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A logic for epistemic two-dimensional semantics

Synthese 190 (10):1753-1770 (2013)

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  1. Questions in Two-Dimensional Logic.Thom van Gessel - 2022 - Review of Symbolic Logic 15 (4):859-879.
    Since Kripke, philosophers have distinguished a priori true statements from necessarily true ones. A statement is a priori true if its truth can be established before experience, and necessarily true if it could not have been false according to logical or metaphysical laws. This distinction can be captured formally using two-dimensional semantics. There is a natural way to extend the notions of apriority and necessity so they can also apply to questions. Questions either can or cannot be resolved before experience, (...)
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  • Actual Issues for Relevant Logics.Shawn Standefer - 2020 - Ergo: An Open Access Journal of Philosophy 7.
    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.
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  • The Logic of Sequence Frames.Fabio Lampert - 2022 - Review of Symbolic Logic 15 (1):101-132.
    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.
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  • Hyperintensionality and Normativity.Federico L. G. Faroldi - 2019 - Cham, Switzerland: Springer Verlag.
    Presenting the first comprehensive, in-depth study of hyperintensionality, this book equips readers with the basic tools needed to appreciate some of current and future debates in the philosophy of language, semantics, and metaphysics. After introducing and explaining the major approaches to hyperintensionality found in the literature, the book tackles its systematic connections to normativity and offers some contributions to the current debates. The book offers undergraduate and graduate students an essential introduction to the topic, while also helping professionals in related (...)
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  • Semantic monsters.Brian Rabern - 2021 - In Heimir Geirsson & Stephen Biggs (eds.), The Routledge Handbook of Linguistic Reference. New York: Routledge. pp. 515-532.
    This chapter provides a general overview of the issues surrounding so-called semantic monsters. In section 1, I outline the basics of Kaplan’s framework and spell out how and why the topic of “monsters” arises within that framework. In Section 2, I distinguish four notions of a monster that are discussed in the literature, and show why, although they can pull apart in different frameworks or with different assumptions, they all coincide within Kaplan’s framework. In Section 3, I discuss one notion (...)
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  • Rabern’s Semantics for Metaphysical and Epistemic Modalities and the Nesting Problem.Fabian Heimann - 2020 - Journal of Philosophical Logic 49 (3):497-507.
    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.
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  • Modal Epistemology.Juhani Yli-Vakkuri & John Hawthorne - manuscript
    Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles.
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  • (1 other version)Natural Deduction for Diagonal Operators.Fabio Lampert - 2017 - In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics: The CSHPM 2016 Annual Meeting in Calgary, Alberta. New York: Birkhäuser. pp. 39-51.
    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 (...)
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  • The Epistemology of Modality.Margot Strohminger & Juhani Yli-Vakkuri - 2017 - Analysis 77 (4):825-838.
    This article surveys recent developments in the epistemology of modality.
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  • Actuality, Tableaux, and Two-Dimensional Modal Logics.Fabio Lampert - 2018 - Erkenntnis 83 (3):403-443.
    In this paper we present tableau methods for two-dimensional modal logics. Although models for such logics are well known, proof systems remain rather unexplored as most of their developments have been purely axiomatic. The logics herein considered contain first-order quantifiers with identity, and all the formulas in the language are doubly-indexed in the proof systems, with the upper indices intuitively representing the actual or reference worlds, and the lower indices representing worlds of evaluation—first and second dimensions, respectively. The tableaux modulate (...)
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  • Actuality and the a priori.Fabio Lampert - 2018 - Philosophical Studies 175 (3):809-830.
    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.
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  • Propositional apriority and the nesting problem.Jens Kipper - 2017 - Philosophical Studies 174 (5):1091-1104.
    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 (...)
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  • Closure of A Priori Knowability Under A Priori Knowable Material Implication.Jan Heylen - 2015 - Erkenntnis 80 (2):359-380.
    The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict it (...)
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  • Two-dimensional semantics and the nesting problem.David J. Chalmers & Brian Rabern - 2014 - Analysis 74 (2):210-224.
    Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the two-dimensional (...)
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  • What is the correct logic of necessity, actuality and apriority?Peter Fritz - 2014 - Review of Symbolic Logic 7 (3):385-414.
    This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two (...)
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  • The Logic of Contingent Actuality.Martin Glazier & Stephan Krämer - 2024 - Ergo: An Open Access Journal of Philosophy 11.
    Current orthodoxy in modal logic and metaphysics has it that actuality is non-contingent in the following sense: for all p, if actually, p, then necessarily, actually, p. Call this thesis (Actuality) Necessitism and its negation (Actuality) Contingentism. Thus, according to Contingentism, there is at least one proposition p which is actually true but which could have been actually false. In another paper, one of us (Glazier 2023) has recently defended Contingentism. The present paper explores the logic of actuality under Contingentism. (...)
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  • A two-dimensional logic for diagonalization and the a priori.Melissa Fusco - 2020 - Synthese 198 (9):8307-8322.
    Two-dimensional semantics, which can represent the distinction between a priority and necessity, has wielded considerable influence in the philosophy of language. In this paper, I axiomatize the dagger operator of Stalnaker’s “Assertion” in the formal context of two-dimensional modal logic. The language contains modalities of actuality, necessity, and a priority, but is also able to represent diagonalization, a conceptually important operation in a variety of contexts, including models of the relative a priori and a posteriori often appealed to Bayesian and (...)
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  • Two-Dimensional Tableaux.David Gilbert - 2016 - Australasian Journal of Logic 13 (7).
    We present two-dimensional tableau systems for the actuality, fixedly, and up-arrow operators. All systems are proved sound and complete with respect to a two-dimensional semantics. In addition, a decision procedure for the actuality logics is discussed.
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  • The nesting problem of two‐dimensional semantics.Zhaoqing Xu - 2021 - Philosophical Forum 52 (2):177-183.
    Two‐dimensional semantics is probably the most significant development in contemporary philosophy of language. Among its various versions, it is Chalmers's epistemic two‐dimensionalism that received most widely discussions and most severe criticisms. Here I consider one such criticism, namely, “the nesting problem,” which concerns the interaction between modality and apriority. I propose a solution to the problem and defend it through comparison with other approaches in the literature, as well as rebut with some potential objections. It turns out that my solution (...)
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  • Questions & Indexicality.Thom van Gessel - 2024 - Journal of Philosophical Logic 53 (3):593-621.
    The truth conditions of sentences with indexicals like ‘I’ and ‘here’ cannot be given directly, but only relative to a context of utterance. Something similar applies to questions: depending on the semantic framework, they are given truth conditions relative to an actual world, or support conditions instead of truth conditions. Two-dimensional semantics can capture the meaning of indexicals and shed light on notions like apriority, necessity and context-sensitivity. However, its scope is limited to statements, while indexicals also occur in questions. (...)
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  • Analyticity, Necessity and Belief : Aspects of two-dimensional semantics.Johannesson Eric - 2017 - Dissertation, Stockholm University
    A glass couldn't contain water unless it contained H2O-molecules. Likewise, a man couldn't be a bachelor unless he was unmarried. Now, the latter is what we would call a conceptual or analytical truth. It's also what we would call a priori. But it's hardly a conceptual or analytical truth that if a glass contains water, then it contains H2O-molecules. Neither is it a priori. The fact that water is composed of H2O-molecules was an empirical discovery made in the eighteenth century. (...)
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  • Variability, Rigidity and the Nesting Problem.Olga Poller - 2021 - Theoria 87 (1):230-246.
    In order to block controversial predictions of 2D semantics (The Nesting Problem), Chalmers and Rabern (2014) propose adding an additional constriction called “the liveness constraint” in definitions of epistemic modals. Without this constraint, all scenario‐world pairs counterfactual to a scenario‐world pair considered as actual in a 2D matrix for a contingenta prioripropositionϕappear problematic for 2D semantics. This is because, although it is false thatϕin such pairs, it isa prioritrue thatϕ. I consider two versions of 2D semantics, those with unstructured and (...)
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