Matrices and Modalities: On the Logic of Two-Dimensional Semantics

Abstract
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.
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David J. Chalmers (2006). The Foundations of Two-Dimensional Semantics. In Manuel Garcia-Carpintero & Josep Macia (eds.), Two-Dimensional Semantics: Foundations and Applications. Oxford University Press. 55-140.
Laura Schroeter, Two-Dimensional Semantics. Stanford Encyclopedia of Philosophy.
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