Logic in pragmatics

Abstract

Relevance Theory assumes that the deductive device for spontaneous inferences never uses the introduction rules for logical connectives, such as & introduction. Two motivations for this are (I) the overgeneration of propositions expressed and (II) non-terminating inferences, both of which are claimed to be caused by logical introduction rules. However, having both logical introduction rules and elimination rules is essential for the completeness of the inference system. Although a sound and complete inference system is not as strongly preferred in the theory of human reasoning as it is in proof theoretic logic, missing one of the two essential rules for the logical connectives leaves too many holes in the data coverage. Naturally, Relevance Theory has additional rules for covering some of these holes. However, without introduction rules, these additional rules are ⿿non-logical⿿ and therefore create other holes which would then require even more non-logical rules with no principled limit. Also, banning introduction rules to solve particular data problems without independent motivations is stipulative. Based on such considerations, this paper discusses a theory that deals with problems (I) and (II) above without banning introduction rules. After explaining the problems with the ban on introduction rules, I provide a pragmatic solution for the overgeneration problem. I then show that non-terminating inferences arise independently of introduction rules and therefore, removing introduction rules does not provide the right solution. Finally, I substantiate my arguments in the earlier sections by briefly showing that a sound and complete sequent calculus can be used as the deductive system with its performance pragmatically controlled in the way that has been discussed in the previous sections.