Work in progress by Leon Commandeur
Bergen Logic Seminar: Information-gain from deductive inference in a dialogical framework
Information-gain from deductive inference in a dialogical framework
A deductive inference is one often defined as one where the truth of the premises guarantees the truth of the conclusion. In other words, if the premises are true, the necessarily so is the conclusion. This, however, has generated a well-known problem about the informativeness of such an inference, often referred to as the scandal of deduction. If the conclusion in a deductive argument necessarily follows from the premises, then it appears to be that when one has the premises available, one also already has the conclusion available. Drawing a deductive inference then becomes essentially uninformative, or useless. The problem has generated wide-ranging secondary literature, offering various solutions to the problem, but a definitive solution arguably is still not available. In this paper I will argue that a different, recently articulated, conception of the nature of deduction does allow us to understand in what sense drawing a deductive inference is informative and thereby useful. This conception of the nature of deduction is that of the dialogical conception, recently articulated by Dutilh Novaes (2021). I will argue that within such a framework, the information-gain from deductive inference can best be understood via the notions of Common Knowledge and Distributed Knowledge, taken from the literature on Dynamic Epistemic Logic (DEL).