Multiple Conclusions

“Multiple Conclusions,” in Logic, Methodology and Philosophy of Science: Proceedings of the Twelfth International Congress, edited by Petr Hajek, Luis Valdes-Villanueva and Dag Westerstahl, Kings’ College Publications, 2005, 189–205.

I argue for the following four theses. (1) Denial is not to be analysed as the assertion of a negation. (2) Given the concepts of assertion and denial, we have the resources to analyse 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.

This paper has now been reprinted in Analysis and Metaphysics, 6, 2007, 14-34.