How do people make difficult decisions in situations involving substantial risk and uncertainty? In this study, we presented a difficult medical decision to three expert physicians in a combined “thinking aloud” and “cross examination” experiment. Verbatim transcripts were analyzed using script analysis to observe the process of constructing and making the decision, and using referring phrase analysis to determine the representation of knowledge of likelihoods. These analyses are compared with a formal decision analysis of the same problem to highlight (...) similarities and differences. The process of making the decision resembles an incremental, sequential‐refinement planning algorithm, where a complex decision is broken into a sequence of choices to be made with a simplified description of the alternatives. This strategy results in certain kinds of relevant information being underweighted in the final decision. Knowledge of likelihood appears to be represented as symbolic descriptions capturing categorical and ordinal relations with “landrhark” likelihoods, only some of which are described numerically. Numerical probabilities, capable of being combined and compared arithmetically, were not observed. These observations suggest an explanation for the heuristics and biases in human decision making under uncertainty in terms of the processes that manipulate symbolic descriptions of likelihoods and construct plans of action for situations involving risk and uncertainty. (shrink)

An increasingly prevalent approach to studying human cognition is to construe the mind as optimally allocating limited cognitive resources among cognitive processes. Under this bounded rationality approach (Icard in Philos Sci 85(1):79–101, 2018; Simon in Utility and probability, Palgrave Macmillan, 1980), it is common to assume that resource-bounded cognitive agents approximate normative solutions to statistical inference problems, and that much of the bias and variability in human performance can be explained in terms of the approximation strategies we employ. In this (...) paper, we argue that this approach restricts itself to an unnecessarily narrow scope of cognitive models, which limits its ability to explain how humans flexibly adapt their representations to novel environments. We argue that more attention should be paid to how we form our cognitive representations in the first place, and advocate for pluralistic framework which jointly optimizes over both representations and algorithms for manipulating them. We identify several fundamental trade-offs that manifest in this joint optimization, and draw on recent work to motivate a unified formal framework for this analysis. We illustrate a simplified version of this analysis with a case study in social cognition, and outline several new directions for research that this approach suggests. (shrink)

Media coverage of migration and migrants can exert considerable influence on the public’s understanding of and attitudes towards migration. During the peak of what has been called ‘the refugee crisis’ in 2015, heated discussions about immigration and its possible impact filled the media landscape. This study focuses specifically on the news framing of insecurities regarding immigration, exploring what we have termed ‘uncertainty frames’ in the coverage of refugees, asylum seekers and immigrants. This study will thus lend empirical support to (...) a novel attempt to combine the concepts of uncertainty, risk, and framing. These frames were analyzed within French and Austrian media from 2015 to 2016. Drawing on a content analysis of tabloid and broadsheet articles, different types of uncertainty frames (economy, values, society, etc.) as well as different types of solution frames (the kind of solutions provided for the issue of immigration) were examined. Results suggest that even though all frames decrease in salience over time, important variations in different types of uncertainty frames do appear. It is argued that frames related to abstract issues seem to stay more salient throughout time in both countries. (shrink)

The Bristol Inquiry is arguably one of the most important cases of judicial medical investigation held in the United Kingdom, which continues to raise important insights into the social construction of medical and scientific risks. As a way of marking the inquiry’s tenth anniversary year, this article returns to an important conversation held between noted pediatric cardiothoracic and cardiovascular specialists, on days 49 and 50 of the inquiry’s proceedings. Their conversance principally describes a pathway of scientific advancement across four decades. (...) Risks, and the avoidance of medical error, represent important subtopics of the ensuing historical narrative, within which the experts describe opportunities for error as diminishing in-line with paradigmatic advancement. The telling of this story of risk mitigation involves the expurgation of considerable sensitivities to scientific uncertainty. In analyzing this example of expert scientific witness testimony, the article primarily considers how representations of uncertainty are formulated in language. The article concludes that, in this instance, the social construction of risk and uncertainty were heteroglossically premised upon language catalysts, cognitive metaphors, and logic-based mathematical rubrics. (shrink)

The auditory system is able to recognize auditory objects and is thought to form predictive models of them even though the acoustic information arriving at our ears is often imperfect, intermixed, or distorted. We investigated implicit regularity extraction for acoustically intact versus disrupted six-tone sound patterns via event-related potentials. In an exact-repetition condition, identical patterns were repeated; in two distorted-repetition conditions, one randomly chosen segment in each sound pattern was replaced either by white noise or by a wrong pitch. In (...) a roving-standard paradigm, sound patterns were repeated 1–12 times in a row before a new pattern occurred. The participants were not informed about the roving rule and had to detect rarely occurring loudness changes. Behavioral detectability of pattern changes was assessed in a subsequent behavioral task. Pattern changes elicited mismatch negativity and P3a, and were behaviorally detected above the chance level in all conditions, suggesting that the auditory system extracts regularities despite distortions in the acoustic input. However, MMN and P3a amplitude were decreased by distortions. At the level of MMN, both types of distortions caused similar impairments, suggesting that auditory regularity extraction is largely determined by the stimulus statistics of matching information. At the level of P3a, wrong-pitch distortions caused larger decreases than white-noise distortions. Wrong-pitch distortions likely prevented the engagement of restoration mechanisms and the segregation of disrupted from true pattern segments, causing stronger informational interference with the relevant pattern information. (shrink)

The uncertainty associated with paradigmatic families has been shown to correlate with their phonetic characteristics in speech, suggesting that representations of complex sublexical relations between words are part of speaker knowledge. To better understand this, recent studies have used two-layer neural network models to examine the way paradigmatic uncertainty emerges in learning. However, to date this work has largely ignored the way choices about the representation of inflectional and grammatical functions in models strongly influence what they subsequently learn. (...) To explore the consequences of this, we investigate how representations of IFS in the input-output structures of learning models affect the capacity of uncertainty estimates derived from them to account for phonetic variability in speech. Specifically, we examine whether IFS are best represented as outputs to neural networks or as inputs by building models that embody both choices and examining their capacity to account for uncertainty effects in the formant trajectories of word final [ɐ], which in German discriminates around sixty different IFS. Overall, we find that formants are enhanced as the uncertainty associated with IFS decreases. This result dovetails with a growing number of studies of morphological and inflectional families that have shown that enhancement is associated with lower uncertainty in context. Importantly, we also find that in models where IFS serve as inputs—as our theoretical analysis suggests they ought to—its uncertainty measures provide better fits to the empirical variance observed in [ɐ] formants than models where IFS serve as outputs. This supports our suggestion that IFS serve as cognitive cues during speech production, and should be treated as such in modeling. It is also consistent with the idea that when IFS serve as inputs to a learning network. This maintains the distinction between those parts of the network that represent message and those that represent signal. We conclude by describing how maintaining a “signal-message-uncertainty distinction” can allow us to reconcile a range of apparently contradictory findings about the relationship between articulation and uncertainty in context. (shrink)

I discuss the application of the Model of Pragmatic Information to the study of spontaneous anomalystic mental phenomena like telepathy, precognition, etc. In these phenomena the most important effects are related to anomalous information gain by the subjects. I consider the basic ideas of the Model, as they have been applied to experimental anomalystic phenomena and to spontaneous phenomena that have strong physical effects, like poltergeist cases, highlighting analogies and differences. Moreover, I point out that in such cases we cannot (...) assign a probability of being accepted to every proposition, and so we cannot use standard formulas for pragmatic information and other relevant measures. To overcome the problem, I propose that qualitative possibility theory could be used to describe the situation. In such theory, the confidence in a proposition is expressed using a scale. Basic concepts like epistemic states, belief revision, information gain, pragmatic information etc. are discussed in this frame. Finally an application to some specific cases is sketched. (shrink)

We investigate the conflict between the ex ante and ex post criteria of social welfare in a new framework of individual and social decisions, which distinguishes between two sources of uncertainty, here interpreted as an objective and a subjective source respectively. This framework makes it possible to endow the individuals and society not only with ex ante and ex post preferences, as is usually done, but also with interim preferences of two kinds, and correspondingly, to introduce interim forms of (...) the Pareto principle. After characterizing the ex ante and ex post criteria, we present a first solution to their conflict that extends the former as much possible in the direction of the latter. Then, we present a second solution, which goes in the opposite direction, and is also maximally assertive. Both solutions translate the assumed Pareto conditions into weighted additive utility representations, and both attribute to the individuals common probability values on the objective source of uncertainty, and different probability values on the subjective source. We discuss these solutions in terms of two conceptual arguments, i.e., the by now classic spurious unanimity argument and a novel informational argument labelled complementary ignorance. The paper complies with the standard economic methodology of basing probability and utility representations on preference axioms, but for the sake of completeness, also considers a construal of objective uncertainty based on the assumption of an exogeneously given probability measure. JEL classification: D70; D81. (shrink)

Scientific knowledge is the most solid and robust kind of knowledge that humans have because of its inherent self-correcting character. Nevertheless, anti-evolutionists, climate denialists, and anti-vaxxers, among others, question some of the best-established scientific findings, making claims unsupported by empirical evidence. A common aspect of these claims is reference to the uncertainties of science concerning evolution, climate change, vaccination, and so on. This is inaccurate: whereas the broad picture is clear, there will always exist uncertainties about the details of the (...) respective phenomena. This book shows that uncertainty is an inherent feature of science that does not devalue it. In contrast, uncertainty advances science because it motivates further research. This is the first book on this topic that draws on philosophy of science to explain what uncertainty in science is and how it makes science advance. It contrasts evolution, climate change, and vaccination, where the uncertainties are exaggerated, and genetic testing and forensic science, where the uncertainties are usually overlooked. The goal is to discuss the scientific, psychological, and philosophical aspects of uncertainty in order to explain what it really is, what kinds of problems it actually poses, and why in the end it makes science advance. Contrary to public representations of scientific findings and conclusions that produce an intuitive but distorted view of science as certain, people need to understand and learn to live with uncertainty in science. This book is intended for anyone who wants to get a clear view of the nature of science. (shrink)

An important epistemic issue in climate modelling concerns structural uncertainty: uncertainty about whether the mathematical structure of a model accurately represents its target. How does structural uncertainty affect our knowledge and predictions about the climate? How can we identify sources of structural uncertainty? Can we manage the effect of structural uncertainty on our knowledge claims? These are some of the questions that an epistemology of structural uncertainty faces, and these questions are also important for (...) climate scientists and policymakers. I develop three desiderata for an epistemological account of structural uncertainty. In my view, an account of structural uncertainty should identify sources of structural uncertainty, explain how these sources limit the applicability of a model, and show how the severity of structural uncertainty depends on the questions that can be asked of a model. I argue that analyzing structural uncertainty by paying attention to the details of model building can satisfy these desiderata. I focus on parametrizations, which are representations of important processes occurring at scales that are not resolved by climate models. Parametrizations are often thought to be ad-hoc, but I show that some important parametrizations are theoretically justified by explicit or implicit scale separation assumptions. These assumptions can also be supported empirically. Analyzing these theoretical and empirical justificatory roles of the scale separation assumptions can provide insights into how parametrizations contribute to structural uncertainty. I conclude by sketching how my approach can satisfy the desiderata I set out at the beginning, highlighting its importance for policy-relevant scientific statements about the climate. (shrink)

According to Richard Jeffrey’s value-free ideal, scientists should avoid making value judgments about inductive risks by offering explicit representations of scientific uncertainty to decision-makers, who can use these to make decisions according to their own values. Some philosophers have responded by arguing that higher-order inductive risks arise in the process of producing representations of uncertainty. This chapter explores this line of argument and its limits, arguing that the Jeffreyan value-free ideal is achievable in contexts where methodological decisions introduce (...) minimal higher-order uncertainty and where communications of uncertainty are unlikely to be manipulated or misunderstood by scientists or decision-makers. This chapter illustrates the limits of the Jeffreyan ideal with reference to climate science and argues that the context of climate science is not conducive to the Jeffreyan ideal, so the argument that climate modeling is value-laden due to higher-order inductive risks withstands recent criticisms. (shrink)

Epistemic states of uncertainty play important roles in ethical and political theorizing. Theories that appeal to a “veil of ignorance,” for example, analyze fairness or impartiality in terms of certain states of ignorance. It is important, then, to scrutinize proposed conceptions of ignorance and explore promising alternatives in such contexts. Here, I study Lerner’s probabilistic egalitarian theorem in the setting of imprecise probabilities. Lerner’s theorem assumes that a social planner tasked with distributing income to individuals in a population is (...) “completely ignorant” about which utility functions belong to which individuals. Lerner models this ignorance with a certain uniform probability distribution, and shows that, under certain further assumptions, income should be equally distributed. Much of the criticism of the relevance of Lerner’s result centers on the representation of ignorance involved. Imprecise probabilities provide a general framework for reasoning about various forms of uncertainty including, in particular, ignorance. To what extent can Lerner’s conclusion be maintained in this setting? (shrink)

Our uncertainty about matters of fact can often be adequately represented by probabilities, but there are also cases in which we, intuitively speaking, know too little even to assign meaningful probabilities. In many of these cases, other formal representations can be used to capture some of the prominent features of our uncertainty. This is a non-technical overview of some of these representations, including probability intervals, belief functions, fuzzy sets, credal sets, weighted credal sets, and second order probabilities.

The last 20 years or so has seen an intense search carried out within Dempster–Shafer theory, with the aim of finding a generalization of the Shannon entropy for belief functions. In that time, there has also been much progress made in credal set theory—another generalization of the traditional Bayesian epistemic representation—albeit not in this particular area. In credal set theory, sets of probability functions are utilized to represent the epistemic state of rational agents instead of the single probability function of (...) traditional Bayesian theory. The Shannon entropy has been shown to uniquely capture certain highly intuitive properties of uncertainty, and can thus be considered a measure of that quantity. This article presents two measures developed with the purpose of generalizing the Shannon entropy for (1) unordered convex credal sets and (2) possibly non-convex credal sets ordered by second order probability, thereby providing uncertainty measures for such epistemic representations. There is also a comparison with the results of the measure AU developed within Dempster–Shafer theory in a few instances where unordered convex credal set theory and Dempster–Shafer theory overlap. (shrink)

A common reducible representation space of the Lie algebras su and su is equipped with two different types of scalar products. The representation bases are labeled by the azimuthal and magnetic quantum numbers. The generators of su are the x-, y- and z-components of the orbital angular momentum operator. The representation of each of these Lie algebras is unitary with respect to only one of the scalar products. To each positive magnetic quantum number a family of the su-Barut–Girardello coherent states (...) is associated. The normalization and resolution of the identity condition for the coherent states are realized in two different approaches, i.e. the unitary and the non-unitary approaches. For the coherent states of the non-unitary case we calculate the uncertainty relation for the Hermitian x- and y-components of the angular momentum operator. While the unitary case leads to the known uncertainty relation for the Hermitian x- and y-components of su Lie algebra. (shrink)

ABSTRACT Objectives There is little research on moral uncertainties and distress of palliative and hospice care providers (PHCPs) working in jurisdictions anticipating legalising voluntary assisted dying (VAD). This study examines the perception and anticipated concerns of PHCPs in providing VAD in the State of Queensland, Australia prior to legalisation of the practice in 2021. The findings help inform strategies to facilitate training and support the health and well-being of healthcare workers involved in VAD. Design The study used a qualitative approach (...) to examine and analyse the perception and anticipated concerns of PHCPs regarding challenges of providing assisted dying in Queensland. Fourteen PHCPs were recruited using a purposive sampling strategy to obtain a broad representation of perspectives including work roles, geographical locations and workplace characteristics. Data were collected via one in-depth interview per participant. The transcripts were coded for patterns and themes using an inductive analysis approach following the tradition of Grounded Theory. Setting The study was conducted in hospital, hospice, community and residential aged care settings in Queensland, Australia. These included public and private facilities, secular and faith-based facilities, and regional/rural and urban facilities. Participants Interviews were conducted with fourteen PHCPs: 10 nurses and 4 physicians; 11 female and 3 male. The median number of years of palliative care practice was 17, ranging from 2 to 36 years. For inclusion, participants had to be practising palliative and hospice care providers. Results PHCPs are divided on whether VAD should be considered part of palliative care. Expectations of moral distress and uncertainty about practising VAD were identified in five areas: handling requests, assessing patient capacity, arranging patient transfers and logistical issues, managing unsuccessful attempts, and dealing with team conflicts and stigma. Conclusions The possibility of having to practise VAD causes moral distress and uncertainty for some PHCPs. Procedural clarity can address some uncertainties; moral and psychological distress, however, remains a source of tension that needs support to ensure ongoing care of both patients and PHCPs. The introduction of VAD post-legalisation may present an occasion for further moral education and development of PHCPs. (shrink)

This book is an extensive survey and critical examination of the literature on the use of expert opinion in scientific inquiry and policy making. The elicitation, representation, and use of expert opinion is increasingly important for two reasons: advancing technology leads to more and more complex decision problems, and technologists are turning in greater numbers to "expert systems" and other similar artifacts of artificial intelligence. Cooke here considers how expert opinion is being used today, how an expert's uncertainty is (...) or should be represented, how people do or should reason with uncertainty, how the quality and usefulness of expert opinion can be assessed, and how the views of several experts might be combined. He argues for the importance of developing practical models with a transparent mathematic foundation for the use of expert opinion in science, and presents three tested models, termed "classical," "Bayesian," and "psychological scaling." Detailed case studies illustrate how they can be applied to a diversity of real problems in engineering and planning. (shrink)

How ought you to evaluate your options if you're uncertain about what's fundamentally valuable? A prominent response is Expected Value Maximisation (EVM)—the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected value across axiologies. But the expected value of an option depends on quantitative probability and value facts, and in particular on value comparisons across axiologies. We need to explain what it is for such facts to hold. Also, (...) EVM is by no means self-evident. We need an argument to defend that it’s true. This book introduces an axiomatic approach to answer these worries. It provides an explication of what EVM means by use of representation theorems: intertheoretic comparisons can be understood in terms of facts about which options are better than which, and mutatis mutandis for intratheoretic comparisons and axiological probabilities. And it provides a systematic argument to the effect that EVM is true: the theory can be vindicated through simple axioms. The result is a formally cogent and philosophically compelling extension of standard decision theory, and original take on the problem of axiological or normative uncertainty. (shrink)

Feminism, poststructuralism, postcolonialism, and Marxism, among other critical approaches, have undermined traditional notions of aesthetics in recent decades. But questions of aesthetic judgment and pleasure persist, and many critics now seek a "return to aesthetics" or a "return to beauty." Janet Wolff advances a "postcritical" aesthetics grounded in shared values that are negotiated in the context of community. She relates this approach to contemporary debates about a committed politics similarly founded on the abandonment of certainty. Neither universalist nor relativist, the (...) "aesthetics of uncertainty" provides a discourse on beauty that contemporary critics can engage with and offers a basis for judgment that is committed to assigning value to works of art. Wolff explores her position through a range of topics: the question of beauty in relation to feminist critique; the problematic status of twentieth-century English art, visual representations of the Holocaust, Jewish identity as portrayed by the artist R. B. Kitaj, refugee artists and modernism in 1940s Britain, and the nature and appeal of imagistic thinking in sociology. She addresses the desire for certainty and the timeliness of doubt and concludes with a meditation on the intersection of aesthetics and ethics, arguing that ethical issues are very much implicated in aesthetic discourse. (shrink)

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }$$\end{document} be a set of outcomes, and let I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{I }$$\end{document} be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} on XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }^\mathcal{I }$$\end{document} admits an additive representation. That is: there exists a linearly ordered abelian group R\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document} and a ‘utility function’ u:X⟶R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u:\mathcal{X }{{\longrightarrow }}\mathcal{R }$$\end{document} such that, for any x,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document} which differ in only finitely many coordinates, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∑i∈Iu-u≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i\in \mathcal{I }} \left[u-u\right]\ge 0$$\end{document}. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document}, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∗∑i∈Iu≥∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u\ge {}^*\!\sum _{i\in \mathcal{I }}u$$\end{document}. Here, ∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u$$\end{document} represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\mathcal{R }$$\end{document}, which is an ultrapower extension of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document}. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. (shrink)

The article discusses the theoretical status of the category of uncertainty. Instead of the classical definitions of uncertainty as an ontological or epistemological concept, a composite theoretical construct is proposed. In classical science, the objectivist representation of the subject of research was preferred. With the nonclassical type of rationality, there rises problem of including subjective elements in a theoretical description. Attention to subject-subject-object methodologies is increasing due to the complication of communicative interactions in science and society in the (...) digital era. One of the consequences of active innovative projective activity on a planetary scale and increasing risks is the perception in the public mind of uncertainty as a challenge. The author considers it appropriate to study the uncertainty-certainty as a paired category. The category of uncertainty was considered in philosophy, science, and management. The status of uncertainty as infinity and formlessness was recognized by Greek natural philosophers. Classical science developed the methodology of knowing the “infinite limit” through the construction of theoretical schemes (forms) and types of empirical testing. The paradox served as a means of destroying dogmatic schemes. In the context of increasingly complex communications in science, the importance of cognitive problems in the study of collective thinking and the personal beginning of creativity is increasing. Modern economic positivism is distinguished by its rejection of objective uncertainty, and the installation of the ability to efficiently manage exclusively accurate calculations is brought to extremes. (shrink)

A coherent account of the connections and contrasts between the principles of complementarity and uncertainty is developed starting from a survey of the various formalizations of these principles. The conceptual analysis is illustrated by means of a set of experimental schemes based on Mach-Zehnder interferometry. In particular, path detection via entanglement with a probe system and (quantitative) quantum erasure are exhibited to constitute instances of joint unsharp measurements of complementary pairs of physical quantities, path and interference observables. The analysis (...) uses the representation of observables as positive-operator-valued measures (POVMs). The reconciliation of complementary experimental options in the sense of simultaneous unsharp preparations and measurements is expressed in terms of uncertainty relations of different kinds. The feature of complementarity, manifest in the present examples in the mutual exclusivity of path detection and interference observation, is recovered as a limit case from the appropriate uncertainty relation. It is noted that the complementarity and uncertainty principles are neither completely logically independent nor logical consequences of one another. Since entanglement is an instance of the uncertainty of quantum properties (of compound systems), it is moot to play out uncertainty and entanglement against each other as possible mechanisms enforcing complementarity. (shrink)

Feminism, poststructuralism, postcolonialism, and Marxism, among other critical approaches, have undermined traditional notions of aesthetics in recent decades. But questions of aesthetic judgment and pleasure persist, and many critics now seek a "return to aesthetics" or a "return to beauty." Janet Wolff advances a "postcritical" aesthetics grounded in shared values that are negotiated in the context of community. She relates this approach to contemporary debates about a committed politics similarly founded on the abandonment of certainty. Neither universalist nor relativist, the (...) "aesthetics of uncertainty" provides a discourse on beauty that contemporary critics can engage with and offers a basis for judgment that is committed to assigning value to works of art. Wolff explores her position through a range of topics: the question of beauty in relation to feminist critique; the problematic status of twentieth-century English art, visual representations of the Holocaust, Jewish identity as portrayed by the artist R. B. Kitaj, refugee artists and modernism in 1940s Britain, and the nature and appeal of imagistic thinking in sociology. She addresses the desire for certainty and the timeliness of doubt and concludes with a meditation on the intersection of aesthetics and ethics, arguing that ethical issues are very much implicated in aesthetic discourse. (shrink)

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

Value and uncertainty are the critical components of decision and action. To think of the affective system as at the core of action is to draw attention to the role of affect in representing and combining these two dimensions, and orchestrating a wide range of mental capacities—attention, perception, memory, inference, motivation, and monitoring—in light of these evaluative representations. The commentators have helpfully enriched our appreciation of the various ways in which affect can contribute to the attunement, cuing, motivation, control, (...) and ongoing assessment of decision and action. (shrink)

Symmetry in biological and physical systems is a product of self-organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry-based feature extraction or representation by neural networks may unravel the most informative contents in large image databases. Despite significant achievements of artificial intelligence in recognition and classification of regular patterns, the problem of uncertainty remains a major challenge in ambiguous data. In this study, we present an artificial neural network that detects symmetry uncertainty states in human observers. (...) To this end, we exploit a neural network metric in the output of a biologically inspired Self- Organizing Map Quantization Error (SOM-QE). Shape pairs with perfect geometry mirror symmetry but a non-homogenous appearance, caused by local variations in hue, saturation, or lightness within and/or across the shapes in a given pair produce, as shown here, a longer choice response time (RT) for “yes” responses relative to symmetry. These data are consistently mirrored by the variations in the SOM-QE from unsupervised neural network analysis of the same stimulus images. The neural network metric is thus capable of detecting and scaling human symmetry uncertainty in response to patterns. Such capacity is tightly linked to the metric’s proven selectivity to local contrast and color variations in large and highly complex image data. (shrink)

It is important to have an adequate model of uncertainty, since decisions must be made before the uncertainty can be resolved. For instance, flood defenses must be designed before we know the future distribution of flood events. It is standardly assumed that probability theory offers the best model of uncertain information. I think there are reasons to be sceptical of this claim. I criticise some arguments for the claim that probability theory is the only adequate model of (...) class='Hi'>uncertainty. In particular I critique Dutch book arguments, representation theorems, and accuracy based arguments. Then I put forward my preferred model: imprecise probabilities. These are sets of probability measures. I offer several motivations for this model of uncertain belief, and suggest a number of interpretations of the framework. I also defend the model against some criticisms, including the so-called problem of dilation. I apply this framework to decision problems in the abstract. I discuss some decision rules from the literature including Levi’s E-admissibility and the more permissive rule favoured by Walley, among others. I then point towards some applications to climate decisions. My conclusions are largely negative: decision making under such severe uncertainty is inevitably difficult. I finish with a case study of scientific uncertainty. Climate modellers attempt to offer probabilistic forecasts of future climate change. There is reason to be sceptical that the model probabilities offered really do reflect the chances of future climate change, at least at regional scales and long lead times. Indeed, scientific uncertainty is multi-dimensional, and difficult to quantify. I argue that probability theory is not an adequate representation of the kinds of severe uncertainty that arise in some areas in science. I claim that this requires that we look for a better framework for modelling uncertainty. (shrink)

There are two main approaches in the phenomenological understanding of the unconscious. The first explores the intentional theory of the unconscious, while the second develops a non-representational way of understanding consciousness and the unconscious. This paper aims to outline a general theoretical framework for the non-representational approach to the unconscious within the phenomenological tradition. In order to do so, I focus on three relevant theories: Maurice Merleau-Ponty’s phenomenology of perception, Thomas Fuchs’ phenomenology of body memory, and Edmund Husserl’s phenomenology of (...) affectivity. Both Merleau-Ponty and Fuchs understand the unconscious as a “sedimented practical schema” of subjective being in the world. This sedimented unconscious contributes to the way we implicitly interpret reality, fill in the gaps of uncertainty, and invest our social interactions with meaning. Husserl, however, approaches the unconscious in terms of affective non-vivacity, as a sphere of sedimentation and the horizon of the distant past which stays affectively connected to the living present. Drawing on these ideas, I argue that these two accounts can reinforce one another and provide the ground for a phenomenological understanding of the unconscious in terms of the horizontal dimension of subjective experience and a non-representational relation to the past. (shrink)

An uncertainty report describes the extent of an agent’s uncertainty about some matter. We identify two basic requirements for uncertainty reports, which we call faithfulness and completeness. We then discuss two pitfalls of uncertainty assessment that often result in reports that fail to meet these requirements. The first involves adopting a one-size-fits-all approach to the representation of uncertainty, while the second involves failing to take account of the risk of surprises. In connection with the latter, (...) we respond to the objection that it is impossible to account for the risk of genuine surprises. After outlining some steps that both scientists and the bodies who commission uncertainty assessments can take to help avoid these pitfalls, we explain why striving for faithfulness and completeness is important. (shrink)

This chapter responds to Michael Tamir and Elay Shech’s chapter “Understanding from Deep Learning Models in Context.”.

Drawing from field theory, Gestalt therapy conceives psychological suffering and psychotherapy as two intentional field phenomena, where unprocessed and chaotic experiences seek the opportunity to emerge and be assimilated through the contact between the patient and the therapist (i.e., the intentionality of contacting). This therapeutic approach is based on the therapist’s aesthetic experience of his/her embodied presence in the flow of the healing process because (1) the perception of beauty can provide the therapist with feedback on the assimilation of unprocessed (...) experiences; (2) the therapist’s attentional focus on intrinsic aesthetic diagnostic criteria can facilitate the modification of rigid psychopathological fields by supporting the openness to novel experiences. The aim of the present manuscript is to review recent evidence from psychophysiology, neuroaesthetic research, and neurocomputational models of cognition, such as the free energy principle (FEP), which support the notion of the therapeutic potential of aesthetic sensibility in Gestalt psychotherapy. Drawing from neuroimaging data, psychophysiology and recent neurocognitive accounts of aesthetic perception, we propose a novel interpretation of the sense of beauty as a self-generated reward motivating us to assimilate an ever-greater spectrum of sensory and affective states in our predictive representation of ourselves and the world and supporting the intentionality of contact. Expecting beauty, in the psychotherapeutic encounter, can help therapists tolerate uncertainty avoiding impulsive behaviours and to stay tuned to the process of change. (shrink)

Purpose Uncertainty is an under-respected issue when it comes to automatic assessment of human emotion by machines. The purpose of this paper is to highlight the existent approaches towards such measurement of uncertainty, and identify further research need. Design/methodology/approach The discussion is based on a literature review. Findings Technical solutions towards measurement of uncertainty in automatic emotion recognition exist but need to be extended to respect a range of so far underrepresented sources of uncertainty. These then (...) need to be integrated into systems available to general users. Research limitations/implications Not all sources of uncertainty in automatic emotion recognition including emotion representation and annotation can be touched upon in this communication. Practical implications AER systems shall be enhanced by more meaningful and complete information provision on the uncertainty underlying their estimates. Limitations of their applicability should be communicated to users. Social implications Users of automatic emotion recognition technology will become aware of their limitations, potentially leading to a fairer usage in crucial application context. Originality/value There is no previous discussion including the technical view point on extended uncertainty measurement in automatic emotion recognition. (shrink)

In this paper I argue that two domains of uncertainty should inform our strategies for making social policy on new genetic technologies. The first is biological complexity, which includes both unknown consequences on known variables and unknown unknowns. The second is value pluralism, which includes both moral conflict and moral pluralism. This framework is used to investigate policy on genetically modified food and suggests that adaptive management is required to track changes in biological knowledge of these interventions and that (...) less simplistic, polemic representations of scientific knowledge are required to permit democratic decision making. (shrink)

Most nonmonotonic logics are assumed to be cumulative, which is often regarded as the minimum requirement for a logic. We argue that cumulativity, in particular, cumulative transitivity can be abandoned, in order to better characterize reasoning in uncertainty. But giving up cumulative transitivity makes it hard to obtain representation results for these logics. Borrowing the idea from strict-tolerant logics, we give some representation results for nonmonotonic logics that are not cumulatively transitive.

How ought you to evaluate your options if you’re uncertain about which axiology is true? One prominent response is Expected Moral Value Maximisation, the view that under axiological uncertainty, an option is better than another if and only if it has the greater expected moral value across axiologies. EMVM raises two fundamental questions. First, there’s a question about what it should even mean. In particular, it presupposes that we can compare moral value across axiologies. So to even understand EMVM, (...) we need to explain what it is for such comparisons to hold. Second, assuming that we understand it, there’s a question about whether EMVM is true. Since there are many plausible rivals, we need an argument to defend it. In this paper, I’ll introduce a representation theorem for axiological uncertainty to answer these two questions. Roughly, the theorem shows that if all our axiologies satisfy the von Neumann–Morgenstern axioms, and if the facts about which options are better than which in light of your uncertainty also satisfy these axioms as well as a Pareto condition, then these facts have a relevantly unique expected utility representation. If I’m right, this theorem at once affords us a compelling way to understand EMVM—and specifically intertheoretic comparisons—and a systematic argument for its truth. (shrink)

The concept of time discounting introduces weights on future goods to make these less valu- able. Famously, both the specic functional form of time discounting and its normative sta- tus are contested. To address these problems, this paper provides a measurement-theoretic framework of representation for time discounting. The general representation theorem char- acterises time discounting factors as ratio-scale representations of dierences in temporally extended prospects. This framework of representation is used to reconsider interpretations of time discounting factors such as time (...) preferences, uncertainty and preference change. It also allows to compare these interpretations with regards to their normative appeal, the kinds of reductionism regarding time and preference they imply and the specic functional form of time discounting they suggest. Farther, multiple-self interpretations of decision-makers become available, such that a time discounting factor represents the degree of connectedness between temporal selves in a person. (shrink)

This paper axiomatizes a recursive utility model that captures both intertemporal utility smoothing defined across time and ambiguity aversion defined over states. The resulting representation adapts Wakai model of intertemporal utility smoothing as an aggregator function, where the utility of the certainty equivalent of future uncertainty is computed by Gilboa and Schmeidler multiple-priors utility. The model also permits the separation of intertemporal utility smoothing from ambiguity aversion.

The book contains a collection of eight survey papers written by some of the best researchers in foundations of knowledge representation and reasoning. It covers topics like theories of uncertainty, nonmonotonic and causal reasoning, logic programming, abduction, inductive logic programming, description logics, complexity in Artificial Intelligence, and model-based diagnosis. It thus provides an up-to-date coverage of recent approaches to some of the most challenging problems underlying knowledge representation and Artificial Intelligence in general.

The book contains a collection of eight survey papers written by some of the most excellent researchers in foundations of knowledge representation and reasoning. It covers topics like theories of uncertainty, nonmonotonic and causal reasoning, logic programming, abduction, inductive logic programming, description logics, complexity in Artificial Intelligence, and model based diagnosis. It thus provides an up-to-date coverage of recent approaches to some of the most challenging problems underlying knowledge representation and Artificial Intelligence in general.

Hierarchical models are commonly used for modelling uncertainty. They arise whenever there is a `correct' or `ideal' uncertainty model but the modeller is uncertain about what it is. Hierarchical models which involve probability distributions are widely used in Bayesian inference. Alternative models which involve possibility distributions have been proposed by several authors, but these models do not have a clear operational meaning. This paper describes a new hierarchical model which is mathematically equivalent to some of the earlier, possibilistic (...) models and also has a simple behavioural interpretation, in terms of betting rates concerning whether or not a decision maker will agree to buy or sell a risky investment for a specified price. We give a representation theorem which shows that any consistent model of this kind can be interpreted as a model for uncertainty about the behaviour of a Bayesian decision maker. We describe how the model can be used to generate buying and selling prices and to make decisions. (shrink)

Conviction Narrative Theory (CNT) is a theory of choice underradical uncertainty– situations where outcomes cannot be enumerated and probabilities cannot be assigned. Whereas most theories of choice assume that people rely on (potentially biased) probabilistic judgments, such theories cannot account for adaptive decision-making when probabilities cannot be assigned. CNT proposes that people usenarratives– structured representations of causal, temporal, analogical, and valence relationships – rather than probabilities, as the currency of thought that unifies our sense-making and decision-making faculties. According to (...) CNT, narratives arise from the interplay between individual cognition and the social environment, with reasoners adopting a narrative that feels “right” to explain the available data; using that narrative to imagine plausible futures; and affectively evaluating those imagined futures to make a choice. Evidence from many areas of the cognitive, behavioral, and social sciences supports this basic model, including lab experiments, interview studies, and econometric analyses. We identify 12 propositions to explain how the mental representations (narratives) interact with four inter-related processes (explanation, simulation, affective evaluation, and communication), examining the theoretical and empirical basis for each. We conclude by discussing how CNT can provide a common vocabulary for researchers studying everyday choices across areas of the decision sciences. (shrink)

In many real-world gambles, a non-trivial amount of time passes before the uncertainty is resolved but after a choice is made. An individual may have a preference between gambles with identical probability distributions over final outcomes if they differ in the timing of resolution of uncertainty. In this domain, utility consists not only of the consumption of outcomes, but also the psychological utility induced by an unresolved gamble. We term this utility anxiety. Since a reflective decision maker may (...) want to include anxiety explicitly in analysis of unresolved lotteries, a multiple-outcome model for evaluating lotteries with delayed resolution of uncertainty is developed. The result is a rank-dependent utility representation (e.g., Quiggin, 1982), in which period weighting functions are related iteratively. Substitution rules are proposed for evaluating compound temporal lotteries. The representation is appealing for a number of reasons. First, probability weights can be interpreted as the cognitive attention allocated to certain outcomes. Second, the model disaggregates strength of preference from temporal risk aversion and thus provides some insight into the old debate about the relationship between von Neumann–Morgenstern utility functions and strength of preference value functions. (shrink)

Measurement is said to be the basis of exact sciences as the process of assigning numbers to matter (things or their attributes), thus making it possible to apply the mathematically formulated laws of nature to the empirical world. Mathematics and empiria are best accorded to each other in laboratory experiments which function as what Nancy Cartwright calls nomological machine: an arrangement generating (mathematical) regularities. On the basis of accounts of measurement errors and uncertainties, I will argue for two claims: 1) (...) Both fundamental laws of physics, corresponding to ideal nomological machine, and phenomenological laws, corresponding to material nomological machine, lie, being highly idealised relative to the empirical reality; and also laboratory measurement data do not describe properties inherent to the world independently of human understanding of it. 2) Therefore the naive, representational view of measurement and experimentation should be replaced with a more pragmatic or practice-based view. (shrink)

An approach to describing risk analysis, risk perception and risk interpretation under a single umbrella starting with a general definition of risk as "adverse consequences under uncertainty." The idea of risk representation is introduced as an omnibus term for many different ways of conceptualizing risk and deploying risk messages in science, government or society.

Five studies replicate and extend recent experimental findings on a divergence between theoretical and subjectively-experienced decision freedom. While conditions like conflict, uncertainty, or com...

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.