Two-Dimensional Semantics

I consider the application of possibility semantics to the modeling of the indeterminacy of the future. I argue that interesting problems arise in connection to the addition of object-language determinacy operator. I show that adding a two-dimensional layer to possibility semantics can help solve these problems.

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in the category of sets is identifiable with the elementary embeddings of large cardinal axioms. A modal coalgebraic automata's mappings are further argued to account for both reinterpretations of quantifier domains as well as the ontological expansion effected by the elementary embeddings in the category of sets. The interaction between the interpretational and (...) objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile of $\Omega$-logical validity, and thus the generic invariance of mathematical truth, modal coalgebraic automata are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual engineering for intensions and (...) hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

This paper endeavors to establish foundations for the interaction between hyperintensional semantics and two-dimensional indexing. I examine the significance of the semantics, by developing three, novel interpretations of the framework. The first interpretation provides a characterization of the distinction between fundamental and derivative truths. The second interpretation demonstrates how the elements of decision theory are definable within the semantics, and provides a novel account of the interaction between probability measures and hyperintensional grounds. The third interpretation concerns the contents of the (...) types of intentional action, and the semantics is shown to resolve a puzzle concerning the role of intention in action. Topic-sensitive two-dimensional truthmaker semantics can be interpreted epistemically and metasemantically as well. (shrink)

This paper aims to provide modal foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed by (...) Hale and Wright and examined in Hale (2013); and demonstrate how a two-dimensional approach to the epistemology of mathematics is consistent with Hale and Wright's notion of there being non-evidential epistemic entitlement rationally to trust that abstraction principles are true. A choice point that I flag is that between availing of intensional or hyperintensional semantics. The hyperintensional semantic approach that I advance is a topic-sensitive epistemic two-dimensional truthmaker semantics. Epistemic and metaphysical states and possibilities may thus be shown to play a constitutive role in vindicating the reality of mathematical objects and truth, and in providing a conceivability-based route to the truth of abstraction principles as well as other axioms and propositions in mathematics. (shrink)

This paper aims to contribute to the analysis of the nature of mathematical modality, and to the applications of the latter to unrestricted quantification and absolute decidability. Rather than countenancing the interpretational type of mathematical modality as a primitive, I argue that the interpretational type of mathematical modality is a species of epistemic modality. I argue, then, that the framework of two-dimensional semantics ought to be applied to the mathematical setting. The framework permits of a formally precise account of the (...) priority and relation between epistemic mathematical modality and metaphysical mathematical modality. The discrepancy between the modal systems governing the parameters in the two-dimensional intensional setting provides an explanation of the difference between the metaphysical possibility of absolute decidability and our knowledge thereof. I also advance a topic-sensitive epistemic two-dimensional truthmaker semantics, if hyperintensional approaches are to be preferred to possible worlds semantics. I examine the relation between two-dimensional hyperintensional states and epistemic set theory. (shrink)

I argue that the two-dimensional intensions of epistemic two-dimensional semantics provide a compelling solution to the access problem.

This essay aims to redress the contention that epistemic possibility cannot be a guide to the principles of modal metaphysics. I introduce a novel epistemic two-dimensional truthmaker semantics. I argue that the interaction between the two-dimensional framework and the mereological parthood relation enables epistemic possibilities and truthmakers to be a guide to the metaphysical profiles of the qualitative haecceitistic properties of individuals, assuming mereological essentialism and the claim that essential properties are haecceitistic properties. I specify a two-dimensional formula encoding the (...) relation between the epistemic possibility and verification of essential properties obtaining and their metaphysical possibility or verification. I then generalize the approach to haecceitistic properties. I also examine the Julius Caesar problem as a test case. I conclude by addressing objections from the indeterminacy of ontological principles relative to the space of epistemic possibilities, and from the consistency of epistemic modal space. (shrink)

Modal dualism is the claim that there is a space of epistemically possible worlds that exceeds the space of metaphysically possible worlds. In the present paper, I argue that modal dualism is false. I do so via an argument that differs from most previous arguments against modal dualism in that it does not rely on controversial semantic or epistemological assumptions like descriptivism, internalism or modal rationalism. The point of my argument is, instead, that modal dualism is internally inconsistent because it (...) is the result of the failure to draw the proper conclusions from the abandonment of these semantic and epistemological assumptions. The relevant inconsistency manifests itself in the modal dualist notion of epistemic modality. For this notion to play the explanatory roles assigned to it by modal dualists, it has to be a notion of a genuinely epistemic kind of modality. But the only way to make sense of such a notion is via just those semantic or epistemological assumptions that the modal dualist is keen to avoid. Anyone willing to abandon these assumptions has to go further and detach the epistemic from the modal altogether. (shrink)

This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction.

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of rational intuition; and (...) to the types of intention, when the latter is interpreted as a modal mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter \textbf{3} provides an abstraction principle for epistemic intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4 (i.e. the KK principle). Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's "criterial" identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapter \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapters \textbf{8-12} provide cases demonstrating how the two-dimensional intensions of epistemic two-dimensional semantics solve the access problem in the epistemology of mathematics. Chapter \textbf{8} examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter \textbf{9} examines the modal profile of $\Omega$-logic in set theory. Chapter \textbf{10} examines the interaction between epistemic two-dimensional truthmaker semantics, epistemic set theory, and absolute decidability. Chapter \textbf{11} avails of modal coalgebraic automata to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. Chapter \textbf{12} provides a modal logic for rational intuition and provides four models of hyperintensional semantics. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory. The multi-hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters \textbf{2} and \textbf{4} is applied in chapters \textbf{7}, \textbf{8}, \textbf{10}, \textbf{11}, \textbf{12}, and \textbf{14}. (shrink)

Chalmers has argued that Bayesianism supports the existence of a priori truths, since it entails that scrutability conditionals are not rationally revisable. However, as we argue, Chalmers's arguments leave open that every proposition is rationally deniable, which would be devastating for large parts of his philosophical program. We suggest that Chalmers should appeal to well-known convergence theorems to argue that ideally rational subjects converge on the truth of scrutability conditionals. However, our discussion reveals that showing that these theorems apply in (...) effect requires assuming scrutability. Consequently, Bayesianism doesn't conflict with Chalmers's scrutability framework, but it doesn't support it, either. (shrink)

According to two-dimensional semantics, primary intension and secondary intension can play the role of reflecting the cognitive aspect of an expression like Fregean sense does. The aim of this paper is to argue that this role is likely a myth. To argue for this, I attempt to show that cognitive aspects of fictional names cannot be explained within the framework of two-dimensional semantics. To be more specific, I consider four ontological theories about fictional characters that two-dimensional semanticists might be tempted (...) to choose. And then, I argue that none of them can be combined with two-dimensional semantics in a satisfactory way. (shrink)

David Chalmers’ two-dimensionalism is an ambitious philosophical program that aims to “ground” or “construct” Fregean meanings and restore “the golden triangle” of apriority, necessity, and meaning that Kripke seemingly broke. This paper aims to examine critically what Chalmers’ theory can in reality achieve. It is argued that the theory faces severe challenges. There are some gaps in the overall arguments, and the reasoning is in some places somewhat circular. Chalmers’ theory is effectively founded on certain strong philosophical assumptions. It is (...) concluded that it is unclear whether the theory can deliver all it promises. (shrink)

In contrast to standard possible worlds semantics, possible worlds in a two-dimensional semantic framework play two kinds of roles, rather than just one. This allows the framework to assign two kinds of intensions to expressions, rather than just one. Its fruitful use in explicating modal operators and the meanings of referential expressions like indexicals has led to two-dimensional accounts that seek to revive the Fregean conception of meaning, or more specifically the descriptivist view of reference, which has fallen into disrepute (...) due to intense criticisms, most famously, by Saul Kripk’s seminal work Naming and Necessity (1972). This entry provides a critical overview of the two most prominent of such accounts, proposed by Frank Jackson and David Chalmers. Unfortunately, there is not space to describe either account in detail, so I rely largely on brief descriptions and plenty of references to primary and secondary sources. More importantly, I rely on focusing on how the accounts explain the phenomenon of necessary a posteriori identity that Kripke’s well-known examples (such as ‘Hesperus is Phosphorus’) have brought to light. Focusing on and structuring our discussions around this phenomenon is by no means just an expository convenience. These cases are of central importance in themselves. They epitomize a large part of the contribution of Naming and Necessity to the theory of reference. This is why section 2 outlines Kripke’s critique of the Fregean theory of referential expressions and section 3 explains rigid designation and identity statements. Section 4 discusses rigidification and the notion of a world considered as actual, leading to the introduction of two-dimensional functions in Section 5. I discuss, finally, Frank Jackson’s and David Chalmers’ two-dimensionalism in Sections 6 and 7. Section 8 makes a few critical remarks on Jackson’s handling of the semantic argument. I conclude (Section 8) by discussing the important distinction between semantics and metasemantics. (shrink)

Philosophy and Phenomenological Research, EarlyView.

In a recent paper, Brian Rabern suggests a semantics for languages with two kinds of modality, standard Kripkean metaphysical modality as well as epistemic modality. This semantics presents an alternative to two-dimensionalism, which was developed in the last decades. Both Rabern’s semantics and two-dimensionalism are subject to a puzzle that Chalmers and Rabern, 210–224 2014) call the nesting problem. I will investigate how Rabern’s semantics answers this puzzle.

In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition.

Epistemic two-dimensional semantics, advocated by Chalmers and Jackson, among others, aims to restore the link between necessity and a priority seemingly broken by Kripke, by showing how armchair access to semantic intensions provides a basis for knowledge of necessary a posteriori truths. The most compelling objections to E2D are that, for one or other reason, the requisite intensions are not accessible from the armchair. As we substantiate here, existing versions of E2D are indeed subject to such access-based objections. But, we (...) moreover argue, the difficulty lies not with E2D but with the typically presupposed conceiving-based epistemology of intensions. Freed from that epistemology, and given the right alternative—one where inference to the best explanation provides the operative guide to intensions—E2D can meet access-based objections, and fulfill its promise of restoring the desirable link between necessity and a priority. This result serves as a central application of Biggs and Wilson, according to which abduction is an a priori mode of inference. (shrink)

ABSTRACT This paper defends a controversial view about personal identity. It argues that it is possible to endorse both Phenomenalism and Materialism about persons. Phenomenalism is the view that personal identity is grounded in phenomenal consciousness. Materialism is the view that we are material objects. Many believe that the two views are incompatible. In this paper, I show that it is possible to accept both. I consider two objections against their combination—the argument from disembodiment and an important objection by Tim (...) Bayne. My responses are based on Kripke’s analysis of necessary a posteriori and contingent a priori statements. I make the case that both objections rest on different kinds of modal illusions. This strategy can be applied to other arguments, and the paper is intended to advocate a general approach to personal identity. (shrink)

How should modal reasoning proceed? Here we compare abduction-based and conceiving-based modal epistemologies, and argue that an abduction-based approach is preferable, and by a wide margin.

ABSTRACTTwo-dimensional accounts of speech and thought make use of so-called ‘diagonal’ propositions. If diagonals are indeed propositions, they can be negated: an ‘anti-diagonal’ is the negation o...

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 →.

Many authors have noted that there are types of English modal sentences cannot be formalized in the language of basic first-order modal logic. Some widely discussed examples include “There could have been things other than there actually are” and “Everyone who is actually rich could have been poor.” In response to this lack of expressive power, many authors have discussed extensions of first-order modal logic with two-dimensional operators. But claims about the relative expressive power of these extensions are often justified (...) only by example rather than by rigorous proof. In this paper, we provide proofs of many of these claims and present a more complete picture of the expressive landscape for such languages. (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)

We consider a natural-language sentence that cannot be formally represented in a first-order language for epistemic two-dimensional semantics. We also prove this claim in the “Appendix” section. It turns out, however, that the most natural ways to repair the expressive inadequacy of the first-order language render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.

One well known problem regarding quantifiers, in particular the 1storder quantifiers, is connected with their syntactic categories and denotations. The unsatisfactory efforts to establish the syntactic and ontological categories of quantifiers in formalized first-order languages can be solved by means of the so called principle of categorial compatibility formulated by Roman Suszko, referring to some innovative ideas of Gottlob Frege and visible in syntactic and semantic compatibility of language expressions. In the paper the principle is introduced for categorial languages generated (...) by the Ajdukiewicz’s classical categorial grammar. The 1st-order quantifiers are typically ambiguous. Every 1st-order quantifier of the type k > 0 is treated as a two-argument functorfunction defined on the variable standing at this quantifier and its scope (the sentential function with exactly k free variables, including the variable bound by this quantifier); a binary function defined on denotations of its two arguments is its denotation. Denotations of sentential functions, and hence also quantifiers, are defined separately in Fregean and in situational semantics. They belong to the ontological categories that correspond to the syntactic categories of these sentential functions and the considered quantifiers. The main result of the paper is a solution of the problem of categories of the 1st-order quantifiers based on the principle of categorial compatibility. (shrink)

According to the modal account of propositional apriority, a proposition is a priori if it is possible to know it with a priori justification. Assuming that modal truths are necessarily true and that there are contingent a priori truths, this account has the undesirable consequence that a proposition can be a priori in a world in which it is false. Epistemic two-dimensionalism faces the same problem, since on its standard interpretation, it also entails that a priori propositions are necessarily a (...) priori. In response to this problem, Chalmers and Rabern propose an alternative conception of propositional apriority as well as two-dimensional truth-conditions for apriority statements. Their proposal is also supposed to avoid another problem for the modal account, namely that it entails the existence of false instances of ‘φ iff actually φ’. I discuss Chalmers and Rabern’s account and point out a number of problems with it. I then develop my own account of propositional apriority that solves the problems in question, that can be accepted by friends and foes of two-dimensionalism alike, and that is also neutral with respect to the question of how one construes the objects of propositional apriority. (shrink)

We present a sound and complete Fitch-style natural deduction system for an S5 modal logic containing an actuality operator, a diagonal necessity operator, and a diagonal possibility operator. The logic is two-dimensional, where we evaluate sentences with respect to both an actual world (first dimension) and a world of evaluation (second dimension). The diagonal necessity operator behaves as a quantifier over every point on the diagonal between actual worlds and worlds of evaluation, while the diagonal possibility quantifies over some point (...) on the diagonal. Thus, they are just like the epistemic operators for apriority and its dual. We take this extension of Fitch’s familiar derivation system to be a very natural one, since the new rules and labeled lines hereby introduced preserve the structure of Fitch’s own rules for the modal case. (shrink)

This paper argues for a particular view about in what metaphysical equivalence consists: namely, that any two metaphysical theories are metaphysically equivalent if and only if those theories are strongly hyperintensionally equivalent. It is consistent with this characterisation that said theories are weakly hyperintensionally distinct, thus affording us the resources to model the content of propositional attitudes directed towards metaphysically equivalent theories in such a way that non-ideal agents can bear different propositional attitudes towards metaphysically equivalent theories.

A common view relating compositional semantics and the objects of assertion holds the following: Sentences φ and ψ expresses the same proposition iff φ and ψ have the same modal profile. Following Dummett, Evans, and Lewis, Stanley argues that this view is fundamentally mistaken. According to Dummett, we must distinguish the semantic contribution a sentence makes to more complex expressions in which it occurs from its assertoric content. Stojnić insists that views which distinguish the roles of content and semantic value (...) must nevertheless ensure a tight connection between the two. But, she contends, there is a crucial disanalogy between the views that follow Lewis and the views that follow Dummett. Stanley’s Dummettian view is argued to contain a fatal flaw: On such views, there is no way to secure an appropriate connection between semantic value and a theoretically motivated notion of assertoric content. I will review the background issues from Dummett, Evans, Lewis, and Stanley, and provide a principled way of bridging the gap between semantic value and a theoretically motivated notion of assertoric content. (shrink)

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)

Self-locating attitudes and assertions provide a challenge to the received view of mental and linguistic intentionality. In this paper I try to show that the best way to meet this challenge is to adopt relativistic, centred possible worlds accounts for both belief and communication. First, I argue that self-locating beliefs support a centred account of belief. Second, I argue that self-locating utterances support a complementary centred account of communication. Together, these two claims motivate a unified centred conception of belief and (...) communication. (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)

In this paper, I mainly pursue the following two goals: on the one hand, I want to show how a central Fregean insight is tried to be captured within a two-dimensional strategy. On the other hand, I want to show that, in the light of Saul Kripke’s arguments against descriptivism, this strategy is faced with a fundamental problem. I proceed in four steps: in a first step, I bring together the passages that contain a central Fregean insight as a source (...) of inspiration for a two-dimensional reconstruction and that suggest a descriptivist reading of Frege’s view. In a second step, I shortly present Kripke’s threefold argumentation against two versions of descriptivism, which is also the basis for Kripke’s view that proper names are rigid designators. In a third step, I explain the basic idea of a Frege-inspired two-dimensional strategy which is used to reconcile theories of definite descriptions with theories of rigid designation and which is sometimes characterized as ‘neo-descriptivism’. Since the two-dimensional strategy is dependent on rigidified definite descriptions, I argue, in a fourth step, that, in the light of Kripke’s epistemological and semantic arguments, the two-dimensional strategy is problematic and untenable – though it is, nevertheless, motivated by Kripke’s modal argument. (shrink)

It is a core commitment of Epistemic Two-Dimensionalism that an utterance is 1-necessary iff it is a priori. But Jeff Speaks's Argument from Misclassification proves that, on a natural interpretation, E2D assigns necessary 1-intensions to many utterances that speakers deem a posteriori. Given that 1-intensions are meant to formalize a speaker's own understanding of the words she utters, this proof raises serious difficulties for E2D. In response, Elliott, McQueen, and Weber point out that the Argument from Misclassification presupposes a controversial (...) theory of reference-fixation for proper names and argue that E2Dists ought to reject this theory. They discuss three alternatives to the theory that render E2D immune to the Argument from Misclassification. I demonstrate here that each of these alternatives either replicates the faults of the original theory by assigning necessary 1-intensions to a posteriori utterances, or makes 1-intensions creatures of darkness. I argue that, although the A.. (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, 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)

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)

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)

I distinguish two notions of agreement in belief: believing the same content versus having beliefs that necessarily coincide/diverge in normative status. The second notion of agreement,, is clearly significant for the communication of beliefs amongst thinkers. Thus there would seem to be some prima facie advantage to choosing the conception of content operative in in such a way that the normative status of beliefs supervenes on their content, and this seems to be the prevailing assumption of many semanticists. I shall (...) argue that de se beliefs and assertions provide a motivation to depart from this assumption, and so do beliefs and assertions concerning what is epistemically possible. I conclude by offering two models of assertoric communication that are compatible with the abandonment of the assumption, and suggesting schematically that each model applies to different cases. (shrink)

Some opponents of epistemic two-dimensionalism say that the view should be rejected on the grounds that it misclassifies certain a posteriori claims as a priori. Elliott, McQueen, & Weber [2013] have argued that any argument of this form must fail. I argue that this conclusion is mistaken, and defend my argument [Speaks (2010] against their criticisms.

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)

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)

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)

This note argues that Laura Schroeter's [2005] critique of David Chalmers's epistemic two-dimensional semantics is not touched by a reply by Edward Elliott, Kelvin McQueen, and Clas Weber [2013].

In recent years, two‐dimensional semantics has been used to develop a broadly descriptivist approach to meaning that seeks to accommodate externalists’ counterexamples to traditional descriptivism. The 2D possible worlds framework can be used to capture a speaker’s implicit dispositions to identify the reference of her words on the basis of empirical information about her actual environment. Proponents of 2D semantics argue that this aspect of linguistic understanding plays the core theoretical role of meanings: 2D semantics allows us to specify a (...) reference‐fixing criterion implicit mastery of which constitutes semantic competence a particular meaning. (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)