Multiple-conclusion Logical Consequence: from a Perspective of Speech Acts

Logical consequence is one of important topics discussed in research of logic. It is generally accepted that logical consequence is a binary relation between the set of premises and a single conclusion, while multiple-conclusion logical consequence is often considered to be unintuitive. Restall (2005) defended the multiple-conclusion logical consequence from a perspective of bilateralism. In that paper, logical consequence is understood as constraints on the two speech acts, "assertion" and "denial", and on their related cognitive states, namely: A1, ..., A(n) proves B-1, ..., B-k, if and only if, asserting "A(1), ..., A(n)" but denying "B-1, ..., B-k" is incoherent. Different logics are different in virtue of the different criteria for "coherence." To defend the arguments given in Restal 1(2005), this paper will give replies to the criticisms from the view of inferentialism made in Steinberg (2011).