The problem of probabilities of conditionals is one of the long-standing puzzles in philosophy of language. We defend and update Adams' solution to the puzzle: the probability of an epistemic conditional is not the probability of a proposition, but a probability under a supposition. -/- Close inspection of how a triviality result unfolds in a concrete scenario does not provide counterexamples to the view that probabilities of conditionals are conditional probabilities: instead, it supports the conclusion that probabilities of conditionals violate (...) standard probability theory. -/- This does not call into question probability theory per se; rather, it calls for a more careful understanding of its role: probability theory is a theory of probabilities of propositions; but as conditionals do not express propositions, their probabilities are not subject to the standard laws. -/- We argue that both conditional probabilities and probabilities of conditionals are best understood in terms of the dynamics of supposing, modeled as a restriction operation on a probability space. This version of the suppositionalist view allows us to connect Adams' Thesis to the widely held restrictor view of the semantics of conditionals. -/- We address two common objections to Adams' view: that the relevant probabilities are ‘probabilities only in name’, and that giving up conditional propositions puts us at a disadvantage when it comes to interpreting compounds. -/- Finally, we argue that some putative counterexamples to Adams' Thesis can be diagnosed as fallacies of probabilistic reasoning: they arise from applying to conditionals laws of standard probability theory which are invalid for them. (shrink)

In ‘Sly Pete’ or ‘standoff’ cases, reasonable speakers accept incompatible conditionals, and communicate them successfully to a trusting hearer. This paper uses the framework of dynamic semantics to offer a new model of the conversational dynamics at play in standoffs, and to articulate several puzzles posed by such cases. The paper resolves these puzzles by embracing a dynamic semantics for conditionals, according to which indicative conditionals require that their antecedents are possible in their local context, and update this body of (...) information by eliminating the possibilities where the antecedent is true and the consequent is false. In this way, the dynamic analysis draws on insights from the material conditional and contextualist analyses, while explaining how standoffs are genuine disagreements. (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)

Holmes exists is false. How can this be, when there is no one for the sentence to misdescribe? Part of the answer is that a sentence’s topic depends on context. The king of France is bald, normally unevaluable, is false qua description of the bald people. Likewise Holmes exists is false qua description of the things that exist; it misdescribes those things as having Holmes among them. This does not explain, though, how Holmes does not exist differs in cognitive content (...) from, say, Vulcan does not exist. Our answer builds on an observation of Kripke’s: even if Holmes exists, he is not in this room, for we were all born too late. (shrink)

The ex ante Pareto principle has an intuitive pull, and it has been a principle of central importance since Harsanyi’s defence of utilitarianism. The principle has been used to criticize and refine a range of positions in welfare economics, including egalitarianism and prioritarianism. But this principle faces a serious problem. I have argued elsewhere :303-323 2017) that the concept of ex ante Pareto superiority is not well defined, because its application in a choice situation concerning a fixed population can depend (...) on how the members of that population are designated. I show in this paper that in almost all cases of policy choice, there will be numerous sets of rival designators for the same fixed population. I explore two ways that we might complete the definition of ex ante Pareto superiority. I call these the ‘supervaluationist’ reading and the ‘subvaluationist’ reading. I reject the subvaluationist reading as uncharitable, and argue that the supervaluationist reading is the most promising interpretation of the ex ante Pareto principle. I end by exploring some of the implications of this principle for prioritarianism and egalitarianism. (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)

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.

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)

ABSTRACT Quine insisted that the satisfaction of an open modalised formula by an object depends on how that object is described. Kripke's ‘objectual’ interpretation of quantified modal logic, whereby variables are rigid, is commonly thought to avoid these Quinean worries. Yet there remain residual Quinean worries for epistemic modality. Theorists have recently been toying with assignment-shifting treatments of epistemic contexts. On such views an epistemic operator ends up binding all the variables in its scope. One might worry that this yields (...) the undesirable result that any attempt to ‘quantify in’ to an epistemic environment is blocked. If quantifying into the relevant constructions is vacuous, then such views would seem hopelessly misguided and empirically inadequate. But a famous alternative to Kripke's semantics, namely Lewis' counterpart semantics, also faces this worry since it also treats the boxes and diamonds as assignment-shifting devices. As I'll demonstrate, the mere fact that a variable is bound is no obstacle to binding it. This provides a helpful lesson for those modelling de re epistemic contexts with assignment sensitivity, and perhaps leads the way toward the proper treatment of binding in both metaphysical and epistemic contexts: Kripke for metaphysical modality, Lewis for epistemic modality. (shrink)

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)

This paper proposes a new model of graded modal judgment. It begins by problematizing the phenomenon: given plausible constraints on the logic of epistemic modality, it is impossible to model graded attitudes toward modal claims as judgments of probability targeting epistemically modal propositions. This paper considers two alternative models, on which modal operators are non-proposition-forming: (1) Moss (2015), in which graded attitudes toward modal claims are represented as judgments of probability targeting a “proxy” proposition, belief in which would underwrite belief (...) in the modal claim. (2) A model on which graded attitudes toward modal claims are represented as judgments of credence taking as their objects (non-propositional) modal representations (rather than proxy propositions). The second model, like Moss’ model, is shown to be semantically and mathematically tractable. The second model, however, can be straightforwardly integrated into a plausible model of the role of graded attitudes toward modal claims in cognition and normative epistemology. (shrink)

A series of recent studies have explored the impact of people's judgments regarding physical law, morality, and probability. Surprisingly, such studies indicate that these three apparently unrelated types of judgments often have precisely the same impact. We argue that these findings provide evidence for a more general hypothesis about the kind of cognition people use to think about possibilities. Specifically, we suggest that this aspect of people's cognition is best understood using an idea developed within work in the formal semantics (...) tradition, namely the notion of modality. On the view we propose, people may have separate representations for physical, moral and probabilistic considerations, but they also integrate these various considerations into a unified representation of modality. (shrink)

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information you have genuinely (...) learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

Dynamic semantics violates numerous classical laws, including Non-Contradiction. Proponents of dynamic semantics have offered no explanation for this behavior, and some critics consider this result to be strong evidence against the tenability of the dynamic program. I defend and explain failures of Non-Contradiction by comparing dynamic semantics and classical, truth conditional semantics in terms of their idealizing assumptions. I demonstrate that dynamic semantics rejects context fixity, an idealizing assumption that truth-conditional semantics typically adopts. I then argue that any semantics which (...) rejects context fixity should, by the classical semanticist’s own lights, violate Non-Contradiction under certain circumstances. I then demonstrate that dynamic semantics violates Non-Contradiction in all and only those circumstances. I subsequently appeal to this insight to vindicate some of dynamic semantics’ more controversial predictions. I close by suggesting that discussion of idealizing assumptions, common in the sciences, is similarly crucial to fruitful discussion in natural language semantics. (shrink)

The past decade has seen a protracted debate over the semantics of epistemic modals. According to contextualists, epistemic modals quantify over the possibilities compatible with some contextually determined group’s information. Relativists often object that contextualism fails to do justice to the way we assess utterances containing epistemic modals for truth or falsity. However, recent empirical work seems to cast doubt on the relativist’s claim, suggesting that ordinary speakers’ judgments about epistemic modals are more closely in line with contextualism than relativism (...) (Knobe & Yalcin 2014; Khoo 2015). This paper furthers the debate by reporting new empirical research revealing a previously overlooked dimension of speakers’ truth-value judgments concerning epistemic modals. Our results show that these judgments vary systematically with the question under discussion in the conversational context in which the utterance is being assessed. We argue that this ‘QUD effect’ is difficult to explain if contextualism is true, but is readily explained by a suitably flexible form of relativism. (shrink)

I review Ninan’s Hundred Tickets case pertaining to quantification into epistemic modal contexts, and his counterpart theoretic way to address it (Ninan, Philos Rev, 2018). Ninan’s solution employs a ‘counterpart relation’ parameter intended to reflect how the domain of quantification is thought of in a context. This approach theoretically rules out the possibility of contexts where different ways of thinking about the domain can be deployed through different quantificational noun phrases. I bring out the case of the multiply de re (...) modal statement "Any ticket in photo #2 might be any ticket in photo #1" to challenge Ninan’s approach. I propose a different approach adapting a more complex ‘counterpart relation’ parameter due to Rabern (Inquiry, 2021). I attempt to flesh it out by relating it to a finer grained notion of epistemic possibility involving assignments to discourse referents. My approach can account for the aforementioned multiply de re statement, as well as address the Hundred Tickets case. (shrink)

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.

Recent challenges to Kratzer’s canonical contextualist semantics for modal expressions are united by a shared methodological practice: Each requires the assessment of the truth or warrant of a sentence in a scenario. The default evidential status accorded these judgments is a constraining one: It is assumed that, to be plausible, a semantic hypothesis must vindicate the reported judgments. Fully assessing the extent to which these cases do generate data that puts pressure on the canonical semantics, then, requires an understanding of (...) this methodological practice. Here I argue that not all assessments are fit to play this evidential role. To play it, we need reason to think that speakers’ assessments can be reasonably expected to be reliable. Minimally, having such grounds requires that assessments are given against the background of non-defectively characterized points of evaluation. Assessing MacFarlane’s central challenge case to contextualism about deontic modals in light of this constraint shows that his judgments do not have the needed evidential significance. In addition, new experimental data shows that once the needed scenario is characterized non-defectively, none of the resulting range of cases provides data that cannot be accommodated by a Kratzer-style contextualism. (shrink)

Epistemic modals have peculiar logical features that are challenging to account for in a broadly classical framework. For instance, while a sentence of the form $$p\wedge \Diamond \lnot p$$ (‘p, but it might be that not p’) appears to be a contradiction, $$\Diamond \lnot p$$ does not entail $$\lnot p$$, which would follow in classical logic. Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing attempts to account for these facts generally either under- or over-correct. (...) Some theories predict that $$ p\wedge \Diamond \lnot p$$, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of entailment that does not always allow us to replace $$p\wedge \Diamond \lnot p$$ with a contradiction; these theories underpredict the infelicity of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded middle, De Morgan’s laws, and disjunction introduction, which intuitively remain valid for epistemic modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a possibility semantics, based on partial possibilities related by compatibility. Both semantics yield the same consequence relation, which we axiomatize. We then show how to lift an arbitrary possible worlds model for a non-modal language to a possibility model for a language with epistemic modals. The goal throughout is to retain what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary. (shrink)

We distinguish three ways that a theory of linguistic meaning and communication might be considered dynamic in character. We provide some examples of systems which are dynamic in some of these senses but not others. We suggest that separating these notions can help to clarify what is at issue in particular debates about dynamic versus static approaches within natural language semantics and pragmatics.

I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of (...) spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: that a conditional is logically independent from its antecedent; that a sequence of antecedents behaves like a single conjunctive antecedent ; and that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart. (shrink)