ABSTRACT. I argue for the following four theses: (1) Denial is not to be analyzed as the assertion of a negation. (2) Given the concepts of assertion and denial, we have the resources to analyze logical consequence as relating arguments with multiple premises and multiple conclusions. Gentzen's multiple conclusion calculus can be understood in a straightforward, motivated, non-question-begging way. (3) If a broadly anti-realist or inferentialist justification of a logical system works, it works just as well for classical logic as it does for intuitionistic logic. The special case for an anti-realist justification of intuitionistic logic over and above a justification of classical logic relies on an unjustified assumption about the shape of proofs. Finally, (4) this picture of logical consequence provides a relatively neutral shared vocabulary which can help us understand and adjudicate debates between proponents of classical and non-classical logics.



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