Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of (...) the main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some (...) suggest that there is a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

Reasoning about mental states and processes is important in various subareas of the legal domain. A trial lawyer might need to reason and the beliefs, reasoning and other mental states and processes of members of a jury; a police officer might need to reason about the conjectured beliefs and reasoning of perpetrators; a judge may need to consider a defendant's mental states and processes for the purposes of sentencing and so on. Further, the mental states in question (...) may themselves be about the mental states and processes of other people. Therefore, if AI systems are to assist with reasoning tasks in law, they may need to be able to reason about mental states and processes. Such reasoning is riddled with uncertainty, and this is true in particular in the legal domain. The article discusses how various different types of uncertainty arise, and shows how they greatly complicate the task of reasoning about mental states and processes. The article concentrates on the special case of states of belief and processes of reasoning, and sketches an implemented, prototype computer program (ATT-Meta) that copes with the various types of uncertainty in reasoning about beliefs and reasoning. In particular, the article outlines the system's facilities for handling conflict between different lines of argument, especially when these lie within the reasoning of different people. The system's approach is illustrated by application to a real-life mugging example. [NB: The date on the archived preprint avail via this Phil* page has an incorrect date, 2011, on it. The correct date is 2001.]. (shrink)

This thesis consists of a collection of five papers on naturalized formal epistemology of uncertain reasoning. In all papers I apply coherence based probability logic to make fundamental epistemological questions precise and propose new solutions to old problems. I investigate the rational evaluation of uncertain arguments, develop a new measure of argument strength, and explore the semantics of uncertain indicative conditionals. Specifically, I study formally and empirically the semantics of negated apparently selfcontradictory conditionals (Aristotle’s theses), resolve (...) a number of paradoxes of the material conditional in a purely semantical way without employing pragmatics and investigate the psychological plausibility of the proposed semantics. Moreover, I defend the formalization of defeasible inferences within a probabilistic framework of nonmonotonic reasoning and empirically justify the formalizations by a series of psychological experiments. I investigate general properties of uncertain argument forms and the interrelations among logical validity, Adams’ p-validity and probabilistic informativeness. (shrink)

When a new piece of information contradicts a currently held belief, one has to modify the set of beliefs in order to restore its consistency. In the case where it is necessary to give up a belief, some of them are less likely to be abandoned than others. The concept of epistemic entrenchment is used by some AI approaches to explain this fact based on formal properties of the belief set (e.g., transitivity). Two experiments were designed to test the hypothesis (...) that contrary to such views, (i) belief is naturally represented by degrees rather than in an all-or-nothing manner, (ii) entrenchment is primarily a matter of content and not only a matter of form, and (iii) consequently prior degree of belief is a powerful factor of change. The two experiments used Elio and Pelletier's (1997) paradigm in which participants were presented with full simple deductive arguments whose conclusion was denied, following which they were asked to decide which premise to revise. (shrink)

The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.

The paper describes and proves completeness theorems for a series of proof systems formalizing common sense reasoning about uncertain knowledge in the case where this consists of sets of linear constraints on a probability function.

Conditionals are most important objects in knowledge representation, commonsense reasoning and belief revision. Due to their non-classical nature, however, they are not easily dealt with. This paper presents a new approach to conditionals, which is apt to capture their dynamic power particularly well. We show how this approach can be applied to represent conditional knowledge inductively, and to guide revisions of epistemic states by sets of beliefs. In particular, we generalize system-Z* as an appropriate counterpart to maximum entropy-representations in (...) a semi-quantitative setting, and provide a theoretical justification to make its basic ideas usable also for belief revision. (shrink)

Subjects are reported as being somewhat Bayesian, but as violating the normative ideal on occasion. To abjure probability altogether is difficult. To use Bayes' Theorem scrupulously when weighing evidence can incur costs without corresponding benefits. The subjects' evident nuanced probabilism appears both realistic and reasonable.

A new criterion is introduced for judging the suitability of various fuzzy logics for practical uncertain reasoning in a probabilistic world and the relationship of this criterion to several established criteria, and its consequences for truth functional belief, are investigated.

When a new piece of information contradicts a currently held belief, one has to modify the set of beliefs in order to restore its consistency. In the case where it is necessary to give up a belief, some of them are less likely to be abandoned than others. The concept of epistemic entrenchment is used by some AI approaches to explain this fact based on formal properties of the belief set (e.g., transitivity). Two experiments were designed to test the hypothesis (...) that contrary to such views, (i) belief is naturally represented by degrees rather than in an all-or-nothing manner, (ii) entrenchment is primarily a matter of content and not only a matter of form, and (iii) consequently prior degree of belief is a powerful factor of change. The two experiments used Elio and Pelletier's (1997) paradigm in which participants were presented with full simple deductive arguments whose conclusion was denied, following which they were asked to decide which premise to revise. (shrink)

We motivate and formalize the idea of sameness by default: two objects are considered the same if they cannot be proved to be different. This idea turns out to be useful for a number of widely different applications, including natural language processing, reasoning with incomplete information, and even philosophical paradoxes. We consider two formalizations of this notion, both of which are based on Reiter’s Default Logic. The first formalization is a new relation of indistinguishability that is introduced by default. (...) We prove that the corresponding default theory has a unique extension, in which every two objects are indistinguishable if and only if their non-equality cannot be proved from the known facts. We show that the indistinguishability relation has some desirable properties: it is reflexive, symmetric, and, while not transitive, it has a transitive “flavor.” The second formalization is an extension (modification) of the ordinary language equality by a similar default: two objects are equal if and only if their non-equality cannot be proved from the known facts. It appears to be less elegant from a formal point of view. In particular, it gives rise to multiple extensions. However, this extended equality is better suited for most of the applications discussed in this paper. (shrink)

There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory (...) provide appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view. (shrink)

Probabilistic models have started to replace classical logic as the standard reference paradigm in human deductive reasoning. Mental probability logic emphasizes general principles where human reasoning deviates from classical logic, but agrees with a probabilistic approach (like nonmonotonicity or the conditional event interpretation of conditionals). -/- This contribution consists of two parts. In the first part we discuss general features of reasoning systems including consequence relations, how uncertainty may enter argument forms, probability intervals, and probabilistic informativeness. These (...) concepts are of central importance for the psychological task analysis. In the second part we report new experimental data on the paradoxes of the material conditional, the probabilistic modus ponens, the complement task, and data on the probabilistic truth table task. The results of the experiments provide evidence for the hypothesis that people represent indicative conditionals by conditional probability assertions. (shrink)

Four experiments investigated uncertainty about a premise in a deductive argument as a function of the expertise of the speaker and of the conversational context. The procedure mimicked everyday reasoning in that participants were not told that the premises were to be treated as certain. The results showed that the perceived likelihood of a conclusion was greater when the major or the minor premise was uttered by an expert rather than a novice (Experiment 1). The results also showed that (...) uncertainty about the conclusion was higher when the major premise was uttered by a novice and an alternative premise by an expert, compared to when the major premise was uttered by an expert and the alternative by a novice (Experiment 2). Similarly, the believability of a conclusion was considerably lower when the minor premise was uttered by a novice and denied by an expert, as opposed to when an expert uttered the minor premise and a novice denied it (Experiment 3). Experiment 4 showed that the nature of the uncertainty induced by a denial of the minor premise depended on whether or not the context was a conversation. These results pose difficult problems for current theories of reasoning, as current theories are based on the results of experiments in which the premises are treated as certain. Our discussion of the results emphasises the importance of pragmatics in reasoning, namely, the role of general knowledge about the world in assessing the probability of a premise uttered by an expert or a novice and the role of interpretations of the premise based on pragmatic inferences in revising these initial probabilities. (shrink)

Previous studies have shown that 1 participants are reluctant to accept a conclusion as certainly true when it is derived from a valid conditional argument that includes a doubtful premise, and 2 participants typically link the degree of uncertainty found in a given premise set to its conclusion. Two experiments were designed to further investigate these phenomena. Ninety adult participants in Experiment 1 were first asked to judge the validity of three conditional arguments Modus Ponens, Denial of the Antecedent, and (...) Affirmation of the Consequent . They were then required to evaluate conclusion uncertainty as a function of two degrees of asserted uncertainty in the major conditional premise If p then it is very probable that q and if p then it is not very probable that q of the arguments from the first task that were otherwise unchanged. Results revealed an effect for asserted-uncertainty in two of the three argument forms. Marginal support was found for the hypothesis that perceived argument validity would be a predictor of performance. Experiment 2 investigated the way 40 adult participants combined two sources of asserted uncertainty, one in the major premise and another in the minor premise, when they had to score the uncertainty of the conclusion. The two most prominent kinds of responses were to choose the same likelihood as the weaker of the two expressed in the premises, or a lower one. However, the within-subject consistency was poor. Theoretical implications are discussed. (shrink)

Five experiments investigated how people use categories to make inductions about objects whose categorisation is uncertain. Normatively, they should consider all the categories the object might be in and use a weighted combination of information from all the categories: bet-hedging. The experiments presented people with simple, artificial categories and asked them to make an induction about a new object that was most likely in one category but possibly in another. The results showed that the majority of people focused on (...) the most likely category in making inductions, although there was a group of consistently normative responders who used information from both categories (about 25% of our college population). Across experiments the overall pattern of results suggests that performance in the task is improved not by understanding the underlying principles of bet-hedging but by increasing the likelihood that multiple categories are in working memory at the time of the induction. We discuss implications for improving everyday inductions. (shrink)

Bayesian accounts are currently popular in the field of inductive reasoning. This commentary briefly reviews the limitations of one such account, the Rational Model (Anderson 1991b), in explaining how inferences are made about objects whose category membership is uncertain. These shortcomings are symptomatic of what Jones & Love (J&L) refer to as Bayesian approaches.

The current special issue focuses on logical and probabilistic approaches to reasoning in uncertain environments, both from a formal, conceptual and argumentative perspective as well as an empirical point of view. In the present introduction we give an overview of the types of problems addressed by the individual contributions of the special issue, based on fundamental distinctions employed in this area. We furthermore describe some of the general features of the special issue.

According to probabilistic theories of reasoning in psychology, people's degree of belief in an indicative conditional `if A, then B' is given by the conditional probability, P(B|A). The role of language pragmatics is relatively unexplored in the new probabilistic paradigm. We investigated how consequent relevance a ects participants' degrees of belief in conditionals about a randomly chosen card. The set of events referred to by the consequent was either a strict superset or a strict subset of the set of (...) events referred to by the antecedent. We manipulated whether the superset was expressed using a disjunction or a hypernym. We also manipulated the source of the dependency, whether in long-term memory or in the stimulus. For subset-consequent conditionals, patterns of responses were mostly conditional probability followed by conjunction. For superset-consequent conditionals, conditional probability responses were most common for hypernym dependencies and least common for disjunction dependencies, which were replaced with responses indicating inferred consequent irrelevance. Conditional probability responses were also more common for knowledge-based than stimulus-based dependencies. We suggest. (shrink)

People can be uncertain in their moral judgments. Philosophers have argued that such uncertainty can either refer to the underlying empirical facts (empirical uncertainty) or to the normative evaluation of these facts itself (normative uncertainty). Psychological investigations of this distinction, however, are rare. In this paper, we combined factor-analytical and experimental approaches to show that empirical and normative uncertainty describe two related but different psychological states. In Study 1, we asked N = 265 participants to describe a case of (...) moral uncertainty and to rate different aspects of their uncertainty about this case. Across this wide range of moral scenarios, our items loaded onto three reliable factors: lack of information, unclear consequences, and normative uncertainty. In Study 2, we confirmed this factor structure using predefined stimulus material. N = 402 participants each rated eight scenarios that systematically varied in their degree of uncertainty regarding the consequences of the described actions and in the value conflict that was inherent to them. The empirical uncertainty factors were mainly affected by the introduction of uncertainty regarding consequences, and the normative uncertainty factor was mainly affected by the introduction of value conflict. Our studies provide evidence that the distinction between empirical and normative uncertainty accurately describes a psychological reality. We discuss the relevance of our findings for research on moral judgments and decision-making, and folk metaethics. (shrink)

ABSTRACTThe new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of probability that (...) contained non-numerical expressions and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, the rate of conjunction fallacy was consistently low (not exceeding 20%,.. (shrink)

We offer thoughts on Shadmehr and Ahmed's foundational assumption that behavioral intensity (vigor) is proportional to the perceived value of outcomes driving behavior (incentives). The assumption is reasonable considering classical motivational thought and scholarship in related literatures but called into question by an influential contemporary theory of motivation by Brehm. Brehm's theory suggests that the assumption is warranted in some, but not all, performance circumstances. Furthermore, proportionality between vigor and value might be generated through a deliberative goal-setting process rather than (...) through intrinsic neural linkages. (shrink)

Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the (...) book will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science. (shrink)

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by Cooper (1968) and Belnap (1973) and it yields two logics of conditional reasoning: (i) a logic C of certainty-preserving inference; and (ii) a logic U for uncertain reasoning that preserves the probability of the premises. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, (...) and we use the distinction between the two systems to cast light on the validity of inferences such as Modus Ponens, Or-To-If, and Conditional Excluded Middle. Specifically, the conditional behaves monotonically in C, but non-monotonically in U; Modus Ponens is valid in C, but valid in U only for non-nested conditionals. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences. (shrink)

Introduction -- Fallibilism -- Contextualism -- Knowledge and reasons -- Justification -- Belief -- The value and importance of knowledge -- Infallibilism or pragmatic encroachment? -- Appendix I: Conflicts with bayesian decision theory? -- Appendix II: Does KJ entail infallibilism?

Conditionals are basic for human reasoning. In our paper, we present two experiments, which for the first time systematically compare how people reason about indicative conditionals (Experiment 1) and counterfactual conditionals (Experiment 2) in causal and non-causal task settings (N = 80). The main result of both experiments is that conditional probability is the dominant response pattern and thus a key ingredient for modeling causal, indicative, and counterfactual conditionals. In the paper, we will give an overview of the main (...) experimental results and discuss their relevance for understanding how people reason about conditionals. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability (...) bounds imposed by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

We should now be able to come to some general conclusions about the main lines of Cuvier's development as a naturalist after his departure from Normandy. We have seen that Cuvier arrived in Paris aware of the importance of physiology in classification, yet without a fully worked out idea of how such an approach could organize a whole natural order. He was freshly receptive to the ideas of the new physiology developed by Xavier Bichat.Cuvier arrived in a Paris also torn (...) by many overlapping debates on the nature of classification, and in particular that between the natural and artificial systems. The very validity of the enterprise of classification was questioned in many quarters. Cuvier's achievement on his entry into the Parisian world of science was not simply to establish himself as a highly competent anatomist: far more important, he also began to use ideas from many different specialties to change completely the notion of what was involved in natural history.124 At the same time that he himself swung away from the guiding image of the field naturalist as the ideal of the specialty, he took ideas from the new physiology to answer questions about the order of the animal world, and from comparative anatomy to resurrect extinct creation — and to come to conclusions from that creation about the history of the forms of life and the manner of their succession. He showed himself able to alter the relationships between natural history and many other fields of study in a way that implied, rightly or wrongly, his own complete mastery over such a movement. Partly he was able to do this because the ideas he borrowed were not themselves logically articulated and thus could be easily adapted and refocused for many different specific purposes. The value of the heuristic possibilities inherent in the idea of life, for example, far outweighed its inability to generate full systems of classification. Cuvier also consistently refused to consider in science matters relating to the first causes of events. Freed from the consideration of first-order phenomena, he was able to use second-order explanations across a far wider field of applicability. Personal doubts about the validity of a theology that had used science in order to bolster its own claims were combined here with the strong influence of the Kantian critique of the limits of human reason.125Cuvier's characteristic mode of procedure was that of intellectual appropriation and a bold capacity for altering the relationships between different fields of knowledge, rather than, with the exception of taxonomy, the technique of expanding their subject matter. His claims to originality came, first, from this reappropriation and reorientation and, second, from the sheer scope of his work, which aimed at nothing less than the cataloging and classification of all animate objects.126 They rested also on his acute use of his assertion of a certain relationship with the past of his subject. Very often he would present this history in such a way as to obscure his own intellectual genealogy, and often too he would give differing accounts of the priority of use of an idea in order to distract attention from the questionable exactitude of his own claims to originality. Cuvier came to Paris at precisely the time when society and institutions were most profitably malleable for a newcomer; it was also a time when many scientific disciplines had reached a stage advanced in terms of their factual content, yet relatively inadequate in conceptual organization. They were ripe for takeover by large-scale organizing ideas such as the animal economy and the subordination of characteristics. Paleontology is a particularly good example of a specialty in this particular form of underdevelopment in 1795.Cuvier paid a high price for his initial success. His electic applications of large-scale organizing ideas tended to mean that little of his own work had complete coherence at all levels. Ideas, as we have seen, that proved capable of providing a complete reform of the larger groups of the animal kingdom were incapable of producing its detailed working-out in the taxonomy of smaller groups, which had to be supplied from observed analogical correlations. Further, his physiological approach to classification involved the breakdown of strict correspondence between organs and functions, which left the way open for workers such as Geoffroy St. Hilaire gradually to tilt the balance away from the study of the correlations of hierarchies of functions, and toward morphology as the basis of the order of nature. Cuvier's brilliant appropriations from physiology from the beginning, therefore, contained the seeds of conflict with Geoffroy.Cuvier's eclectic approach made it very nearly impossible for him to present a clear idea of the ways in which the life sciences could be said to be lawful. In spite of his efforts to assimilate them to the position of the physical sciences in this respect, he was forced in the end to accord only an ambiguous status as “laws” to observational correlations. From this area of failure came much of the attempt to give his own two laws — the correlation of parts and the subordination of characteristics — predictive qualities, particularly in relation to paleontological research.It is not surprising that Cuvier's title as the “legislator” of natural history should represent more a claim than a reality. How, then, was he able to emerge as the leading French naturalist of his day? First of all must be adduced the sheer scale of his undertakings. Then comes his expertise as a practical anatomist, and the range of different topics toward which he turned his interest. His collaborators cannot be given credit for his output nor, as we have seen, for slavish adherence to his ideas. Cuvier was able to successfully claim to have dominated the underdeveloped specialties, such as paleontology, and turned them into a major heuristic input into both geology and comparative anatomy; but in other fields, such as physiology, he appropriated concepts and encouraged research but made little impact on the field himself. His attempts in 1812 to head off, or neutralize and absorb the growth of morphological studies landed him in a dangerously rigid position, which despite his encouragement of the new physiological research under the Restoration made further elaboration of his own conceptual underpinnings almost impossible.Cuvier's authority in the scientific world would in any case have been great because of his substantive achievement in taxonomy, but the rest of his work had enough ambiguities and dislocations for it to need the support of his political and social power. Cuvier's detractors seized on a vital fragment of the truth when they accused him of finding the political dimension all-important: it obscured the disjunctions in his theories and at the same time gave him the authority to make new claims for the status of the observational sciences - and for their relations of power with their surrounding specialties. Cuvier's science both thrived on and was halted by the power games of intellectual appropriation, manipulation of the past to confirm the present, and continual claims for hegemony. (shrink)

Background Massively parallel sequencing techniques, such as whole exome sequencing (WES) and whole genome sequencing (WGS), may reveal unsolicited findings (UFs) unrelated to the diagnostic aim. Such techniques are frequently used for diagnostic purposes in pediatric cases of developmental delay (DD). Yet policy guidelines for informed consent and return of UFs are not well equipped to address specific moral challenges that may arise in these children’s situations. Discussion In previous empirical studies conducted by our research group, we found that it (...) is sometimes uncertain how children with a DD will develop and whether they could come to possess capacities for autonomous decision-making in the future. Parents sometimes felt this brought them into a Catch-22 like situation when confronted with choices about UFs before undergoing WES in trio-analysis (both the parents’ and child’s DNA are sequenced). An important reason for choosing to consent to WES was to gain more insight into how their child might develop. However, to make responsible choices about receiving or declining knowledge of UFs, some idea of their child’s future development of autonomous capacities is needed. This undesirable Catch-22 situation was created by the specific policy configuration in which parents were required to make choices about UFs before being sequencing (trio-analysis). We argue that this finding is relevant for reconfiguring current policies for return of UFs for WES/WGS and propose guidelines that encompass two features. First, the informed consent process ought to be staged. Second, differing guidelines are required for withholding/disclosing a UF in cases of DD appropriate to the level of confidence there is about the child’s future developmental of autonomous capacities. Conclusion When combined with a dynamic consent procedure, these two features of our guidelines could help overcome significant moral challenges that present themselves in the situations of children undergoing genomic sequencing for clarifying a DD. (shrink)

This paper considers the demand for insurance in a model with uncertain indemnity. Uncertain indemnity tends to increase the demand for insurance for precautionary reasons, but it also tends to decrease the demand due to the risk created by indemnity uncertainty. When the coefficient of relative prudence is not too large, uncertain indemnity reduces the demand for insurance and partial coverage is optimal even at actuarially fair premiums. In addition, insurance may be an inferior good or a (...) normal good, depending on the behavior of absolute risk aversion and the magnitude of the coefficient of relative risk aversion. (shrink)

Expert probability forecasts can be useful for decision making . But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty . Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language . But Bayesian epistemology comes in three main varieties. (...) Strictly subjective Bayesianism and empirically-based subjective Bayesianism have difficulty in justifying the use of a forecaster’s probabilities for decision making . On the other hand, objective Bayesianism can justify the use of these probabilities, at least when the probabilities are consistent with the agent’s evidence . Hence objective Bayesianism offers the most promise overall for explaining how testimony of uncertainty can be useful for decision making. Interestingly, the objective Bayesian analysis provided in Sect. 5 can also be used to justify a version of the Principle of Reflection. (shrink)

The Covid-19 pandemic has shaken the world. It has presented us with a series of new challenges, but the policy response may be difficult due to the severe uncertainty of our circumstances. While pressure to take timely action may push towards less inclusive decision procedures, in this paper I argue that precisely our current uncertainty provides reasons to include stakeholders in collective decision-making. Decision-making during the pandemic faces uncertainty that goes beyond the standard, probabilistic one of Bayesian decision theory. Agents (...) may be uncertain not just about factual properties of the world, but also about how to model their decision problems and about the values of the possible consequences of their options. As different stakeholders may have irreconcilable disagreement about how to resolve these uncertainties, decision-making procedures should take everybody’s perspectives into account. Moreover, those communities that are hit harder by the pandemic are also those that are typically excluded from knowledge production. Thus, in the face of Covid-19 uncertainty, both democratic and epistemic considerations highlight the importance of stakeholders’ inclusion in policy decision-making. (shrink)

Philosophers and psychologists routinely explore questions surrounding reasoning, inquiry, and bias, though typically in disciplinary isolation. What is the source of our intellectual errors? When can we trust information others tell us? This volume brings together researchers from across the two disciplines to present ideas and insights for addressing the challenges of knowing well in a complicated world in four parts: how to best describe the conceptual and empirical terrain of reason and bias; how reasoning and bias influence (...) basic perception of the physical world; how to assess knowledge and expertise in ourselves and others; and how people approach reasoning and knowledge among and about groups. Together, the chapters show what philosophers and psychologists can do together when they shine light on the challenges of reaching the truth and avoiding errors. Reason, Bias, and Inquiry is a multidisciplinary meditation for readers who are awash in information but are uncertain how to manage it to make informed decisions. (shrink)

The obligation to provide reasons may appear rather a simple and straightforward, but in actual practice—as the mutually antagonistic Weiss rulings of the CJEU and the German Bundesverfassungsgericht amply demonstrate—is fraught with constitutional complication. On the one side, there lies the concern with a deeply intrusive form of judicial review which substitutes judicially determined “good” reasons for those of the reviewee decisionmaker—legislatures, administrative agencies, or, as in Weiss, the European Central Bank. On the other side lies the concern with judicial (...) abdication in the face of technical expertise, uncertainty and complexity, turning the reason-giving requirement into a mere façade thereby placing democratic accountability in the modern administrative state beyond law’s remit. Either way, normatively and conceptually, we seem left with a half-way house only. Drawing on the recent US administrative law discourse—the neo-Fullerian concept of an “internal morality of law” and democratic experimentalism —this paper explores the concept of process review as tertium datur. Process review responds to concerns over the rule of law and administrative discretion through indirect, procedural safeguards, by imposing requirements of reasoned justification, rather than through wholesale invalidation or aggressive substantive review. (shrink)

We should adopt the following principle with regard to compensatory justice. (1) If an unjust act benefits an innocent person and there is no reasonable way to assess the amount of damages to the victim, then compensatory justice does not require that the innocent beneficiary pay compensation for those damages. We cannot reasonably assess the amount of damages to current racial minorities that have resulted from past discriminatory acts. Problems arise in determining the identity of the injured parties, the identity (...) of the injuring agents and injuring acts (and omissions), and the degree of injury that directly resulted from these acts (or omissions). Since such compensable damages cannot be accurately estimated and since white male applicants are innocent beneficiaries of past discriminatory acts, the value of compensatory justice does not justify strong affirmative action programs. (shrink)

When forecasting events, multiple types of uncertainty are often inherently present in the modeling process. Various uncertainty typologies exist, and each type of uncertainty has different implications a scientist might want to convey. In this work, we focus on one type of distinction betweendirect quantitative uncertaintyandindirect qualitative uncertainty. Direct quantitative uncertainty describes uncertainty about facts, numbers, and hypotheses that can be communicated in absolute quantitative forms such as probability distributions or confidence intervals. Indirect qualitative uncertainty describes the quality of knowledge (...) concerning how effectively facts, numbers, or hypotheses represent reality, such as evidence confidence scales proposed by the Intergovernmental Panel on Climate Change. A large body of research demonstrates that both experts and novices have difficulty reasoning with quantitative uncertainty, and visualizations of uncertainty can help with such traditionally challenging concepts. However, the question of if, and how, people may reason with multiple types of uncertainty associated with a forecast remains largely unexplored. In this series of studies, we seek to understand if individuals can integrate indirect uncertainty about how “good” a model is (operationalized as a qualitative expression of forecaster confidence) with quantified uncertainty in a prediction (operationalized as a quantile dotplot visualization of a predicted distribution). Our first study results suggest that participants utilize both direct quantitative uncertainty and indirect qualitative uncertainty when conveyed as quantile dotplots and forecaster confidence. In manipulations where forecasters were less sure about their prediction, participants made more conservative judgments. In our second study, we varied the amount of quantified uncertainty (in the form of the SD of the visualized distributions) to examine how participants’ decisions changed under different combinations of quantified uncertainty (variance) and qualitative uncertainty (low, medium, and high forecaster confidence). The second study results suggest that participants updated their judgments in the direction predicted by both qualitative confidence information (e.g., becoming more conservative when the forecaster confidence is low) and quantitative uncertainty (e.g., becoming more conservative when the variance is increased). Based on the findings from both experiments, we recommend that forecasters present qualitative expressions of model confidence whenever possible alongside quantified uncertainty. (shrink)

ABSTRACTTreating conditionals as probabilistic statements has been referred to as a defining feature of the “new paradigm” in cognitive psychology. Doing so is attractive for several reasons, but it complicates the problem of assessing the merits of conditional arguments. We consider several variables that relate to judging the persuasiveness of conditional arguments with uncertain premises. We also explore ways of judging the consistency of people's beliefs as represented by components of conditional arguments. Experimental results provide evidence that inconsistencies in (...) beliefs are more prevalent if the arguments’ components are spatially and temporally dispersed than if they are contiguous in space and time. This supports the idea that assuring the consistency among even a small number of beliefs is difficult to do, especially if the beliefs in question are not brought into consciousness at the same time; but consistency can be enhanced when beliefs are considered simultaneously or nea... (shrink)