sensitivity, some of which consider an extension of the 2-D model explained in, for example, D. Kaplan’s article “Demonstratives” (Kaplan 1989, cited under Context Sensitivity in Natural Language Semantics) to other kinds of natural language expressions.

                    • Garcia-Carpintero, Manuel, and Josep Macià, eds. Two-Dimensional Semantics. New York: Oxford University Press, 2006.

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                      This collection includes some papers originally written for a conference on the 2-D framework but also includes some specially commissioned papers. Topics considered include foundations of the 2-D framework and its applications in semantics, pragmatics, phenomenal and indexical concepts, epistemology, and ethics.

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                      • Gendler, T. S., and J. Hawthorne, eds. Conceivability and Possibility. New York: Oxford University Press, 2002.

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                        This collection of original essays includes some considering the application of the 2-D framework. See in particular papers by George Bealer, David Chalmers, Stephen Yablo, and Crispin Wright.

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                        • Preyer, G., and G. Peter, eds. Context Sensitivity and Semantic Minimalism: New Essays on Semantics and Pragmatics. New York: Oxford University Press, 2007.

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                          New defenses of a variety of strategies of explaining the role of context in the determination of the complete meaning of an utterance, including explicitly two-dimensionalist approaches and alternatives.

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                          • Stalnaker, R. C. Context and Content. New York: Oxford University Press, 1999.

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                            This volume of mostly previously published essays includes papers that introduce Stalnaker’s application of the 2-D framework in semantics, pragmatics, and belief ascription and content and a helpful introductory essay that presents the 2-D framework.

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                            • Stalnaker, R. C. Ways a World Might Be. New York: Oxford University Press, 2003.

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                              This volume contains fourteen essays in metaphysics, all but two of which are previously published. It includes three essays on the 2-D framework that focus on interpretations rather than applications.

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

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                                This volume arose from papers and commentaries at a 2002 conference on the 2-D framework and is consequently focused on the themes arising in the main conference papers due to Robert Stalnaker, David Chalmers, Frank Jackson, Martin Davies, and Lloyd Humberstone.

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                                Bibliographies

                                Davies and Stoljar 2004 and Humberstone 2004 contain comprehensive bibliographies of classic sources on the framework and its applications. Although not a bibliography per se, PhilPapers is a free searchable database of online scholarship in philosophy. Papers are organized by topic and subtopic, and many topic headings (including the one on 2-D semantics) are edited for completeness and relevance.

                                • 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.0000019540.28979.7aSave Citation »Export Citation »E-mail Citation »

                                  This introductory essay contains a concise bibliography of classic sources on the 2-D framework and applications.

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                                  • 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.d1Save Citation »Export Citation »E-mail Citation »

                                    The exhaustive bibliography included in this overview essay considers applications of the 2-D framework outside the familiar problem space.

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                                    • Philpapers.

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                                      Edited by David Chalmers and David Bourget, Philpapers is a continuously updated directory of online papers and books in all areas of philosophy. Many topic areas, including 2-D semantics, are edited, in this case by Chalmers.

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                                      Reference Works

                                      The few reference works on 2-D semantics are listed in General Overviews. Entries here provide background to the problems to which the framework is commonly applied. The free online Stanford Encyclopedia of Philosophy contains comprehensive entries on several relevant subjects here, including Garson 2009, Braun 2007, and Korta and Perry 2006. Lepore and Smith 2006 and Horn and Ward 2004 include many useful background entries, the former situated in a philosophical context and the latter in a linguistic one. Soames 2007 introduces a criticism of the 2-D framework in semantics and metasemantics developed by the author in a subsequent book (Soames 2005, cited under Generalized Two-Dimensional Semantics). McLaughlin 2011 contains several introductions to questions in the philosophy of mind that the 2-D framework is sometimes invoked to settle or state.

                                      Precursors to the Debate

                                      The 2-D framework was introduced in Kamp 1971 and further elaborated in Vlach 1971 for tense logic and in Segerberg 1973, Aqvist 1973, and van Fraassen 1977 for modal logic. Montague 1994 offers a semantics for indexicals that is formally equivalent to the later approach in D. Kaplan’s article “Demonstratives” (Kaplan 1989, cited under Context Sensitivity in Natural Language Semantics). Crossley and Humberstone 1977 introduces a 2-D operator “fixedly,” which is invoked in further work to distinguish different sorts of necessity. The original source for several examples and problems driving debate about the 2-D framework is Kripke 1980.

                                      Context Sensitivity in Natural Language Semantics

                                      Two-dimensional (2-D) modal logic is a natural vehicle for representing certain types of context sensitivity in natural language. Lewis 1970 gives a general sketch of this sort of semantic theory, and work in this area draws heavily on the sort of picture found there. Kaplan 1989 and Stalnaker 1978 develop this picture in a way that gives the diagonal a theoretical role, although in each case the roles are quite different. Kaplan 1989 uses the framework to give a semantics for indexical and demonstrative pronouns. The diagonal content of an indexical expression (that is, the character in D. Kaplan’s terms) corresponds with its cognitive significance, and Kaplan invokes it to address some questions about the epistemology of indexical and demonstrative belief. Many philosophers have hoped to extend Kaplan’s picture to treat other cases of natural language context sensitivity. (In many cases these applications do not make theoretical use of the diagonal proposition, so they are excluded from this bibliography.) Stalnaker 1978 argues that the informational content of an assertion is a subset of the open possibilities in the conversation in which it takes place. Both the horizontal and the diagonal propositions the assertion determines can be candidates for its informational content. Lewis 1981 compares the approaches in Stalnaker 1978 and Kaplan 1989 and defends a picture very much like R. C. Stalnaker’s. Perry 2001 embeds a 2-D approach to language and thought content within situation semantics. Stalnaker 1987 applies the framework to propositional attitude ascriptions and shows how it can shed light on traditional puzzles about belief. Stalnaker 1998 revisits the original motivation for the 2-D framework in pragmatics and the picture of the role of context in determining utterance content that motivates it. Weatherson 2001 is less concerned with context sensitivity than with the distinction between a priority and necessity as captured in the 2-D framework (see Davies and Humberstone 1980, cited under A Posteriori Necessity). B. Weatherson argues that this distinction sheds light on the distinction between indicative and subjunctive conditionals and invokes it to give a unified semantics for both.

                                      • Kaplan, D. “Demonstratives.” In Themes from Kaplan. Edited by J. Almog, J. Perry, and H. Wettstein, 481–563. New York: Oxford University Press, 1989.

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                                        Determines that indexical and demonstrative pronouns are directly referential and that their reference is determined as a function of the context of utterance.

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                                        • Lewis, David K. “General Semantics.” Synthese 22 (1970): 18–67.

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                                          Lewis sketches a general model for a referential semantic theory suitable for adaptation to natural languages and considers the proper incorporation of context sensitivity and the basic notion of evaluation of a sentence relative to an index.

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                                          • Lewis, David K. “Index, Context, and Content.” In Philosophy and Grammar. Edited by S. Kanger and S. Ohman, 79–100. Dordrecht, The Netherlands: Reidel, 1981.

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                                            This overview of the structure and motivation for the 2-D framework compares Stalnaker 1978 and Kaplan 1989 and sketches a more general application of the 2-D framework to context sensitivity in natural language.

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                                            • Perry, John. Reference and Reflexivity. Stanford, CA: Center for the Study of Language and Information, 2001.

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                                              Utterances have both familiar referential contents and reflexive contents, which are roughly the information audiences get from an utterance if they know what the words mean but lack the background or contextual information to recover the referential content.

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                                              • Stalnaker, R. C. “Assertion.” In Syntax and Semantics, Vol. 9, Pragmatics. Edited by P. Cole, 315–332. New York: Academic, 1978.

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                                                Stalnaker uses the 2-D framework to give an account of assertion content and argues that the informative content of an utterance may be understood as the diagonal proposition of the 2-D matrix for that utterance.

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                                                • Stalnaker, R. C. “Semantics for Belief.” Philosophical Topics 15 (1987): 177–190.

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                                                  Stalnaker applies the 2-D framework to familiar problems about the semantics for belief ascriptions. Also contains a helpful contrast of Stalnaker 1978 and Kaplan 1989.

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                                                  • Stalnaker, R. C. “On the Representation of Context.” Journal of Logic, Language, and Information 7.1 (1998): 3–19.

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                                                    This paper considers what discourse contexts must be if they are to play the dual roles of affecting and being affected by speech acts. It also considers and responds to a criticism concerning the framework’s treatment of pronouns with indefinite antecedents.

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                                                    • Weatherson, B. “Indicative and Subjunctive Conditionals.” Philosophical Quarterly 203 (2001): 200–216.

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                                                      The 2-D framework is used to give a unified account of the truth conditions of indicative and subjunctive conditionals.

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                                                      A Posteriori Necessity

                                                      Backgrounding discussions of modality and the 2-D framework is S. Kripke’s Naming and Necessity (Kripke 1980; see Precursors to the Debate), in particular his attack on the traditional identification of necessary truths with those known a priori and contingent truths with those known a posteriori. Tichy 1983 defends the traditional identification of necessity with a priority and contingency with a posteriority against Kripke’s arguments. Evans 1979 distinguishes deep and superficial necessity and argues that Kripke’s examples of the necessary a posteriori are necessary in the superficial sense only. Davies and Humberstone 1980 uses the 2-D framework to give a formal rendering of G. Evans’s distinction. Davies 2004 returns to the central problem in Davies and Humberstone 1980 and clarifies the relationship between the notions sketched there and a priority. Baldwin 2001 and Stalnaker 2001 consider the suitability of the 2-D framework to account for the necessary a posteriori and contingent a priori. R. C. Stalnaker ends up skeptical, but T. Baldwin argues that it can account for a certain sort of contingent a priori knowledge arising from stipulations. Wong 1996 defends a sentence-relative account of a priority, on which a proposition can be a priori relative to a sentence that determines a necessary diagonal proposition.

                                                      Generalized Two-Dimensional Semantics

                                                      While applications of the 2-D framework to straightforward linguistic context sensitivity and to modal operators is quite widely accepted, generalized applications are more controversial. Chalmers 2006, Chalmers 2002, and Jackson 1998 have used the 2-D framework to give a semantics for both language and thought, although their work serves different philosophical projects. For Frank Jackson, the diagonal intension (in Jackson’s terms, the A-intension) for a concept reveals reference-fixing criteria that are known a priori to speakers and that are generally shared by all members of the speaker’s linguistic community. Furthermore, a successful metaphysical reduction of, for example, mental facts or moral facts to physical facts must be faithful to the A-intension of the higher-level concept (otherwise the reduction would not be explanatory). For Chalmers, the 2-D framework allows us to trace the constitutive connections among reason, meaning, and possibility while accommodating the core insights of the direct reference picture. Some have suggested that generalized 2-D semantics of either stripe resurrects semantic descriptivism and faces many of its problems (see Byrne and Pryor 2006). Some philosophers have found the 2-D framework useful in stating questions or positions in metasemantics as well as semantics, though others have claimed that the framework can confuse the two sorts of questions. Stalnaker 2003 rejects the generalized two-dimensionalism of Chalmers and Jackson, which Stalnaker distinguishes from his own metasemantic interpretation. Soames 2005, while endorsing the limited applications in D. Kaplan’s article “Demonstratives” (Kaplan 1989, cited under Context Sensitivity in Natural Language Semantics) and the application to modal operators in Martin Davies and Lloyd Humberstone’s article “Two Notions of Necessity” (Davies and Humberstone 1980, cited under A Posteriori Necessity), criticizes the application in the context of the more ambitious projects of R. C. Stalnaker, Chalmers, and Jackson. Schroeter 2003 and Marconi 2005 offer more targeted criticisms of Chalmers’s and Jackson’s 2-D approaches to meaning and thought content.

                                                      • Byrne, A., and J. Pryor. “Bad Intensions.” In Two-Dimensional Semantics. Edited by Manuel Garcia-Carpintero and Josep Macià, 38–54. New York: Oxford University Press, 2006.

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                                                        David Chalmers’s 2-D semantics for natural kind terms is a version of descriptivism and as such faces descriptivism’s many problems.

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                                                        • Chalmers, David. “On Sense and Intension.” In Philosophical Perspectives, Vol. 16, Language and Mind. Edited by James E. Tomberlin, 135–182. Oxford: Blackwell, 2002.

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                                                          Chalmers offers an interpretation of the 2-D framework that respects a Fregean picture of intension, according to which the intension of an expression determines both its reference and its cognitive value.

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                                                          • Chalmers, David. “The Foundations of Two-Dimensional Semantics.” In Two-Dimensional Semantics. Edited by Manuel Garcia-Carpintero and Josep Macià, 55–140. New York: Oxford University Press, 2006.

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                                                            Chalmers lays out an ambitious program that appeals to the 2-D framework to restore the connection among meaning, reason, and modality that accommodates S. Kripke’s arguments in Kripke 1980 (cited under Precursors to the Debate).

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                                                            • Jackson, Frank. From Metaphysics to Ethics. New York: Oxford University Press, 1998.

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                                                              Jackson defends conceptual analysis as a method of uncovering a priori knowledge and rejects the familiar materialist claim that mind-brain identities are known only a posteriori. Jackson also offers a robust defense of descriptivism and invokes the 2-D framework to distinguish two propositions associated with a sentence. He claims that one gives the truth conditions of the sentence and the other its cognitive value.

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                                                              • Marconi, D. “Two-Dimensional Semantics and the Articulation Problem.” Synthese 143.3 (2005): 321–349.

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                                                                Contra David Chalmers, the 2-D framework does not help us assimilate a Kripkean causal theory of reference for natural kind terms with Fregean intuitions that different co-referring terms will differ in cognitive significance.

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                                                                • Schroeter, Laura. “Gruesome Diagonals.” Philosophers’ Imprint 3 (2003).

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                                                                  Schroeter takes issue with David Chalmers’s and Frank Jackson’s semantic thesis that the diagonal or primary intension associated with a word or thought characterizes its meaning or content. Meanings so construed, first, are too holistic and, second, cannot slot into explanations of behavior, communication, or deliberation.

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                                                                  • Soames, Scott. Reference and Description. Princeton, NJ: Princeton University Press, 2005.

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                                                                    In this book-length salvo against certain interpretations and applications of the 2-D framework, Soames offers a careful exposition of descriptivism about reference and its problems, direct reference alternative, and what he sees as the revival of descriptivism in what he calls “ambitious” two-dimensionalism of Frank Jackson and David Chalmers as well as the weaker two-dimensionalism of R. C. Stalnaker.

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                                                                    • Stalnaker, R. C. “Conceptual Truth and Metaphysical Necessity.” In Ways a World Might Be. By R. C. Stalnaker, 201–215. New York: Oxford University Press, 2003.

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                                                                      Stalnaker outlines the 2-D framework and contrasts generalized interpretations (for example, Chalmers 1996 [cited under Mental Content and Consciousness], Chalmers 2002, Jackson 1998) with his own metasemantic interpretation of it. He argues that only the former sort of interpretation can give an account of truth in virtue of meaning but that this account is compromised by the implausible assumptions about intentionality that underwrite it.

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                                                                      Conceivability and Possibility

                                                                      Debate in this area has focused on two issues: whether conceivability entails possibility and how we can tell what we are conceiving in the first place. In the 2-D literature, both issues are commonly addressed in the service of criticizing or shoring up conceivability arguments against a posteriori physicalism. One argument that backgrounds debate in this area is S. Kripke’s argument that the mind-brain identity theory faces a problem in explaining away the fact that we seem to be able to conceive that it is false (see Kripke 1980, cited under Precursors to the Debate). David Chalmers’s The Conscious Mind (Chalmers 1996, cited under Mental Content and Consciousness) and Frank Jackson’s From Metaphysics to Ethics (Jackson 1998, cited under Generalized Two-Dimensional Semantics) give Kripke’s argument a 2-D interpretation. Chalmers 2009 also offers a version of the conceivability argument familiar from the more compressed presentation in The Conscious Mind. Lewis 1994 takes the same sorts of considerations to be decisive against a posteriori physicalism but parts company with Chalmers in defending physicalism of the a priori variety. Papineau 2007 argues that the Chalmers-Jackson line misinterprets Kripke, and Yablo 2000 attacks the Chalmers-Jackson argument on its own terms, arguing that it incorrectly supposes that all mistakes about the content of our conceptions fit a certain form. Howell 2008 argues that Chalmers’s metaphysical two-dimensionalism contains the seeds of its own undoing, specifically in the assumption that there is a genuine possible world answering to every coherent primary intension. Yablo 2002 offers a different criticism of the general picture of the relation among conceivability, a priority, meaning, and possibility due to Chalmers and Jackson. He argues that although we can use the 2-D framework to characterize conceptual necessity, the resulting notion cannot characterize the intuitive notion of a priori knowledge. Perry 2001 invokes the 2-D framework in defense of a posteriori physicalism, saying that we can close the epistemic gap between phenomenal knowledge and physical knowledge by appealing to the diagonal content of the former. Block and Stalnaker 1999 argues that we can close the gap between phenomenal and physical knowledge without conceptual analysis, the same way other epistemic gaps have been closed. Questions about conceivability and possibility overlap with questions about the proper understanding of a posteriori necessities, thus many of the entries in A Posteriori Necessity are also relevant here.

                                                                      • Block, N., and R. C. Stalnaker. “Conceptual Analysis, Dualism, and the Explanatory Gap.” Philosophical Review 108.1 (January 1999): 1–46.

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                                                                        Conceptual analysis is not the only way to close the explanatory gap between consciousness and the physical. We can close other explanatory gaps (about life, for example) without conceptual analysis, and the gap in explanations of consciousness could be closed in similar fashion.

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                                                                        • Chalmers, David. “The Two-Dimensional Argument against Materialism.” In The Oxford Handbook of Philosophy of Mind. Edited by Brian P. McLaughlin, 313–338. New York: Oxford University Press, 2009.

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                                                                          A more careful and explicit presentation of the conceivability argument against materialism from Chalmers 1996 (cited under Mental Content and Consciousness), with objections and replies, and comparison of this argument to other arguments against materialism that move from an epistemic gap to a metaphysical one.

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                                                                          • Howell, R. “The Two-Dimensionalist Reductio.” Pacific Philosophical Quarterly 89.3 (2008): 348–358.

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                                                                            Howell argues that metaphysical two-dimensionalism is self-defeating. The culprit is the assumption that every coherent primary intension is verified in some metaphysically possible world.

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                                                                            • Lewis, David. “Lewis, David: Reduction of Mind.” In A Companion to the Philosophy of Mind. Edited by Samuel Guttenplan, 412–430. Cambridge, MA: Blackwell, 1994.

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                                                                              In this overview of Lewis’s own approach to central questions in philosophy of mind, Lewis defends a priori physicalism and shows a posteriori physicalism to be incompatible with the popular view that necessary a posteriori knowledge involves a priori inferences from contingent a posteriori knowledge.

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                                                                              • Papineau, David. “Kripke’s Proof is Ad Hominem not Two-Dimensional.” Philosophical Perspectives 21.1 (2007): 475–494.

                                                                                DOI: 10.1111/j.1520-8583.2007.00133.xSave Citation »Export Citation »E-mail Citation »

                                                                                Papineau takes issue with the two-dimensionalist interpretation of the Kripke 1980 (see Precursors to the Debate) argument against the identity theory, arguing that S. Kripke’s point is instead that the identity theorist, who endorses identities such as pain = Brain state B, cannot at the same time explain the apparent contingency of these claims.

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                                                                                • Perry, John. Knowledge, Possibility, and Consciousness. Cambridge, MA: MIT Press, 2001.

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                                                                                  Perry defends physicalism against the challenge posed by consciousness. Perry appeals to a 2-D account of content of phenomenal beliefs in his reply to the dualist, arguing that the reflexive (similar to the diagonal) content of beliefs about what experiences are like can carry information that their referential content does not carry.

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                                                                                  • Yablo, Stephen. “Textbook Kripkeanism and the Open Structure of Concepts.” Pacific Philosophical Quarterly 81.1 (2000): 98–122.

                                                                                    DOI: 10.1111/1468-0114.00097Save Citation »Export Citation »E-mail Citation »

                                                                                    Textbook Kripkeanism says that mistakes about the content of our conceptions always result from the confusion of diagonal intensions with horizontal ones. Yablo rejects textbook Kripkeanism, because it makes meaning and modality too closely intertwined.

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                                                                                    • Yablo, Stephen. “Coulda Woulda Shoulda.” In Conceivability and Possibility. Edited by T. S. Gendler and J. Hawthorne, 441–491. New York: Oxford University Press, 2002.

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                                                                                      Yablo uses the 2-D framework to characterize conceptual necessity and argues that the notion so construed does not line up with the intuitive notion of a priority. For a wide range of expressions, we are simply in no position to tell whether they would apply given a complete world description.

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                                                                                      Mental Content and Consciousness

                                                                                      Since the 2-D framework has proved useful in characterizing linguistic content, it is natural to extend the 2-D treatment to other types of intentional content, such as the content of thought and experience. White 1982 develops a Kaplan-style 2-D picture of thought content and uses it to carve out a role for beliefs and desires in psychological explanation. Chalmers 1996 offers a generalized 2-D semantics for language and thought and uses it in the service of an argument against materialism, which is developed in more detail in David Chalmers’s article “The Two Dimensional Argument against Materialism” (Chalmers 2009, cited under Conceivability and Possibility). Chalmers develops a 2-D account of thought content in Chalmers 2002 and of phenomenal content in Chalmers 2003. Nida-Rümelin 2006 appeals to a 2-D account of phenomenal content to argue that it is implausible that phenomenal qualities are only contingently associated with their realizers. Stalnaker 1990 is skeptical of the extension of the 2-D picture from linguistic content to thought content on the ground that it commits us to internalism, although Stalnaker 2008 argues that phenomenal content is analogous to indexical thought content and appeals to the 2-D framework to develop the analogy in an externalist framework. Schiffer 2003 is also critical of the 2-D approach to mental content, though S. Schiffer’s criticism moves from considerations about what it is to know the meaning of an expression. For further background, see the separate Oxford Bibliographies article on “Consciousness.”

                                                                                      • Chalmers, David. The Conscious Mind. New York: Oxford University Press, 1996.

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                                                                                        Chalmers argues that facts about consciousness force us to accept mind-body dualism. He defends a 2-D semantics for mental and physical kind terms and concepts and uses it to argue that materialists cannot escape his arguments by endorsing a posteriori physicalism.

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                                                                                        • Chalmers, David. “The Components of Content.” In Philosophy of Mind: Classical and Contemporary Readings. Edited by David Chalmers, 608–633. New York: Oxford University Press, 2002.

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                                                                                          An influential exposition of the 2-D framework and its application to many long-standing puzzles about belief.

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                                                                                          • Chalmers, David. “The Content and Epistemology of Phenomenal Belief.” In Consciousness: New Philosophical Essays. Edited by Q. Smith and A. Jokic, 220–272. New York: Oxford University Press, 2003.

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                                                                                            Chalmers distinguishes between various kinds of concepts to which experience gives rise and offers a 2-D treatment of their meanings. He uses the treatment to address some core questions about phenomenal beliefs.

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                                                                                            • Nida-Rümelin, Martine. “Phenomenal Belief, Phenomenal Concepts, and Phenomenal Properties in a Two-Dimensional Framework.” In Two-Dimensional Semantics. Edited by Manuel Garcia-Carpintero and Josep Macià, 205–219. Oxford: Oxford University Press, 2006.

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                                                                                              Phenomenal concepts (concepts that pick out the phenomenal qualities of experience by their phenomenal feel) pick out the same property in all possible worlds, consequently a certain route to explaining away the intuition that phenomenal qualities are only contingently associated with their physical realizers is blocked.

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                                                                                              • Schiffer, S. The Things We Mean. New York: Oxford University Press, 2003.

                                                                                                DOI: 10.1093/0199257760.001.0001Save Citation »Export Citation »E-mail Citation »

                                                                                                Considerations about what it is to know the meaning of an expression tell against the 2-D approach to expression, meaning, and thought content due to Chalmers 2002 and Jackson 1998 (both cited under Generalized Two-Dimensional Semantics).

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                                                                                                • Stalnaker, R. C. “Narrow Content.” In Propositional Attitudes. Edited by C. A. Anderson and J. Owens, 131–146. Stanford, CA: Center for the Study of Language and Information, 1990.

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                                                                                                  An externalist about content argues that 2-D semantics does not offer a clear or coherent notion of narrow or internal thought content, mainly because we cannot always identify particular thoughts across possible worlds and ask what their contents would have been in those worlds.

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                                                                                                  • Stalnaker, R. C. Our Knowledge of the Internal World. New York: Oxford University Press, 2008.

                                                                                                    DOI: 10.1093/acprof:oso/9780199545995.001.0001Save Citation »Export Citation »E-mail Citation »

                                                                                                    Stalnaker defends an externalist approach to knowledge of the contents of our thoughts and our experience. He likens knowledge of what it is like to have a particular experience to indexical knowledge. He invokes the 2-D framework to display the context sensitivity of both kinds of knowledge.

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                                                                                                    • White, S. “Partial Character and the Language of Thought.” Pacific Philosophical Quarterly 63 (1982): 347–365.

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                                                                                                      White appeals to a Kaplan-style (see Kaplan 1989, cited under Context Sensitivity in Natural Language Semantics) 2-D account of thought content to carve out a role for beliefs and desires in psychological explanation and to argue that the “partial character,” analogous to the diagonal proposition, has a theoretical use in explaining meaning change and the language of thought.

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