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