CEFISES Seminar: Alberto Naibo, “Stability in Proof-Theoretic Semantics: some comparisons and some remarks”

Series: Explanatory Inference

Abstract: According to proof-theoretic semantics, the meaning of linguistic expressions, and in particular of logical connectives, should be explained in terms of the rules governing the inferential use of these expressions. Following Dummett, there are two fundamental conditions that the inference rules of a logical connective must satisfy in order to completely determine the meaning of such a connective: harmony and stability. In this talk, we will focus our attention on the latter. More specifically, we will draw a comparison between two formalizations of stability that have been recently proposed: one due to Jacinto and Read, and the other due to Tranchini. We will analyze them with respect to the problematic case of quantum disjunction. A specific attention will be addressed to the proof-transformations that they induce. In particular, we claim that Tranchini’s formalization can be decomposed into two different operation on proofs, a local one (expansion) and a global one (permutation). This means that there are two ways of showing that the rules of a certain connective are not stable: either by showing that they do not allow for a proof-expansion, or by showing that they do not allow for a proof-permutation.