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Two-Dimensional Semantics

Edited by David Chalmers (Australian National University, New York University)
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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. Thomas Baldwin (2001). On Considering a Possible World as Actual. 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 (...)
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  2. Derek Ball (2013). Two-Dimensionalism and the Social Character of Meaning. Erkenntnis: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. (...)
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  3. Hagit Benbaji (2008). Two-Dimensionalism and the “Knowing Which” Requirement. 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 (...)
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  4. Stephen Biggs & Jessica M. Wilson, Abductive Two-Dimensionalism: A New Route to the A Priori Identification of Necessary Truths.
    Chalmers and Jackson (2001) offer an epistemic interpretation of the two-dimensional semantic framework advanced by Kaplan (1979, 1989), Stalnaker (1978), and others. Epistemic two-dimensional semantics (E2D) aims to re-forge the link between necessity and a priority seemingly broken by Kripke (1972/1980). On the E2D strategy, a priori knowledge of certain semantic intensions provides a route to a priori knowledge of a wide range of modal truths---nice outcome, if we can get it. E2D faces the serious challenge, however, that we typically (...)
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  5. Gregory Bochner (2013). The Metasyntactic Interpretation of Two-Dimensionalism. 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: (...)
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  6. Berit Brogaard (2012). Context and Content: Pragmatics in Two-Dimensional Semantics. 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 (...)
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  7. Berit Brogaard (2007). That May Be Jupiter: A Heuristic for Thinking Two-Dimensionally. 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 (...)
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  8. Alex Byrne & James Pryor (2006). Bad Intensions. In Manuel Garcia-Carpintero & Maci (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. 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.
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  9. David Chalmers, Soames on Two-Dimensionalism.
    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.
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  10. David Chalmers (forthcoming). Intensions and Indeterminacy: Reply to Soames, Turner, and Wilson. Philosophy and Phenomenological Research.
    A reply to Scott Soames, Jason Turner, and Mark Wilson, for a symposium in Philosophy and Phenomenological Research on Constructing the World.
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  11. David J. Chalmers (2011). Propositions and Attitude Ascriptions: A Fregean Account. 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?
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  12. David J. Chalmers (2009). The Two-Dimensional Argument Against Materialism. 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 (...)
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  13. David J. Chalmers, Response to Scott Soames on Two-Dimensionalism.
    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 (...)
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  14. David J. Chalmers, Scott Soames' Two-Dimensionalism.
    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 (...)
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  15. David J. Chalmers (2006). The Foundations of Two-Dimensional Semantics. In Manuel Garcia-Carpintero & Josep Macia (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. 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 (...)
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  16. David J. Chalmers (2006). Two-Dimensional Semantics. In E. Lepore & B. Smith (eds.), Oxford Handbook of 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 (...)
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  17. David J. Chalmers (2004). Epistemic Two-Dimensional Semantics. Philosophical Studies 118 (1-2):153-226.
  18. David J. Chalmers (2002). On Sense and Intension. 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.
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  19. David J. Chalmers & Brian Rabern (2014). Two-Dimensional Semantics and the Nesting Problem. 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 (...)
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  20. Daniel Cohnitz (2003). Two-Dimensionalism and the Metaphysical Possibility of Zombies. 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. 55--62.
  21. Juan Comesaña (2002). The Diagonal and the Demon. Philosophical Studies 110 (3):249 - 266.
    Reliabilism about epistemic justification – thethesis that what makes a belief epistemicallyjustified is that it was produced by a reliableprocess of belief-formation – must face twoproblems. First, what has been called ``the newevil demon problem'', which arises from the ideathat the beliefs of victims of an evil demonare as justified as our own beliefs, althoughthey are not – the objector claims – reliablyproduced. And second, the problem of diagnosingwhy skepticism is so appealing despite beingfalse. I present a special version ofreliabilism, (...)
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  22. Eros Corazza (2005). Reference and Description: The Case Against Two-Dimensionalism (Review of Scott Soames' Book). Philosophy Reviews.
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  23. Martin Davies (2004). Reference, Contingency, and the Two-Dimensional Framework. 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 (...)
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  24. Martin Davies & Lloyd Humberstone (1980). Two Notions of Necessity. Philosophical Studies 38 (1):1-31.
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  25. Louis deRosset (2010). Reference and Response. 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. (...)
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  26. Josh Dever (2007). Low-Grade Two-Dimensionalism. 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.
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  27. Iris Einheuser (2005). Two Types of Rigid Designation. 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 (...)
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  28. Edward Elliott, Kelvin McQueen & Clas Weber (2013). Epistemic Two-Dimensionalism and Arguments From Epistemic Misclassification. 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 (...)
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  29. Gareth Evans (2004). Comment on 'Two Notions of Necessity'. Philosophical Studies 118 (1-2):11 - 16.
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  30. Graeme Forbes (2011). The Problem of Factives for Sense Theories. 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 (...)
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  31. Peter Fritz, Matrices and Modalities: On the Logic of Two-Dimensional Semantics.
    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 (...)
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  32. Peter Fritz, What is the Correct Logic of Necessity, Actuality and Apriority?
    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 (...)
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  33. Peter Fritz (2013). A Logic for Epistemic Two-Dimensional Semantics. 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 (...)
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  34. Manuel García-Carpintero (2006). Two-Dimensionalism: A Neo-Fregean Interpretation. In Manuel García-Carpintero & Josep Macià (eds.), Two-Dimensional Semantics. Oxford: Clarendon Press.
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  35. Manuel Garcia-Carpintero & Josep Macia (eds.) (2006). Two-Dimensional Semantics. 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 (...)
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  36. David R. Gilbert & Edwin D. Mares (2012). Completeness Results for Some Two-Dimensional Logics of Actuality. 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.
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  37. John Hawthorne & Ofra Magidor (2009). Assertion, Context, and Epistemic Accessibility. 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 (...)
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  38. Tim Henning (2011). Moral Realism and Two-Dimensional Semantics. 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 (...)
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  39. Robert J. Howell (2008). The Two-Dimensionalist Reductio. 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 (...)
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  40. Lloyd Humberstone (2004). Two-Dimensional Adventures. 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.
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  41. Frank Jackson (2004). Why We Need A-Intensions. 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.
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  42. Jacek Jarocki (2013). David Chalmers’ Argument for the Logical Possibility of Zombies. Roczniki Filozoficzne 61 (1):23-42.
    This paper presents a reconstruction of the argument for the logical possibility of zombies, proposed by David Chalmers, which has been debated in analytical philosophy for at least fifteen years now. Beside discussing it, I’m trying to analyze every of its premises. My aim is, especially, to present how the reasoning can show that: (a) zombies/zombie worlds are genuinely conceivable; (b) conceivability is a good guide to possibility; (c) the possibility of zombies is philosophically significant. I’m particularly putting emphasis on (...)
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  43. Jens Kipper (2012). A Two-Dimensionalist Guide to Conceptual Analysis. Ontos.
    According to epistemic two-dimensionalism, or simply two-dimensionalism, linguistic expressions are associated with two intensions, one of which represents an expression’s a priori implications. The author investigates the prospects of conceptual analysis on the basis of a two-dimensionalist theory of meaning. He discusses a number of arguments for and against two-dimensional semantics and argues that properly construed, two-dimensionalism provides a potent and plausible account of meaning. Against the background of this account, the author then goes on to assess the value of (...)
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  44. Frederick W. Kroon (2004). A-Intensions and Communication. Philosophical Studies 118 (1-2):279-298.
    In his 'Why We Need A-Intensions', Frank Jackson argues that "representational content [is] how things are represented to be by a sentence in the communicative role it possesses in virtue of what it means," a type of content Jackson takes to be broadly descriptive. I think Jackson overstates his case. Even if we agree that such representational properties play a crucial reference-fixing role, it is much harder to argue the case for a crucial communicative role. I articulate my doubts about (...)
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  45. Penelope Mackie (2002). Deep Contingency and Necessary a Posteriori Truth. Analysis 62 (3):225-236.
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  46. José Tomás Alvarado Marambio (2007). Bidimensionalismo Epistémico y El Espacio Ontológico Modal (Epistemic Two-Dimensionalism and the Ontological Modal Space). Crítica 39 (117):3 - 18.
    Este trabajo presenta las líneas centrales del bidimensionalismo epistémico defendido recientemente por David Chalmers, y considera, en particular, las motivaciones a las que la semántica debería servir en la conexión entre modalidad metafísica y epistémica. Después de esta presentación, se indican tres dificultades: (i) no se ha diferenciado suficientemente de las semánticas bidimensionales contextuales tradicionales; (ii) la noción de justificación a priori sobre la que se ha desarrollado requiere urgentemente mayor precisión; y (iii) los defensores del esquema han olvidado completamente (...)
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  47. Diego Marconi (2005). Two-Dimensional Semantics and the Articulation Problem. Synthese 143 (3):321-49.
    . David Chalmerss version of two-dimensional semantics is an attempt at setting up a unified semantic framework that would vindicate both the Fregean and the Kripkean semantic intuitions. I claim that there are three acceptable ways of carrying out such a project, and that Chalmerss theory does not coherently fit any of the three patterns. I suggest that the theory may be seen as pointing to the possibility of a double reading for many linguistic expressions (a double reading which, however, (...)
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  48. Robert Michels (2013). Erratum To: Soames's Argument 1 Against Strong Two-Dimensionalism. [REVIEW] Philosophical Studies 163 (2):575-575.
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  49. Robert Michels (2012). Soames's Argument 1 Against Strong Two-Dimensionalism. Philosophical Studies 161 (3):403-420.
    This paper criticizes Soames’s main argument against a variant of two-dimensionalism that he calls strong two-dimensionalism. The idea of Soames’s argument is to show that the strong two-dimensionalist’s semantics for belief ascriptions delivers wrong semantic verdicts about certain complex modal sentences that contain both such ascriptions and claims about the truth of the ascribed beliefs. A closer look at the formal semantics underlying strong two-dimensionalism reveals that there are two feasible ways of specifying the truth conditions for claims of the (...)
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  50. Friederike Moltmann (2006). Presuppositions and Quantifier Domains. Synthese 149 (1):179 - 224.
    In this paper, I will argue for a new account of presuppositions which is based on double indexing as well as minimal representational contexts providing antecedent material for anaphoric presuppositions, rather than notions of context defined in terms of the interlocutors’ pragmatic presuppositions or the information accumulated from the preceding discourse. This account applies in particular to new phenomena concerning the presupposition of quantifier domains. But it is also intended to be an account of presuppositions in general. The account differs (...)
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