Expressive Incompleteness of Two-Dimensional Modal Logic

Fabio Lampert (University of California, Davis)

Fabio Lampert (UC Davis) will present "Expressive Incompleteness of Two-Dimensional Modal Logic" at 11am in Old Quad G14. 

Abstract: We consider a natural-language sentence which cannot be formally represented by the apparatus of a quantified two-dimensional modal logic, or even two-dimensional semantics broadly construed. This was firstly conjectured in a previous work, but here we present a proof. The problem is very similar to the one motivating the introduction of an actuality operator into S5 modal logic. It turns out, however, that the most natural ways to repair the expressive inadequacy in the two-dimensional case, i.e. by adding a stronger actuality operator into the language, or by appealing to plural quantification, render moot the original philosophical motivation of formalizing a priori knowability as necessity along the diagonal.