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Summary Two-dimensional semantic theories postulate two "dimensions" of meaning or content, each understood in terms of possible worlds.  The second dimension is typically depends on the external referents of expressions involved, while the first dimension captures the way that reference depends on the world.  There are many different two-dimensional frameworks.  David Kaplan develops a framework involving "character" and "content" to understand the meaning of indexicals and demonstratives.  Robert Stalnaker develops a framework involving "diagonal propositions" and "propositions expressed" to understand assertion and its relation to context.  David Chalmers and Frank Jackson develop frameworks involving "primary intensions" and "secondary intensions" (or "A-" and "C-intensions") to understand the relation between apriority and necessity and also to understand an internal Fregean dimension of content. 
Key works The origins of 2D semantics lie in work on 2D modal logic by  Kamp 1968 and Vlach 1973.  Various 2D analyses of meaning and content are given by Kaplan 1989, Stalnaker 1978, Evans 1979, Davies & Humberstone 1980, Chalmers 1996, and Jackson 1998Soames 2005 is a book-length critique of many different versions.  Numerous papers are collected in Garcia-Carpintero & Macia 2006.
Introductions Chalmers 2006 and Schroeter 2010 give overviews of various different two-dimensional semantic frameworks, along with their motivations and objections to them.
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  1. Semántica bidimensional: desarrollos recientes. [REVIEW]J. J. Acero - 2008 - Teorema: International Journal of Philosophy 27 (2).
  2. Soames. 2008. Reference and Description: The Case Against Two-Dimensionalism.Juan José Acero - unknown
  3. Assertability Conditions of Epistemic (and Fictional) Attitudes and Mood Variation.Mari Alda - unknown - Proceedings of SALT 26.
    Italian is a well-known exception to the cross-linguistic generalization according to which `belief' predicates are indicative selectors across languages. We newly propose that languages that select the subjunctive with epistemic predicates allow us to see a systematic polysemy between what we call an expressive-`belief' (featuring only a doxastic dimension) and an inquisitive-`belief' (featuring both a doxastic and an epistemic dimension conveying doxastic certainty (in the assertion) and epistemic uncertainty (in the presupposition)). We offer several previously unseen contrasts proving this distinction (...)
  4. On Considering a Possible World as Actual.Thomas Baldwin - 2001 - Aristotelian Society Supplementary Volume 75 (1):157–174.
    [Robert Stalnaker] Saul Kripke made a convincing case that there are necessary truths that are knowable only a posteriori as well as contingent truths that are knowable a priori. A number of philosophers have used a two-dimensional model semantic apparatus to represent and clarify the phenomena that Kripke pointed to. According to this analysis, statements have truth-conditions in two different ways depending on whether one considers a possible world 'as actual' or 'as counterfactual' in determining the truth-value of the statement (...)
  5. Two-Dimensionalism and the Social Character of Meaning.Derek Nelson Ball - 2013 - Erkenntnis (S3):1-29.
    This paper develops and critiques the two-dimensionalist account of mental content developed by David Chalmers. I first explain Chalmers’s account and show that it resists some popular criticisms. I then argue that the main interest of two-dimensionalism lies in its accounts of cognitive significance and of the connection between conceivability and possibility. These accounts hinge on the claim that some thoughts have a primary intension that is necessarily true. In this respect, they are Carnapian, and subject to broadly Quinean attack. (...)
  6. Two-Dimensionalism and the “Knowing Which” Requirement.Hagit Benbaji - 2008 - Acta Analytica 23 (1):55-67.
    Two-dimensional semantics aims to eliminate the puzzle of necessary a posteriori and contingent a priori truths. Recently many argue that even assuming two-dimensional semantics we are left with the puzzle of necessary and a posteriori propositions. Stephen Yablo (Pacific Philosophical Quarterly, 81, 98–122, 2000) and Penelope Mackie (Analysis, 62(3), 225–236, 2002) argue that a plausible sense of “knowing which” lets us know the object of such a proposition, and yet its necessity is “hidden” and thus a posteriori. This paper answers (...)
  7. The Metasyntactic Interpretation of Two-Dimensionalism.Gregory Bochner - 2013 - Philosophical Studies 163 (3):611-626.
    Robert Stalnaker contrasts two interpretations, semantic and metasemantic, of the two-dimensionalist framework. On the semantic interpretation, the primary intension or diagonal proposition associated with an utterance is a semantic value that the utterance has in virtue of the actual linguistic meaning of the corresponding sentence, and that primary intension is both what a competent speaker grasps and what determines different secondary intensions or horizontal propositions relative to different possible worlds considered as actual. The metasemantic interpretation reverses the order of explanation: (...)
  8. Context and Content: Pragmatics in Two-Dimensional Semantics.Berit Brogaard - 2012 - In Keith Allan & Kasia Jaszczolt (eds.), Cambridge Handbook of Pragmatics. Cambridge University Press.
    Context figures in the interpretation of utterances in many different ways. In the tradition of possible-worlds semantics, the seminal account of context-sensitive expressions such as indexicals and demonstratives is that of Kaplan's two-dimensional semantics (the content- character distinction), further pursued in various directions by Stalnaker, Chalmers, and others. This chapter introduces and assesses the notion of context-sensitivity presented in this group of approaches, with a special focus on how it relates to the notion of cognitive significance and whether it includes (...)
  9. That May Be Jupiter: A Heuristic for Thinking Two-Dimensionally.Berit Brogaard - 2007 - American Philosophical Quarterly 44 (4):315 - 328.
    According to epistemic two-dimensionalism, every expression is associated with two kinds of meaning: a primary intension (a “Fregean” component) and a secondary intension (a “Russellian” component). While the rst kind of meaning lines up with the speaker’s abilities to pick out referents of correctly employed expressions in hypothetical scenarios, the second kind of meaning is a version of what standard semanticists call “semantic content”—a kind of content which does not pivot on speaker abilities. Despite its conciliatory temperament, epistemic two-dimensionalism has (...)
  10. Bad Intensions.Alex Byrne & James Pryor - 2006 - In Manuel Garcia-Carpintero & Maci (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. pp. 38--54.
    _the a priori role_ (for word T). For instance, perhaps anyone who understands the word _water_ is able to know, without appeal to any further a posteriori information, that _water_ refers to the clear, drinkable natural kind whose instances are predominant in our oceans and lakes (if _water_ refers at all.
  11. Soames on Two-Dimensionalism.David Chalmers - manuscript
    Here the extension of a sentence token is a truth-value, the extension of a name is an individual, and so on. Scenarios are most often understood as centered possible worlds – i.e. ordered triples of worlds, individuals, and times - although they may also be understood in other ways.
  12. Intensions and Indeterminacy: Reply to Soames, Turner, and Wilson.David J. Chalmers - 2014 - Philosophy and Phenomenological Research 89 (1):249-269.
  13. Propositions and Attitude Ascriptions: A Fregean Account.David J. Chalmers - 2011 - Noûs 45 (4):595-639.
    When I say ‘Hesperus is Phosphorus’, I seem to express a proposition. And when I say ‘Joan believes that Hesperus is Phosphorus’, I seem to ascribe to Joan an attitude to the same proposition. But what are propositions? And what is involved in ascribing propositional attitudes?
  14. The Two-Dimensional Argument Against Materialism.David J. Chalmers - 2009 - In Brian P. McLaughlin & Sven Walter (eds.), Oxford Handbook to the Philosophy of Mind. Oxford University Press.
    A number of popular arguments for dualism start from a premise about an epistemic gap between physical truths about truths about consciousness, and infer an ontological gap between physical processes and consciousness. Arguments of this sort include the conceivability argument, the knowledge argument, the explanatory-gap argument, and the property dualism argument. Such arguments are often resisted on the grounds that epistemic premises do not entail ontological conclusion. My view is that one can legitimately infer ontological conclusions from epistemic premises, if (...)
  15. Response to Scott Soames on Two-Dimensionalism.David J. Chalmers - manuscript
    At the April 2006 meeting of the Central Division of the American Philosophical Association, in an author-meets-critics session on Scott Soames' book _Reference and Description: The Case Against Two-Dimensionalism_ , I presented a comment on Soames' book, "Scott Soames' Two-Dimensionalism" . The other critic was Robert Stalnaker. Soames presented his response to critics . Below is a reply to Soames' response to me, for those who were at the session and interested others. Note that this response was mostly written before (...)
  16. Scott Soames' Two-Dimensionalism.David J. Chalmers - manuscript
    Scott Soames’ Reference and Description contains arguments against a number of different versions of two-dimensional semantics. After early chapters on descriptivism and on Kripke’s anti-descriptivist arguments, a chapter each is devoted to the roots of twodimensionalism in “slips, errors, or misleading suggestions” by Kripke and Kaplan, and to the two-dimensional approaches developed by Stalnaker (1978) and by Davies and Humberstone (1981). The bulk of the book (about 200 pages) is devoted to “ambitious twodimensionalism”, attributed to Frank Jackson, David Lewis, and (...)
  17. The Foundations of Two-Dimensional Semantics.David J. Chalmers - 2006 - In Manuel Garcia-Carpintero & Josep Macia (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. pp. 55-140.
    Why is two-dimensional semantics important? One can think of it as the most recent act in a drama involving three of the central concepts of philosophy: meaning, reason, and modality. First, Kant linked reason and modality, by suggesting that what is necessary is knowable a priori, and vice versa. Second, Frege linked reason and meaning, by proposing an aspect of meaning (sense) that is constitutively tied to cognitive signi?cance. Third, Carnap linked meaning and modality, by proposing an aspect of meaning (...)
  18. Two-Dimensional Semantics.David J. Chalmers - 2006 - In E. Lepore & B. Smith (eds.), The Oxford Handbook to the Philosophy of Language. Oxford University Press.
    Two-dimensional approaches to semantics, broadly understood, recognize two "dimensions" of the meaning or content of linguistic items. On these approaches, expressions and their utterances are associated with two different sorts of semantic values, which play different explanatory roles. Typically, one semantic value is associated with reference and ordinary truth-conditions, while the other is associated with the way that reference and truth-conditions depend on the external world. The second sort of semantic value is often held to play a distinctive role in (...)
  19. Epistemic Two-Dimensional Semantics.David J. Chalmers - 2004 - Philosophical Studies 118 (1-2):153-226.
  20. On Sense and Intension.David J. Chalmers - 2002 - Philosophical Perspectives 16 (s16):135-82.
    What is involved in the meaning of our expressions? Frege suggested that there is an aspect of an expression.
  21. Two-Dimensional Semantics and the Nesting Problem.David J. Chalmers & Brian Rabern - 2014 - Analysis 74 (2):210-224.
    Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the two-dimensional (...)
  22. Two-Dimensionalism and the Metaphysical Possibility of Zombies.Daniel Cohnitz - 2003 - In B. Löwe, W. Malzkorn & T. Räsch (eds.), Foundations of The Formal Sciences II. Applications of Mathematical Logic in Philosophy and Linguistics [Trends in Logic]. Kluwer Academic Publishers. pp. 55--62.
  23. The Diagonal and the Demon.Juan Comesaña - 2002 - Philosophical Studies 110 (3):249 - 266.
    Reliabilism about epistemic justification - the thesis that what makes a belief epistemically justified is that it was produced by a reliable process of belief-formation - must face two problems. First, what has been called "the new evil demon problem", which arises from the idea that the beliefs of victims of an evil demon are as justified as our own beliefs, although they are not - the objector claims - reliably produced. And second, the problem of diagnosing why skepticism is (...)
  24. Reference and Description: The Case Against Two-Dimensionalism (Review of Scott Soames' Book).Eros Corazza - 2005 - Philosophy Reviews.
  25. Reference, Contingency, and the Two-Dimensional Framework.Martin Davies - 2004 - Philosophical Studies 118 (1-2):83-131.
    I review and reconsider some of the themes of ‘Two notions of necessity’ (Davies and Humberstone, 1980) and attempt to reach a deeper understanding and appreciation of Gareth Evans’s reflections (in ‘Reference and contingency’, 1979) on both modality and reference. My aim is to plot the relationships between the notions of necessity that Humberstone and I characterised in terms of operators in two-dimensional modal logic, the notions of superficial and deep necessity that Evans himself described, and the epistemic notion of (...)
  26. Two Notions of Necessity.Martin Davies & Lloyd Humberstone - 1980 - Philosophical Studies 38 (1):1-31.
  27. Dual Content Semantics, Privative Adjectives and Dynamic Compositionality.Guillermo Del Pinal - 2015 - Semantics and Pragmatics 8 (7):1-53.
    This paper defends the view that common nouns have a dual semantic structure that includes extension-determining and non-extension-determining components. I argue that the non-extension-determining components are part of linguistic meaning because they play a key compositional role in certain constructions, especially in privative noun phrases such as "fake gun" and "counterfeit document". Furthermore, I show that if we modify the compositional interpretation rules in certain simple ways, this dual content account of noun phrase modification can be implemented in a type-driven (...)
  28. Reference and Response.Louis deRosset - 2010 - Australasian Journal of Philosophy 99999 (1):1-18.
    A standard view of reference holds that a speaker's use of a name refers to a certain thing in virtue of the speaker's associating a condition with that use that singles the referent out. This view has been criticized by Saul Kripke as empirically inadequate. Recently, however, it has been argued that a version of the standard view, a _response-based theory of reference_, survives the charge of empirical inadequacy by allowing that associated conditions may be largely or even entirely implicit. (...)
  29. Low-Grade Two-Dimensionalism.Josh Dever - 2007 - Philosophical Books 48 (1):1-16.
    As tends to be the way with philosophical positions, there are at least as many two-dimensionalisms as there are two-dimensionalists. But painting with a broad brush, there are core epistemological and metaphysical commitments which underlie the two-dimensionalist project, commitments for which I have no sympathies. A sketch of three signi?cant points of disagreement.
  30. Two Types of Rigid Designation.Iris Einheuser - 2005 - Dialectica 59 (3):367–374.
    The notion of a rigid designator was originally introduced with respect to a modal semantics in which only one world, the world of evaluation, is shifted. Several philosophical applications employ a modal semantics which shifts not just the world of evaluation, but also the world considered as actual. How should the notion of a rigid designator be generalized in this setting? In this note, I show that there are two options and argue that, for the currently most popular application of (...)
  31. Epistemic Two-Dimensionalism and Arguments From Epistemic Misclassification.Edward Elliott, Kelvin McQueen & Clas Weber - 2013 - Australasian Journal of Philosophy 91 (2):375-389.
    According to Epistemic Two-Dimensional Semantics (E2D), expressions have a counterfactual intension and an epistemic intension. Epistemic intensions reflect cognitive significance such that sentences with necessary epistemic intensions are a priori. We defend E2D against an influential line of criticism: arguments from epistemic misclassification. We focus in particular on the arguments of Speaks [2010] and Schroeter [2005]. Such arguments conclude that E2D is mistaken from (i) the claim that E2D is committed to classifying certain sentences as a priori, and (ii) the (...)
  32. Comment on ‘Two Notions of Necessity’.Gareth Evans - 2006 - In Manuel Garcia-Carpintero & Josep Macià (eds.), Two-Dimensional Semantics. Clarendon Press.
  33. Comment on 'Two Notions of Necessity'.Gareth Evans - 2004 - Philosophical Studies 118 (1-2):11 - 16.
  34. Actuality, Tableaux, and Two-Dimensional Modal Logics.Lampert Fabio - 2018 - Erkenntnis 83 (3):403-443.
    In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate (...)
  35. The Problem of Factives for Sense Theories.Graeme Forbes - 2011 - Analysis 71 (4):654-662.
    This paper discusses some recent responses to Kripke’s modal objections to descriptivism about names. One response, due to Gluer-Pagin and Pagin, involves employing "actually" operators in a new way. Another, developed mainly by Chalmers, involves distinguishing the dimension of meaning modal operators affect from the dimension other operators, especially epistemic ones, affect. I argue that both these moves run into problems with "mixed" contexts involving factive verbs such as "know", "establish", "prove", etc. In mixed contexts there are both modal and (...)
  36. Matrices and Modalities: On the Logic of Two-Dimensional Semantics.Peter Fritz - manuscript
    Two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. Usually, this theory is presented in an informal manner. In this thesis, I take first steps in formalizing it, and use the formalization to present some considerations in favor of two-dimensional semantics. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that (...)
  37. What is the Correct Logic of Necessity, Actuality and Apriority?Peter Fritz - 2014 - Review of Symbolic Logic 7 (3):385-414.
    This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...)
  38. A Logic for Epistemic Two-Dimensional Semantics.Peter Fritz - 2013 - Synthese 190 (10):1753-1770.
    Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe (...)
  39. Two-Dimensionalism: A Neo-Fregean Interpretation.Manuel García-Carpintero - 2006 - In Manuel García-Carpintero & Josep Macià (eds.), Two-Dimensional Semantics. Oxford: Clarendon Press.
    The truth of a statement depends on the world in two ways: what the statement says is true if the world is as the statement says it is; on the other hand, what the expressions in the statement mean depends on what the world is like (for instance, on what conventions are in place). Each of these two kinds of dependence of truth on the world corresponds to one of the dimensions on the two-dimensional semantic framework, developed in the 1970’ (...)
  40. Two-Dimensional Semantics.Manuel Garcia-Carpintero & Josep Macia (eds.) - 2006 - Oxford: Clarendon Press.
    Two-dimensional semantics is a framework that helps us better understand some of the most fundamental issues in philosophy: those having to do with the relationship between the meaning of words, the way the world is, and our knowledge of the meaning of words. This selection of new essays by some of the world's leading authorities in this field sheds fresh light both on foundational issues regarding two-dimensional semantics and on its specific applications. Contributors: Richard Breheny, Alex Byrne, David Chalmers, Martin (...)
  41. Completeness Results for Some Two-Dimensional Logics of Actuality.David R. Gilbert & Edwin D. Mares - 2012 - Review of Symbolic Logic 5 (2):239-258.
    We provide a Hilbert-style axiomatization of the logic of , as well as a two-dimensional semantics with respect to which our logics are sound and complete. Our completeness results are quite general, pertaining to all such actuality logics that extend a normal and canonical modal basis. We also show that our logics have the strong finite model property and permit straightforward first-order extensions.
  42. Assertion, Context, and Epistemic Accessibility.John Hawthorne & Ofra Magidor - 2009 - Mind 118 (470):377-397.
    In his seminal paper 'Assertion', Robert Stalnaker distinguishes between the semantic content of a sentence on an occasion of use and the content asserted by an utterance of that sentence on that occasion. While in general the assertoric content of an utterance is simply its semantic content, the mechanisms of conversation sometimes force the two apart. Of special interest in this connection is one of the principles governing assertoric content in the framework, one according to which the asserted content ought (...)
  43. If-Clauses as Postsemantic Context-Shifters.Benj Hellie - manuscript
    A mainstay assumption in natural-language semantics is that \emph{if}-clauses bind indexical argument-places in \emph{then}-clauses. Unfortunately, recent work (compare \citealt{santorio12}) suggests that \emph{if}-clauses can somehow act to `shift the context'. On the framework of Kaplan's `Demonstratives' \citep{kaplan77}, that would be `monstrous' and somehow impossible `in English'. The superseding framework of Lewis's `Index, context, and content' \citep{lewis80icc} instead maintains that an indexical argument-place is just one that is bindable (compare~\citealt[ch.~1]{stalnaker14}), but maintains that these are rare---whereas the lesson of recent work is that (...)
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  44. Moral Realism and Two-Dimensional Semantics.Tim Henning - 2011 - Ethics 121 (4):717-748.
    Moral realists can, and should, allow that the truth-conditional content of moral judgments is in part attitudinal. I develop a two-dimensional semantics that embraces attitudinal content while preserving realist convictions about the independence of moral facts from our attitudes. Relative to worlds “considered as counterfactual,” moral terms rigidly track objective, response-independent properties. But relative to different ways the actual world turns out to be, they nonrigidly track whatever properties turn out to be the objects of our relevant attitudes. This theory (...)
  45. Scott Soames, Reference and Description. The Case against Two-Dimensionalism. Princeton, Princeton University Press, 2005. [REVIEW]Jan Heylen - 2006 - Tijdschrift Voor Filosofie 68 (2):406-408.
  46. The Two-Dimensionalist Reductio.Robert J. Howell - 2008 - Pacific Philosophical Quarterly 89 (3):348-358.
    Abstract: In recent years two-dimensional semantics has become one of the most serious alternatives to Millianism for the proper interpretation of modal discourse. It has origins in the works of a diverse group of philosophers, and it has proven popular as an interpretation of both language and thought. It has probably received most of its attention, however, because of its use by David Chalmers in his arguments against materialism. It is this more metaphysical application of two-dimensionalism that is the concern (...)
  47. Two-Dimensional Adventures.Lloyd Humberstone - 2004 - Philosophical Studies 118 (1-2):17--65.
    This paper recalls some applications of two-dimensional modal logic from the 1980s, including work on the logic of Actually and on a somewhat idealized version of the indicative/subjunctive distinction, as well as on absolute and relative necessity. There is some discussion of reactions this material has aroused in commentators since. We also survey related work by Leslie Tharp from roughly the same period.
  48. Why We Need A-Intensions.Frank Jackson - 2004 - Philosophical Studies 118 (1-2):257-277.
    I think recent discussions of content and reference have not paid enough attention to the role of language as a convention-governed system of communication. With this as a background theme, I explain the role of A-intensions in elucidating one important notion of content and correlative notions of reference.
  49. The A Priori‐Operator and the Nesting Problem.Eric Johannesson & Sara Packalén - 2016 - Thought: A Journal of Philosophy 5 (3):169-176.
    Many expressions intuitively have different epistemic and modal profiles. For example, co-referring proper names are substitutable salva veritate in modal contexts but not in belief-contexts. Two-dimensional semantics, according to which terms have both a so-called primary and a secondary intension, is a framework that promises to accommodate and explain these diverging intuitions. The framework can be applied to indexicals, proper names or predicates. Graeme Forbes argues that the two-dimensional semantics of David Chalmers fails to account for so-called nested contexts. These (...)
  50. Semantics, Two-Dimensional.Jens Kipper - 2018 - Internet Encyclopedia of Philosophy.
    Two-dimensional semantic theories distinguish between two different aspects, or ‘dimensions’, of the meaning of linguistic expressions. Many other theories identify the meaning of an expression with a dependency of its extension on the state of the world. (The extension of a sentence is its truth-value, and the extension of a sub-sentential expression … Continue reading Semantics, Two-Dimensional →.
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