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Ian Rumfitt (2000) developed a bilateralist account of logic in which the meaning of the connectives is given by conditions on asserted and rejected sentences. An additional set of inference rules, the coordination principles, determines the interaction of assertion and rejection. Fernando Ferreira (2008) found this account defective, as Rumfitt must state the coordination principles for arbitrary complex sentences. Rumfitt (2008) has a reply, but we argue that the problem runs deeper than he acknowledges and is in fact related to the challenge of establishing proof-theoretic harmony. We motivate a distinctively bilateral criterion for harmony and show how the bilateralist can meet it. This also resolves Ferreira's complaint.

Recent advances in the Super Linguistics of pictures have laid the Super Semantic foundation for modelling the phenomena of narrative sequencing and co-reference in pictorial and mixed linguistic-pictorial discourses. We take up the question of how one arrives at the pragmatic interpretations of such discourses. In particular, we offer an analysis of: (i) the discourse composition problem: how to represent the joint meaning of a multi-picture discourse, (ii) observed differences in narrative sequencing in prima facie equivalent linguistic vs pictorial discourses, and (iii) the phenomenon of co-referencing across pictures. We extend Segmented Discourse Representation Theory to spell out a formal Super Pragmatics that applies to linguistic, pictorial and mixed discourses, while respecting the particular ‘genius’ of either medium and computing their distinctive pragmatic interpretations.

Minimalism about truth is one of the main contenders for our best theory of truth, but minimalists face the charge of being unable to properly state their theory. Donald Davidson incisively pointed out that minimalists must generalize over occurrences of the same expression placed in two different contexts, which is futile. In order to meet the challenge, Paul Horwich argues that one can nevertheless characterize the axioms of the minimalist theory. Sten Lindström and Tim Button have independently argued that Horwich’s attempt to formulate minimalism remains unsuccessful. We show how to properly state Horwich’s axioms by appealing to propositional functions that are given by definite descriptions. Both Lindström and Button discuss proposals similar to ours and conclude that they are unsuccessful. Our new suggestion avoids these objections.

Data involving epistemic modals suggest that some classically valid argument forms, such as reductio, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a de re–de dicto collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic.

We present an inferentialist account of the epistemic modal operator might. Our starting point is the bilateralist programme. A bilateralist explains the operator not in terms of the speech act of rejection; we explain the operator might in terms of weak assertion, a speech act whose existence we argue for on the basis of linguistic evidence. We show that our account of might provides a solution to certain well-known puzzles about the semantics of modal vocabulary whilst retaining classical logic. This demonstrates that an inferentialist approach to meaning can be successfully extended beyond the core logical constants.

This chapter develops a novel solution to the negation version of the Frege–Geach problem by taking up recent insights from the bilateral programme in logic. Bilateralists explain the meaning of negation in terms of a primitive B-type inconsistency involving the attitudes of assent and dissent. Some may demand an explanation of this inconsistency in simpler terms, but here it is argued that bilateralism’s assumptions are no less explanatory than those of A-type semantics that only require a single primitive attitude, but must stipulate inconsistency elsewhere. A version of B-type expressivism called inferential expressivism—a novel semantic framework that characterizes meanings by inferential roles that define which attitudes one can infer from the use of terms—is developed. This framework is applied to normative vocabulary, thereby solving the Frege–Geach problem generally and comprehensively. The chapter includes a semantics for epistemic modals, thereby also explaining normative terms under epistemic modals.

The knowledge norm of assertion is the subject of a lively debate on when someone is in a position to assert something. However, not much has been said about the logic that underlies such debate. In this paper, I propose a formalisation of the knowledge norm in a deontic logic that aims to be explanatory and conceptually sound. Afterwards, I investigate some problems that this formalisation makes visible. This reveals some significant limitations of the underlying logic: it can neither contain Axiom 4 (transitivity) nor Axiom C4 (density). Moreover, sentences of the form p and I have not asserted that p appear to licence a violation of deontic rules.

This paper presents a novel account of focal stress and pitch contour in English dialogue. We argue that one should analyse and treat focus and pitch contour jointly, since (i) some pragmatic interpretations vary with contour (e.g., whether an utterance accepts or rejects; or whether it implicates a positive or negative answer); and (ii) there are utterances with identical prosodic focus that in the same context are infelicitous with one contour, but felicitous with another. We offer an account of two distinct pitch contours that predicts the correct felicity judgements and implicatures, outclassing other models in empirical coverage or formality. Prosodic focus triggers a presupposition, where what is presupposed and how the presupposition is resolved depends on prosodic contour. If resolving the presupposition entails the proffered content, then the proffered content is uninteresting and hence the utterance is in-felicitous. Otherwise, resolving the presupposition may lead to an implicature. We regiment this account in SDRT. EARLY ACCESS

Linguistic evidence supports the claim that certain, weak rejections are less specific than assertions. On the basis of this evidence, it has been argued that rejected sentences cannot be premisses and conclusions in inferences. We give examples of inferences with weakly rejected sentences as premisses and conclusions. We then propose a logic of weak rejection which accounts for the relevant phenomena and is motivated by principles of coherence in dialogue. We give a semantics for which this logic is sound and complete, show that it axiomatizes the modal logic KD45 and prove that it still derives classical logic on its asserted fragment. Finally, we defend previous logics of strong rejection as being about the linguistically preferred interpretations of weak rejections.