What does ‘Smith knows that it might be raining’ mean? Expressivism here faces a challenge, as its basic forms entail a pernicious type of transparency, according to which ‘Smith knows that it might be raining’ is equivalent to ‘it is consistent with everything that Smith knows that it is raining’ or ‘Smith doesn’t know that it isn’t raining’. Pernicious transparency has direct counterexamples and undermines vanilla principles of epistemic logic, such as that knowledge entails true belief and that something can (...) be true without one knowing it might be. I re-frame the challenge in precise terms and propose a novel expressivist formal semantics that meets it by exploiting (i) the topic-sensitivity and fragmentation of knowledge and belief states and (ii) the apparent context-sensitivity of epistemic modality. The resulting form of assertibility semantics advances the state of the art for state-based bilateral semantics by combining attitude reports with context-sensitive modal claims, while evading various objectionable features. In appendices, I compare the proposed system to Beddor and Goldstein’s ‘safety semantics’ and discuss its analysis of a modal Gettier case due to Moss. (shrink)

Expressivists about epistemic modals deny that ‘Jane might be late’ canonically serves to express the speaker’s acceptance of a certain propositional content. Instead, they hold that it expresses a lack of acceptance. Prominent expressivists embrace pragmatic expressivism: the doxastic property expressed by a declarative is not helpfully identified with that sentence’s compositional semantic value. Against this, we defend semantic expressivism about epistemic modals: the semantic value of a declarative from this domain is the property of doxastic attitudes it canonically serves (...) to express. In support, we synthesize data from the critical literature on expressivism—largely reflecting interactions between modals and disjunctions—and present a semantic expressivism that readily predicts the data. This contrasts with salient competitors, including: pragmatic expressivism based on domain semantics or dynamic semantics; semantic expressivism à la Moss [2015]; and the bounded relational semantics of Mandelkern [2019]. (shrink)

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. (shrink)

Asserting is the act of claiming that something is the case—for instance, that oranges are citruses, or that there is a traffic congestion on Brooklyn Bridge (at some time). We make assertions to share information, coordinate our actions, defend arguments, and communicate our beliefs and desires. Because of its central role in communication, assertion has been investigated in several disciplines. Linguists, philosophers of language, and logicians rely heavily on the notion of assertion in theorizing about meaning, truth and inference. -/- (...) The nature of assertion and its relation to other speech acts and linguistic phenomena (implicatures, presuppositions, etc.) have been subject to much controversy. This entry will situate assertion within speech act theory and pragmatics more generally, and then go on to present the current main accounts of assertion. (shrink)

In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...) multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives. (shrink)

We develop a novel solution to the negation version of the Frege-Geach problem by taking up recent insights from the bilateral programme in logic. Bilateralists derive the meaning of negation from a primitive *B-type* inconsistency involving the attitudes of assent and dissent. Some may demand an explanation of this inconsistency in simpler terms, but we argue 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. Based (...) on these insights, we develop a version of B-type expressivism called *inferential expressivism*. This is a novel semantic framework that characterises meanings by inferential roles that define which *attitudes* one can *infer* from the use of terms. We apply this framework to normative vocabulary, thereby solving the Frege-Geach problem generally and comprehensively. Our account moreover includes a semantics for epistemic modals, thereby also explaining normative terms under epistemic modals. (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. Thus, supervaluationists (...) can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

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. (shrink)

This paper overviews some recent work on the semantics and pragmatics of arguments.

According to dialectical disposition expressivism about conjunction, disjunction, and negation, the function of these connectives is to convey dispositions speakers have with respect to challenging and meeting challenges to assertions. This paper investigates the view’s implications for logic. An interpretation in terms of dialectical dispositions is proposed for the proof rules of a bilateral sequent system. Rules that are sound with respect to this interpretation can be seen as generating an intrinsic logic of dialectical dispo- sition expressivism. It is argued (...) that such a logic will be very weak —weaker than the intersection of minimal logic and FDE. (shrink)

In a series of works, Pablo Cobreros, Paul Égré, David Ripley and Robert van Rooij have proposed a nontransitive system (call it ‘_K__3__L__P_’) as a basis for a solution to the semantic paradoxes. I critically consider that proposal at three levels. At the level of the background logic, I present a conception of classical logic on which _K__3__L__P_ fails to vindicate classical logic not only in terms of structural principles, but also in terms of operational ones. At the level of (...) the theory of truth, I raise a cluster of philosophical difficulties for a _K__3__L__P_-based system of naive truth, all variously related to the fact that such a system proves things that would seem already by themselves repugnant, even in the absence of transitivity. At the level of the theory of validity, I consider an extension of the _K__3__L__P_-based system of naive validity that is supposed to certify that validity in that system does not fall short of naive validity, argue that such an extension is untenable in that its nontriviality depends on the inadmissibility of a certain irresistible instance of transitivity (whence the advertised “final cut”) and conclude on this basis that the _K__3__L__P_-based system of naive validity cannot coherently be adopted either. At all these levels, a crucial role is played by certain metaentailments and by the extra strength they afford over the corresponding entailments: on the one hand, such strength derives from considerations that would seem just as compelling in a general nontransitive framework, but, on the other hand, such strength wreaks havoc in the particular setting of _K__3__L__P_. (shrink)

Stephen Read presented harmonious inference rules for identity in classical predicate logic. I demonstrate here how this approach can be generalised to a setting where predicate logic has been extended with epistemic modals. In such a setting, identity has two uses. A rigid one, where the identity of two referents is preserved under epistemic possibility, and a non-rigid one where two identical referents may differ under epistemic modality. I give rules for both uses. Formally, I extend Quantified Epistemic Multilateral Logic (...) with two identity signs. I argue that a uniform meaning for identity tout court can be given by adopting Maria Aloni’s account of reference using conceptual covers. We obtain a harmonious set of rules for identity that is sound and complete for Aloni’s model theory. (shrink)

A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of ‘global’ expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege–Geach problem). The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed (...) ICL (‘Indicative Conditional Logic’). The expressivist framework extends the AGM (after Alchourron, Gärdenfors, Makinson) framework for belief revision and so provides a categorical (‘yes’–‘no’) epistemology for conditionals that complements McGee’s probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data (as pooled by linguists and from psychological experiments) while integrating both expressivist and semanticist perspectives. (shrink)

It’s commonly thought that, in conversation, speakers accept and reject propositions that have been asserted by others. Do speakers accept and reject questions as well? Intuitively, it seems that they do. But what does it mean to accept or reject a question? What is the relationship between these acts and those of asking and answering questions? Are there clear and distinct classes of reasons that speakers have for acceptance and rejection of questions? This chapter seeks to address these issues. Beyond (...) their intrinsic interest to those working on the nature of questions, solutions to these problems may aid the extension of inferentialist approaches to logic and language. Inferentialists who think that inferences should be conceived in terms of the norms we are subject to in virtue of both the sentences we accept or assert as well as those we reject or deny are known as bilateralists. A coherent account of accepting and rejecting questions raises the prospects for a bilateralism that interprets question-involving or erotetic inferences according to these additional primitives. While a full-blown bilateralism for erotetic inferences and ultimately for question-forming operators themselves far exceeds this chapter’s scope, the work presented here does sketch the first steps in that direction. (shrink)

I argue that standard explanationist solutions to the problem of creeping minimalism are largely on the right track, but they fail to correctly specify the kind of explanation that is relevant to distinguishing realism from quasirealism. Quasirealism should not be distinguished from realism in terms of the explanations it gives of why a normative judgment—a normative sentence or attitude—has the semantic content that it has. Rather, it should be distinguished in terms of the explanations it offers of what the semantic (...) content of a normative judgment is. (shrink)

This paper has two related goals. First, we develop an expressivist account of negation which, in the spirit of Alan Gibbard, treats disagreement as semantically primitive. Our second goal is to make progress toward a unified expressivist treatment of modality. Metaethical expressivists must be expressivists about deontic modal claims. But then metaethical expressivists must either extend their expressivism to include epistemic and alethic modals, or else accept a semantics for modal expressions that is radically disjunctive. We propose that expressivists look (...) to Amie Thomasson’s work for a general strategy for offering a unified expressivist account of modality. Modals in general, we propose, are devices for expressing metalinguistic commitments within the object language, with deontic, epistemic, and metaphysical modals all expressing different kinds of metalinguistic commitments. (shrink)

Incurvati and Schlöder (Journal of Philosophical Logic, 51(6), 1549–1582, 2022) have recently proposed to define supervaluationist logic in a multilateral framework, and claimed that this defuses well-known objections concerning supervaluationism’s apparent departures from classical logic. However, we note that the unconventional multilateral syntax prevents a straightforward comparison of inference rules of different levels, across multi- and unilateral languages. This leaves it unclear how the supervaluationist multilateral logics actually relate to classical logic, and raises questions about Incurvati and Schlöder’s response to (...) the objections. We overcome the obstacle, by developing a general method for comparisons of strength between multi- and unilateral logics. We apply it to establish precisely on which inferential levels the supervaluationist multilateral logics defined by Incurvati and Schlöder are classical. Furthermore, we prove general limits on how classical a multilateral logic can be while remaining supervaluationistically acceptable. Multilateral supervaluationism leads to sentential logic being classical on the levels of theorems and regular inferences, but necessarily strictly weaker on meta- and higher-levels, while in a first-order language with identity, even some classical theorems and inferences must be forfeited. Moreover, the results allow us to fill in the gaps of Incurvati and Schlöder’s strategy for defusing the relevant objections. (shrink)

Drawing on the puzzling behavior of ordinary knowledge ascriptions that embed an epistemic (im)possibility claim, we tentatively conclude that it is untenable to jointly endorse (i) an unfettered classical logic for epistemic language, (ii) the general veridicality of knowledge ascription, and (iii) an intuitive ‘negative transparency’ thesis that reduces knowledge of a simple negated ‘might’ claim to an epistemic claim without modal content. We motivate a strategic trade-off: preserve veridicality and (generalized) negative transparency, while abandoning the general validity of contraposition. (...) We criticize various approaches to incorporating veridicality into domain semantics, a paradigmatic ‘information-sensitive’ framework for capturing negative transparency and, more generally, the non-classical behavior of sentences with epistemic modals. We then present a novel information-sensitive semantics that successfully executes our favored strategy: stable acceptance semantics, extending a vanilla bilateral state-based semantics for epistemic modals with a knowledge operator loosely inspired by the defeasibility theory of knowledge. (shrink)

I argue that rejection is a speech act that cannot be reduced to assertion. Adapting an argument by Huw Price, I conclude that rejection is best conceived of as the speech act that is used to register that some other speech act is (or would be) violating a rule of the conversation game. This can be naturally understood as registering *norm violations* where speech acts are characterised by their essential norms. However, I argue that rejection itself is not to be (...) characterised by a norm. Instead, registering violations is a necessary condition for understanding the normative framework in the first place. The core observation is that the concept of an 'illegal move' is intelligible, so a speech act can be (say) an assertion, despite violating the essential norm of asserting. Rejection has the function of pointing out that a move is illegal. But registering rule violations is a precondition of playing games with rules (it is part of the concept 'game'), not itself a rule in a game. A similar special role of rejection (that it is not explicable in the terms provided by a framework, but needed to conceptualise these terms) likely occurs in other frameworks as well, e.g. characterising speech acts by commitments or their effect on a common ground. (shrink)

One of the challenges that any theorist of vagueness faces is to account for there being two kinds of disagreement over vague predicates like “tall” and “rich”: canonical disagreements concerning clear cases and faultless disagreements concerning borderline cases. I’ll argue that one needs to maintain that the illocutionary force of borderline utterances is different from that of clear utterances. Whereas the latter might be correct assertions, the former should be assertives weaker than assertions, since they express only a weak belief (...) of the speaker. The degree of commitment to the truth of what is said in a borderline utterance is lower and neither speaker of two opposing verdicts makes a mistake. (shrink)

Incurvati and Schlöder (_Journal of Philosophical Logic, 51_(6), 1549–1582, 2022) have recently proposed to define supervaluationist logic in a multilateral framework, and claimed that this defuses well-known objections concerning supervaluationism’s apparent departures from classical logic. However, we note that the unconventional multilateral syntax prevents a straightforward comparison of inference rules of different levels, across multi- and unilateral languages. This leaves it unclear how the supervaluationist multilateral logics actually relate to classical logic, and raises questions about Incurvati and Schlöder’s response to (...) the objections. We overcome the obstacle, by developing a general method for comparisons of strength between multi- and unilateral logics. We apply it to establish precisely on which inferential levels the supervaluationist multilateral logics defined by Incurvati and Schlöder are classical. Furthermore, we prove general limits on how classical a multilateral logic can be while remaining supervaluationistically acceptable. Multilateral supervaluationism leads to sentential logic being classical on the levels of theorems and regular inferences, but necessarily strictly weaker on meta- and higher-levels, while in a first-order language with identity, even some classical theorems and inferences must be forfeited. Moreover, the results allow us to fill in the gaps of Incurvati and Schlöder’s strategy for defusing the relevant objections. (shrink)

Indicative and subjunctive conditionals are in non-complimentary distribution: there are conversational contexts at which both are licensed (Stalnaker 1975; Karttunen and Peters 1979; von Fintel 1998). This means we can ask an important, but under-explored, question: in contexts which license both, what relations hold between the two? In this paper, I’ll argue for an initially surprising conclusion: when attention is restricted to the relevant contexts, indicatives and subjunctives are co-entailing. §1 introduces the indicative/subjunctive distinction, along with a discussion of the (...) relevant notion of entailment; §2 presents the main argument of the paper, and §3 considers some of the philosophical implications of the argument in §2. Finally, §4 argues that we can reconcile the equivalence of indicatives and subjunctives with apparently conflicting judgements. (shrink)

In this paper, we propose a new approach to absurdity in the context of natural deduction for intuitionistic and classical logic. It combines the aspects of both the logical approach, which treats absurdity as a propositional constant, and the structural approach, which treats absurdity as a structural punctuation mark signalling the dead end of derivations. In particular, we will treat absurdity as an impossible command, that is, a speech act composed of an imperative force indicator, and the false propositional constant, (...) that is, a proposition that cannot be true by definition. In return, we obtain a framework that constitutes a middle ground between the logical and structural approaches. For example, it allows us to consider the ex falso quodlibet rule as a kind of structural rule, specifically, a semi‐structural rule, and at the same time also maintain that negation can be reduced to implication of absurdity, specifically, to its propositional content. (shrink)

Epistemic contradictions are now a well-known and often discussed phenomenon among those who study epistemic modals. These contradictions are expressed by sentences like ‘It is raining and it might not be raining’ whose oddness to the common ear demands an explanation. However, it has turned out to be a rather controversial enterprise to provide such an explanation in a sufficiently precise and general manner. According to pragmatic explanations, epistemic contradictions are semantically consistent but pragmatically defective. According to semantic explanations, one (...) should regard epistemic contradictions as plain semantic inconsistencies. Endorsing such a semantic solution is, however, tantamount to rejecting classical logic, which predicts the consistency of epistemic contradictions. After arguing that all existing solutions to this problem face as yet unmet challenges, I will present a new solution that adequately overcomes these challenges. I will propose to view epistemic contradictions as semantically consistent but epistemically defective sentences. The main thesis emerging will be that we need neither abandon the inference rules of classical logic nor the classical truth-conditional approach to semantics to deal adequately with epistemic contradictions. (shrink)