We introduce the rejection game, designed to formalize the interaction between interlocutors in a Stalnakerian conversation: a speaker who asserts something and a listener who may accept or reject. The rejection game is similar to other signalling games known to the literature in economics and biology. We point out similarities and differences, and propose an application in linguistics. We uncover basic conditions under which the Gricean maxim of quality emerges from incentives among the players, providing evidence for a functionalist understanding (...) of the Gricean program. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

Deflationists about truth hold that the function of the truth predicate is to enable us to make certain assertions we could not otherwise make. Pragmatists claim that the utility of negation lies in its role in registering incompatibility. The pragmatist insight about negation has been successfully incorporated into bilateral theories of content, which take the meaning of negation to be inferentially explained in terms of the speech act of rejection. We implement the deflationist insight in a bilateral theory by taking (...) the meaning of the truth predicate to be explained by its inferential relation to assertion. We combine this account of the meaning of the truth predicate with a new diagnosis of the liar paradox: its derivation requires the truth rules to preserve evidence, but these rules only preserve commitment. The result is a novel inferential deflationist theory of truth, which solves the liar paradox in a principled manner. We end by showing that our theory and simple extensions thereof have the resources to axiomatize the internal logic of several supervaluational hierarchies, including Cantini’s. This solves open problems of Halbach (2011) and Horsten (2011). (shrink)

Bilateral proof systems, which provide rules for both affirming and denying sentences, have been prominent in the development of proof-theoretic semantics for classical logic in recent years. However, such systems provide a substantial amount of freedom in the formulation of the rules, and, as a result, a number of different sets of rules have been put forward as definitive of the meanings of the classical connectives. In this paper, I argue that a single general schema for bilateral proof rules has (...) a reasonable claim to inferentially articulating the core meaning of all of the classical connectives. I propose this schema in the context of a bilateral sequent calculus in which each connective is given exactly two rules: a rule for affirmation and a rule for denial. Positive and negative rules for all of the classical connectives are given by a single rule schema, harmony between these positive and negative rules is established at the schematic level by a pair of elimination theorems, and the truth-conditions for all of the classical connectives are read off at once from the schema itself. (shrink)

This paper discusses a set of observations, many of which are novel, concerning differences between the adjectival modals _certain_ and _possible_ and their adverbial counterparts _certainly_ and _possibly_. It argues that the observations can be derived from a standard interpretation of _certain_/_certainly_ as universal and _possible_/_possibly_ as existential quantifiers over possible worlds, in conjunction with the hypothesis that the adjectives quantify over knowledge and the adverbs quantify over belief. The claims on which the argument relies include the following: (i) knowledge (...) implies belief, (ii) agents have epistemic access to their belief, (iii) relevance is closed under speakers’ belief, and (iv) commitment is pragmatically inconsistent with explicit denial of belief. (shrink)

The main goal of my text is to generalize Alexy's explicative argument against human rights skeptics in order to minimize the overall room for their escape. This argument tries to show that any attempt to intersubjectively justify the nonexistence of human rights as moral rights necessarily commits the so‐called performative self‐contradiction. Alexy worries that the effect of his argument can be weakened by a group reduction of discourse. But I will argue that this worry is overstated because the price of (...) such a reduction is much higher than Alexy estimates. I will then turn to the issue of moral relativism. I will try to show that the explicative argument, if suitably generalized, can cope even with human rights skeptics who think in terms of moral relativism. (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)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

The ability to express negation in language may have been the result of an adaptive process. However, there are different accounts of adaptation in linguistics, and more than one of them may describe the case of negation. In this paper, I distinguish different versions of the claim that negation is adaptive and defend a proposal, based on recent work by Steinert-Threlkeld (2016) and Incurvati and Sbardolini (2021), on which negation is an indirect adaptation.

Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if $$\wedge $$ ∧ and $$\vee $$ ∨ are duals, and the negation of the latter can be expressed lexically (nor), why not the negation (...) of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language. (shrink)

The aim of this paper is to provide a philosophical interpretation of bilateralism in terms of probabilism. In particular, to interpret the main concepts of bilateralism –acceptance, rejection and incoherence– in terms of the probabilistic notions of degree of belief and coherence. According to bilateralism, the meaning of logical connectives is determined by the acceptance and rejection conditions of the sentences in which they are involved, where acceptance and rejection cannot be reduced to one another. I will focus on a (...) variant of bilateralism that understands logical consequence as the statement that it is incoherent to accept all the premises of a valid argument while rejecting all its conclusions. On the other hand, probabilism states that it is possible to interpret our degrees of belief in terms of probabilities. The aim of this work is then to interpret the concept of incoherence in terms of probability functions and determine when it is coherent to accept or to reject a proposition according to some threshold defined in terms of degrees of belief. To achieve this goal, we need both an interpretation of the concept of incoherence coined by the bilateralists as well as an interpretation of acceptance and rejection. I will show that a good interpretation of coherence in probabilistic terms can already be found in the literature. Then, I will give an interpretation of acceptance and rejection in terms of degrees of belief. In particular, I will show that it is possible to interpret these concepts in accordance with Locke’s thesis, the thesis that states that there is some threshold r such that if you believe some sentence in degree equal or higher than r you should accept it, without falling into epistemic paradoxes. (shrink)

The logical analysis of Nāgārjuna’s catuṣkoṭi has remained a heated topic for logicians in Western academia for nearly a century. At the heart of the catuṣkoṭi, the four corners’ formalization typically appears as: A, Not A, Both, and Neither. The pulse of the controversy is the repetition of negations in the catuṣkoṭi. Westerhoff argues that Nāgārjuna in the Mūlamadhyamakakārikā uses two different negations: paryudāsa and prasajya-pratiṣedha. This paper builds off Westerhoff’s account and presents some subtleties of Nāgārjuna’s use of these (...) negations regarding their scope. This is achieved through an analysis of the Sanskrit and Tibetan Madhyamaka commentarial tradition and through a grammatical analysis of Nāgārjuna’s use of na and a- within a diverse variety of the catuṣkoṭi within the Mūlamadhyamakakārikā. (shrink)

Our linguistic communication is, in part, the exchange of truths. It is an empirical fact that in daily conversation we aim at truths, not falsehoods. This fact may lead us to assume that ordinary, assertion-based communication is the only possible communicative system for truth-apt information exchange, or at least has priority over any alternatives. This assumption is underwritten in three traditional doctrines: that assertion is a basic notion, in terms of which we define denial; that to predicate truth of a (...) sentence is to assert the content it expresses; and that one should, in the context of radical interpretation, try to maximize the truth of what foreigners believe or utter. However, I challenge this assumption via a thought experiment: imagine a language game in which everyone aims to exchange only falsehoods. I argue that information exchange is possible in this game, and so truth-guided communication and falsity-guided communication are conceptually on a par. As a consequence, we should reject the three doctrines, based as they are on the conceptual priority of assertion-based communication. (shrink)

We discuss a well-known puzzle about the lexicalization of logical operators in natural language, in particular connectives and quantifiers. Of the many logically possible operators, only few appear in the lexicon of natural languages: the connectives in English, for example, are conjunction _and_, disjunction _or_, and negated disjunction _nor_; the lexical quantifiers are _all, some_ and _no_. The logically possible nand (negated conjunction) and Nall (negated universal) are not expressed by lexical entries in English, nor in any natural language. Moreover, (...) the lexicalized operators are all upward or downward monotone, an observation known as the Monotonicity Universal. We propose a logical explanation of lexical gaps and of the Monotonicity Universal, based on the dynamic behaviour of connectives and quantifiers. We define update potentials for logical operators as procedures to modify the context, under the assumption that an update by \( \phi \) depends on the logical form of \( \phi \) and on the speech act performed: assertion or rejection. We conjecture that the adequacy of update potentials determines the limits of lexicalizability for logical operators in natural language. Finally, we show that on this framework the Monotonicity Universal follows from the logical properties of the updates that correspond to each operator. (shrink)

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. (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)

Starting from the case of insurance claims, I investigate the dynamics of acceptance, rejection and denial. I show that disagreement can be more varied than one might think. I illustrate this by looking at the Warren/Sanders controversy in the 2020 democratic primaries and at religious agnosticism.

We present epistemic multilateral logic, a general logical framework for reasoning involving epistemic modality. Standard bilateral systems use propositional formulae marked with signs for assertion and rejection. Epistemic multilateral logic extends standard bilateral systems with a sign for the speech act of weak assertion (Incurvati and Schlöder 2019) and an operator for epistemic modality. We prove that epistemic multilateral logic is sound and complete with respect to the modal logic S5 modulo an appropriate translation. The logical framework developed provides the (...) basis for a novel, proof-theoretic approach to the study of epistemic modality. To demonstrate the fruitfulness of the approach, we show how the framework allows us to reconcile classical logic with the contradictoriness of so-called Yalcin sentences and to distinguish between various inference patterns on the basis of the epistemic properties they preserve. (shrink)

The paper introduces the formula structure of poly-sequents, allowing the expression of poly-positions: positions with any number of stances, of which bilateralism and trilateralism are special cases. The paper also puts forward the view that s-coherence of such poly-positions can be defined inferentially, without appealing to their validity under interpretations of the object language.

We provide a framework for understanding agnosticism. The framework accounts for the varieties of agnosticism while vindicating the unity of the phenomenon. This combination of unity and plurality is achieved by taking the varieties of agnosticism to be represented by several agnostic stances, all of which share a common core provided by what we call the minimal agnostic attitude. We illustrate the fruitfulness of the framework by showing how it can be applied to several philosophical debates. In particular, several philosophical (...) positions can be aptly conceived of as instances of agnosticism whilst retaining their differences and distinguishing features. (shrink)

In this paper we investigate whether and to what extent scientists (e.g. inquirers such as epidemiologists or virologists) can have rational and fruitful disagreement with what we call post-enquirers (e.g. conspiratorial anti-vaxxers) on topics of scientific relevance such as the safety and efficacy of vaccines. In order to accomplish this aim, we will rely and expand on the epistemological framework developed in detail in Ferrari & Moruzzi (2021) to study the underlying normative profile of enquiry and post-enquiry. We take it (...) that our analysis provides an effective explanation of why standard argumentative strategies such as fact-checking and debunking cannot work in the context of disagreement between scientists and denialists unless they are coupled with a discussion of the values that are endorsed by the scientific community. (shrink)

Can someone who suspends judgement about a certain proposition <p> be in a relational state of disagreement with someone who believes <p> as well as with some- one who disbelieves <p>? This paper argues for an af- firmative answer. It develops an account of the notions of suspended judgement and disagreement that explains how and why the suspender is in a relational state of disagreement with both the believer and the disbeliever about the very same proposition <p>. More specifically, the (...) paper first provides a characterisation of the norma- tive profile associated with the state of suspended judge- ment in terms of the set of normative commitments that it engenders in the context of inquiry. It then provides a characterisation of the notion of disagreement in terms the incompatibility between the sets of normative com- mitments characteristic of the three states in question— belief, disbelief, and suspension. (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)

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...) We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (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)

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)

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)

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)

What is the relation of logic to thinking? My dissertation offers a new argument for the claim that logic is constitutive of thinking in the following sense: representational activity counts as thinking only if it manifests sensitivity to logical rules. In short, thinking has to be minimally logical. An account of thinking has to allow for our freedom to question or revise our commitments – even seemingly obvious conceptual connections – without loss of understanding. This freedom, I argue, requires that (...) thinkers have general abilities to respond to support and tension among their thoughts. And these abilities are constituted by following logical rules. So thinkers have to follow logical rules. But there isn’t just one correct logic for thinking. I show that my view is consistent with logical pluralism: there are a range of correct logics, any one of which a thinker might follow. A logic for thinking does, however, have to contain certain minimal principles: Modus Ponens and Non-Contradiction, and perhaps others. We follow logical rules by exercising logical capacities, which display a distinctive first-person/third-person asymmetry: a subject can find the instances of a rule compelling without seeing them as instances of a rule. As a result, there are two limits on illogical thinking. First, thinkers have to tend to find instances of logical rules compelling. Second, thinkers can’t think in obviously illogical ways. So thinking has to be logical – but not perfectly so. When we try to think, but fail, we produce nonsense. But our failures to think are often subjectively indistinguishable from thinking. To explain how this occurs, I offer an account of nonsense. To be under the illusion that some nonsense makes sense is to enter a pretence that the nonsense is meaningful. Our use of nonsense within the pretence relies on the role of logical form in understanding. Finally, while the normativity of logic doesn’t fall directly out of logical constitutivism, it’s possible to build an attractive account of logical normativity which has logical constitutivism as an integral part. I argue that thinking is necessary for human flourishing, and that this is the source of logical normativity. (shrink)