Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

THE INDICATIVE CONDITIONAL. A PROBABILISTIC CRITERION OF SOUNDNESS FOR DEDUCTIVE INFERENCES Our objective in this section is to establish a prima facie case ...

Conditional sentences are among the most intriguing and puzzling features of language, and analysis of their meaning and function has important implications for, and uses in, many areas of philosophy. Jonathan Bennett, one of the world's leading experts, distils many years' work and teaching into this book, making it the fullest and most authoritative treatment of the subject.

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)

The standard use of the propositional calculus ('P.C.?) in analyzing the validity of inferences involving conditionals leads to fallacies, and the problem is to determine where P.C. may be ?safely? used. An alternative analysis of criteria of reasonableness of inferences in terms of conditions of justification rather than truth of statements is proposed. It is argued, under certain restrictions, that P. C. may be safely used, except in inferences whose conclusions are conditionals whose antecedents are incompatible with the premises in (...) the sense that if the antecedent became known, some of the previously asserted premises would have to be withdrawn. (shrink)

The last section made it clear that an analysis which at first seems to fail is viable after all. It is viable if we let it depend on a partition function to be provided by the context of conversation. This analysis leaves certain traits of the partition function open. I have tried to show that this should be so. Specifying these traits as Pollock does leads to wrong predictions. And leaving them open endows counterfactuals with just the right amount of (...) variability and vagueness. (shrink)

I develop an account of counterfactual conditionals using “causal models”, and argue that this account is preferable to the currently standard account in terms of “similarity of possible worlds” due to David Lewis and Robert Stalnaker. I diagnose the attraction of counterfactual theories of causation, and argue that it is illusory.

What are facts, situations, or events? When Situation Semantics was born in the eighties, I objected because I could not swallow the idea that situations might be chunks of information. For me, they had to be particulars like sticks or bricks. I could not imagine otherwise. The first manuscript of “An Investigation of the Lumps of Thought” that I submitted to Linguistics and Philosophy had a footnote where I distanced myself from all those who took possible situations to be units (...) of information. In that context and at that time, this meant Jon Barwise and John Perry. (shrink)

A normative framework for modeling causal and counterfactual reasoning has been proposed by Spirtes, Glymour, and Scheines. The framework takes as fundamental that reasoning from observation and intervention differ. Intervention includes actual manipulation as well as counterfactual manipulation of a model via thought. To represent intervention, Pearl employed the do operator that simplifies the structure of a causal model by disconnecting an intervened-on variable from its normal causes. Construing the do operator as a psychological function affords predictions about how people (...) reason when asked counterfactual questions about causal relations that we refer to as undoing, a family of effects that derive from the claim that intervened-on variables become independent of their normal causes. Six studies support the prediction for causal arguments but not consistently for parallel conditional ones. Two of the studies show that effects are treated as diagnostic when their values are observed but nondiagnostic when they are intervened on. These results cannot be explained by theories that do not distinguish interventions from other sorts of events. (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).

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)

This paper investigates the interpretation of counterfactual conditionals. The main goal of the paper is to provide an account of the semantic role of similarity in the evaluation of counterfactuals. The paper proposes an analysis according to which counterfactuals are treated as predications “ de re ” over past situations in the actual world. The relevant situations enter semantic composition via the interpretation of tense. Counterfactuals are treated as law-like conditionals with de re predication over particular facts. Similarity with respect (...) to particular facts is ensured by the semantics of tense in interaction with the modal, while the modal itself is responsible for invoking laws. In the paper, various arguments are provided to support a local view of similarity over the global approach found in semantics along the line of Lewis’s and Stalnaker’s. Arguments are also provided tying the evaluation of similarity to the interpretation of tense. Finally, arguments are provided to show that in key cases, the approaches make comparable predictions. (shrink)

Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left early. This article compares two proposed Bayes net theories as models of people's understanding of counterfactuals. Experiments 1-3 show that neither theory makes correct predictions about backtracking counterfactuals (in which the event of the if-clause (...) occurs after the event of the then-clause), and Experiment 4 shows the same is true of forward counterfactuals. An amended version of one of the approaches, however, can provide a more accurate account of these data. (shrink)

This paper deals with the truth conditions of conditional sentences. It focuses on a particular class of problematic examples for semantic theories for these sentences. I will argue that the examples show the need to refer to dynamic, in particular causal laws in an approach to their truth conditions. More particularly, I will claim that we need a causal notion of consequence. The proposal subsequently made uses a representation of causal dependencies as proposed in Pearl to formalize a causal notion (...) of consequence. This notion inserted in premise semantics for counterfactuals in the style of Veltman and Kratzer will provide a new interpretation rule for conditionals. I will illustrate how this approach overcomes problems of previous proposals and end with some remarks on remaining questions. (shrink)

Many languages allow for “fake” uses of their past tense marker: the marker: can occur in certain contexts without conveying temporal pastness. Instead it appears to bear a modal meaning. Iatridou :231–270, 2000) has dubbed this phenomenon Fake Tense. Fake Tense is particularly common to conditional constructions. This paper analyzes Fake Tense in English conditional sentences as a certain kind of ambiguity: the past tense morphology can mark the presence of a temporal operator, but it can also signal a specific (...) modal operator. The ambiguity is proposed to be the result of recategorization: the Simple Past develops a second, modal meaning because of structural similarities between the temporal and the modal/epistemic domain. The proposal is spelled out in the generative semantics framework, using the restrictor approach to conditionals Semantics from different points of view, 1979; in: A. von Stechow and D. Wunderlich Semantics: an international handbook of contemporary research, 1991), and building on von Stechows et al.’s recent work on the English tense system The expression of time in language, 2010; Romero and von Stechow, Tense: introduction, 2008). (shrink)

P. B. Downing; VII.—Subjunctive Conditionals, Time Order, and Causation, Proceedings of the Aristotelian Society, Volume 59, Issue 1, 1 June 1959, Pages 125–140.

The goal of this paper is to offer a compositional semantics for subjunctive and indicative will conditionals, and to derive the projection properties of the types of conditionals we consider and in particular those of counterfactual conditionals. It is argued that subjunctive conditionals are "bare" conditional embedded under temporal and aspectural operators, which constrain the interpretation of the modal operators in the embedded conditional. Furthermore, it is argued that a theory of presupposition projection à la Heim together with the present (...) proposal about their logical form explains the projection facts. (shrink)

In opposition to a common assumption, this paper defends the idea that the auxiliary verb will has no other semantic contribution in contemporary English than a temporal shift towards the future with respect to the utterance time. Strong reasons for rejecting the idea that will quantifies over possible worlds are presented. Given the adoption of Lewis’s and Kratzer’s views on modality, the alleged ‘modal’ uses of will are accounted for by a pragmatic mechanism which restricts the domain of the covert (...) epistemic necessity operator scoping over the sentence. (shrink)

" It is the connected presentation of Jespersen's views of the general principles of grammar based on years of studying various languages through both direct ...

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)

This note is a reply to ‘On the Lumping Semantics of Counterfactuals’ by Makoto Kanazawa, Stefan Kaufmann and Stanley Peters. It shows first that the first triviality result obtained by Kanazawa, Kaufmann, and Peters is already ruled out by the constraints on admissible premise sets listed in Kratzer (1989). Second, and more importantly, it points out that the results obtained by Kanazawa, Kaufmann, and Peters are obsolete in view of the revised analysis of counterfactuals in Kratzer (1990, 2002).

Differences in the interpretation of would-conditionals with simple (perfective) and perfect antecedent clauses are marked enough to discourage a unified view. However, this paper presents a unified, Lewis–Stalnaker style semantics for the modal in such constructions. Differences in the interpretation of the conditionals are derived from the interaction between the interpretation of different types of aspect and the modal. The paper makes a distinction between perfective and perfect aspect in terms of whether they make reference to or quantify over Lewis-style (...) events. In making reference to Lewis-events, perfective aspect is shown to be incompatible with counterfactual would-conditionals. The so-called ‘epistemic flavor’ of perfective conditionals about the future is derived from the use of diagonalization as an interpretive strategy called upon to resolve reference. (shrink)

Conditional sentences pose a problem for semantic accounts in terms of truth conditions. On the one hand, evidence about the validity of inference patterns suggests that there is a close relationship between conditionals and conditional probability. On the other hand, while probability is typically interpreted as the probability that a proposition is true, that connection has proven elusive in the case of conditionals. Some probabilistic accounts accommodate these obstacles by concluding either that conditionals do not have truth conditions, or that (...) the usual connection between truth and probability does not hold for them. Both of these approaches remain problematic; moreover, definitions of the probability of conditionals directly in terms of conditional probability do not extend easily to complex and embedded conditionals, a limitation of coverage imposed solely by the probabilistic calculus. ;In this dissertation I develop a way to reinstate the connection between conditional probability and probability of truth by adopting a new definition of the latter. Building on previous work on the formal aspects of the problem, I suggest that conditionals denote random variables which, unlike the denotations of other sentences, may take values between 1 and 0 ; the probability of a conditional is the expectation of its values. I explore the rationale for such values and the predictions made by the theory in detail for three common types of conditionals: epistemic, predictive, and counterfactual. Under the proposed theory, conditionals are interpreted in models of the evolution of objective chance and subjective probabilities, both of which are the sources of the values of different kinds of conditionals. The time of evaluation thus plays a crucial part in determining those values. ;The theory predicts values for complex and embedded conditionals as well, but the expectation of these values in a given situation does not always accord with intuitions about what the probability of the sentence should be. I show that this problem can be successfully addressed by making the interpretation sensitive to causal dependencies. This addition opens up new insights into the relationship between counterfactual conditionals and their epistemic and predictive counterparts: They are equivalent but not equiprobable. (shrink)