There is a plethora of confirmation measures in the literature. Zalabardo considers four such measures: PD, PR, LD, and LR. He argues for LR and against each of PD, PR, and LD. First, he argues that PR is the better of the two probability measures. Next, he argues that LR is the better of the two likelihood measures. Finally, he argues that LR is superior to PR. I set aside LD and focus on the trio of PD, PR, and (...) LR. The question I address is whether Zalabardo succeeds in showing that LR is superior to each of PD and PR. I argue that the answer is negative. I also argue, though, that measures such as PD and PR, on one hand, and measures such as LR, on the other hand, are naturally understood as explications of distinct senses of confirmation. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Zalabardo focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by the likelihood ratio measure but not by any of (...) the other three measures. Glass and McCartney, hereafter “G&M,” accept the conclusion of Zalabardo’s argument along with each of the premises in it. They nonetheless try to improve on Zalabardo’s argument by replacing his third adequacy condition with a weaker condition. They do this because of a worry to the effect that Zalabardo’s third adequacy condition runs counter to the idea behind his first adequacy condition. G&M have in mind confirmation in the sense of increase in probability: the degree to which E confirms H is a matter of the degree to which E increases H’s probability. I call this sense of confirmation “IP.” I set out four ways of precisifying IP. I call them “IP1,” “IP2,” “IP3,” and “IP4.” Each of them is based on the assumption that the degree to which E increases H’s probability is a matter of the distance between p and a certain other probability involving H. I then evaluate G&M’s argument in light of them. (shrink)

Peter Achinstein has argued at length and on many occasions that the view according to which evidential support is defined in terms of probability-raising faces serious counterexamples and, hence, should be abandoned. Proponents of the positive probabilistic relevance view have remained unconvinced. The debate seems to be in a deadlock. This paper is an attempt to move the debate forward and revisit some of the central claims within this debate. My conclusion here will be that while Achinstein may be (...) right that his counterexamples undermine probabilistic relevance views of what it is for e to be evidence that h, there is still room for a defence of a related probabilistic view about an increase in being supported, according to which, if p > p, then h is more supported given e than it is without e. My argument relies crucially on an insight from recent work on the linguistics of gradable adjectives. (shrink)

Peter Achinstein has argued at length and on many occasions that the view according to which evidential support is defined in terms of probability-raising faces serious counterexamples and, hence, should be abandoned. Proponents of the positive probabilistic relevance view have remained unconvinced. The debate seems to be in a deadlock. This paper is an attempt to move the debate forward and revisit some of the central claims within this debate. My conclusion here will be that while Achinstein may be (...) right that his counterexamples undermine probabilistic relevance views of what it is for e to be evidence that h, there is still room for a defence of a related probabilistic view about an increase in being supported, according to which, if p > p, then h is more supported given e than it is without e. My argument relies crucially on an insight from recent work on the linguistics of gradable adjectives. (shrink)

Evidential support is often equated with confirmation, where evidence supports hypothesis H if and only if it increases the probability of H. This article argues against this received view. As the author shows, support is a comparative notion in the sense that increase-in-probability is not. A piece of evidence can confirm H, but it can confirm alternatives to H to the same or greater degree; and in such cases, it is at best misleading to conclude that the (...) evidence supports H. The author puts forward an alternative view that defines support in terms of measures of degree of confirmation. The proposed view is both sufficiently comparative and able to accommodate the increase-in-probability aspect of support. The author concludes that the proposed measure-theoretic approach to support provides a superior alternative to the standard confirmatory approach. (shrink)

Psychologists and philosophers who pose moral dilemmas to understand moral judgment typically specify outcomes as certain to occur in them. This contrasts with real-life moral decision-making, which is almost always infused with probabilities (e.g., the probability of a given outcome if an action is or is not taken). Seven studies examine sensitivity to the size and location of shifts in probabilities of outcomes that would result from action in moral dilemmas. We find that moral judgments differ between actions that (...) result in an equal increase in probability of harm (equal size), but have different end-states (e.g., an increase in harm probability from 25% to 50% or from 50% to 75%). This deviation from expected value is robust under separate evaluation, and increases when the comparison between shifts is made explicit under simultaneous evaluation. Consistent with the centrality of perceived harm in some models of moral judgment, perceived harm partially mediates sensitivity to location of harm probability shift. Unlike for shifts in harm probabilities, participants are insensitive to the location of shifts in probability of beneficial outcomes. They are also insensitive to the location of shifts in probability of analogous monetary losses and gains, suggesting an asymmetry between harm and benefit in moral reasoning, as well as an asymmetry between moral and monetary decision-making more broadly. Implications for normative philosophical theory and moral psychological theory, as well as practical applications, are discussed. (shrink)

We examine change across U.S. cohorts born between 1920 and 2000 in their probability of having had sex with same-sex partners in the last year and since age 18. Using data from the 1988–2018 General Social Surveys, we explore how trends differ by gender, race, and class background. We find steep increases across birth cohorts in the proportion of women who have had sex with both men and women since age 18, whereas increases for men are less steep. We (...) suggest that the trends reflect an increasingly accepting social climate, and that women’s steeper trend is rooted in a long-term asymmetry in gender change, in which nonconformity to gender norms is more acceptable for women than men. We also find evidence that, among men, the increase in having had sex with both men and women was steeper for black than for white men, and for men of lower socioeconomic status; we speculate that the rise of mass incarceration among less privileged men may have influenced this trend. (shrink)

What is required for an action to promote the satisfaction of a desire? We reject extant answers and propose an alternative. Our account differs from competing answers in two ways: first, it is contrastive, in that actions promote the satisfaction of desires only as contrasted with other possible actions. Second, it employs a notion of expected fit between desire and world, defined as the weighted sum of the fit between the desire and the world in all possible outcomes, where each (...) weight is given by the probability of the agent’s obtaining the relevant outcome. According to our proposal, then, an action promotes a desire when the expected fit for the desire given that the agent performs the action is greater than the expected fit of the desire given that the agent performs the contrasting action. We highlight this account’s attractive features and explain how it improves on its competitors. (shrink)

For a finite universe of discourse, if Φ → and ~(Ψ → Φ) , then P(Ψ) > P(Φ), i.e., there is always a loss of information, there is an increase in probability, in a non reversible implication. But consider the two propositions, "All ravens are black", (i.e., "(x)(Rx ⊃ Bx)"), and "Some ravens are black" (i.e., "(∃x)(Rx & Bx)"). In a world of one individual, called "a", these two propositions are equivalent to "~Ra ∨ Ba" and "Ra & (...) Ba" respectively. However, (Ra & Ba) → (~Ra ∨ Ba) and ~[(~Ra ∨ Ba) → (Ra & Ba)]. Consequently, in a world of one individual it is more probable that all ravens are black than that some ravens are black! (shrink)

In a quantum universe with a strong arrow of time, it is standard to postulate that the initial wave function started in a particular macrostate---the special low-entropy macrostate selected by the Past Hypothesis. Moreover, there is an additional postulate about statistical mechanical probabilities according to which the initial wave function is a ''typical'' choice in the macrostate. Together, they support a probabilistic version of the Second Law of Thermodynamics: typical initial wave functions will increase in entropy. Hence, there are (...) two sources of randomness in such a universe: the quantum-mechanical probabilities of the Born rule and the statistical mechanical probabilities of the Statistical Postulate. I propose a new way to understand time's arrow in a quantum universe. It is based on what I call the Thermodynamic Theories of Quantum Mechanics. According to this perspective, there is a natural choice for the initial quantum state of the universe, which is given by not a wave function but by a density matrix. The density matrix plays a microscopic role: it appears in the fundamental dynamical equations of those theories. The density matrix also plays a macroscopic / thermodynamic role: it is exactly the projection operator onto the Past Hypothesis subspace. Thus, given an initial subspace, we obtain a unique choice of the initial density matrix. I call this property "the conditional uniqueness" of the initial quantum state. The conditional uniqueness provides a new and general strategy to eliminate statistical mechanical probabilities in the fundamental physical theories, by which we can reduce the two sources of randomness to only the quantum mechanical one. I also explore the idea of an absolutely unique initial quantum state, in a way that might realize Penrose's idea of a strongly deterministic universe. (shrink)

Studies investigating compliance-gaining procedures have shown that the feeling that someone is free to comply or not with a request is a requirement to obtain compliance. In this study, participants were asked for money for a charitable organization. In the experimental condition, people first heard a sentence saying that they would probably refuse to help, and then they were asked to make a donation. In the control condition, participants were just asked for money. Findings showed that more participants complied with (...) the request in the experimental condition. Reactance theory was used to explain these results. (shrink)

The contributions to this special collection concern issues and problems discussed in or related to the work of Wesley C. Salmon. Salmon has long been noted for his important work in the philosophy of science, which has included research on the interpretation of probability, the nature of explanation, the character of reasoning, the justification of induction, the structure of space/time and the paradoxes of Zeno, to mention only some of the most prominent. During a time of increasing preoccupation with (...) historical and sociological approaches to under standing science (which characterize scientific developments as though they could be adequately analysed from the perspective of political movements, even mistaking the phenomena of conversion for the rational appraisal of scientific theories), Salmon has remained stead fastly devoted to isolating and justifying those normative standards distinguishing science from non-science - especially through the vindi cation of general principles of scientific procedure and the validation of specific examples of scientific theories - without which science itself cannot be (even remotely) adequately understood. In this respect, Salmon exemplifies and strengthens a splendid tradi tion whose most remarkable representatives include Hans Reichenbach, Rudolf Carnap and Carl G. Hempel, all of whom exerted a profound influence upon his own development. (shrink)

The contributions to this special collection concern issues and problems discussed in or related to the work of Wesley C. Salmon. Salmon has long been noted for his important work in the philosophy of science, which has included research on the interpretation of probability, the nature of explanation, the character of reasoning, the justification of induction, the structure of space/time and the paradoxes of Zeno, to mention only some of the most prominent. During a time of increasing preoccupation with (...) historical and sociological approaches to under standing science (which characterize scientific developments as though they could be adequately analysed from the perspective of political movements, even mistaking the phenomena of conversion for the rational appraisal of scientific theories), Salmon has remained stead fastly devoted to isolating and justifying those normative standards distinguishing science from non-science - especially through the vindi cation of general principles of scientific procedure and the validation of specific examples of scientific theories - without which science itself cannot be (even remotely) adequately understood. In this respect, Salmon exemplifies and strengthens a splendid tradi tion whose most remarkable representatives include Hans Reichenbach, Rudolf Carnap and Carl G. Hempel, all of whom exerted a profound influence upon his own development. (shrink)

It is increasingly common in cognitive science and philosophy of perception to regard perceptual processing as a probabilistic engine, taking into account uncertainty in computing representations of the distal environment. Models of this kind often postulate probabilistic representations, or what we will call probabilistic states,. These are states that in some sense mark or represent information about the probabilities of distal conditions. It has also been argued that perceptual experience itself in some sense represents uncertainty (Morrison _Analytic Philosophy_ 57 (1): (...) 15 48, 2016 ). In this article, we will first consider three models of sensory activity from perceptual neuroscience, namely signal detection theory (SDT), probabilistic population codes (PPC), and sampling. We will then reflect on the sense in which the probabilistic states introduced in these models are probabilistic representations. To sharpen this discussion, we will compare and contrast these probabilistic states to credences as they are understood in epistemology. We will suggest that probabilistic representation, in an appropriately robust sense, can be understood as a form of analog representation. In the last part of the paper, we apply this to the issue of whether conscious experience represents uncertainty—we will interpret this as the claim that there are phenomenal features of experience that serve as analog probabilistic representations. (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)

Many groups make decisions over multiple interconnected propositions. The “doctrinal paradox” or “discursive dilemma” shows that propositionwise majority voting can generate inconsistent collective sets of judgments, even when individual sets of judgments are all consistent. I develop a simple model for determining the probability of the paradox, given various assumptions about the probability distribution of individual sets of judgments, including impartial culture and impartial anonymous culture assumptions. I prove several convergence results, identifying when the probability of the (...) paradox converges to 1, and when it converges to 0, as the number of individuals increases. Drawing on the Condorcet jury theorem and work by Bovens and Rabinowicz , I use the model to assess the “truth-tracking” performance of two decision procedures, the premise- and conclusion-based procedures. I compare the present results with existing results on the probability of Condorcet’s paradox. I suggest that the doctrinal paradox is likely to occur under plausible conditions. (shrink)

We present a model for studying communities of epistemically interacting agents who update their belief states by averaging the belief states of other agents in the community. The agents in our model have a rich belief state, involving multiple independent issues which are interrelated in such a way that they form a theory of the world. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that (...) end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. It is shown that, under the assumptions of our model, an agent always has a probability of less than 2% of ending up in an inconsistent belief state. Moreover, this probability can be made arbitrarily small by increasing the number of independent issues the agents have to judge or by increasing the group size. A real-world situation to which this model applies is a group of experts participating in a Delphi-study. (shrink)

A diagnostic judgment of a teacher can be seen as an inference from manifest observable evidence on a student’s behavior to his or her latent traits. This can be described by a Bayesian model of in-ference: The teacher starts from a set of assumptions on the student (hypotheses), with subjective probabilities for each hypothesis (priors). Subsequently, he or she uses observed evidence (stu-dents’ responses to tasks) and knowledge on conditional probabilities of this evidence (likelihoods) to revise these assumptions. Many systematic (...) deviations from this model (biases, e.g. base-rate neglect, inverse fallacy) are reported in literature on Bayesian reasoning. In a teacher’s situation the information (hypotheses, priors, likelihoods) is usually not explicitly represented numerically (as in most research on Bayesian reasoning), but only by qualitative esti-mations in the mind of the teacher. In our study, we ask to which extent individuals (approximately) apply a rational Bayesian strategy or resort on other biased strategies of processing information for their diagnostic judgments. We explicitly pose this question with respect to non-numerical settings. To investigate this question, we developed a scenario that visually displays all relevant information (hypotheses, priors, likelihoods) in a graphically displayed hypothesis space (called “hypothegon”) – without recurring to numerical representations or mathematical procedures. 42 pre-service teach-ers were asked to judge the plausibility of different misconceptions of six students based on their responses to decimal comparison tasks (e.g. 3.39 > 3.4). Applying a Bayesian classification proce-dure, we identified three updating strategies: A Bayesian update strategy (BUS, processing all probabilities), a combined evidence strategy (CES, ignoring the prior probabilities but including all likelihoods), and a single evidence strategy (SES, only using the likelihood of the most probable hypothesis). In study 1, an instruction on the relevance of using all probabilities (priors and likelihoods) only weakly increased the processing of more information. In study 2, we found strong evidence that a visual explication of the prior-likelihood interaction led to an increase of processing the interaction of all relevant information. These results show that the phenomena found in general research on Bayesian reasoning in numerical settings extend to diagnostic judgments in non-numerical settings. (shrink)

Notions of probability and uncertainty have been increasingly prominant in modern economics. This book considers the philosophical and practical difficulties inherent in integrating these concepts into realistic economic situations. It outlines and evaluates the major developments, indicating where further work is needed. This book addresses: * probability, utility and rationality within current economic thought and practice * concepts of ignorance and indeterminancy * experimental economics * econometrics, with particular reference inference and estimation.

Markov models of evolution describe changes in the probability distribution of the trait values a population might exhibit. In consequence, they also describe how entropy and conditional entropy values evolve, and how the mutual information that characterizes the relation between an earlier and a later moment in a lineage’s history depends on how much time separates them. These models therefore provide an interesting perspective on questions that usually are considered in the foundations of physics—when and why does entropy (...) class='Hi'>increase and at what rates do changes in entropy take place? They also throw light on an important epistemological question: are there limits on what your observations of the present can tell you about the evolutionary past? (shrink)

Two-stage voting is prone to majority inversions, a situation in which the outcome of an election is not backed by a majority of popular votes. We study the probability of majority inversion in a model with two candidates, three states and uniformly distributed fractions of supporters for each candidate. The model encompasses equal or distinct population sizes, with equal, population-based or arbitrary voting weights in the second stage. We prove that, when no state can dictate the outcome of the (...) election by commanding a voting weight in excess of one half, the probability of majority inversion increases with the size disparity among the states. (shrink)

Science aims at the discovery of general principles of special kinds that are applicable for the explanation and prediction of the phenomena of the world in the form of theories and laws. When the phenomena themselves happen to be general, the principlesinvolved assume the form of theories; and when they are p- ticular, they assume the form of general laws. Theories themselves are sets of laws and de nitions that apply to a common domain, which makes laws indispensable to science. (...) Understanding science thus depends upon understanding the nature of theories and laws, the logical structure of explanations and predictions based upon them, and the principles of inference and decision that apply to theories and laws. Laws and theories can differ in their form as well as in their content. The laws of quantum mechanics are indeterministic, for example, while those of classical mechanics are deterministic instead. The history of science re ects an increasing role for probabilities as properties of the world but also as measures of evidential support and as degrees of subjective belief. Our purpose is to clarify and illuminate the place of probability in science. (shrink)

For more than 20 years, research has proven the beneficial effect of natural frequencies when it comes to solving Bayesian reasoning tasks (Gigerenzer & Hoffrage, 1995). In a recent meta-analysis, McDowell & Jacobs (2017) showed that presenting a task in natural frequency format increases performance rates to 24% compared to only 4% when the same task is presented in probability format. Nevertheless, on average three quarters of participants in their meta-analysis failed to obtain the correct solution for such a (...) task in frequency format. In this paper, we present an empirical study on what participants typically do wrong when confronted with natural frequencies. We found that many of them did not actually use natural frequencies for their calculations, but translated them back into complicated probabilities instead. This switch from the intuitive presentation format to a less intuitive calculation format will be discussed within the framework of psychological theories (e.g., the Einstellung effect). (shrink)

The response mode bias, in which subjects exhibit different risk attitudes when assessing certainty equivalents versus indifference probabilities, is a well-known phenomenon in the assessment of utility functions. In this empirical study, we develop and apply a cardinal measure of risk attitudes to analyze not only the existence, but also the strength of this phenomenon. Since probability levels involved in decision problems are already known to have a strong impact on behavior, we use this approach to study the impact (...) of probabilities on the extent of the response mode bias. We find that the direction in which probabilities influence measured risk aversion is the opposite in the certainty equivalence (CE) method versus in the probability equivalence (PE) method. Utilizing the CE elicitation approach leads to an increase of risk seeking for gambles involving high probabilities. For the PE method, subjects tend to behave risk averse with gambles of high probabilities. This behavior is reversed in the gain domain. This “tailwhip” effect is consistently replicated in several experiments, involving both loss and gain domains of lotteries. (shrink)

Although memories are more retrievable if observers’ emotional states are consistent between encoding and retrieval, it is unclear whether the consistency of emotional states increases the likelihood of successful memory retrieval, the precision of retrieved memories, or both. The present study tested visual long-term memory for everyday objects while consistent or inconsistent emotional contexts between encoding and retrieval were induced using background grey-scale images from the International Affective Picture System. In the study phase, participants remembered colours of sequentially presented objects (...) in a negative or positive context. In the test phase, participants estimated the colours of previously studied objects in either negative versus neutral or positive versus neutral contexts. Note, IAPS images in the test phase were always visually different from those initially paired with the studied objects. We found that reinstating negative context and positive context at retrieval resulted in better mnemonic precision and a higher probability of successful retrieval, respectively. Critically, these effects could not be attributed to a negative or positive context at retrieval alone. Together, these findings demonstrated dissociable effects of emotion on the quantitative and qualitative aspects of visual long-term memory retrieval. (shrink)

It was Hume's concept of knowledge that marked Masaryk's philosophy more than influential Kant. Masaryk devoted Hume his inaugural lecture The Probability Calculus and Hume's Scepticism at Prague University in 1882. He tried to face his scepticism concerning causation and induction by a formula P = n: or P = : where P means the increasing probability that an event that had happened n times in the past will happen again. Hume stresses that there is an essential difference (...) between probability and certainty, and we have no logical reason to presuppose that the past experience is legitimate for expectation that the future will resemble to the past. Only our belief, not knowledge, leads us to that. Although Masaryk did not accept Hume's scepticism, he had deep understanding for his way of thinking. Reflection of Hume's influence on Masaryk in Czech philosophy is unsatisfactory, which is stated in this article. (shrink)

In management research, theory testing confronts a paradox described by Meehl in which designing studies with greater methodological rigor puts theories at less risk of falsification. This paradox exists because most management theories make predictions that are merely directional, such as stating that two variables will be positively or negatively related. As methodological rigor increases, the probability that an estimated effect will differ from zero likewise increases, and the likelihood of finding support for a directional prediction boils down to (...) a coin toss. This paradox can be resolved by developing theories with greater precision, such that their propositions predict something more meaningful than deviations from zero. This article evaluates the precision of theories in management research, offers guidelines for making theories more precise, and discusses ways to overcome barriers to the pursuit of theoretical precision. (shrink)

Research suggests that moral evaluations change during adulthood. Older adults (75+) tend to judge accidentally harmful acts more severely than younger adults do, and this age‐related difference is in part due to the greater negligence older adults attribute to the accidental harmdoers. Across two studies (N = 254), we find support for this claim and report the novel discovery that older adults’ increased attribution of negligence, in turn, is associated with a higher perceived likelihood that the accident would occur. We (...) propose that, because older adults perceive accidents as more likely than younger adults do, they condemn the agents and their actions more and even infer that the agents’ omission to exercise due care is intentional. These findings refine our understanding of the cognitive processes underpinning moral judgment in older adulthood and highlight the role of subjective probability judgments in negligence attribution. (shrink)

Bayesian confirmation theory is rife with confirmation measures. Many of them differ from each other in important respects. It turns out, though, that all the standard confirmation measures in the literature run counter to the so-called “Reverse Matthew Effect” (“RME” for short). Suppose, to illustrate, that H1 and H2 are equally successful in predicting E in that p(E | H1)/p(E) = p(E | H2)/p(E) > 1. Suppose, further, that initially H1 is less probable than H2 in that p(H1) < p(H2). (...) Then by RME it follows that the degree to which E confirms H1 is greater than the degree to which it confirms H2. But by all the standard confirmation measures in the literature, in contrast, it follows that the degree to which E confirms H1 is less than or equal to the degree to which it confirms H2. It might seem, then, that RME should be rejected as implausible. Festa (2012), however, argues that there are scientific contexts in which RME holds. If Festa’s argument is sound, it follows that there are scientific contexts in which none of the standard confirmation measures in the literature is adequate. Festa’s argument is thus interesting, important, and deserving of careful examination. I consider five distinct respects in which E can be related to H, use them to construct five distinct ways of understanding confirmation measures, which I call “Increase in Probability”, “Partial Dependence”, “Partial Entailment”, “Partial Discrimination”, and “Popper Corroboration”, and argue that each such way runs counter to RME. The result is that it is not at all clear that there is a place in Bayesian confirmation theory for RME. (shrink)

Wilcox proposed an argument against imprecise probabilities and for the principle of indifference based on a thought experiment where he argues that it is very intuitive to feel that one’s confidence in drawing a ball of a given colour out of an unknown urn should decrease while the number of potential colours in the urn increases. In my response to him, I argue that one’s intuitions may be unreliable because it is very hard to truly feel completely ignorant in such (...) a situation. I further argue that Wilcox must also account for the conflicting intuition that it is absurd to have to feel completely convinced that a specific claim about reality is true _in the absence of any evidence_ in order to avoid being irrational. It is dubious that this intuition is considerably less universal and strongly-held than Wilcox’s own intuition. Finally, I point out that even if Wilcox’s intuition were to be universally shared among members of our biological species, it is far from being clear that someone refusing to let that intuition dictate his or her beliefs would be irrational. For all these reasons, I believe that Wilcox was not successful in proving that philosophers and scientists representing uncertainty through imprecise probabilities are violating the principles of rationality. (shrink)

Subjective probability plays an increasingly important role in many fields concerned with human cognition and behavior. Yet there have been significant criticisms of the idea that probabilities could actually be represented in the mind. This paper presents and elaborates a view of subjective probability as a kind of sampling propensity associated with internally represented generative models. The resulting view answers to some of the most well known criticisms of subjective probability, and is also supported by empirical work (...) in neuroscience and behavioral psychology. The repercussions of the view for how we conceive of many ordinary instances of subjective probability, and how it relates to more traditional conceptions of subjective probability, are discussed in some detail. (shrink)

Relations between physics and biology have been always difficult. One reason is that physical approaches to the phenomena of life have frequently been conceived by their authors as alternatives to biological explanations. My argument is that molecular descriptions and explanations have been pushed so far that they have reached their limits: these limits constitute a favourable niche in which physical explanations can develop. I will focus on the field of molecular and cell biology and give many examples of these recent (...) physical studies made possible by the precision of molecular observations. The nature of these niches is probably diverse. I consider that it is too early to have a global view of the interactions between biological and physical explanations, and to organize them into different categories. Such interactions are not new within the life sciences: the history of biology reveals a complex, permanently moving landscape of interactions between biological and physical explanations. (shrink)

China has long enjoyed its position as the world's cheapest production country. However, this position is being shaken due to the increasingly rising costs in China in pace with China's rapid economic development. China's New Labour Contract Law which took effect from 1 January 2008 has further pushed the labour costs in China in general. The purpose of this article is to arrive at an in-depth understanding of why foreign firms conduct sourcing in China where sourcing is becoming increasingly expensive. (...) The experiences of four Swedish companies in the textile and clothing industry (TCI) conducting sourcing in China are presented. Our findings show that sourcing in China is becoming both cost-and strategy-driven. Companies purely chasing the cheapest production would most probably consider leaving China, whereas companies with a long-term strategic intent and a high level of business ethics and corporate social responsibility (CSR) practices will retain all or most of their sourcing activities on the Chinese soil despite the rising costs. (shrink)

The University of Michigan conference “Where Religion, Policy, and Bioethics Meet: An Interdisciplinary Conference on Islamic Bioethics and End-of-Life Care” in April 2011 addressed the issue of brain death as the prototype for a discourse that would reflect the emergence of Islamic bioethics as a formal field of study. In considering the issue of brain death, various Muslim legal experts have raised concerns over the lack of certainty in the scientific criteria as applied to the definition and diagnosis of brain (...) death by the medical community. In contrast, the medical community at large has not required absolute certainty in its process, but has sought to eliminate doubt through cumulative diagnostic modalities and supportive scientific evidence. This has recently become a principal model, with increased interest in data analysis and evidence-based medicine with the intent to analyze and ultimately improve outcomes. Islamic law has also long employed a systematic methodology with the goal of eliminating doubt from rulings regarding the question of certainty. While ample criticism of the scientific criteria of brain death (Harvard criteria) by traditional legal sources now exists, an analysis of the legal process in assessing brain death, geared toward informing the clinician’s perspective on the issue, is lacking. In this article, we explore the role of certainty in the diagnostic modalities used to establish diagnoses of brain death in current medical practice. We further examine the Islamic jurisprudential approach vis-à-vis the concept of certainty (yaqīn). Finally, we contrast the two at times divergent philosophies and consider what each perspective may contribute to the global discourse on brain death, understanding that the interdependence that exists between the theological, juridical, ethical, and medical/scientific fields necessitates an open discussion and active collaboration between all parties. We hope that this article serves to continue the discourse that was successfully begun by this initial interdisciplinary endeavor at the University of Michigan. (shrink)

It is well known that classical, aka ‘sharp’, Bayesian decision theory, which models belief states as single probability functions, faces a number of serious difficulties with respect to its handling of agnosticism. These difficulties have led to the increasing popularity of so-called ‘imprecise’ models of decision-making, which represent belief states as sets of probability functions. In a recent paper, however, Adam Elga has argued in favour of a putative normative principle of sequential choice that he claims to be (...) borne out by the sharp model but not by any promising incarnation of its imprecise counterpart. After first pointing out that Elga has fallen short of establishing that his principle is indeed uniquely borne out by the sharp model, I cast aspersions on its plausibility. I show that a slight weakening of the principle is satisfied by at least one, but interestingly not all, varieties of the imprecise model and point out that Elga has failed to motivate his stronger commitment. (shrink)

Epistemic closure under known implication is the principle that knowledge of "p" and knowledge of "p implies q", together, imply knowledge of "q". This principle is intuitive, yet several putative counterexamples have been formulated against it. This paper addresses the question, why is epistemic closure both intuitive and prone to counterexamples? In particular, the paper examines whether probability theory can offer an answer to this question based on four strategies. The first probability-based strategy rests on the accumulation of (...) risks. The problem with this strategy is that risk accumulation cannot accommodate certain counterexamples to epistemic closure. The second strategy is based on the idea of evidential support, that is, a piece of evidence supports a proposition whenever it increases the probability of the proposition. This strategy makes progress and can accommodate certain putative counterexamples to closure. However, this strategy also gives rise to a number of counterintuitive results. Finally, there are two broadly probabilistic strategies, one based on the idea of resilient probability and the other on the idea of assumptions that are taken for granted. These strategies are promising but are prone to some of the shortcomings of the second strategy. All in all, I conclude that each strategy fails. Probability theory, then, is unlikely to offer the account we need. (shrink)

Algorithmic probability and friends: Proceedings of the Ray Solomonoff 85th memorial conference is a collection of original work and surveys. The Solomonoff 85th memorial conference was held at Monash University's Clayton campus in Melbourne, Australia as a tribute to pioneer, Ray Solomonoff, honouring his various pioneering works - most particularly, his revolutionary insight in the early 1960s that the universality of Universal Turing Machines could be used for universal Bayesian prediction and artificial intelligence. This work continues to increasingly influence (...) and under-pin statistics, econometrics, machine learning, data mining, inductive inference, search algorithms, data compression, theories of intelligence and philosophy of science - and applications of these areas. Ray not only envisioned this as the path to genuine artificial intelligence, but also, still in the 1960s, anticipated stages of progress in machine intelligence which would ultimately lead to machines surpassing human intelligence. Ray warned of the need to anticipate and discuss the potential consequences - and dangers - sooner rather than later. Possibly foremostly, Ray Solomonoff was a fine, happy, frugal and adventurous human being of gentle resolve who managed to fund himself while electing to conduct so much of his paradigm-changing research outside of the university system. The volume contains 35 papers pertaining to the abovementioned topics in tribute to Ray Solomonoff and his legacy. (shrink)

Analyses of singular causation often make use of the idea that a cause increases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analysed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way, it becomes clearer that the ‘behaviour’ of (...) probability functions in small intervals about the times in question ought to be of concern. In this article, I make an extended case that causal theorists employing the ‘probability raising’ idea should pay attention to the continuity question. Specifically, if the probability functions are ‘jumping about’ in ways typical of discontinuous functions, then the stability of the relevant probability increase is called into question. The rub, however, is that sweeping requirements for either continuity or discontinuity are problematic and, as I argue, this constitutes a ‘continuity bind’. Hence more subtle considerations and constraints are needed, two of which I consider: utilizing discontinuous first derivatives of continuous probability functions, and abandoning point probability for imprecise probability. _1_ Introduction _2_ Probability Trajectories and Continuity _2.1_ Probability trajectories _2.2_ Causation as discontinuous jumps _2.3_ Against systematic discontinuity _3_ Broader Discontinuity Concerns _4_ The Continuity Bind _4.1_ Retaining continuity with discontinuous first derivatives _4.2_ Imprecise probability trajectories _5_ Concluding Remarks Appendix. (shrink)

Will future lethal autonomous weapon systems (LAWS), or ‘killer robots’, be a threat to humanity? The European Parliament has called for a moratorium or ban of LAWS; the ‘Contracting Parties to the Geneva Convention at the United Nations’ are presently discussing such a ban, which is supported by the great majority of writers and campaigners on the issue. However, the main arguments in favour of a ban are unsound. LAWS do not support extrajudicial killings, they do not take responsibility away (...) from humans; in fact they increase the abil-ity to hold humans accountable for war crimes. Using LAWS in war would probably reduce human suffering overall. Finally, the availability of LAWS would probably not increase the probability of war or other lethal conflict—especially as compared to extant remote-controlled weapons. The widespread fear of killer robots is unfounded: They are probably good news. (shrink)

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, (...) indicated by an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability to be the conditional probability. In our approach, however, we avoid triviality because the import-export principle is invalid. We then analyze an example of reasoning under partial knowledge where, given a conditional if A then Cas information, the probability of A should intuitively (...) increase. We explain this intuition by making some implicit background information explicit. We consider several iterated conditionals, which allow us to formalize different kinds of latent information. We verify that for these iterated conditionals the prevision is greater than or equal to the probability of A. We also investigate the lower and upper bounds of the Affirmation of the Consequent inference. We conclude our study with some remarks on the supposed "independence" of two conditionals, and we interpret this property as uncorrelation between two random quantities. 2020 Elsevier Inc. All rights reserved. (shrink)

One hears increasingly from philosophers that statistical inference is a technical study that is well in control by statisticians and should be left to them; and one hears, increasingly, from mathematical statisticians that all this talk about interpretations of probability is so much philosophical frosting that is utterly irrelevant to the serious business of producing mathematical statistics. “The more interpretations of probability there are, the wider the scope of applications of our purely mathematical theories.” The point of this (...) paper is to present, in detail, a situation in which an individual withgivendegrees of belief,givenevidence, andgivenvalues, will have three differentand contrarycourses of action recommended to him, each according to one of the three most popular interpretations of probability. (shrink)

Probability theory is a key tool of the physical, mathematical, and social sciences. It has also been playing an increasingly significant role in philosophy: in epistemology, philosophy of science, ethics, social philosophy, philosophy of religion, and elsewhere. This Handbook encapsulates and furthers the influence of philosophy on probability, and of probability on philosophy. Nearly forty articles summarise the state of play and present new insights in various areas of research at the intersection of these two fields. The (...) articles will be of special interest to practitioners of probability who seek a greater understanding of its mathematical and conceptual foundations, and to philosophers who want to get up to speed on the cutting edge of research in this area. The volume begins with a primer on those parts of probability theory that we believe are most important for philosophers to know, and the rest is divided into seven main sections: History; Formalism; Alternatives to Standard Probability Theory; Interpretations and Interpretive Issues; Probabilistic Judgment and Its Applications; Applications of Probability: Science; and Applications of Probability: Philosophy. (shrink)

& Carnegie Mellon University Abstract The rationality of human causal judgments has been the focus of a great deal of recent research. We argue against two major trends in this research, and for a quite different way of thinking about causal mechanisms and probabilistic data. Our position rejects a false dichotomy between "mechanistic" and "probabilistic" analyses of causal inference -- a dichotomy that both overlooks the nature of the evidence that supports the induction of mechanisms and misses some important probabilistic (...) implications of mechanisms. This dichotomy has obscured an alternative conception of causal learning: for discrete events, a central adaptive task is to induce causal mechanisms in the environment from probabilistic data and prior knowledge. Viewed from this perspective, it is apparent that the probabilistic norms assumed in the human causal judgment literature often do not map onto the mechanisms generating the probabilities. Our alternative conception of causal judgment is more congruent with both scientific uses of the notion of causation and observed causal judgments of untutored reasoners. We illustrate some of the relevant variables under this conception, using a framework for causal representation now widely adopted in computer science and, increasingly, in statistics. We also review the formulation and evidence for a theory of human causal induction (Cheng, 1997) that adopts this alternative conception. (shrink)

Adolescence has been linked to an enhanced tolerance of uncertainty and risky behavior and is possibly connected to an increased response toward rewards. However, previous research has produced inconsistent findings. To investigate whether these findings are due to different reward probabilities used in the experimental design, we extended a monetary incentive delay task by including three different reward probabilities. Using functional magnetic resonance imaging, 25 healthy adolescents and 22 adults were studied during anticipation of rewards in the VS. Differently colored (...) cue stimuli indicated either a monetary or verbal trial and symbolized different reward probabilities, to which the participants were blinded. Results demonstrated faster reaction times for lower reward probabilities in both age groups. Adolescents were slower through all conditions and had less activation on a neural level. Imaging results showed a three-way interaction between age group x condition x reward probability with differences in percent signal change between adolescents and adults for the high reward probabilities while adolescents demonstrated differences for the lowest. Therefore, previous inconsistent findings could be due to different reward probabilities, which makes examining these crucial for a better understanding of adolescent and adult behavior. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better (...) than C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)