How do we ascribe subjective probability? In decision theory, this question is often addressed by representation theorems, going back to Ramsey (1926), which tell us how to define or measure subjective probability by observable preferences. However, standard representation theorems make strong rationality assumptions, in particular expected utility maximization. How do we ascribe subjective probability to agents which do not satisfy these strong rationality assumptions? I present a representation theorem with weak rationality assumptions which can be used to define or measure (...) subjective probability for partly irrational agents. (shrink)

The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...) high but non-maximal and might \ that \\) is significantly greater than 0. Drawing on several observations concerning the behavior of must, might and similar epistemic operators in evidential contexts, deductive inferences, downplaying and retractions scenarios, and expressions of epistemic tension, I argue that those two influential accounts have systematic descriptive shortcomings. To better make sense of their complex behavior, I propose instead a broadly Kratzerian account according to which must \ entails that \ = 1\) and might \ that \ > 0\), given a body of evidence and a set of normality assumptions about the world. From this perspective, must and might are vehicles for expressing a common mode of reasoning whereby we draw inferences from specific bits of evidence against a rich set of background assumptions—some of which we represent as defeasible—which capture our general expectations about the world. I will show that the predictions of this Kratzerian account can be substantially refined once it is combined with a specific yet independently motivated ‘grammatical’ approach to the computation of scalar implicatures. Finally, I discuss some implications of these results for more general discussions concerning the empirical and theoretical motivation to adopt a probabilisitic semantic framework. (shrink)

This paper investigates the link between informational consequence and credence. I first suggest a natural constraint, namely that informational consequence should preserve certainty: on any rational credence distribution, when the premises of an informational inferences have credence 1, the conclusion also has credence 1. Then I show that the certainty‐preserving constraint leads to triviality. In particular, the following three claims are incompatible: (i) informational consequence is extensionally distinct from classical consequence; (ii) informational inferences preserve certainty; (iii) credences obey (a subset (...) of) classical Bayesian constraints. The proof is straightforward, but the theoretical implications are substantial. Informational theorists need to either give up the idea that credence applies to epistemic discourse, or develop a nonclassical theory of credence and credal update. Moreover, the result also suggests that there is a connection between informational consequence and triviality results, including classical triviality results like Lewis's. (shrink)

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to (...) undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (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)

Many recent theories of epistemic discourse exploit an informational notion of consequence, i.e. a notion that defines entailment as preservation of support by an information state. This paper investigates how informational consequence fits with probabilistic reasoning. I raise two problems. First, all informational inferences that are not also classical inferences are, intuitively, probabilistically invalid. Second, all these inferences can be exploited, in a systematic way, to generate triviality results. The informational theorist is left with two options, both of them radical: (...) they can either deny that epistemic modal claims have probability at all, or they can move to a nonstandard probability theory. (shrink)

I present unexplored and unaccounted for uses of 'wants'. I call them advisory uses, on which information inaccessible to the desirer herself helps determine what she wants. I show that extant theories by Stalnaker, Heim, and Levinson fail to predict these uses. They also fail to predict true indicative conditionals with 'wants' in the consequent. These problems are related: intuitively valid reasoning with modus ponens on the basis of the conditionals in question results in unembedded advisory uses. I consider two (...) fixes, and end up endorsing a relativist semantics, according to which desire attributions express information-neutral propositions. On this view, 'wants' functions as a precisification of 'ought', which exhibits similar unembedded and compositional behavior. I conclude by sketching a pragmatic account of the purpose of desire attributions that explains why it made sense for them to evolve in this way. (shrink)

We advocate and develop a states-based semantics for both nominal and adjectival confidence reports, as in "Ann is confident/has confidence that it's raining", and their comparatives "Ann is more confident/has more confidence that it's raining than that it's snowing". Other examples of adjectives that can report confidence include "sure" and "certain". Our account adapts Wellwood's account of adjectival comparatives in which the adjectives denote properties of states, and measure functions are introduced compositionally. We further explore the prospects of applying these (...) tools to the semantics of probability operators. We emphasize three desirable and novel features of our semantics: (i) probability claims only exploit qualitative resources unless there is explicit compositional pressure for quantitative resources; (ii) the semantics applies to both probabilistic adjectives (e.g., "likely") and probabilistic nouns (e.g., "probability"); (iii) the semantics can be combined with an account of belief reports that allows thinkers to have incoherent probabilistic beliefs (e.g. thinking that A & B is more likely than A) even while validating the relevant purely probabilistic claims (e.g. validating the claim that A & B is never more likely than A). Finally, we explore the interaction between confidence-reporting discourse (e.g., "I am confident that...") and belief-reports about probabilistic discourse (e.g.,"I think it's likely that.."). (shrink)

Recently, there has been a shift away from traditional truth-conditional accounts of meaning towards non-truth-conditional ones, e.g., expressivism, relativism and certain forms of dynamic semantics. Fueling this trend is some puzzling behavior of modal discourse. One particularly surprising manifestation of such behavior is the alleged failure of some of the most entrenched classical rules of inference; viz., modus ponens and modus tollens. These revisionary, non-truth-conditional accounts tout these failures, and the alleged tension between the behavior of modal vocabulary and classical (...) logic, as data in support of their departure from tradition, since the revisionary semantics invalidate some of these patterns. I, instead, offer a semantics for modality with the resources to accommodate the puzzling data while preserving classical logic, thus affirming the tradition that modals express ordinary truth-conditional content. My account shows that the real lesson of the apparent counterexamples is not the one the critics draw, but rather one they missed: namely, that there are linguistic mechanisms, reflected in the logical form, that affect the interpretation of modal language in a context in a systematic and precise way, which have to be captured by any adequate semantic account of the interaction between discourse context and modal vocabulary. The semantic theory I develop specifies these mechanisms and captures precisely how they affect the interpretation of modals in a context, and do so in a way that both explains the appearance of the putative counterexamples and preserves classical logic. (shrink)

This paper motivates and develops a novel semantic framework for deontic modals. The framework is designed to shed light on two things: the relationship between deontic modals and substantive theories of practical rationality and the interaction of deontic modals with conditionals, epistemic modals and probability operators. I argue that, in order to model inferential connections between deontic modals and probability operators, we need more structure than is provided by classical intensional theories. In particular, we need probabilistic structure that interacts directly (...) with the compositional semantics of deontic modals. However, I reject theories that provide this probabilistic structure by claiming that the semantics of deontic modals is linked to the Bayesian notion of expectation. I offer a probabilistic premise semantics that explains all the data that create trouble for the rival theories. (shrink)

In this paper, I consider a variant of the ancient Idle Argument involving so‐called “unconditionals” with interrogative antecedents. This new Idle Argument provides an ideal setting for probing the logic of these close relatives of if‐conditionals, which has been comparatively underexplored. In the course of refuting the argument, I argue that contrary to received wisdom, many unconditionals do not entail their main clauses, yet modus ponens is still unrestrictedly valid for this class of expressions. I make these lessons precise in (...) a formal system drawing on recent work in inquisitive semantics. My larger aim is to challenge standard truth preservation accounts of logic and deductive argumentation. (shrink)

Recent ideas about epistemic modals and indicative conditionals in formal semantics have significant overlap with ideas in modal logic and dynamic epistemic logic. The purpose of this paper is to show how greater interaction between formal semantics and dynamic epistemic logic in this area can be of mutual benefit. In one direction, we show how concepts and tools from modal logic and dynamic epistemic logic can be used to give a simple, complete axiomatization of Yalcin's [16] semantic consequence relation for (...) a language with epistemic modals and indicative conditionals. In the other direction, the formal semantics for indicative conditionals due to Kolodny and MacFarlane [9] gives rise to a new dynamic operator that is very natural from the point of view of dynamic epistemic logic, allowing succinct expression of dependence (as in dependence logic) or supervenience statements. We prove decidability for the logic with epistemic modals and Kolodny and MacFarlane's indicative conditional via a full and faithful computable translation from their logic to the modal logic K45. (shrink)

The problem of inferring probability comparisons between events from an initial set of comparisons arises in several contexts, ranging from decision theory to artificial intelligence to formal semantics. In this paper, we treat the problem as follows: beginning with a binary relation ≥ on events that does not preclude a probabilistic interpretation, in the sense that ≥ has extensions that are probabilistically representable, we characterize the extension ≥+ of ≥ that is exactly the intersection of all probabilistically representable extensions of (...) ≥. This extension ≥+ gives us all the additional comparisons that we are entitled to infer from ≥, based on the assumption that there is some probability measure of which ≥ gives us partial qualitative information. We pay special attention to the problem of extending an order on states to an order on events. In addition to the probabilistic interpretation, this problem has a more general interpretation involving measurement of any additive quantity: e.g., given comparisons between the weights of individual objects, what comparisons between the weights of groups of objects can we infer? (shrink)