A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in the study (...) of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

A number of recent authors (Galles and Pearl, Found Sci 3 (1):151–182, 1998; Hiddleston, Noûs 39 (4):232–257, 2005; Halpern, J Artif Intell Res 12:317–337, 2000) advocate a causal modeling semantics for counterfactuals. But the precise logical significance of the causal modeling semantics remains murky. Particularly important, yet particularly under-explored, is its relationship to the similarity-based semantics for counterfactuals developed by Lewis (Counterfactuals. Harvard University Press, 1973b). The causal modeling semantics is both an account of the truth conditions of counterfactuals, and (...) an account of which inferences involving counterfactuals are valid. As an account of truth conditions, it is incomplete. While Lewis's similarity semantics lets us evaluate counterfactuals with arbitrarily complex antecedents and consequents, the causal modeling semantics makes it hard to ascertain the truth conditions of all but a highly restricted class of counterfactuals. I explain how to extend the causal modeling language to encompass a wider range of sentences, and provide a sound and complete axiomatization for the extended language. Extending the truth conditions for counterfactuals has serious consequences concerning valid inference. The extended language is unlike any logic of Lewis's: modus ponens is invalid, and classical logical equivalents cannot be freely substituted in the antecedents of conditionals. (shrink)

This paper defends a counterexample to Modus Tollens, and uses it to draw some conclusions about the logic and semantics of indicative conditionals and probability operators in natural language. Along the way we investigate some of the interactions of these expressions with 'knows', and we call into question the thesis that all knowledge ascriptions have truth-conditions.

Early commentators on David Lewis's account of counterfactuals noted that certain examples suggest that some counterfactuals with true antecedents and true consequents are false. Lewis's account has the consequence that all such counterfactuals are true, leaving us to choose between explaining away our intuitions about the examples in question or offering an alternative to Lewis's account. Here I argue that a simple modification of the familiar Lewisian truth conditions yields the intuitively correct verdicts about these examples, and so we can (...) take our intuitions about these examples at face value without any major departure from Lewis's approach to counterfactuals. (shrink)

Abstract Utterances of counterfactual conditionals are typically attended by the information that their antecedents are false. But there is as yet no account of the source of this information that is both detailed and complete. This paper describes the problem of counterfactual antecedent falsity and argues that the problem can be addressed by appeal to an adequate account of the presuppositions of various competing conditional constructions. It argues that indicative conditionals presuppose that their antecedents are epistemically possible, while subjunctive conditionals (...) bear no presupposition. Given this arrangement, utterance of the counterfactual results in an antipresupposition, that is, a scalar implicature generated from the presuppositions of competing alternatives rather than from the at-issue content of competing alternatives. The content of the antipresupposition is the negation of the presupposition of the competing indicative, i.e., that the antecedent of the conditional is known to be false by the speaker. (shrink)

Lewis (1973) gave a short argument against conditional excluded middle, based on his treatment of ‘might’ counterfactuals. Bennett (2003), with much of the recent literature, gives an alternative take on ‘might’ counterfactuals. But Bennett claims the might-argument against CEM still goes through. This turns on a specific claim I call Bennett’s Hypothesis. I argue that independently of issues to do with the proper analysis of might-counterfactuals, Bennett’s Hypothesis is inconsistent with CEM. But Bennett’s Hypothesis is independently objectionable, so we should (...) resolve this tension by dropping the Hypothesis, not by dropping CEM. (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)

Frank Ramsey was the greatest of the remarkable generation of Cambridge philosophers and logicians which included G. E. Moore, Bertrand Russell, Ludwig Wittgenstein and Maynard Keynes. Before his tragically early death in 1930 at the age of twenty-six, he had done seminal work in mathematics and economics as well as in logic and philosophy. This volume, with a new and extensive introduction by D. H. Mellor, contains all Ramsey's previously published writings on philosophy and the foundations of mathematics. The latter (...) gives the definitive form and defence of the reduction of mathematics to logic undertaken in Russell and Whitehead's Principia Mathematica; the former includes the most profound and original studies of universals, truth, meaning, probability, knowledge, law and causation, all of which are still constantly referred to, and still essential reading for all serious students of these subjects. (shrink)

We consider a paradox involving indicative conditionals (‘ifs’) and deontic modals (‘oughts’). After considering and rejecting several standard options for resolv- ing the paradox—including rejecting various premises, positing an ambiguity or hidden contextual sensitivity, and positing a non-obvious logical form—we offer a semantics for deontic modals and indicative conditionals that resolves the paradox by making modus ponens invalid. We argue that this is a result to be welcomed on independent grounds, and we show that rejecting the general validity of modus (...) ponens is compatible with vindicating most ordinary uses of modus ponens in reasoning. (shrink)

This paper provides an update semantics for counterfactual conditionals. It does so by giving a dynamic twist to the ‘Premise Semantics’ for counterfactuals developed in Veltman (1976) and Kratzer (1981). It also offers an alternative solution to the problems with naive Premise Semantics discussed by Angelika Kratzer in ‘Lumps of Thought’ (Kratzer, 1989). Such an alternative is called for given the triviality results presented in Kanazawa et al. (2005, this issue).

Why are some conditionals subjunctive? It is often assumed that at least one crucial difference is that subjunctive conditionals presuppose that their antecedent is false, that they are counterfactual (Lakoff 1970). The traditional theory has apparently been refuted. Perhaps the clearest counter-example is one given by Alan Anderson (1951: 37): If Jones had taken arsenic, he would have shown just exactly those symptoms which he does in fact show. A typical place to use such a subjunctive conditional would be in (...) the course of an argument that tries to bolster the hypothesis that Jones did in fact take arsenic. But then it would of course be self-defeating to presuppose that the hypothesis is false. Thus, something else must be going on. (shrink)

In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this (...) new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG. (shrink)

This paper will be concerned with the conjunctive interpretation of a family of disjunctive constructions. The relevant conjunctive interpretation, sometimes referred to as a “free choice effect,” (FC) is attested when a disjunctive sentence is embedded under an existential modal operator. I will provide evidence that the relevant generalization extends (with some caveats) to all constructions in which a disjunctive sentence appears under the scope of an existential quantifier, as well as to seemingly unrelated constructions in which conjunction appears under (...) the scope of negation and a universal quantifier. (shrink)

The score was tied in the bottom of the ninth, I was on third base, and there was only one out when Bubba hit a towering fly ball to deep left-center. Although I’m no speed-demon, the ball was hammered so far that I easily could have scored the winning run if I had tagged up. But I didn’t. I got caught up in the excitement and stupidly played it half way, standing between third and home until I saw the center (...) fielder make his spectacular catch, after which I had to return sheepishly to third. The next batter grounded out, and we lost the game in extra innings. (shrink)

One criticism of David Lewis's account of counterfactuals is that it sometimes assigns the wrong truth-value to a counterfactual when both antecedent and consequent happen to be true. Lewis has suggested a possible remedy to this situation, but commentators have found this to be unsatisfactory. I suggest an alternative solution which involves a modification of Lewis's truth conditions, but which confines itself to the resources already present in his account. This modification involves the device of embedding one counterfactual within another. (...) On the revised set of truth conditions, counterfactuals with true components are sometimes true and sometimes false, in a way that is more in keeping with our intuitive judgments about such statements. (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.

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

Russell and Strawson sparked a well known debate on the subject of Linguistic Presupposition inspiring many linguists and philosophers to follow suit, including Frege, whose work initiated the modern study in this area. Beaver begins with the most comprehensive overview and critical discussion of this burgeoning field published to date. He then goes on to motivate and develop his own account based on a Dynamic Semantics. This account is a recent line of theoretical work in which the Tarskian emphasis on (...) truth conditions is questioned. The central plank of the theory of meaning is a formal account of the change in information effected by use of language on hearers or readers. The proposal thus consolidates ideas of Stalnaker, Karttunen and Heim, all of whom had suggested that such an account was needed. At the same time it provides a new impulse and motivation to Dynamic Semantics itself. (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)

This paper offers a unified semantic explanation of two observations that prove to be problematic for classical analyses of modals, conditionals, and disjunctions: the fact that disjunctions scoping under possibility modals give rise to the free choice effect and the fact that counterfactuals license simplification of disjunctive antecedents. It shows that the data are well explained by a dynamic semantic analysis of modals and conditionals that uses ideas from the inquisitive semantic tradition in its treatment of disjunction. The analysis explains (...) why embedding a disjunctive possibility under negation reverts disjunction to its classical behavior, is general enough to predict less studied simplification patterns, and also makes progress toward a unified perspective on the distinction between informative, inquisitive, and attentive content. (shrink)

Letting denote ‘would’ counterfactual conditionals like If I had looked in my pocket, I would have found a penny and letting denote ‘might’ counterfactual conditionals like If I had looked in my pocket, I might have found a penny,David Lewis’s thesis regarding the connection between these two types of conditionals is that.

This paper proposes a semantics for free choice permission that explains both the non-classical behavior of modals and disjunction in sentences used to grant permission, and their classical behavior under negation. It also explains why permissions can expire when new information comes in and why free choice arises even when modals scope under disjunction. On the proposed approach, deontic modals update preference orderings, and connectives operate on these updates rather than propositions. The success of this approach stems from its capacity (...) to capture the difference between expressing the preferences that give rise to permissions and conveying propositions about those preferences. (shrink)

This paper refutes the widespread view that disjunctions of imperatives invariably grant free choice between the actions named by their disjuncts. Like other disjunctions they can also express a correlation with some factual distinction, but as with modalized declaratives used for non-assertive speech acts this needs to be indicated explicitly. A compositional analysis of one such indicator, depending on, constitutes the point of departure for a uniform analysis of disjunctions across clause types. Disjunctions are analyzed as sets of propositional alternatives (...) that correlate with a partition that the speaker may or may not be able to indicate explicitly. Free choice arises as the specific case where the partition is induced by the preferences of the addressee. (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)

Free choice permission, a crucial test case concerning the semantics/ pragmatics boundary, usually receives a pragmatic treatment. But its pragmatic features follow from its semantics. We observe that free choice inferences are defeasible, and defend a semantics of free choice permission as strong permission expressed in terms of a modal conditional in a nonmonotonic logic.

I propose a unified solution to two puzzles: Ross's puzzle and free choice permission. I begin with a pair of cases from the decision theory literature illustrating the phenomenon of act dependence, where what an agent ought to do depends on what she does. The notion of permissibility distilled from these cases forms the basis for my analysis of 'may' and 'ought'. This framework is then combined with a generalization of the classical semantics for disjunction — equivalent to Boolean disjunction (...) on the diagonal, but with a different two-dimensional character — that explains the puzzling facts in terms of semantic consequence. (shrink)

The standard Lewis–Stalnaker semantics of counterfactuals, given the Strong Centering Thesis, implies that all true–true counterfactuals are trivially true. McGlynn developed a theory, based on Penczek, to rehabilitate the non-triviality of true–true counterfactuals. I show here that counterfactuals with true but irrelevant components are counterexamples to McGlynn’s account. I argue that an extended version of the connection hypothesis is sustainable, and grounds a full theory of counterfactuals explicable in a broadly standard way, if an indispensable asymmetry between semifacuals and other (...) counterfactuals is acknowledged. (shrink)

Advocates of Expressivism about basically any kind of language are best-served by abandoning a traditional content-centric approach to semantic theorizing, in favor of an update-centric or dynamic approach (or so this paper argues). The type of dynamic approach developed here — in contrast to the content-centric approach — is argued to yield canonical, if not strictly classical, "explanations" of the core semantic properties of the connectives. (The cases on which I focus most here are negation and disjunction.) I end the (...) paper by describing a distinctive sense in which mental states might play a fundamental role in the practice of semantic theorizing (as I understand it), and I connect this to a distinctive account of the pragmatic function of, e.g., a normatively laden claim in discourse. (shrink)

How do hearers manage to understand speakers? And how do speakers manage to shape hearers' understanding? Lepore and Stone show that standard views about the workings of semantics and pragmatics are unsatisfactory. They advance an alternative view which better captures what is going on in linguistic communication.

Robert Stalnaker explores the contexts in which speech takes place, the ways we represent them, and the roles they play in explaining the interpretation and dynamics of speech. His central thesis is the autonomy of pragmatics: the independence of theory about structure and function of discourse from theory about mechanisms serving those functions.

A dynamic semantics for iffy oughts offers an attractive alternative to the folklore that Chisholm's paradox enforces an unhappy choice between the intuitive inference rules of factual and deontic detachment. The first part of the story told here shows how a dynamic theory about ifs and oughts gives rise to a nonmonotonic perspective on deontic discourse and reasoning that elegantly removes the air of paradox from Chisholm's puzzle without sacrificing any of the two detachment principles. The second part of the (...) story showcases two bonus applications of the framework suggested here: it offers a response to Forrester's gentle murder paradox and avoids Kolodny and MacFarlane's miners paradox about deontic reasoning under epistemic uncertainty. A comparison between the dynamic semantic proposal made in this paper and a more conservative approach combining a static semantics with a dynamic pragmatics is provided. (shrink)