Consequence in Context: Two-Dimensional Semantics meets Logical Consequence

Two-dimensional semantics is a formal framework used to characterize the meaning of sentences and sub-sentential expressions and distinguished by the view according to which the extension of an expression depends on two dimensions. Contextual philosophical interpretations of that framework intend to capture how the extension of an expression depends on context. These interpretations have been argued to provide insight into questions related to logical consequence. This thesis is concerned with problems having to do with logical consequence and the role of context in the determination of truth – with contextual interpretations of two-dimensional semantics constituting theories in which solutions to those problems can be devised. The main problem that will be addressed is the logically possible cases problem, the problem of what are the logically possible cases – that is, what are those things x such that, if the premise of an argument is true relative to x while the conclusion of an argument is false relative to x, an argument is logically invalid. Linked to the logically possible cases problem, and thus also of interest in the present thesis, is the relata problem, the problem of what are the things that the relation of logical consequence relates. In particular, the interest will reside in whether the contexts as cases thesis – the thesis that logically possible cases are just contexts / context-related entities – and the context-sensitive relata thesis – the thesis that the relata of logical consequence are context-sensitive, in the sense that their truth is determined relative to contexts / context-related entities – hold. I will argue that the contexts as cases thesis does not hold, and that the context-sensitive relata thesis does.