When embedding data are used to argue against semantic theory A and in favor of semantic theory B, it is important to ask whether A could make sense of those data. It is possible to ask that question on a case-by-case basis. But suppose we could show that A can make sense of all the embedding data which B can possibly make sense of. This would, on the one hand, undermine arguments in favor of B over A on the basis (...) of embedding data. And, provided that the converse does not hold—that is, that A can make sense of strictly more embedding data than B can—it would also show that there is a precise sense in which B is more constrained than A, yielding a pro tanto simplicity-based consideration in favor of B. In this paper I develop tools which allow us to make comparisons of this kind, which I call comparisons of potential expressive power. I motivate the development of these tools by way of exploration of the recent debate about epistemic modals. Prominent theories which have been developed in response to embedding data turn out to be strictly less expressive than the standard relational theory, a fact which necessitates a reorientation in how to think about the choice between these theories. (shrink)

The Identity principle says that conditionals with the form 'If p, then p' are logical truths. Identity is overwhelmingly plausible, and has rarely been explicitly challenged. But a wide range of conditionals nonetheless invalidate it. I explain the problem, and argue that the culprit is the principle known as Import-Export, which we must thus reject. I then explore how we can reject Import-Export in a way that still makes sense of the intuitions that support it, arguing that the differences between (...) indicative and subjunctive conditionals play a key role in solving this puzzle. (shrink)

Mind &Language, Volume 35, Issue 1, Page 115-138, February 2020.

I show that standard dynamic approaches to the semantics of epistemic modals invalidate the classical laws of excluded middle and non-contradiction, as well as the law of epistemic non-contradiction. I argue that these facts pose a serious challenge.

What does 'might' mean? One hypothesis is that 'It might be raining' is essentially an avowal of ignorance like 'For all I know, it's raining'. But it turns out these two constructions embed in different ways, in particular as parts of larger constructions like Wittgenstein's 'It might be raining and it's not' and Moore's 'It's raining and I don't know it', respectively. A variety of approaches have been developed to account for those differences. All approaches agree that both Moore sentences (...) and Wittgenstein sentences are classically consistent. In this paper I argue against this consensus. I adduce a variety of new data which I argue can best be accounted for if we treat Wittgenstein sentences as being classically inconsistent. This creates a puzzle, since there is decisive reason to think that 'Might p' is classically consistent with 'Not p'. How can it also be that 'Might p and not p' and 'Not p and might p' are classically inconsistent? To make sense of this situation, I propose a new theory of epistemic modals and their interaction with embedding operators. This account makes sense of the subtle embedding behavior of epistemic modals, shedding new light on their meaning and, more broadly, the dynamics of information in natural language. -/- . (shrink)

McGee argued that modus ponens was invalid for the natural language conditional ‘If…then…’. Many subsequent responses have argued that, while McGee’s examples show that modus ponens fails to preserve truth, they do not show that modus ponens fails to preserve rational full acceptance, and thus modus ponens may still be valid in the latter informational sense. I show that when we turn our attention from indicative conditionals to subjunctive conditionals, we find that modus ponens does not preserve either truth or (...) rational full acceptance, and thus is not valid in either sense. In concluding I briefly consider how we can account for these facts. (shrink)

In this paper, I show that, given seemingly plausible assumptions about the epistemic ‘might’ and conditionals, we cannot explain why in some circumstances it is appropriate to utter conditional ‘might’-sentences, like “If Angelica has crumbs in her pocket, then she might be the thief” and not the corresponding simple ones, like “Angelica might be the thief.” So, one of our assumptions must be incorrect. I argue that the root of the problem is an umbrella thesis about the pragmatics of ‘might’-communication (...) - one that says that the communicative impact of an utterance of a ‘might’-sentence is the performance of a consistency check on the information of the context. I conclude that we must reject this thesis. And I close the paper by sketching an alternative view about what assertive uses of ‘might’-sentences typically do - one which avoids the problem. Such uses typically present a possibility as a serious option in reasoning and deliberation. (shrink)

I argue against a simple contextualist account of epistemic modals. My argument, like the argument on which it is based , charges that simple contextualism cannot explain all of the conversational data about uses of epistemic modals. My argument improves on its predecessor by insulating itself from recent contextualist attempts by Janice Dowell and Igor Yanovich to get around that argument. In particular, I use linguistic data to show that an utterance of an epistemic modal sentence can be warranted, while (...) an utterance of its suggested simple contextualist paraphrase is not. (shrink)

I generalize the notion of a conditional attitude by bringing together two topics of inquiry. One is the ordinary inquiry into conditional attitudes. The other topic is the inquiry into the attitude of thinking that a proposition is likely, or having a high credence in a proposition. For instance, what is it to intend to go to the game if it is likely that Kershaw pitches? Being likely that Kershaw pitches is the condition of the attitude. Given a natural position (...) about statements like “It is likely that Kershaw pitches,” the target attitude looks different from ordinary conditional attitudes. (shrink)

This paper makes explicit the way in which many theorists of the epistemology of uncertainty, or formal epistemologists, are committed to a version of noncognitivism—one about thoughts that something is likely. It does so by drawing an analogy with metaethical noncognitivism. I explore the degree to which the motivations for both views are similar and how both views have to grapple with the Frege‐Geach Problem about complex thoughts. The major upshot of recognizing this noncognitivism is that it presents challenges and (...) opportunities not only in the philosophy of mind and language but also in epistemology itself. I present some examples where attention to the implicit noncognitivism in formal epistemology has affected or should affect epistemological theory. And I suggest that it is likely that further examples of this sort will arise. (shrink)

What we can call asymmetric disagreement occurs when one agent is in disagreement with another, but not vice-versa. In this paper, I give an example of and develop a framework for understanding this phenomenon. One pivotal feature of my example is that one of the agents in the scenario has a belief about what might be the case—a might-belief. I show that a traditional account of might-beliefs and disagreement cannot explain the initially surprising phenomenon of asymmetric disagreement. In order to (...) provide an explanation, I develop a dynamic account of might-beliefs and a corresponding account of disagreement. I close by exploring a choice point for our account—showing that the simple dynamic account has some controversial (though, perhaps, true) consequences. I explore how revisionary notions of validity, inconsistency, and disagreement can allow us to avoid these consequences if we wish. (shrink)

Contextualism about many expressions faces a common objection: in some discourses it appears that there is no single interpretation which can explain how a speaker is justified in making her assertion and how a hearer with different information or standards is justified in negatively evaluating what the speaker said. According to the Multiple Proposition Strategy , contextualists may attempt to explain these competing features pragmatically in terms of different propositions in play. In this paper I argue against the Multiple Proposition (...) Strategy, first focusing on epistemic modals and then generalising the results to other expressions. I show how when purportedly contextualist terms are embedded in belief reports, we get similar problems but that the Multiple Proposition Strategy does not provide a satisfactory explanation of such cases. I suggest, therefore, that we reject the Multiple Proposition Strategy in favour of a theory that explains the unembedded and embedded cases in similar ways. (shrink)

This paper presents corpus and experimental data that problematize the traditional analysis of must as a strong necessity modal, as recently revived and defended by von Fintel and Gillies :351–383, 2010). I provide naturalistic examples showing that must p can be used alongside an explicit denial of knowledge of p or certainty in p, and that it can be conjoined with an expression indicating that p is not certain or that not-p is possible. I also report the results of an (...) experiment involving lotteries, where most participants endorsed a sentence of the form must not-p despite being instructed that p is a possibility. Crucially, endorsement was much higher for must in this context than for matched sentences with knowledge or certainty expressions. These results indicate that the requirements for felicitous use of must are weaker than for know and certain rather than being at least as strong, as the epistemic necessity theory would predict. However, it is possible to account for these data while retaining the key insights of von Fintel and Gillies’ analysis of the evidential component of must. I discuss several existing accounts that could be construed in this way and explain why none is completely satisfactory. I then propose a new model that embeds an existing scalar theory into a probabilistic model of informational dynamics structured around questions and answers. (shrink)

Epistemic and deontic comparatives differ in how they interact with disjunction. I argue that this difference provides a compelling empirical argument against the semantics of Kratzer, which predicts that all modal comparatives should interact with disjunction in the same way. Interestingly, an identical distinction is found in the semantics of non-modal adjectives: additive adjectives like ‘heavy’ behave logically like epistemic comparatives, and intermediate adjectives like ‘hot’ behave like deontic comparatives. I characterize this distinction formally and argue that the divergence between (...) epistemic and deontic modals explained if we structure their semantics around scalar concepts: epistemic modals should be analyzed using probability , and deontic modals using expected value. (shrink)

Plural definite descriptions across many languages display two well-known properties. First, they can give rise to so-called non-maximal readings, in the sense that they ‘allow for exceptions’. Second, while they tend to have a quasi-universal quantificational force in affirmative sentences, they tend to be interpreted existentially in the scope of negation. Building on previous works, we offer a theory in which sentences containing plural definite expressions trigger a family of possible interpretations, and where general principles of language use account for (...) their interpretation in various contexts and syntactic environments. Our theory solves a number of problems that these previous works encounter, and has broader empirical coverage in that it offers a precise analysis for sentences that display complex interactions between plural definites, quantifiers and bound variables, as well as for cases involving non-distributive predicates. The resulting proposal is briefly compared with an alternative proposal by Križ, which has similar coverage but is based on a very different architecture and sometimes makes subtly different predictions. (shrink)

Counterfactual scepticism holds that most ordinary counterfactuals are false. The main argument for this view appeals to a ‘chance undermines would’ principle: if ψ would have some chance of not obtaining had ϕ obtained, then ϕ □→ ψ is false. This principle seems to follow from two fairly weak principles, namely, that ‘chance ensures could’ and that ϕ □→ ψ and ϕ ⋄→ ¬ ψ clash. Despite their initial plausibility, I show that these principles are independently problematic: given some modest (...) closure principles, they entail absurdities. Moreover, on the most promising strategy for saving these principles, they do not, in the relevant sense, entail the chance-undermines-would principle. Instead, they entail a principle that only supports counterfactual indeterminism, the view that most ordinary counterfactuals are chancy, that is, not settled true. I demonstrate this by developing an indeterminist semantics that vindicates the clash and chance-ensures-could principles but not the chance-undermines-would principle. This view, I argue, offers a better account of our credal and linguistic judgements than counterfactual scepticism. (shrink)

There are certain uses of and and or that cannot be explained by their normal meanings as truth-functional connectives, even with sophisticated pragmatic resources. These include examples such as The cops show up, and a fight will break out (‘If the cops show up, a fight will break out’), and I have no friends, or I would throw a party (‘I have no friends. If I did have friends, I would throw a party.’). We argue that these uses are indeed (...) distinct from the more ordinary uses of and and or, but that they are nonetheless related in a principled way. To explain them we give an analysis of what we call the dynamic effects of connectives, which arise in all their uses. The special uses at issue are then argued to be instances where the connectives exhibit their dynamic effects without their truth-conditional meaning. (shrink)

By maintaining that a conditional sentence can be taken to express the validity of a rule of inference, we offer a solution to the Miners Paradox that leaves both modus ponens and disjunction elimination intact. The solution draws on Sundholm's recently proposed account of Fitch's Paradox.

In this paper I will argue, contrary to common assumptions, that rational atheistic prayer is possible. I will formulate and respond to two powerful arguments against the possibility of atheistic prayer: first, an argument that the act of prayer involves an intention to communicate to God, precluding disbelief in God’s existence; second, an argument claiming that reaching out to God through prayer requires believing God might exist, precluding rational disbelief in God. In showing options for response to these arguments, I (...) will describe a model on which atheistic prayer is not only possible, but is on a par with theistic prayer in many more ways than one might expect. (shrink)

In the pair of articles of which this is the second, I present a set of problems and philosophical proposals that have in recent years been associated with the term “relativism”. These problems are related to the question of how we should represent thought and speech about certain topics. The main issue is whether we should model such mental states or linguistic acts as involving representational contents that are absolutely correct or incorrect, or whether, alternatively, their correctness should be thought (...) of as varying with some (more or less surprising) factor. In the first article, “Relativism 1: Representational Content”, I discussed the general issue of relativism about representational content. I argued for the conciliatory view that both relativist and absoutist conceptions of representational content can be legitimate. In the present continuation, I look in more detail at a special case of the general issue, namely the question of whether semantic contents, i.e. the contents assigned to linguistic utterances in the semantics of natural language, should be construed in an absolutist or in a relativist way. (shrink)

It is often assumed that when one party felicitously rejects an assertion made by an- other party, the first party thinks that the proposition asserted by the second is false. This assumption underlies various disagreement arguments used to challenge contex- tualism about some class of expressions. As such, many contextualists have resisted these arguments on the grounds that the disagreements in question may not be over the proposition literally asserted. The result appears to be a dialectical stalemate, with no independent (...) method of determining whether any particular instance of disagreement is over the proposition literally asserted. In this paper, I propose an independent method for assessing whether a disagreement is about what’s literally asserted. Focusing on epistemic modals throughout, I argue that this method provides evidence that some epistemic modal disagreements are in fact not over the proposition literally asserted by the utterance of the epistemic modal sentence. This method provides a way to break the stalemate, and reveals a new data point for theories of epistemic modals to predict—that is, how there can be such modal disagreements. In the rest of the paper, I motivate a general theory of how to predict these kinds of disagreements, and then offer some brief remarks about how contextualist, relativist, and expressivist theories of epistemic modals might accommodate this new data point. (shrink)

When speakers utter conflicting moral sentences, it seems clear that they disagree. It has often been suggested that the fact that the speakers disagree gives us evidence for a claim about the semantics of the sentences they are uttering. Specifically, it has been suggested that the existence of the disagreement gives us reason to infer that there must be an incompatibility between the contents of these sentences. This inference then plays a key role in a now-standard argument against certain theories (...) in moral semantics. In this paper, we introduce new evidence that bears on this debate. We show that there are moral conflict cases in which people are inclined to say both that the two speakers disagree and that it is not the case at least one of them must be saying something incorrect. We then explore how we might understand such disagreements. As a proof of concept, we sketch an account of the concept of disagreement and an independently motivated theory of moral semantics which, together, explain the possibility of such cases. (shrink)

According to long-standing orthodoxy in contemporary analytic philosophy of language, the content of a sentence (that is, the information it encodes and what on.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (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)

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)

I compare Stalnaker’s early take on assertoric content with the one expressed in his recent book (2014). I discern in the latter some striking implications about the semantics of proper names and assertoric content’s relation to semantics.

Accounts of scientific explanation disagree about what’s required for a cause, law, or other fact to be a reason why an event occurs. In short, they disagree about the conditions for explanatory relevance. Nonetheless, most accounts presuppose that claims about explanatory relevance play a descriptive role in tracking reality. By rejecting the need for this descriptivist assumption, I develop an expressivist account of explanatory relevance and explanation: to judge that an answer is explanatory is to express an attitude ofbeing for (...) being satisfied by that answer. I show how expressivism vindicates ordinary scientific discourse about explanation, including claims about the objectivity and mind-independence of explanations. By avoiding commitment to ontic relevance relations, I rehabilitate an irrealist conception of explanation. (shrink)

When are you in a position to rely on p in practical reasoning? Existing accounts say that you must know that p, or be in a position to know that p, or be justified in believing that p, or be in a position to justifiably believe it, and so on. This paper argues that all of these proposals face important problems, which I call the Problems of Negative Bootstrapping and of Level Confusions. I offer a diagnosis of these problems, and (...) I argue that an adequate epistemic norm must be transparent in the following sense: According to the correct epistemic norm, a consideration counts in favor of (or against) relying on p in practical reasoning iff, and to the extent that, this consideration also counts in favor of (or against) p being true. I introduce a candidate epistemic norm that satisfies this condition. According to this norm, one should rely on p in practical reasoning only if it must be that p. If we adopt a non-factualist account of “must”, this amounts to a novel and attractive proposal, a proposal that satisfies the transparency condition. (shrink)

A direct realist theory of perceptual justification. I take a ground-up approach, beginning with a theory of subjective rationality understood in terms of first-person rational explicability of the stream of consciousness. I mathematize this picture via a Tractarian spin on a semantical framework developed by Rayo. Perceptual states justify by being 'receptive': rationally inexplicable intentional states encoded in sentences that are analytic. Direct realists working within this framework should say that when one is taken in by hallucination one's overall picture (...) of the world is incoherent; in this sense, a belief based on delusive hallucination can be provided with exculpation but not with justification. (shrink)

‘Fred must open the door’ concerns Fred’s obligations. This obligative meaning is turned off by adding aspect: ‘Fred must have opened/be opening/have been opening the door’ are one and all epistemic. Why? In a nutshell: obligative ’must’ operates on procedural contents of imperative sentences, epistemic ‘must’ on propositional contents of declarative sentences; and adding aspect converts procedural into propositional content.

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)

We investigate, in a logical setting, the expressivist proposal that assertion primarily functions to express and coordinate doxastic states and that ‘might’ fundamentally expresses lack of belief. We provide a formal model of an agent’s doxastic state and novel assertability conditions for an associated formal language. We thereby prove that an arbitrary assertion always succeeds in expressing a well-defined doxastic state, and propose a fully general and intuitive update operation as a model of an agent coming to accept an arbitrary (...) assertion. Leaving a comprehensive philosophical and linguistic defense for elsewhere, we explore technical aspects of our framework, providing, for instance, a complete logic of assertability and reduction axioms for the novel update operations related to our proposal. Finally, we contrast our work with related proposals in the logic literature. (shrink)

It is tempting to posit an intimate relationship between belief and assertion. The speech act of assertion seems like a way of transferring the speaker’s belief to his or her audience. If this is right, then you might think that the evidential warrant required for asserting a proposition is just the same as the warrant for believing it. We call this thesis entitlement equality. We argue here that entitlement equality is false, because our everyday notion of belief is unambiguously a (...) weak one. Believing something is true, we argue, is compatible with having relatively little confidence in it. Asserting something requires something closer to complete confidence. Specifically, we argue that believing a proposition merely requires thinking it likely, but that thinking that a proposition is likely does not entitle one to assert it. This conclusion conflict with a standard view that ‘full belief’ is the central commonsense non-factive attitude. (shrink)

Crosslinguistically, the same modal words can be used to express a wide range of interpretations. This crosslinguistic trend supports a Kratzerian analysis, where each modal has a core lexical entry and where the difference between an epistemic and a root interpretation is contextually determined. A long-standing problem for such a unified account is the equally robust crosslinguistic correlation between a modal’s interpretation and its syntactic behavior: epistemics scope high (in particular higher than tense and aspect) and roots low, a fact (...) which has led to proposals that hardwire different syntactic positions for epistemics and roots (cf. Cinque’s hierarchy). This paper argues that the range of interpretations a modal receives is even more restricted: a modal must be keyed to certain time-individual pairs, but not others. I show that this can be captured straightforwardly by minimally modifying the Kratzerian account: modals are relative to an event—rather than a world—of evaluation, which readily provides a time (the event’s running time) and (an) individual(s) (the event’s participants). I propose that this event relativity of modals can in turn explain the correlation between type of interpretation and syntactic position, without stipulation of an interpretation-specific height for modals. (shrink)

Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis- Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis- Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.

This essay calls attention to a set of linguistic interactions between counterfactual conditionals, on one hand, and possibility modals like could have and might have, on the other. These data present a challenge to the popular variably strict semantics for counterfactual conditionals. Instead, they support a version of the strict conditional semantics in which counterfactuals and possibility modals share a unified quantificational domain. I’ll argue that pragmatic explanations of this evidence are not available to the variable analysis. And putative counterexamples (...) to the unified strict analysis, on careful inspection, in fact support it. Ultimately, the semantics of conditionals and modals must be linked together more closely than has sometimes been recognized, and a unified strict semantics for conditionals and modals is the only way to fully achieve this. (shrink)

In recent years, a number of theorists have claimed that beliefs about probability are transparent. To believe probably p is simply to have a high credence that p. In this paper, I prove a variety of triviality results for theses like the above. I show that such claims are inconsistent with the thesis that probabilistic modal sentences have propositions or sets of worlds as their meaning. Then I consider the extent to which a dynamic semantics for probabilistic modals can capture (...) theses connecting belief, certainty, credence, and probability. I show that although a dynamic semantics for probabilistic modals does allow one to validate such theses, it can only do so at a cost. I prove that such theses can only be valid if probabilistic modals do not satisfy the axioms of the probability calculus. (shrink)

This paper explores the relationship between dynamic and truth conditional semantics for epistemic modals. It provides a generalization of a standard dynamic update semantics for modals. This new semantics derives a Kripke semantics for modals and a standard dynamic semantics for modals as special cases. The semantics allows for new characterizations of a variety of principles in modal logic, including the inconsistency of ‘p and might not p’. Finally, the semantics provides a construction procedure for transforming any truth conditional semantics (...) for modals into a dynamic semantics for modals with similar properties. (shrink)

Free Choice is the principle that possibly p or q implies and is implied by possibly p and possibly q. A variety of recent attempts to validate Free Choice rely on a nonclassical semantics for disjunction, where the meaning of p or q is not a set of possible worlds. This paper begins with a battery of impossibility results, showing that some kind of nonclassical semantics for disjunction is required in order to validate Free Choice. The paper then provides a (...) positive account of Free Choice, by identifying a family of dynamic semantics for disjunction that can validate the inference. On all such theories, the meaning of p or q has two parts. First, p or q requires that our information is consistent with each of p and q. Second, p or q narrows down our information by eliminating some worlds. It turns out that this second component of or is well behaved: there is a strongest such meaning that p or q can express, consistent with validating Free Choice. The strongest such meaning is the classical one, on which p or q eliminates any world where both p and q are false. In this way, the classical meaning of disjunction turns out to be intimately related to the validity of Free Choice. (shrink)

This paper has three main goals. First, to motivate a puzzle about how ignorance-expressing terms like maybe and if interact: they iterate, and when they do they exhibit scopelessness. Second, to argue that there is an ambiguity in our theoretical toolbox, and that exposing that opens the door to a solution to the puzzle. And third, to explore the reach of that solution. Along the way, the paper highlights a number of pleasing properties of two elegant semantic theories, explores some (...) meta-theoretic properties of dynamic notions of meaning, dips its toe into some hazardous waters, and offers characterization theorems for the space of meanings an indicative conditional can have. (shrink)

Epistemic modal verbs and adverbs of necessity are claimed to be positive polarity items. We study their behavior by examining modal spread, a phenomenon that appears redundant or even anomalous, since it involves two apparent modal operators being interpreted as a single modality. We propose an analysis in which the modal adverb is an argument of the MUST modal, providing a meta-evaluation \ which ranks the Ideal, stereotypical worlds in the modal base as better possibilities than the Non-Ideal worlds in (...) it. MUST and possibility modals differ in that the latter have an empty \, a default that can be negotiated. Languages vary in the malleability of this parameter. Positive polarity is derived as a conflict between the ranking imposed by \—which requires that the Ideal worlds be better possibilities than Non-Ideal worlds—and the effect of higher negation which renders the Ideal set non-homogenous. Applying the ordering over such a non-homogeneous set would express preference towards both p and \ worlds thus rendering the sentence uninformative. Negative polarity MUST and possibility modals, on the other hand, contain an empty \, application of higher negation therefore poses no problem. This account is the first to connect modal spread to positive polarity of necessity modals, and captures the properties of both in a unified analysis. (shrink)

It is widely accepted that when ‘might’ expresses certain kinds of relative modality, the sentence ‘p and it might not be the case that p’ is in some sense inconsistent. It has proven difficult to define a formal semantics that explicates this inconsistency while meeting certain other desiderata, in particular, that p does not imply ‘Must p’. This paper presents such a semantics. The key idea is that background contexts have to have multiple levels, including an inner set consisting of (...) worlds that represent what might be true and an outer set of worlds such that a sentence must be true only if it is true in all of them. This is an open access publication. (shrink)