Negation on the Australian Plan

Abstract: In this talk, I explain the difference between Australian Plan semantics for negation – which treat negation as a kind of negative modality – and semantics based on the American Plan, which conceive of negation in terms of independent truth and falsity conditions. I will update the presentation of the Australian Plan (introduced in the 1970s in early days of the ternary relational semantics for relevant logics), in the light of more recent developments in logic, and defend this updated plan in the face of some recent criticisms due to Michael De and Hitoshi Omori, in their paper “There is More to Negation than Modality.” Along the way, I hope to draw out some insights into what we might want out of a representational semantics for a language with a consequence relation.

This talk is based on joint work with Professor Franz Berto, from the University of Amsterdam.

This is a talk presented at the Melbourne Logic Seminar.