More Reflections on Consequence

This special issue collects together nine new essays on logical consequence :the relation obtaining between the premises and the conclusion of a logically valid argument. The present paper is a partial, and opinionated,introduction to the contemporary debate on the topic. We focus on two in{}uential accounts of consequence, the model-theoretic and the proof-theoretic, and on the seeming platitude that valid arguments necessarilypreserve truth. We brie{}y discuss the main objections these accounts face, as well as Hartry Field\textquoteright{}s contention that such objections show consequenceto be a primitive, inde{}nable notion, and that we must reject the claim that valid arguments necessarily preserve truth. We suggest that the accountsin question have the resources to meet the objections standardly thought to herald their demise and make two main claims: (i) that consequence, as opposed to logical consequence, is the epistemologically signi{}cant relation philosophers should be mainly interested in; and (ii) that consequence is a paradoxical notion if truth is