Inferential Constants

FIORE, CAMILLO; PAILOS, FEDERICO MATÍAS; RUBIN, MARIELA

Journal of Philosophical Logic

Springer Nature

Año: 2022

0022-3611

A metainference is usually understood as a pair consisting of a collection of inferences, called premises, and a single inference, called conclusion. In the last few years,much attention has been paid to the study of metainferences—and, in particular, tothe question of what are the valid metainferences of a given logic. So far, however, thisstudy has been done in quite a poor language. Our usual sequent calculi have no wayto represent, e.g. negations, disjunctions or conjunctions of inferences. In this paperwe tackle this expressive issue. We assume some background sentential language asgiven and define what we call an inferential language, that is, a language whose atomicformulas are inferences. We provide a model-theoretic characterization of validity forthis language, relative to some given characterization of validity for the backgroundsentential language and provide a proof-theoretic analysis of validity. We argue thatour novel language has fruitful philosophical applications. Lastly, we generalize someof our definitions and results to arbitrary metainferential levels.