We discuss the semantic significance of a puzzle concerning ‘ought’ and conditionals recently discussed by Kolodny and MacFarlane. We argue that the puzzle is problematic for the standard Kratzer-style analysis of modality. In Kratzer’s semantics, modals are evaluated relative to a pair of conversational backgrounds. We show that there is no sensible way of assigning values to these conversational backgrounds so as to derive all of the intuitions in Kolodny and MacFarlane’s case. We show that the appropriate verdicts can be (...) derived by extending Kratzer’s framework to feature a third conversational background and claiming that the relevant reading of ‘ought’ is sensitive to this parameter. (shrink)

The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings intuitions about counterfactual conditionals to bear on the interpretation of (...) indicatives and relies on the notion of causal (in)dependence. (shrink)

This paper discusses counterexamples to the thesis that the probabilities of conditionals are conditional probabilities. It is argued that the discrepancy is systematic and predictable, and that conditional probabilities are crucially involved in the apparently deviant interpretations. Furthermore, the examples suggest that such conditionals have a less prominent reading on which their probability is in fact the conditional probability, and that the two readings are related by a simple step of abductive inference. Central to the proposal is a distinction between (...) causal and purely stochastic dependence between variables. (shrink)

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...) conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual conditionals. (shrink)

Philosophers investigating the interpretation and use of conditional sentences have long been intrigued by the intuitive correspondence between the probability of a conditional `if A, then C' and the conditional probability of C, given A. Attempts to account for this intuition within a general probabilistic theory of belief, meaning and use have been plagued by a danger of trivialization, which has proven to be remarkably recalcitrant and absorbed much of the creative effort in the area. But there is a strategy (...) for avoiding triviality that has been known for almost as long as the triviality results themselves. What is lacking is a straightforward integration of this approach in a larger framework of belief representation and dynamics. This paper discusses some of the issues involved and proposes an account of belief update by conditionalization. (shrink)

The rise of causality and the attendant graph-theoretic modeling tools in the study of counterfactual reasoning has had resounding effects in many areas of cognitive science, but it has thus far not permeated the mainstream in linguistic theory to a comparable degree. In this study I show that a version of the predominant framework for the formal semantic analysis of conditionals, Kratzer-style premise semantics, allows for a straightforward implementation of the crucial ideas and insights of Pearl-style causal networks. I spell (...) out the details of such an implementation, focusing especially on the notions of intervention on a network and backtracking interpretations of counterfactuals. (shrink)

Recent work on the interpretation of counterfactual conditionals has paid much attention to the role of causal independencies. One influential idea from the theory of Causal Bayesian Networks is that counterfactual assumptions are made by intervention on variables, leaving all of their causal non-descendants unaffected. But intervention is not applicable across the board. For instance, backtracking counterfactuals, which involve reasoning from effects to causes, cannot proceed by intervention in the strict sense, for otherwise they would be equivalent to their consequents. (...) We discuss these and similar cases, focusing on two factors which play a role in determining whether and which causal parents of the manipulated variable are affected: Speakers' need for an explanation of the hypothesized state of affairs, and differences in the ‘resilience’ of beliefs that are independent of degrees of certainty. We describe the relevant theoretical notions in some detail and provide experimental evidence that these factors do indeed affect speakers' interpretation of counterfactuals. (shrink)

Conditionals with conditional constituents pose challenges for _the Thesis_, the idea that the probability of a conditional is the corresponding conditional probability. This note is concerned with two proposals for overcoming those challenges, both inspired by early work of van Fraassen: the _Bernoulli Semantics_ associated with Stalnaker and Jeffrey, and augmented with a mechanism for obtaining “local probabilities” by Kaufmann; and a proposal by Bacon which I dub _Ordinal Semantics_. Despite differences in mathematical details and emphasis of presentation, both proposals (...) lend themselves for use as a basis for a modal-theoretic interpretation of embedded conditionals. The goal of this note is to compare the two frameworks by implementing a model for the interpretation of conditionals in each, based on the same underlying probability model for non-conditional sentences. I show that in the Ordinal model, certain sentences are assigned probabilities that do not accord with intuitions. This problem is familiar from the literature on Bernoulli models and can be addressed by introducing Kaufmann-style local probabilities into Ordinal models. I then show that Bernoulli Semantics has other limitations, in that it assigns probabilities in violation of the Thesis to certain very complex formulas. The upshot is that a fusion of the theories may be our best shot at getting the predictions right. (shrink)

The papers collected in this volume exemplify some of the trends in current approaches to logic, language and computation. Written by authors with varied academic backgrounds, the contributions are intended for an interdisciplinary audience. The first part of this volume addresses issues relevant for multi-agent systems: reasoning with incomplete information, reasoning about knowledge and beliefs, and reasoning about games. Proofs as formal objects form the subject of Part II. Topics covered include: contributions on logical frameworks, linear logic, and different approaches (...) to formalized reasoning. Part III focuses on representations and formal methods in linguistic theory, addressing the areas of comparative and temporal expressions, modal subordination, and compositionality. (shrink)

The thesis that the probability of a conditional`if A, C' is the corresponding conditional probability of C, given A, enjoys wide currency among philosophers and growing empirical support in psychology. In this paper I ask how a probabilisitic account of conditionals along these lines could be extended to unconditional sentences, i.e., conditionals with interrogative antecedents. Such sentences are typically interpreted as equivalent to conjunctions of conditionals. This raises a number of challenges for a probabilistic account, chief among them the question (...) of what the probability of a conjunction of conditionals should be. I offer an analysis which addresses these issues by extending the interpretation of conditionals in Bernoulli models to the case of unconditionals. (shrink)

This edited book examines conditionals from a number of interdisciplinary perspectives, drawing on research from fields as diverse as linguistics, psychology, philosophy and logic. Across 13 chapters, the authors not only investigate and examine various commonly-held perceptions about conditionals, but they also challenge many of the assumptions underpinning current conditionals scholarship, setting an agenda for future research. Based in part on the papers presented at a unique international summer school - Conditionals in Paris - this volume represents the cutting edge (...) in the study of conditionals, and it will be of interest to scholars in fields including linguistics and psychology, semiotics, philosophy and logic, and artificial intelligence. (shrink)