Two-Dimensional Semantics

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 (...) and offer a new analysis for mood choice cross-linguistically. We argue that the distinction between expressive and inquisitive attitudes is not an idiosyncrasy of non-factive epistemics. We provide novel data, showing that fictional predicates (dream, imagine) license the subjunctive. We explain the indicative/subjunctive alternation by again appealing to epistemic uncertainty and disentangling expressive from inquisitive-fictional meanings. We thus pave the way for a new typology of attitudes relying on this systematic polysemy and propose new criteria to explain mood distribution cross-linguistically. (shrink)

[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 (...) relative to that possible world. There are no necessary a posteriori or contingent a priori propositions: rather, contingent a priori and necessary a posteriori statements are statements that are necessary when evaluated one way, and contingent when evaluated the other way. This paper distinguishes two ways that the two-dimensional framework can be interpreted, and argues that one of them gives the better account of what it means to 'consider a world as actual', but that it provides no support for any notion of purely conceptual a priori truth. /// [Thomas Baldwin] Two-dimensional possible world semantic theory suggests that Kripke's examples of the necessary a posteriori and contingent a priori should be handled by interpreting names as implicitly indexical. Like Stalnaker, I reject this account of names and accept that Kripke's examples have to be accommodated within a metasemantic theory. But whereas Stalnaker maintains that a metasemantic approach undermines the conception of a priori truth, I argue that it offers the opportunity to develop a conception of the a priori aspect of stipulations, conceived as linguistic performances. The resulting position accommodates Kripke's examples in a way which is both intrinsically plausible and fits with Kripke's actual discussion of them. (shrink)

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. (...) The remainder of the paper advances such an attack. I argue that there are possible thinkers who are willing to revise their beliefs in response to expert testimony (in a way familiar by Burge’s famous cases), and that such thinkers will have no thoughts with necessary primary intensions. I even suggest that many actual humans may well be such thinkers. I go on to argue that these possible thinkers show that the two-dimensionalist accounts fail. (shrink)

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 (...) this objection; I argue that given two-dimensional semantics you cannot know a necessary proposition without knowing that it is true. (shrink)

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: (...) an utterance has the primary intension it has because it yields the secondary intensions it yields relative to different possible worlds considered as actual. In these possible worlds, the semantic facts can be different: the metasemantic interpretation is metasemantic in the sense that the secondary intensions are determined relative to possible worlds considered as actual given the meanings the expressions have there. Stalnaker holds a causal picture of the reference of names, according to which names have no meaning over and above their unique referent, and therefore maintains that the semantic interpretation is not an option. He thus endorses the metasemantic interpretation, while insisting that this interpretation does not, contrary to what he originally thought, yield any account of a priori truth and knowledge. My double aim in this paper is to show (i) that the metasemantic interpretation, as sketched by Stalnaker, is not compatible with one natural understanding of the causal picture of reference, on which names are rigid because they have their original bearers essentially , and (ii) that a third kind of interpretation of the framework is available, the metasyntactic interpretation, which grants that names have their bearers essentially and yields some account of a priori knowledge. (shrink)

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 (...) an intuitively plausible range of expressions within its scope. The chapter concludes with a discussion of the prospects of using two-dimensional semantics to account for context-sensitive expressions in dynamic discourse. (shrink)

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 (...) come under recent attack. It has been alleged that it is bound to attribute to speakers a priori identifying knowledge of the referents of correctly employed terms, and bound also to reject valid rules of inference such as exportation: P(a) → λx[P(x)](a) (see, e.g., Soames 2005. (shrink)

_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.

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.

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?

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 (...) one is very careful about how one reasons. To do so, the best way is to reason first from epistemic premises to modal conclusions , and from there to ontological conclusions. Here, the crucial issue is the link between the epistemic and modal domains. How can one reason from theses about what is knowable or conceivable to theses about what is necessary or possible? To bridge the epistemic and modal domains, the framework of two-dimensional semantics can play a central role. I have used this framework in earlier work to mount an argument against materialism. Here, I want to revisit the argument, laying it out in a more explicit and careful form, and responding to a number of objections. In what follows I will concentrate mostly on the conceivability argument. I think that very similar considerations apply to the other arguments mentioned above, however. In the final section of the paper, I show how this analysis might yield a unified treatment of a number of anti-materialist arguments. (shrink)

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 (...) the session, except for one or two paragraphs where the discussion in the session is mentioned. (shrink)

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 (...) me. After a quick overview of two-dimensional approaches, I will focus on Soames’ discussion of ambitious twodimensionalism. I will then turn to a system advocated by Soames that is itself strikingly reminiscent of a two-dimensional approach. Two-dimensional semantic theories are varieties of possible-worlds semantics on which linguistic items can be evaluated relative to possibilities in two different ways, yielding two sorts of intensional semantic values, which can be seen as two “dimensions” of meaning. The second dimension is the familiar sort of Kripkean evaluation in metaphysically possible worlds, so that necessarily coextensive terms (such as ‘Hesperus’ and ‘Phosphorus’ or ‘water’ and ‘H2O’) always have the same semantic value. The first dimension behaves differently, so that there are typically at least some cases where necessarily coextensive terms have different semantic values on the first dimension. For this reason, the two-dimensional framework is sometimes seen as a way of granting many of the insights of a Kripkean approach to meaning (on the second dimension), while retaining elements of a Fregean approach to meaning (on the first dimension). (shrink)

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 (...) (intension) that is constitutively tied to possibility and necessity. (shrink)

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 (...) analyzing matters of cognitive significance and/or context-dependence. (shrink)

What is involved in the meaning of our expressions? Frege suggested that there is an aspect of an expression.

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 (...) semantics for attitude ascriptions developed in Chalmers (2011a) has no trouble accommodating certain forms of the nesting problem that involve factive verbs such as “know” or “establish”. A certain form of the nesting problem involving apriority and necessity operators does raise an interesting puzzle, but we show how a generalized version of the nesting problem arises independently of two-dimensional semantics—it arises, in fact, for anyone who accepts the contingent a priori. We, then, provide a two-dimensional treatment of the apriority operator that fits the two-dimensional treatment of attitude verbs and apply it to the generalized nesting problem. We conclude that two-dimensionalism is not seriously threatened by cases involving the nesting of epistemic and modal operators. (shrink)

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 (...) so appealing despite being false. I present a special version of reliabilism, "indexical reliabilism", based on two-dimensional semantics, and show how it can solve both problems. (shrink)

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 (...) a priority. (shrink)

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 (...) formal semantic framework. In addition, I also argue against traditional accounts of privative noun phrases which can be paired with the assumption that nouns do not have a dual semantic structure. At the most general level, this paper presents a proposal for how we can begin to integrate a psychologically realistic account of lexical semantics with a linguistically plausible compositional semantic framework. (shrink)

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. (...) This paper argues that response-based theories of reference are prey to a variant of the empirical inadequacy objection, because they are ill-suited to accommodate the successful use of proper names by pre-school children. Further, I argue that there is reason to believe that normal adults are, by and large, no different from children with respect to how the referents of their names are determined. I conclude that speakers typically refer _positionally_: the referent of a use of a proper name is typically determined by aspects of the speaker's position, rather than by associated conditions present, however implicitly, in her psychology. (shrink)

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.

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 (...) two-dimensional modal semantics, proper names ought to be treated as rigid relative to the world considered as actual. (shrink)

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 (...) claim that such sentences are a posteriori. We aim to show that these arguments are unsuccessful as (i) and (ii) undercut each other. One must distinguish the general framework of E2D from a specific implementation of it. The framework is flexible enough to avoid commitment to the apriority of any particular sentence; only specific implementations are so committed. Arguments from epistemic misclassification are therefore better understood as arguments for favouring one implementation of E2D over another, rather than as refutations of E2D. (shrink)

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 (...) over different notions of validity such as local, general, and diagonal, besides being general enough for several two-dimensional logics proposed in the literature. We also motivate the introduction of a new operator into two-dimensional languages and explore some of the philosophical questions raised by it concerning the relations there are between actuality, necessity, and the a priori, that seem to undermine traditional intuitive interpretations of two-dimensional operators. (shrink)

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 (...) epistemic operators, and it seems that some contradictory examples, such as "possibly (Hesperus has a moon and someone establishes that Hesperus has no moon)", are classified as true according to these views. (shrink)

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 (...) captures the relevant ideas of two-dimensional semantics. I use this to show that some criticisms of two-dimensional semantics that claim that the theory is incoherent are not justified. I also axiomatize the logic, and compare it to the most important proposals in the literature that define similar logics. To indicate that two-dimensional semantics is a plausible semantic theory, I give an argument that shows that all theorems of the logic can be philosophically justified independently of two-dimensional semantics. (shrink)

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 (...) arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics. (shrink)

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 (...) some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem. (shrink)

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’ (...) in the work of Evans, Kaplan, Kripke and Stalnaker. The introduction provides a systematic overview of the framework, the ideas of its earlier originators, recent developments and criticism. Finally, it gives a brief overview over the contributions to the volume. (shrink)

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 (...) Davies, Gareth Evans, Manuel Garcia-Carpintero, Josep Maci`, Martine Nida-Rumelin, Christopher Peacocke, James Pryor, Francois Recanati, Scott Soames, Cara Spencer, Robert Stalnaker, Kai-Yee Wong, Stephen Yablo. (shrink)

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.

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 (...) to be identical at each world in the context set. In this paper, we present a problem for Stalnaker's meta-semantic framework, by challenging the plausibility of the Uniformity principle. We argue that the interaction of the framework with facts about epistemic accessibility - in particular, failures of epistemic transparency - cause problems for the Uniformity principle and thus for Stalnaker's framework more generally. (shrink)

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 (...) they are pervasive. -/- This brief technical note observes that it is possible to `hack' the Lewis framework to make use of a resource that is doing little work: the `postsemantic' stage, whereby nonpropositional semantic values are transformed into propositional contents. I provide a semantics for \emph{if}-clauses on which they \emph{restrict} the domain of definedness of their operanda to those in which the antecedent is correct, and then \emph{test} for the correctness of the consequent: postsemantically, then, we `seek out' the closest context in which the antecedent is correct; if it is one in which the consequent is correct, the conditional is correct in our context. The result has the structure of a Stalnaker-conditional, but over contexts rather than worlds. -/- The `hack' has the radical consequence that this the mainstay assumption in natural-language semantics is wrong: if \emph{if}-clauses act postsemantically rather than in the course of semantic composition, then nothing about their behavior can teach us anything about the distribution of indexical argument-places. (shrink)

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 (...) provides realists with a satisfactory account of Moral Twin Earth cases and an improved response to Blackburn’s supervenience argument. (shrink)

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 (...) in this paper. For though there is probably something salvageable from two-dimensionalism as a way to explain the content of thought, as a metaphysical tool it should be abandoned. In this paper I aim to establish this point by reductio: if 'metaphysical' two-dimensionalism is assumed, it can be shown to be false. (shrink)

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.

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.

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 (...) are linguistic contexts where a sentence is embedded under both epistemic and modal operators. Chalmers and Rabern suggest a two-dimensional solution to the problem. Their semantics solves the nesting-problem, but at the cost of invalidating certain plausible principles. We suggest a solution that is both simpler and avoids this cost. (shrink)

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 →.