This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle of compositionality, (...) a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

Predicates of personal taste (fun, tasty) and epistemic modals (might, must) share a similar analytical difficulty in determining whose taste or knowledge is being expressed. Accordingly, they have parallel behavior in attitude reports and in a certain kind of disagreement. On the other hand, they differ in how freely they can be linked to a contextually salient individual, with epistemic modals being much more restricted in this respect. I propose an account of both classes using Lasersohn’s (Linguistics and Philosophy 28: (...) 643–686, 2005) “judge” parameter, at the same time arguing for crucial changes to Lasersohn’s view in order to allow the extension to epistemic modals and address empirical problems faced by his account. (shrink)

Moore's paradox pits our intuitions about semantic oddnessagainst the concept of truth-functional consistency. Most solutions tothe problem proceed by explaining away our intuitions. But``consistency'' is a theory-laden concept, having different contours indifferent semantic theories. Truth-functional consistency is appropriateonly if the semantic theory we are using identifies meaning withtruth-conditions. I argue that such a framework is not appropriate whenit comes to analzying epistemic modality. I show that a theory whichaccounts for a wide variety of semantic data about epistemic modals(Update Semantics) buys (...) us a solution to Moore's paradox as a corollary.It turns out that Moorean propositions, when looked at through the lenseof an appropriate semantic theory, are inconsistent after all. (shrink)

We investigate a basic probabilistic dynamic semantics for a fragment containing conditionals, probability operators, modals, and attitude verbs, with the aim of shedding light on the prospects for adding probabilistic structure to models of the conversational common ground.

Seth Yalcin has pointed out some puzzling facts about the behaviour of epistemic modals in certain embedded contexts. For example, conditionals that begin ‘If it is raining and it might not be raining, … ’ sound unacceptable, unlike conditionals that begin ‘If it is raining and I don’t know it, … ’. These facts pose a prima facie problem for an orthodox treatment of epistemic modals as expressing propositions about the knowledge of some contextually specified individual or group. This paper (...) develops an explanation of the puzzling facts about embedding within an orthodox framework. (shrink)

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

David Lewis (1941-2001) was Class of 1943 University Professor of Philosophy at Princeton University. His contributions spanned philosophical logic, philosophy of language, philosophy of mind, philosophy of science, metaphysics, and epistemology. In On the Plurality of Worlds, he defended his challenging metaphysical position, "modal realism." He was also the author of the books Convention, Counterfactuals, Parts of Classes, and several volumes of collected papers.

A very simple contextualist treatment of a sentence containing an epistemic modal, e.g. a might be F, is that it is true iff for all the contextually salient community knows, a is F. It is widely agreed that the simple theory will not work in some cases, but the counterexamples produced so far seem amenable to a more complicated contextualist theory. We argue, however, that no contextualist theory can capture the evaluations speakers naturally make of sentences containing epistemic modals. If (...) we want to respect these evaluations, our best option is a relativist theory of epistemic modals. On a relativist theory, an utterance of a might be F can be true relative to one context of evaluation and false relative to another. We argue that such a theory does better than any rival approach at capturing all the behaviour of epistemic modals. (shrink)

Epistemic modals are standardly taken to be context-dependent quantifiers over possibilities. Thus sentences containing them get truth-values with respect to both a context and an index. But some insist that this relativization is not relative enough: `might'-claims, they say, only get truth-values with respect to contexts, indices, and—the new wrinkle—points of assessment (hence, CIA). Here we argue against such "relativist" semantics. We begin with a sketch of the motivation for such theories and a generic formulation of them. Then we catalogue (...) central problems that any such theory faces. We end by outlining an alternative story. (shrink)

It is a recurring mantra that epistemic must creates a statement that is weaker than the corresponding flat-footed assertion: It must be raining vs. It’s raining. Contrary to classic discussions of the phenomenon such as by Karttunen, Kratzer, and Veltman, we argue that instead of having a weak semantics, must presupposes the presence of an indirect inference or deduction rather than of a direct observation. This is independent of the strength of the claim being made. Epistemic must is therefore quite (...) similar to evidential markers of indirect evidence known from languages with rich evidential systems. We work towards a formalization of the evidential component, relying on a structured model of information states (analogous to some models used in the belief dynamics literature). We explain why in many contexts, one can perceive a lack of confidence on the part of the speaker who uses must. (shrink)

A semantic framework for interpreting dialogue should provide an account of the content that is mutually accepted by its participants. The acceptance by one agent of another’s contribution crucially involves the theory of what that contribution means; A’s acceptance of B’s contribution means that the content of B’s contribution must be integrated into A’s extant commitments.1 For assertions, traditionally assumed to express a proposition formalised as a set of possible worlds, it was clear how the integration should go: acceptance meant (...) intersecting the newly accepted proposition with the set of worlds representing the content of the agent’s prior commitments. Dynamic semantics (e.g., Asher (1989)) refined this picture by replacing intersection with the operation of dynamic update. The way to treat the negative counterpart of acceptance—namely, rejection—is also clear in principle: A s rejection of B’s assertion means that the negation of the content of B’s contribution should be integrated with the content of A’s prior commitments. However, acceptance and rejection don’t just happen with assertions. These speech acts can happen with questions as well. That is, an agent can choose to address the issues raised by the questioner; he can also choose to reject them. The explicit acceptance of a question can be conveyed by providing a direct answer or by an explicit admittance that one doesn’t know an answer; explicit rejection by uttering I won’t answer. (shrink)

The aim of this paper is twofold: (i) to introduce the framework of update semantics and to explain what kind of semantic phenomena may successfully be analysed in it: (ii) to give a detailed analysis of one such phenomenon: default reasoning.

After presenting a simple expressivist account of reports of probabilistic judgements, I explore a classic problem for it, namely the Frege‐Geach problem. I argue that it is a problem not just for expressivism but for any reasonable account of ascriptions of graded judgements. I suggest that the problem can be resolved by appropriately modelling imprecise credences.

In ‘Epistemic Modals’ (2007), Seth Yalcin proposes Stalnaker-style semantics for epistemic possibility. He is inspired by John MacFarlane’s ingenious defence of relativism, in which claims of epistemic possibility are made rigidly from the perspective of the assessor’s actual stock of information (rather than from the speaker’s knowledge base or that of his audience or community). The innovations of MacFarlane and Yalcin independently reinforce the modal collapse espoused by Jaakko Hintikka in his 1962 epistemic logic (which relied on the implausible KK (...) principle and heavy idealizations). I respond to this new challenge with fresh objections to the underlying S4 equivalence: p p . I also propose counter-analyses of the intriguing data which Yalcin cites in support of his new semantics. A key collateral motivation for this defence of irredundant iterations is to ward off a threat to higher order vagueness. (shrink)

way on the information available in the contexts in which they are used, it’s not surprising that there is a minor but growing industry of work in semantics and the philosophy of language concerned with the precise nature of the context-dependency of epistemically modalized sentences. Take, for instance, an epistemic might-claim like..

Philosophers on all sides of the contextualism debates have had an overly narrow conception of what semantic context sensitivity could be. They have conflated context sensitivity (dependence of truth or extension on features of context) with indexicality (dependence of content on features of context). As a result of this conflation, proponents of contextualism have taken arguments that establish only context sensitivity to establish indexicality, while opponents of contextualism have taken arguments against indexicality to be arguments against context sensitivity. Once these (...) concepts are carefully pulled apart, it becomes clear that there is conceptual space in semantic theory for nonindexical forms of contextualism that have many advantages over the usual indexical forms. (shrink)

What we want to be true about ordinary indicative conditionals seems to be more than we can possibly get: there just seems to be no good way to assign truth-conditions to ordinary indicative conditionals. Some take this argument as reason to make our wantings more modest. Others take it to show that indicative conditionals don't have truth-conditions in the first place. But we have overlooked two possibilities for assigning truth-conditions to indicatives. What's more, those possibilities deliver what we want and (...) turn out to be equivalent. CiteULike Connotea Del.icio.us Digg Reddit Technorati What's this? (shrink)

Karttunen observed that, if the complement of an attitude sentence presupposes p, then that sentence as a whole presupposes that the attitude–holder believes p. I attempt to derive some representative instances of this generalization from suitable assumptions about the lexical semantics of attitude predicates. The enterprise is carried out in a framework of context change semantics, which incorporates Stalnaker's suggestion that presupposition projection results from the stepwise fashion in which information is updated in response to complex utterances. The empirical focus (...) is on predicates of desire and on the contribution of counterfactual mood. (shrink)

I respond to comments by David Barnett and Roy Sorensen on my paper ‘Epistemic Modals’.

What I am calling New Age Relativism is usually proposed as a thesis about the truth-conditions of utterances, where an utterance is an actual historic voicing or inscription of a sentence of a certain type. Roughly, it is the view that, for certain discourses, whether an utterance is true depends not just on the context of its making—when, where, to whom, by whom, in what language, and so on—and the “circumstances of evaluation”—the state of the world in relevant respects—but also (...) on an additional parameter: a context of assessment. Vary the latter and the truth-value of the utterance can vary, even though the context of its making and the associated state of the world remain fixed. (shrink)

This paper has two purposes. We first give a new dynamic account of epistemic modal operators that account for both their test-like behaviour with respect to whole information states and their capacity to induce quantificational dependencies across worlds (modal subordination). We then use this theory, together with an analysis of conditionals and irrealis moods, to give a fully compositional semantics of indicative and counterfactual conditionals. In our analysis, the distinction between counterfactual and indicative conditionals follows directly from the interaction between (...) the semantics of the conditional and irrealis operators and the semantics of the particular modals involved in the conditional consequent. We indicate some theoretical and logical consequences of our approach. (shrink)

This paper deals with the truth-Conditions and the logic for vague languages. The use of supervaluations and of classical logic is defended; and other approaches are criticized. The truth-Conditions are extended to a language that contains a definitely-Operator and that is subject to higher order vagueness.

A reconstruction is presented of van der Sandt's theory of presupposition in the framework of update semantics and extended to belief sentences. The resulting view is confronted with earlier approaches to presupposition (especially Heim's) in update semantics, concentrating on the approach to accommodation. It is shown in some detail that the anaphoric view of presupposition can be maintained for only a subclass of presuppositional triggers and must be given up for another class. The paper shows that the treatment of presuppositional (...) anaphora and presuppositional accommodation is compositional with respect to stacks of information states. The brief development of the approach in section 7 shows, however, that, contrary to what one would expect, an approach in terms of stacks of information states is a powerful method in the study of DRT and other dynamic systems. (shrink)

I think that there are good reasons to adopt a relativist semantics for epistemic modal claims such as ``the treasure might be under the palm tree'', according to which such utterances determine a truth value relative to something finer-grained than just a world (or a <world, time> pair). Anyone who is inclined to relativise truth to more than just worlds and times faces a problem about assertion. It's easy to be puzzled about just what purpose would be served by assertions (...) of this kind, and how to understand what we'd be up to in our use of sentences like ``the treasure might be under the palm tree'', if they have such peculiar truth conditions. After providing a very quick argument to motivate a relativist view of epistemic modals, I bring out and attempt to resolve this problem in making sense of the role of assertions with relativist truth conditions. Solving this problem should be helpful in two ways: first, it eliminates an apparently forceful objection to relativism, and second, spelling out the relativist account of assertion and communication will help to make clear just what the relativist position is, exactly, and why it's interesting. (shrink)

In this paper I offer an account of the meaning of must and can within the framework of possible worlds semantics. The paper consists of two parts: the first argues for a relative concept of modality underlying modal words like must and can in natural language. I give preliminary definitions of the meaning of these words which are formulated in terms of logical consequence and compatibility, respectively. The second part discusses one kind of insufficiency in the meaning definitions given in (...) the first part, which arise from the ex falso quodlibet paradox of logical consequence. In stepwise fashion, I make an attempt to avoid most of the consequences of this paradox for the meaning definitions of must and can. (shrink)

This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two (...) types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked. (shrink)

When I tell you that it’s raining, I describe a way the world is—viz., rainy. I say something whose truth turns on how things are with the weather in the world. Likewise when I tell you that the weatherman thinks that it’s raining. Here the truth of what I say turns on how things are with the weatherman’s state of mind in the world. Likewise when I tell you that I think that it’s raining. Here the truth of what I (...) say turns on how things are with my state of mind in the world. (shrink)

By “epistemic modals,” I mean epistemic uses of modal words: adverbs like “necessarily,” “possibly,” and “probably,” adjectives like “necessary,” “possible,” and “probable,” and auxiliaries like “might,” “may,” “must,” and “could.” It is hard to say exactly what makes a word modal, or what makes a use of a modal epistemic, without begging the questions that will be our concern below, but some examples should get the idea across. If I say “Goldbach’s conjecture might be true, and it might be false,” (...) I am not endorsing the Cartesian view that God could have made the truths of arithmetic come out differently. I make the claim not because I believe in the metaphysical contingency of mathematics, but because I know that Goldbach’s conjecture has not yet been proved or refuted. Similarly, if I say “Joe can’t be running,” I am not saying that Joe’s constitution prohibits him from running, or that Joe is essentially a non-runner, or that Joe isn’t allowed to run. My basis for making the claim may be nothing more than that I see Joe’s running shoes hanging on a hook. (shrink)

On Kratzer’s canonical account, modal expressions (like “might” and “must”) are represented semantically as quantifiers over possibilities. Such expressions are themselves neutral; they make a single contribution to determining the propositions expressed across a wide range of uses. What modulates the modality of the proposition expressed—as bouletic, epistemic, deontic, etc.—is context.2 This ain’t the canon for nothing. Its power lies in its ability to figure in a simple and highly unified explanation of a fairly wide range of language use. Recently, (...) though, the canon’s neat story has come under attack. The challenge cases involve the epistemic use of a modal sentence for which no single resolution of the contextual parameter appears capable of accommodating all our intuitions.3 According to these revisionaries, such cases show that the canonical story needs to be amended in some way that makes multiple bodies of information relevant to the assessment of such statements. Here I show that how the right canonical, flexibly contextualist account of modals can accommodate the full range of challenge cases. The key will be to extend Kratzer’s formal semantic account with an account of how context selects values for a modal’s.. (shrink)