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Structural equations and causation

Philosophical Studies 132 (1):109 - 136 (2007)

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  1. Grounding in the image of causation.Jonathan Schaffer - 2016 - Philosophical Studies 173 (1):49-100.
    Grounding is often glossed as metaphysical causation, yet no current theory of grounding looks remotely like a plausible treatment of causation. I propose to take the analogy between grounding and causation seriously, by providing an account of grounding in the image of causation, on the template of structural equation models for causation.
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  • Cause and Norm.Christopher Hitchcock & Joshua Knobe - 2009 - Journal of Philosophy 106 (11):587-612.
    Much of the philosophical literature on causation has focused on the concept of actual causation, sometimes called token causation. In particular, it is this notion of actual causation that many philosophical theories of causation have attempted to capture.2 In this paper, we address the question: what purpose does this concept serve? As we shall see in the next section, one does not need this concept for purposes of prediction or rational deliberation. What then could the purpose be? We will argue (...)
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  • Contrastive causation.Jonathan Schaffer - 2005 - Philosophical Review 114 (3):327-358.
    Causation is widely assumed to be a binary relation: c causes e. I will argue that causation is a quaternary, contrastive relation: c rather than C* causes e rather than E*, where C* and E* are nonempty sets of contrast events. Or at least, I will argue that treating causation as contrastive helps resolve some paradoxes.
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  • Graded Causation and Defaults.Joseph Y. Halpern & Christopher Hitchcock - 2015 - British Journal for the Philosophy of Science 66 (2):413-457.
    Recent work in psychology and experimental philosophy has shown that judgments of actual causation are often influenced by consideration of defaults, typicality, and normality. A number of philosophers and computer scientists have also suggested that an appeal to such factors can help deal with problems facing existing accounts of actual causation. This article develops a flexible formal framework for incorporating defaults, typicality, and normality into an account of actual causation. The resulting account takes actual causation to be both graded and (...)
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  • A Model-Invariant Theory of Causation.J. Dmitri Gallow - 2021 - Philosophical Review 130 (1):45-96.
    I provide a theory of causation within the causal modeling framework. In contrast to most of its predecessors, this theory is model-invariant in the following sense: if the theory says that C caused (didn't cause) E in a causal model, M, then it will continue to say that C caused (didn't cause) E once we've removed an inessential variable from M. I suggest that, if this theory is true, then we should understand a cause as something which transmits deviant or (...)
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  • A Regularity Theory of Causation.Holger Andreas & Mario Günther - 2024 - Pacific Philosophical Quarterly 105 (1):2-32.
    In this paper, we propose a regularity theory of causation. The theory aims to be reductive and to align with our pre‐theoretic understanding of the causal relation. We show that our theory can account for a wide range of causal scenarios, including isomorphic scenarios, omissions, and scenarios which suggest that causation is not transitive.
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  • Interventionist counterfactuals.Rachael Briggs - 2012 - Philosophical Studies 160 (1):139-166.
    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 (...)
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  • Structural equations and causation.Ned Hall - 2007 - Philosophical Studies 132 (1):109 - 136.
    Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
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  • The metaphysics of causation.Jonathan N. D. Schaffer - 2008 - Stanford Encyclopedia of Philosophy.
    Questions about the metaphysics of causation may be usefully divided as follows. First, there are questions about the nature of the causal relata, including (1.1) whether they are in spacetime immanence), (1.2) how fine grained they are individuation), and (1.3) how many there are adicity). Second, there are questions about the metaphysics of the causal relation, including (2.1) what is the difference between causally related and causally unrelated sequences connection), (2.2) what is the difference between sequences related as cause to (...)
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  • Are There Non-Causal Explanations (of Particular Events)?Bradford Skow - 2014 - British Journal for the Philosophy of Science 65 (3):445-467.
    Philosophers have proposed many alleged examples of non-causal explana- tions of particular events. I discuss several well-known examples and argue that they fail to be non-causal.
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  • Are There Non-Causal Explanations (of Particular Events)?Brdford Skow - 2013 - British Journal for the Philosophy of Science (3):axs047.
    Philosophers have proposed many alleged examples of non-causal explanations of particular events. I discuss several well-known examples and argue that they fail to be non-causal. 1 Questions2 Preliminaries3 Explanations That Cite Causally Inert Entities4 Explanations That Merely Cite Laws I5 Stellar Collapse6 Explanations That Merely Cite Laws II7 A Final Example8 Conclusion.
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  • Causal exclusion and the limits of proportionality.Neil McDonnell - 2017 - Philosophical Studies 174 (6):1459-1474.
    Causal exclusion arguments are taken to threaten the autonomy of the special sciences, and the causal efficacy of mental properties. A recent line of response to these arguments has appealed to “independently plausible” and “well grounded” theories of causation to rebut key premises. In this paper I consider two papers which proceed in this vein and show that they share a common feature: they both require causes to be proportional to their effects. I argue that this feature is a bug, (...)
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  • Causal Contextualisms.Jonathan Schaffer - 2013 - In Martijn Blaauw, Contrastivism in philosophy. New York: Routledge/Taylor & Francis Group.
    Causal claims are context sensitive. According to the old orthodoxy (Mackie 1974, Lewis 1986, inter alia), the context sensitivity of causal claims is all due to conversational pragmatics. According to the new contextualists (Hitchcock 1996, Woodward 2003, Maslen 2004, Menzies 2004, Schaffer 2005, and Hall ms), at least some of the context sensitivity of causal claims is semantic in nature. I want to discuss the prospects for causal contextualism, by asking why causal claims are context sensitive, what they are sensitive (...)
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  • A principled approach to defining actual causation.Sander Beckers & Joost Vennekens - 2018 - Synthese 195 (2):835-862.
    In this paper we present a new proposal for defining actual causation, i.e., the problem of deciding if one event caused another. We do so within the popular counterfactual tradition initiated by Lewis, which is characterised by attributing a fundamental role to counterfactual dependence. Unlike the currently prominent definitions, our approach proceeds from the ground up: we start from basic principles, and construct a definition of causation that satisfies them. We define the concepts of counterfactual dependence and production, and put (...)
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  • Essential Structure for Causal Models.Jennifer McDonald - 2025 - Australasian Journal of Philosophy:1-23.
    This paper introduces and defends a new principle for when a structural equation model is apt for analyzing actual causation. Any such analysis in terms of these models has two components: a recipe for reading claims of actual causation off an apt model, and an articulation of what makes a model apt. The primary focus in the literature has been on the first component. But the problem of structural isomorphs has made the second especially pressing (Hall 2007; Hitchcock 2007a). Those (...)
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  • Causation and manipulability.James Woodward - 2008 - Stanford Encyclopedia of Philosophy.
    Manipulablity theories of causation, according to which causes are to be regarded as handles or devices for manipulating effects, have considerable intuitive appeal and are popular among social scientists and statisticians. This article surveys several prominent versions of such theories advocated by philosophers, and the many difficulties they face. Philosophical statements of the manipulationist approach are generally reductionist in aspiration and assign a central role to human action. These contrast with recent discussions employing a broadly manipulationist framework for understanding causation, (...)
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  • Causal counterfactuals without miracles or backtracking.J. Dmitri Gallow - 2022 - Philosophy and Phenomenological Research 107 (2):439-469.
    If the laws are deterministic, then standard theories of counterfactuals are forced to reject at least one of the following conditionals: 1) had you chosen differently, there would not have been a violation of the laws of nature; and 2) had you chosen differently, the initial conditions of the universe would not have been different. On the relevant readings—where we hold fixed factors causally independent of your choice—both of these conditionals appear true. And rejecting either one leads to trouble for (...)
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  • Decision, causality, and predetermination.Boris Kment - 2023 - Philosophy and Phenomenological Research 107 (3):638-670.
    Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that match actuality in (...)
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  • Causal Responsibility and Counterfactuals.David A. Lagnado, Tobias Gerstenberg & Ro'I. Zultan - 2013 - Cognitive Science 37 (6):1036-1073.
    How do people attribute responsibility in situations where the contributions of multiple agents combine to produce a joint outcome? The prevalence of over-determination in such cases makes this a difficult problem for counterfactual theories of causal responsibility. In this article, we explore a general framework for assigning responsibility in multiple agent contexts. We draw on the structural model account of actual causation (e.g., Halpern & Pearl, 2005) and its extension to responsibility judgments (Chockler & Halpern, 2004). We review the main (...)
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  • Response to Strevens.Jim Woodward - 2008 - Philosophy and Phenomenological Research 77 (1):193-212.
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  • (1 other version)Ceteris Paribus Laws.Alexander Reutlinger, Gerhard Schurz, Andreas Hüttemann & Siegfried Jaag - 2011 - Stanford Encyclopedia of Philosophy.
    Laws of nature take center stage in philosophy of science. Laws are usually believed to stand in a tight conceptual relation to many important key concepts such as causation, explanation, confirmation, determinism, counterfactuals etc. Traditionally, philosophers of science have focused on physical laws, which were taken to be at least true, universal statements that support counterfactual claims. But, although this claim about laws might be true with respect to physics, laws in the special sciences (such as biology, psychology, economics etc.) (...)
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  • A Ramsey Test Analysis of Causation for Causal Models.Holger Andreas & Mario Günther - 2021 - British Journal for the Philosophy of Science 72 (2):587-615.
    We aim to devise a Ramsey test analysis of actual causation. Our method is to define a strengthened Ramsey test for causal models. Unlike the accounts of Halpern and Pearl ([2005]) and Halpern ([2015]), the resulting analysis deals satisfactorily with both over- determination and conjunctive scenarios.
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  • Causal Models and Metaphysics—Part 2: Interpreting Causal Models.Jennifer McDonald - 2024 - Philosophy Compass 19 (7):e13007.
    This paper addresses the question of what constitutes an apt interpreted model for the purpose of analyzing causation. I first collect universally adopted aptness principles into a basic account, flagging open questions and choice points along the way. I then explore various additional aptness principles that have been proposed in the literature but have not been widely adopted, the motivations behind their proposals, and the concerns with each that stand in the way of universal adoption. I conclude that the remaining (...)
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  • A Partial Theory of Actual Causation.Brad Weslake - manuscript
    One part of the true theory of actual causation is a set of conditions responsible for eliminating all of the non-causes of an effect that can be discerned at the level of counterfactual structure. I defend a proposal for this part of the theory.
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  • A theory of structural determination.J. Dmitri Gallow - 2016 - Philosophical Studies 173 (1):159-186.
    While structural equations modeling is increasingly used in philosophical theorizing about causation, it remains unclear what it takes for a particular structural equations model to be correct. To the extent that this issue has been addressed, the consensus appears to be that it takes a certain family of causal counterfactuals being true. I argue that this account faces difficulties in securing the independent manipulability of the structural determination relations represented in a correct structural equations model. I then offer an alternate (...)
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  • Just probabilities.Chad Lee-Stronach - 2024 - Noûs 58 (4):948-972.
    I defend the thesis that legal standards of proof are reducible to thresholds of probability. Many reject this thesis because it appears to permit finding defendants liable solely on the basis of statistical evidence. To the contrary, I argue – by combining Thomson's (1986) causal analysis of legal evidence with formal methods of causal inference – that legal standards of proof can be reduced to probabilities, but that deriving these probabilities involves more than just statistics.
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  • Three Concepts of Actual Causation.Enno Fischer - 2024 - British Journal for the Philosophy of Science 75 (1):77-98.
    I argue that we need to distinguish between three concepts of actual causation: total, path-changing, and contributing actual causation. I provide two lines of argument in support of this account. First, I address three thought experiments that have been troublesome for unified accounts of actual causation, and I show that my account provides a better explanation of corresponding causal intuitions. Second, I provide a functional argument: if we assume that a key purpose of causal concepts is to guide agency, we (...)
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  • Causation in terms of production.Holger Andreas & Mario Günther - 2020 - Philosophical Studies 177 (6):1565-1591.
    In this paper, we analyse actual causation in terms of production. The latter concept is made precise by a strengthened Ramsey Test semantics of conditionals: \ iff, after suspending judgement about A and C, C is believed in the course of assuming A. This test allows us to verify or falsify that an event brings about another event. Complementing the concept of production by a weak condition of difference-making gives rise to a full-fledged analysis of causation.
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  • Events and their counterparts.Neil McDonnell - 2016 - Philosophical Studies 173 (5):1291-1308.
    This paper argues that a counterpart-theoretic treatment of events, combined with a counterfactual theory of causation, can help resolve three puzzles from the causation literature. First, CCT traces the apparent contextual shifts in our causal attributions to shifts in the counterpart relation which obtains in those contexts. Second, being sensitive to shifts in the counterpart relation can help diagnose what goes wrong in certain prominent examples where the transitivity of causation appears to fail. Third, CCT can help us resurrect the (...)
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  • Grounding interventionism: Conceptual and epistemological challenges.Amanda Bryant - 2022 - Metaphilosophy 53 (2-3):322-343.
    Philosophers have recently highlighted substantial affinities between causation and grounding, which has inclined some to import the conceptual and formal resources of causal interventionism into the metaphysics of grounding. The prospect of grounding interventionism raises two important questions: exactly what are grounding interventions, and why should we think they enable knowledge of grounding? This paper will approach these questions by examining how causal interventionists have addressed (or might address) analogous questions and then comparing the available options for grounding interventionism. I (...)
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  • (1 other version)Following the FAD: Folk Attributions and Theories of Actual Causation.Jonathan Livengood, Justin Sytsma & David Rose - 2017 - Review of Philosophy and Psychology 8 (2):273-294.
    In the last decade, several researchers have proposed theories of actual causation that make use of structural equations and directed graphs. Many of these researchers are committed to a widely-endorsed folk attribution desideratum, according to which an important constraint on the acceptability of a theory of actual causation is agreement between the deliverances of the theory with respect to specific cases and the reports of untutored individuals about those same cases. In the present article, we consider a small collection of (...)
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  • Actual Causation: Apt Causal Models and Causal Relativism.Jennifer McDonald - 2022 - Dissertation, The Graduate Center, Cuny
    This dissertation begins by addressing the question of when a causal model is apt for deciding questions of actual causation with respect to some target situation. I first provide relevant background about causal models, explain what makes them promising as a tool for analyzing actual causation, and motivate the need for a theory of aptness as part of such an analysis (Chapter 1). I then define what it is for a model on a given interpretation to be accurate of, that (...)
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  • A Probabilistic Analysis of Causation.Luke Glynn - 2011 - British Journal for the Philosophy of Science 62 (2):343-392.
    The starting point in the development of probabilistic analyses of token causation has usually been the naïve intuition that, in some relevant sense, a cause raises the probability of its effect. But there are well-known examples both of non-probability-raising causation and of probability-raising non-causation. Sophisticated extant probabilistic analyses treat many such cases correctly, but only at the cost of excluding the possibilities of direct non-probability-raising causation, failures of causal transitivity, action-at-a-distance, prevention, and causation by absence and omission. I show that (...)
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  • Causation and the Problem of Disagreement.Enno Fischer - 2021 - Philosophy of Science 88 (5):773-783.
    This article presents a new argument for incorporating a distinction between default and deviant values into the formalism of causal models. The argument is based on considerations about how causal reasoners should represent disagreement over causes, and it is defended against an objection that has been raised against earlier arguments for defaults.
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  • Causal Sufficiency and Actual Causation.Sander Beckers - 2021 - Journal of Philosophical Logic 50 (6):1341-1374.
    Pearl opened the door to formally defining actual causation using causal models. His approach rests on two strategies: first, capturing the widespread intuition that X = x causes Y = y iff X = x is a Necessary Element of a Sufficient Set for Y = y, and second, showing that his definition gives intuitive answers on a wide set of problem cases. This inspired dozens of variations of his definition of actual causation, the most prominent of which are due (...)
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  • Structural equations and beyond.Franz Huber - 2013 - Review of Symbolic Logic 6 (4):709-732.
    Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...)
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  • The Transitivity and Asymmetry of Actual Causation.Sander Beckers & Joost Vennekens - 2017 - Ergo: An Open Access Journal of Philosophy 4:1-27.
    The counterfactual tradition to defining actual causation has come a long way since Lewis started it off. However there are still important open problems that need to be solved. One of them is the (in)transitivity of causation. Endorsing transitivity was a major source of trouble for the approach taken by Lewis, which is why currently most approaches reject it. But transitivity has never lost its appeal, and there is a large literature devoted to understanding why this is so. Starting from (...)
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  • A Regularity Theoretic Approach to Actual Causation.Michael Baumgartner - 2013 - Erkenntnis 78 (1):85-109.
    The majority of the currently flourishing theories of actual causation are located in a broadly counterfactual framework that draws on structural equations. In order to account for cases of symmetric overdeterminiation and preemption, these theories resort to rather intricate analytical tools, most of all, to what Hitchcock has labeled explicitly nonforetracking counterfactuals. This paper introduces a regularity theoretic approach to actual causation that only employs material conditionals, standard Boolean minimization procedures, and a stability condition that regulates the behavior of causal (...)
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  • Actual Causation and Simple Voting Scenarios.Jonathan Livengood - 2011 - Noûs 47 (2):316-345.
    Several prominent, contemporary theories of actual causation maintain that in order for something to count as an actual cause (in the circumstances) of some known effect, the potential cause must be a difference-maker with respect to the effect in some restricted range of circumstances. Although the theories disagree about how to restrict the range of circumstances that must be considered in deciding whether something counts as an actual cause of a known effect, the theories agree that at least some counterfactual (...)
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  • A good cause.Carolina Sartorio - 2024 - Philosophical Studies 181 (9):2129-2144.
    I explore the question of how to ground the responsibility of agents in some tricky cases involving multiple agents who act in a non-coordinated fashion. These are scenarios where no single agent has the individual ability to make a difference to a harmful outcome, but where the outcome would have been avoided if they had all acted as they should have (thus, the agents collectively made a difference to the outcome’s occurrence). I argue that an important source of the problem (...)
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  • Causal Models and Causal Relativism.Jennifer McDonald - 2025 - Synthese 205 (108):1 - 26.
    A promising development in the philosophy of causation analyzes actual causation using structural equation models, i.e., “causal models”. This paper carefully considers what it means for an interpreted model to be accurate of its target situation. These considerations show, first, that our existing understanding of accuracy is inadequate. Further, and more controversially, they show that any causal model analysis is committed to a kind of relativism – a view whereby causation is a three-part relation holding between a cause, an effect, (...)
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  • Proportionality in Causation, Part I: Theories.Ezra Rubenstein - 2024 - Philosophy Compass 19 (1):e12957.
    A much-discussed idea in the causation literature is that it is preferable to invoke causes which are proportional to—neither too general nor too specific for—the effect. This article presents various ways of understanding this idea. In what sense are such causal claims ‘preferable’? And what is it for one event to be ‘proportional’ to another? In a companion article, ‘Proportionality in Causation, Part II: Applications and Challenges’, I discuss the principal applications of the resulting theories of proportionality, and the challenges (...)
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  • Two causal theories of counterfactual conditionals.Lance J. Rips - 2010 - Cognitive Science 34 (2):175-221.
    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 (...)
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  • Appropriate causal models and the stability of causation.Joseph Y. Halpern - 2016 - Review of Symbolic Logic 9 (1):76-102.
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  • Structural equations and causation: six counterexamples.Christopher Hitchcock - 2009 - Philosophical Studies 144 (3):391-401.
    Hall [(2007), Philosophical Studies, 132, 109–136] offers a critique of structural equations accounts of actual causation, and then offers a new theory of his own. In this paper, I respond to Hall’s critique, and present some counterexamples to his new theory. These counterexamples are then diagnosed.
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  • Portable Causal Dependence: A Tale of Consilience.Christopher Hitchcock - 2012 - Philosophy of Science 79 (5):942-951.
    This article describes research pursued by members of the McDonnell Collaborative on Causal Learning. A number of members independently converged on a similar idea: one of the central functions served by claims of actual causation is to highlight patterns of dependence that are highly portable into novel contexts. I describe in detail how this idea emerged in my own work and also in that of the psychologist Tania Lombrozo. In addition, I use the occasion to reflect on the nature of (...)
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  • (1 other version)Following the FAD: Folk Attributions and Theories of Actual Causation.Jonathan Livengood, Justin Sytsma & David Rose - 2016
    Using structural equations and directed graphs, Christopher Hitchcock (2007a) proposes a theory specifying the circumstances in which counterfactual dependence of one event e on another event c is necessary and sufficient for c to count as an actual cause of e. In this paper, we argue that Hitchcock is committed to a widely-endorsed folk attribution desideratum (FAD) for theories of actual causation. We then show experimentally that Hitchcock’s theory does not satisfy the FAD, and hence, it is in need of (...)
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  • Conjoined cases.Tomasz Wysocki - 2023 - Synthese 201 (6):1-19.
    Incorporating normality ascriptions into counterfactual theories of causation was supposed to handle isomorphs. It doesn’t—conjoining isomorphs can produce cases that such ascriptions cannot resolve.
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  • Experimental Philosophy and Causal Attribution.Jonathan Livengood & David Rose - 2016 - In Wesley Buckwalter & Justin Sytsma, Blackwell Companion to Experimental Philosophy. Malden, MA: Blackwell. pp. 434–449.
    Humans often attribute the things that happen to one or another actual cause. In this chapter, we survey some recent philosophical and psychological research on causal attribution. We pay special attention to the relation between graphical causal modeling and theories of causal attribution. We think that the study of causal attribution is one place where formal and experimental techniques nicely complement one another.
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  • Causation: Determination and difference-making.Boris Kment - 2010 - Noûs 44 (1):80-111.
    Much of the modern philosophy of causation has been governed by two ideas: (i) causes make their effects inevitable; (ii) a cause is something that makes a difference to whether its effect occurs. I focus on explaining the origin of idea (ii) and its connection to (i). On my view, the frequent attempts to turn (ii) into an analysis of causation are wrongheaded. Patterns of difference-making aren't what makes causal claims true. They merely provide a useful test for causal claims. (...)
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