Using formal systems to represent and reason about uncertainty.

A new approach for defining causality and such related notions as degree of responsibility, degrees of blame, and causal explanation. Causality plays a central role in the way people structure the world; we constantly seek causal explanations for our observations. But what does it even mean that an event C "actually caused" event E? The problem of defining actual causation goes beyond mere philosophical speculation. For example, in many legal arguments, it is precisely what needs to be established in order (...) to determine responsibility. The philosophy literature has been struggling with the problem of defining causality since Hume. In this book, Joseph Halpern explores actual causality, and such related notions as degree of responsibility, degree of blame, and causal explanation. The goal is to arrive at a definition of causality that matches our natural language usage and is helpful, for example, to a jury deciding a legal case, a programmer looking for the line of code that cause some software to fail, or an economist trying to determine whether austerity caused a subsequent depression. Halpern applies and expands an approach to causality that he and Judea Pearl developed, based on structural equations. He carefully formulates a definition of causality, and building on this, defines degree of responsibility, degree of blame, and causal explanation. He concludes by discussing how these ideas can be applied to such practical problems as accountability and program verification. Technical details are generally confined to the final section of each chapter and can be skipped by non-mathematical readers. (shrink)

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 (...) comparative. We then show how our account would handle a number of standard cases. 1 Introduction2 Causal Models3 The HP Definition of Actual Causation4 The Problem of Isomorphism5 Defaults, Typicality, and Normality6 Extended Causal Models7 Examples7.1 Omissions7.2 Knobe effects7.3 Causes versus background conditions7.4 Bogus prevention7.5 Causal chains7.6 Legal doctrines of intervening causes7.7 Pre-emption and short circuits8 Conclusion. (shrink)

We propose a new definition of actual causes, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficulties in the traditional account.

This book offers an in-depth analysis of the cognitive and ethical role of emotion, particularly empathy, in medical practice. The author explains how doctors can use empathy in diagnosing and treating patients without jeopardizing their objectivity or projecting their own values on to patients.

We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion article. Essentially, an explanation is a fact that is not known for certain but, if found to be true, would constitute an actual cause of the fact to be explained, regardless of the agent's initial uncertainty. We show that the definition handles well a number of problematic examples from the literature.

What are the limits of the use of artificial intelligence (AI) in the relational aspects of medical and nursing care? There has been a lot of recent work and applications showing the promise and efficiency of AI in clinical medicine, both at the research and treatment levels. Many of the obstacles discussed in the literature are technical in character, regarding how to improve and optimize current practices in clinical medicine and also how to develop better data bases for optimal parameter (...) adjustments and predictive algorithms. This paper argues that there are also in principle obstacles to the application of AI in clinical medicine and care where empathy is important, and that these problems cannot be solved with any of the technical and theoretical approaches that shape the current application of AI in specific areas of clinical medicine in which care for patients is fundamental. This is important, because it generates specific risks that may be overlooked otherwise, and it justifies the necessity of human monitoring and emotional intervention in clinical medicine. Consequently, difficult issues concerning moral and legal responsibility may ensue if these in principle problems are ignored. (shrink)

Metaphors used to describe new technologies mediate public understanding of the innovations. Analyzing the linguistic, rhetorical, and affective aspects of these metaphors opens the range of issues available for bioethical scrutiny and increases public accountability. This article shows how such a multidisciplinary approach can be useful by looking at a set of texts about one issue, the use of a newly developed technique for genetic modification, CRISPRcas9.

Unrealistic therapeutic beliefs are very common—the majority of patient-subjects enrol in phase 1 trials seeking and expecting significant medical benefit, even though the likelihood of such benefit has historically proven very low. The high prevalence of therapeutic misestimation and unrealistic optimism in particular has stimulated debate about whether unrealistic therapeutic beliefs in early-phase clinical trials preclude adequate informed consent. We seek here to help resolve this controversy by showing that a crucial determination of when such therapeutic beliefs are ethically problematic (...) turns on whether they are causally linked and instrumental to the motivation to participate in the trial. Thus, in practice, it is ethically incumbent on researchers to determine which understanding and beliefs lead to the participant’s primary motivation for enrolling, not to simply assess understanding, beliefs and motivations independently. We further contend that assessing patient-subjects’ appreciation as a component of informed consent—it is already an established component of decision-making capacity assessments—can help elucidate the link between understanding-beliefs and motivation; appreciation refers to an individual’s understanding of the personal significance of both the medical facts and the experience of trial participation. Therefore, we recommend that: in addition to the usual question, ‘Why do you want to participate in this trial?’, all potential participants should be asked the question: ‘What are you giving up by participating in this trial?’ and researchers should consider the settings in which it may be possible and practical to obtain ‘two-point consent’. (shrink)

There is an important gap in philosophical, clinical and bioethical conceptions of decision-making capacity. These fields recognize that when traumatic life circumstances occur, people not only feel afraid and demoralized, but may develop catastrophic thinking and other beliefs that can lead to poor judgment. Yet there has been no articulation of the ways in which such beliefs may actually derail decision-making capacity. In particular, certain emotionally grounded beliefs are systematically unresponsive to evidence, and this can block the ability to deliberate (...) about alternatives. People who meet medico-legal criteria for decision-making capacity can react to health and personal crises with such capacity-derailing reactions. One aspect of this is that a person who is otherwise cognitively intact may be unable to appreciate her own future quality of life while in this complex state of mind. This raises troubling ethical challenges. We cannot rely on the current standard assessment of cognition to determine decisional rights in medical and other settings. We need to understand better how emotionally grounded beliefs interfere with decision-making capacity, in order to identify when caregivers have an obligation to intervene. (shrink)

The appropriateness of S5 as a logic of knowledge has been attacked at some length in the philosophical literature. Here one particular attack based on the interplay between knowledge and belief is considered: Suppose that knowledge satisfies S5, belief satisfies KD45, and both the entailment property (knowledge implies belief) and positive certainty (if the agent believes something, she believes she knows it) hold. Then it can be shown that belief reduces to knowledge: it is impossible to have false beliefs. While (...) the entailment property has typically been viewed as perhaps the least controversial of these assumptions, an argument is presented that it can plausibly be viewed as the culprit. More precisely, it is shown that this attack fails if we weaken the entailment property so that it applies only to objective (nonmodal) formulas, rather than to arbitrary formulas. Since the standard arguments in favor of the entailment property are typically given only for objective formulas, this observation suggests that care must be taken in applying intuitions that seem reasonable in the case of objective formulas to arbitrary formulas. (shrink)

Empathy is an extensively studied construct, but operationalization of effective empathy is routinely debated in popular culture, theory, and empirical research. This article offers a process-focused approach emphasizing the relational functions of empathy in interpersonal contexts. We argue that this perspective offers advantages over more traditional conceptualizations that focus on primarily intrapsychic features. Our aim is to enrich current conceptualizations and empirical approaches to the study of empathy by drawing on psychological, philosophical, medical, linguistic, and anthropological perspectives. In doing so, (...) we highlight the various functions of empathy in social interaction, underscore some underemphasized components in empirical studies of empathy, and make recommendations for future research on this important area in the study of emotion. (shrink)

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems (...) to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. (shrink)

Galles & Pearl (l998) claimed that s [possible-worlds] framework.s framework. Recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures. On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well. The problem with the Galles and Pearl argument is identified: an axiom that they (...) viewed as irrelevant, because it involved disjunction (which was not in their language), is not irrelevant at all. (shrink)

The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last 50 years, is studied here in the framework of epistemic and doxastic logics. Three notions of definability are considered: explicit definability, implicit definability, and reducibility, where explicit definability is equivalent to the combination of implicit definability and reducibility. It is shown that if knowledge satisfies any set of axioms contained in S5, then it cannot be explicitly defined in (...) terms of belief. S5 knowledge can be implicitly defined by belief, but not reduced to it. On the other hand, S4.4 knowledge and weaker notions of knowledge cannot be implicitly defined by belief, but can be reduced to it by defining knowledge as true belief. It is also shown that S5 knowledge cannot be reduced to belief and justification, provided that there are no axioms that involve both belief and justification. (shrink)

Judea Pearl (2000) was the first to propose a definition of actual causation using causal models. A number of authors have suggested that an adequate account of actual causation must appeal not only to causal structure but also to considerations of normality. In Halpern and Hitchcock (2011), we offer a definition of actual causation using extended causal models, which include information about both causal structure and normality. Extended causal models are potentially very complex. In this study, we show how it (...) is possible to achieve a compact representation of extended causal models. (shrink)

The Covid‐19 crisis has accelerated a trend toward burnout in health care workers, making starkly clear that burnout is especially likely when providing health care is not only stressful and sad but emotionally alienating; in such situations, there is no mental space for clinicians to experience authentic clinical empathy. Engaged curiosity toward each patient is a source of meaning and connection for health care providers, and it protects against sympathetic distress and burnout. In a prolonged crisis like Covid‐19, clinicians provide (...) care out of a sense of duty, especially the duty of nonabandonment. We argue that when duty alone is relied on too heavily, with fear and frustration continually suppressed, the risk of burnout is dramatically increased. Even before Covid‐19, clinicians often worked under dehumanizing and unjust conditions, and rates of burnout were 50 percent for physicians and 33 percent for nurses. The Covid‐19 intensification of burnout can serve as a wake‐up call that the structure of health care needs to be improved if we are to prevent the loss of a whole generation of empathic clinicians. (shrink)

In 1960, E. P. Wigner, a joint winner of the 1963 Nobel Prize for Physics, published a paper titled On the Unreasonable Effectiveness of Mathematics in the Natural Sciences [61]. This paper can be construed as an examination and affirmation of Galileo's tenet that “The book of nature is written in the language of mathematics”. To this effect, Wigner presented a large number of examples that demonstrate the effectiveness of mathematics in accurately describing physical phenomena. Wigner viewed these examples as (...) illustrations of what he called the empirical law of epistemology, which asserts that the mathematical formulation of the laws of nature is both appropriate and accurate, and that mathematics is actually the correct language for formulating the laws of nature. At the same time, Wigner pointed out that the reasons for the success of mathematics in the natural sciences are not completely understood; in fact, he went as far as asserting that “… the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it.”. (shrink)

What is an inference rule? This question does not have a unique answer. One usually finds two distinct standard answers in the literature; validity inference $(\sigma \vdash_\mathrm{v} \varphi$ if for every substitution $\tau$, the validity of $\tau \lbrack\sigma\rbrack$ entails the validity of $\tau\lbrack\varphi\rbrack)$, and truth inference $(\sigma \vdash_\mathrm{t} \varphi$ if for every substitution $\tau$, the truth of $\tau\lbrack\sigma\rbrack$ entails the truth of $\tau\lbrack\varphi\rbrack)$. In this paper we introduce a general semantic framework that allows us to investigate the notion of inference (...) more carefully. Validity inference and truth inference are in some sense the extremal points in our framework. We investigate the relationship between various types of inference in our general framework, and consider the complexity of deciding if an inference rule is sound, in the context of a number of logics of interest: classical propositional logic, a nonstandard propositional logic, various propositional modal logics, and first-order logic. (shrink)

ABSTRACT For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. (...) Furthermore, this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. _1_ Introduction _2_ Alternative Updating Policies _3_ Modelling the Situation for Normal Updating _4_ Tracking: A Criterion for Updating Policies _5_ Tracking: Precise Formulation and Relation to Convexity _6_ The Spanning Criterion _7_ Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria _8_ Policies that Violate the Spanning and Tracking Criteria Appendix Appendix. (shrink)

There have been two major lines of research aimed at capturing resource-bounded players in game theory. The first, initiated by Rubinstein (), charges an agent for doing costly computation; the second, initiated by Neyman (), does not charge for computation, but limits the computation that agents can do, typically by modeling agents as finite automata. We review recent work on applying both approaches in the context of decision theory. For the first approach, we take the objects of choice in a (...) decision problem to be Turing machines, and charge players for the “complexity” of the Turing machine chosen (e.g., its running time). This approach can be used to explain well-known phenomena like first-impression-matters biases (i.e., people tend to put more weight on evidence they hear early on) and belief polarization (two people with different prior beliefs, hearing the same evidence, can end up with diametrically opposed conclusions) as the outcomes of quite rational decisions. For the second approach, we model people as finite automata, and provide a simple algorithm that, on a problem that captures a number of settings of interest, provably performs optimally as the number of states in the automaton increases. (shrink)

Natural conditions are provided that are sufficient to ensure that causality as defined by approaches that use counterfactual dependence and structural equations will be transitive.

For changing opinion, represented by an assignment of probabilities to propositions, the criterion proposed is motivated by the requirement that the assignment should have, and maintain, the possibility of matching in some appropriate sense statistical proportions in a population. This ‘tracking’ criterion implies limitations on policies for updating in response to a wide range of types of new input. Satisfying the criterion is shown equivalent to the principle that the prior must be a convex combination of the possible posteriors. Furthermore, (...) this is equivalent to the requirement that prior expected values must fall inside the range spanned by possible posterior expected values. The tracking criterion is liberal; it allows for, but does not require, a policy such as Bayesian conditionalization, and can be offered as a general constraint on policies for managing opinion over time. Examples are given of non-Bayesian policies, both ones that satisfy and ones that violate the criterion. 1 Introduction2 Alternative Updating Policies3 Modelling the Situation for Normal Updating4 Tracking: A Criterion for Updating Policies5 Tracking: Precise Formulation and Relation to Convexity6 The Spanning Criterion7 Non-Bayesian Policies that Satisfy the Spanning and Tracking Criteria8 Policies that Violate the Spanning and Tracking Criteria AppendixAppendix. (shrink)