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A logic for epistemic two-dimensional semantics

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

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  1. Variability, Rigidity and the Nesting Problem.Olga Poller - forthcoming - Theoria.
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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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  • Rabern’s Semantics for Metaphysical and Epistemic Modalities and the Nesting Problem.Fabian Heimann - forthcoming - Journal of Philosophical Logic:1-11.
    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 (2014) call the nesting problem. I will investigate how Rabern’s semantics answers this puzzle.
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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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  • 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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  • 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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  • 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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  • 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. Cham: 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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  • 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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  • 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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  • 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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  • 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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