Maximilian van Remmen

According to inferential expressivism, the meaning of a logical constant is determined by the inferential relations between speech acts directed at sentences in which it occurs. Extant varieties of inferential expressivism focus exclusively on assertoric discourse, thereby neglecting the inferential role of question-directed speech acts such as asking, answering, and rejecting a question. This paper extends the inferential expressivist framework to interrogative discourse. Drawing on inquisitive semantics and the multilateralist methodology, I develop two commitment-preserving proof systems. The first, inquisitive bilateral logic (IBL), generalises assertion and weak rejection to questions as answering and withholding from answering. The second, inquisitive multilateral logic (IML), enriches IBL with force markers for accepting and rejecting a sentence, which coincide with assertion and weak rejection on declaratives but come apart for questions. This allows for a precise characterisation of asking a question as a composite commitment: accepting a question while withholding from answering it. Both systems are given a semantics via translation into systems of inquisitive modal logic and are shown to be sound and complete with respect to the corresponding notions of modal consequence.

In the current literature the issue of the normativity of logic is usually understood as whether logic is autonomously normative, i.e., whether logic provides norms for reasoning over and above the demands of more general epistemic norms. This is generally taken to be a binary question: either logic is autonomously normative or it is not. In the present paper, I provide a more nuanced answer. Against the background of current work on epistemic and zetetic norms, I distinguish between different normative roles coming to logic: On the one hand, logic provides ideal standards for the synchronic evaluation of doxastic states. These norms operate alongside traditional epistemic norms such as evidentialism. On the other hand, facts of logical entailment provide guidance for deductive inferences as part of inquiries. As such these norms are zetetic. Once this distinction is sufficiently appreciated, the issue of the normative autonomy of logic bifurcates. In particular, so I argue, the arguments against the normative autonomy of logic in the literature are only successful as far as an evaluative normative role of logic is concerned. However, when it comes to the role of logic as guiding deductive inference in inquiry, a strong case is to be made in favour of logic being autonomously normative.

According to the traditional view in the philosophy of logic facts of logic bear normative authority regarding how one ought to reason. Usually this is to mean that the relation of logical consequence between statements has some special relevance for how one’s beliefs should cohere. However, as I will argue in this article, this is just one way in which logic is normative for reasoning. For one thing, belief is not the only kind of mental state involved in reasoning. Besides adopting and revising beliefs, rational agents pose and resolve questions. For another thing, the consequence relation of classical logic can be conservatively extended such that it includes logical relations between questions as well. Therefore, there is an argument to be made that not only the inference of new beliefs from extant beliefs but also the process of raising additional questions falls under the normative authority of logic. Accordingly, a nuanced account of the normativity of logic presents itself, which convincingly deals with problems such as clutter-avoidance and the paradox of the preface.