A worldview that does not involve religion or science seems to be incomplete. However, a worldview that includes both religion and science may arouse concern of incompatibility. This paper looks at the particular religion, Christianity, and proceeds to develop a worldview in which Christianity and Science are compatible with each other. The worldview may make use of some ideas of Christianity and may involve some author’s own ideas on Christianity. It is thought that Christianity and Science are in harmony in (...) the sense that science can support beliefs in Christianity and in turn beliefs in Christianity can support science. To avoid future unnecessary conflicts between science and religion, it is suggested that a core faith Christianity worldview should be taken. However, this does not mean that certain parts of scripture are abandoned. (shrink)

The paper aims at analyzing Lambert’s conception of empirical knowledge that is part of scientific learning. Indeed, in the Neues Organon, he claims that science is obtained with the help of both a priori and a posteriori knowledge. Lambert’s originality lies on the application of the analytic and synthetic methods of reasoning, which are traditionally used in formal disciplines, to the realm of experience. Transforming common knowledge into scientific a posteriori knowledge is mainly based on the employment of such demonstrative (...) methods. This allows Lambert to introduce some important theoretical tools in his theory of experience, in particular about the search for the conditions of observations and experimentations as well as the establishment of hypothesis. For Lambert, the synthetic method in empirical deductions requires the use of conjectures and probable principles. (shrink)

This article discusses the dual interpretation of the Jeffreys-Lindley paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to the difficulty of using improper priors while testing. I stress the considerable impact of this paradox on the foundations of both classical and Bayesian statistics. While assessing existing resolutions of the paradox, I focus on a critical viewpoint of the paradox discussed by Spanos in Philosophy (...) of Science. (shrink)

Many of the problems studied in cognitive science are inductive problems, requiring people to evaluate hypotheses in the light of data. The key to solving these problems successfully is having the right inductive biases—assumptions about the world that make it possible to choose between hypotheses that are equally consistent with the observed data. This article explores a novel experimental method for identifying the biases that guide human inductive inferences. The idea behind this method is simple: This article uses the responses (...) produced by a participant on one trial to generate the stimuli that either they or another participant will see on the next. A formal analysis of this “iterated learning” procedure, based on the assumption that the learners are Bayesian agents, predicts that it should reveal the inductive biases of these learners, as expressed in a prior probability distribution over hypotheses. This article presents a series of experiments using stimuli based on a well-studied set of category structures, demonstrating that iterated learning can be used to reveal the inductive biases of human learners. (shrink)

The conflict of narrowness and precision in direct inference occurs if a body of evidence contains estimates for frequencies in a certain reference class and less precise estimates for frequencies in a narrower reference class. To develop a solution to this conflict, I draw on ideas developed by Paul Thorn and John Pollock. First, I argue that Kyburg and Teng’s solution to the conflict of narrowness and precision leads to unreasonable direct inference probabilities. I then show that Thorn’s recent solution (...) to the conflict leads to unreasonable direct inference probabilities. Based on my analysis of Thorn’s approach, I propose a natural distribution for a Bayesian analysis of the data directly obtained from studying members of the narrowest reference class. (shrink)

This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some (...) support to this version of objective Bayesianism. (shrink)

This paper poses a problem for Lewis’ Principal Principle in a subjective Bayesian framework: we show that, where chances inform degrees of belief, subjective Bayesianism fails to validate normal informal standards of what is reasonable. This problem points to a tension between the Principal Principle and the claim that conditional degrees of belief are conditional probabilities. However, one version of objective Bayesianism has a straightforward resolution to this problem, because it avoids this latter claim. The problem, then, offers some (...) support to this version of objective Bayesianism. (shrink)

Consider the hypothesis H that a defendant is guilty, and the evidence E that a majority of h out of n independent jurors have voted for H and a minority of k:=n-h against H. How likely is the majority verdict to be correct? By a formula of Condorcet, the probability that H is true given E depends only on each juror's competence and on the absolute margin between the majority and the minority h-k, but neither on the number n, (...) nor on the proportion h/n. This paper reassesses that result and explores its implications. First, using the classical Condorcet jury model, I derive a more general version of Condorcet's formula, confirming the significance of the absolute margin, but showing that the probability that H is true given E depends also on an additional parameter: the prior probability that H is true. Second, I show that a related result holds when we consider not the degree of belief we attach to H given E, but the degree of support E gives to H. Third, I address the implications for the definition of special majority voting, a procedure used to capture the asymmetry between false positive and false negative decisions. I argue that the standard definition of special majority voting in terms of a required proportion of the jury is epistemically questionable, and that the classical Condorcet jury model leads to an alternative definition in terms of a required absolute margin between the majority and the minority. Finally, I show that the results on the significance of the absolute margin can be resisted if the so-called assumption of symmetrical juror competence is relaxed. (shrink)

While in medicine, comparison of the data supplied by a clinical syndrome with the data supplied by the biological system is used to arrive at the most accurate diagnosis, the same cannot be said of financial economics: the accumulation of statistical results that contradict the Brownian hypothesis used in risk modelling, combined with serious empirical problems in the practical implementation of the Black-Scholes-Merton model, the benchmark theory of mathematical finance founded on the Brownian hypothesis, has failed to change (...) the Brownian representation, which has endured for more than fifty years despite the extent of its invalidation by experience. Without any statistical foundations, one mathematical representation has become the established approach, acting in the minds of practitioners as a “prenotion” in the sense the word is used by Durkheim, i.e. a “schematic, summary representation” which has produced a kind of spontaneous epistemology. The question arises of the persistence of this mathematical representation, which has been the basis for every financial risk modelling approach: how can its long life be explained? How was this spontaneous epistemology formed, and why did it prove to be so persistent? To address this question and offer an answer, I will test the various dynamics of scientific knowledge used with reference to financial modelling. All these dynamics are specific ways of describing the relationship between knowledge of a phenomenon and the phenomenon itself. Observing that it is impossible for the positivist approach to solve the financial puzzle, I turn to the three principal postpositivist dynamics, developed by Kuhn, Lakatos and Quine. I shall try to make to speak these representations of science for financial research, in order to reflect on the dominance of the Brownian representation in finance. We shall see that none of the epistemologies examined can explain why the Brownian representation continues to be used in mathematical finance research. I shall then propose an alternative hypothesis, concerning a significant pervading mental model that has irrigated both academics and practitioners in the financial sector: the “principle of continuity” introduced into economics by Marshall in. I consider that this principle of continuity has become a “persistent idea” in the form of a viral approach to representations, and I give this persistent idea the metaphorical name of the “Brownian virus”. Then, to explain the spread of this Brownian virus through the financial sector, the contamination of financial practices by this mental representation founded on the principle of continuity, I introduce the concept of the “financial Logos”, a discourse that structures practices and organisations, calculations, prudential regulations and accounting standards, leading to a general financialisation of society from the 1980s onwards. (shrink)

Samuel Huntington's influential clash of civilizations hypothesis (Huntington, 1993; Huntington, 1996) has been widely debated, but empirical tests of his ideas about core states remain limited at the micro-level. In this paper, we bring new evidence to bear, focusing on the : Greater Asia and the Pacific. Using the AsiaBarometer, we examine the extent to which publics in the region identify with the core states of the supposedly most contentious civilizations in the region and the factors that influence those (...) perceptions. We give attention to the role of globalization and nationalism and whether both may be subsumed by religiosity as Huntington suggests. Our descriptive evidence affirms some of the tensions between the US, China, and Islamic-predominant Asia identified by Huntington as areas of potential conflict. At the same time, we find no evidence to suggest that attitudes toward core states are zero-sum; Asian publics often see rival powers as mutually good influences. Using multivariate analysis, we find that religiosity, as the clash paradigm surmises, boosts Iranian influence and undermines American influence in several predominantly Islamic states. We also find, contrary to Huntington, that overall exposure to foreign cultures leads to a more positive assessment of American influence among Chinese and Pakistanis, as well as American perceptions of China. When foreign exposure influences perceptions of Iran, the effect is modestly, but consistently, negative. Taken together, the findings raise questions about two key assumptions of the Huntington framework and suggest that alternative approaches in recent civilizations literature show greater empirical promise. (shrink)

This paper is an extended review of the book Error and Inference, edited by Deborah Mayo and Aris Spanos, about their frequentist and philosophical perspective on testing of hypothesis and on the criticisms of alternatives like the Bayesian approach.

We report the results of a dual-task study in which participants performed a tracking and typing task under various experimental conditions. An objective payoff function was used to provide explicit feedback on how participants should trade off performance between the tasks. Results show that participants’ dual-task interleaving strategy was sensitive to changes in the difficulty of the tracking task and resulted in differences in overall task performance. To test the hypothesis that people select strategies that maximize payoff, a Cognitively (...) Bounded Rational Analysis model was developed. This analysis evaluated a variety of dual-task interleaving strategies to identify the optimal strategy for maximizing payoff in each condition. The model predicts that the region of optimum performance is different between experimental conditions. The correspondence between human data and the prediction of the optimal strategy is found to be remarkably high across a number of performance measures. This suggests that participants were honing their behavior to maximize payoff. Limitations are discussed. (shrink)

This article presents preliminary considerations and results from a research project designed to investigate the relation between gestures, graphic traces and perceptions. More specifically, the project aims to test the hypothesis that graphic traces, including handwriting, can set up graphetic empathy between writers and readers of traces across long temporal and spatial distances. Insofar as a graphic trace is lawfully related to the gesture by which it came into being, the trace itself will hold information about the gesture, which (...) may resonate with the sensorimotor system of a perceiver, as if they themselves performed the gesture. If this is in fact so, it will have important and hitherto unanticipated implications for our understanding of the embodiment of reading. As part of the article we will present and discuss the results of a neurophenomenological trial study through which we attempt to operationalize the gesture-trace and trace–perception relations respectively. (shrink)

The contributions in this volume focus on the Bayesian interpretation of natural languages, which is widely used in areas of artificial intelligence, cognitive science, and computational linguistics. This is the first volume to take up topics in Bayesian Natural Language Interpretation and make proposals based on information theory, probability theory, and related fields. The methodologies offered here extend to the target semantic and pragmatic analyses of computational natural language interpretation. Bayesian approaches to natural language semantics and pragmatics (...) are based on methods from signal processing and the causal Bayesian models pioneered by especially Pearl. In signal processing, the Bayesian method finds the most probable interpretation by finding the one that maximizes the product of the prior probability and the likelihood of the interpretation. It thus stresses the importance of a production model for interpretation as in Grice’s contributions to pragmatics or in interpretation by abduction. (shrink)

People are ‘biased toward the future’: all else being equal, we typically prefer to have positive experiences in the future, and negative experiences in the past. Several explanations have been suggested for this pattern of preferences. Adjudicating among these explanations can, among other things, shed light on the rationality of future-bias: For instance, if our preferences are explained by unjustified beliefs or an illusory phenomenology, we might conclude that they are irrational. This paper investigates one hypothesis, according to which (...) future-bias is explained by our having a phenomenology that we describe, or conceive of, as being as of time robustly passing. We empirically tested this hypothesis and found no evidence in its favour. Our results present a puzzle, however, when compared with the results of an earlier study. We conclude that although robust passage phenomenology on its own probably does not explain future-bias, having this phenomenology and taking it to be veridical may contribute to future-bias. (shrink)

Predictivism asserts that novel confirmations carry special probative weight. Epistemic pluralism asserts that the judgments of agents (about, e.g., the probabilities of theories) carry epistemic import. In this paper, I propose a new theory of predictivism that is tailored to pluralistic evaluators of theories. I replace the orthodox notion of use-novelty with a notion of endorsement-novelty, and argue that the intuition that predictivism is true has two roots. I provide a detailed Bayesian rendering of this theory and argue that (...) pluralistic theory evaluation pervades scientific practice. I compare my account of predictivism with those of Maher and Worrall. Introduction Why construction is a red herring for pluralist evaluators The unvirtuous accommodator Virtuous endorsers and the two roots of predictivism The two roots in Bayesian terms: the priors and background beliefs of endorsers Who are the pluralist evaluators? Two contemporary theories of predictivism 7.1 Maher: Reliable methods of theory construction 7.2 Worrall: The confirmation of core ideas Conclusion. (shrink)

Unfortunately, reading Chow's work is likely to leave the reader more confused than enlightened. My preferred solutions to the “controversy” about null- hypothesis testing are: (1) recognize that we really want to test the hypothesis that an effect is “small,” not null, and (2) use Bayesian methods, which are much more in keeping with the way humans naturally think than are classical statistical methods.

The foundations of probability deal with the problem of modelling reasoning in face of uncertainty by a mathematical calculus, usually the standard probability calculus .The three dominating schools in the foundations of probability interpret probabilities as limiting long-run frequencies conceived as an objective property of series of repeatable experiments , or rational betting rates for an individual to bet on the unknown outcome of experiments depending on the individual’s prior assessments updated by evidence , or rational betting rates to bet (...) on the unknown outcome of experiments depending on evidence only, but not on subjective assessments .Apart from the interpretation of probability, frequentism and Bayesianism in particular also differ with respect to the advocated methodology for inference. Frequentists use tests, estimators, and confidence intervals . Bayesians usually start with a prior distribution and use the posterior distribution, which is obtained by conditioning on the evidence, in order to carry out inferences. The prior distribution either models the individual’s personal prior probability assessments or, in objective Bayesianism, is chosen according to some rules in order to allow the evidence to determine the posterior.All three approaches are riddled with difficulties . Frequentism is often accused of circularity, because the assumption of independent identically distributed outcomes is needed in order to connect observations to frequentist probabilities, but ‘iid’ is itself defined probabilistically. Subjective Bayesianism is attacked for being too …. (shrink)

Physical activity counteracts some of the negative consequences associated with chronic neurological diseases. Here, we describe the levels of physical activity and sports activity in patients with multiple sclerosis and chronic stroke and test compliance with the recommendation for health-promoting physical activity of the World-Health Organization. Secondly, we tested for differences between the groups of patients, and thirdly, we examined relationships between PA and Sport with psychological indicators of perceived energy and self-beliefs. Psychological constructs were assessed with validated measures from (...) different disciplines in Psychology. A statistical aim was to describe interpretations gained by parametric Bayesian and Null-Hypothesis-Significance Testing statistics on the example of the conducted tests for differences and relationships. Descriptive analyses revealed that pMS and pStroke complied with recommendations of the WHO, but with large variance indicating that patient groups are not homogenous. Tests for differences showed that the PA difference between pMS and pStroke can be attributed to the higher proportion of women in the pMS sample as they engage more in household chores. Tests for relationships showed that for pStroke, vitality, self-control, and self-efficacy were positively related to the level of sports activity. Furthermore, pStroke who were sport active had lower fatigue and higher self-control and self-efficacy scores than sport inactive people. Although they address slightly different questions, the Bayesian and the NHST approach led to similar general conclusions. (shrink)

It is generally accepted among philosophers of science that hypothesis testing is a key methodological feature of science. As far as philosophical theories of confirmation are con...

Bayesian confirmation theory is a leading theory to decide the confirmation/refutation of a hypothesis based on probability calculus. While it may be much discussed in philosophy of science, is it actually practiced in terms of hypothesis testing by scientists? Since the assignment of some of the probabilities in the theory is open to debate and the risk of making the wrong decision is unknown, many scientists do not use the theory in hypothesis testing. Instead, they use (...) alternative statistical tests that can measure the risk or the reliability in decision making, circumventing some of the theoretical problems in practice. Therefore, the theory is not very popular in hypothesis testing among scientists at present. However, there are some proponents of Bayesian hypothesis testing, and software packages are made available to accelerate utilization by scientists. Time will tell whether Bayesian confirmation theory can become both a leading theory and a widely practiced method. In addition, this theory can be used to model the belief of scientists when testing hypotheses. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Holy Trinity in Ippolito Desideri's Ke ri se ste aṇ kyi chos lugs kyi snying poTrent PomplunOn April 10, 1716, Ippolito Desideri, a Jesuit who had but recently arrived in Tibet, wrote a long letter to another Jesuit missionary, Ildebrando Grassi, who was stationed in Mysuru, India. Desideri recounted his adventures since the two men had last been together, three and a half years earlier, at (...) the Jesuit residence in Goa. He told of his travels to Surat, Delhi, Lahore, Leh, and Lhasa, and recalled his first impressions of Tibetan religion and culture. Tibetans, he told Grassi, were gentle and docile, but coarse and uncultivated. In Desideri's opinion, they had neither arts nor sciences, but they did reject the doctrine of transmigration and appeared to have some knowledge of the Christian faith.1 "Here is what I learned about the Tibetans' religion," he wrote,They call God könchok (dkon mchog), and they appear to have some notion of the adorable Trinity, for at times they call Him könchok chik (dkon mchog gcig), that is, the One God, and at other times they call Him könchok sum (dkon mchog gsum), that is, the Triune God. They also use a kind of chaplet, over which they repeat the words Oṁ ah hūṁ, and they say that the word Oṁ signifies knowledge or an arm, that is, power; ah is the word, and hūṁ is the heart, or love, and that these three words mean God. They also worship a being named Padmasaṃbhava, who was born some seven hundred years ago. When asked if he were God or man, some people replied that he was both God and man, having neither father nor mother, but having been born from a flower. Even so, they have statues representing a woman with a flower in her hand, whom they call Padmasaṃbhava's mother, and they venerate several others whom they treat as saints. In their churches, one finds an altar covered with cloth and ornaments, and a sort of tabernacle sits in the middle of the altar, where they say Padmasaṃbhava dwells, though they also assert that he is in heaven.2This letter, which survives only in a French translation, is noteworthy if only because Ippolito Desideri would later repudiate almost everything he affirmed in it. In a matter of months, the Jesuit missionary would change his mind about Tibetans' capacities for art, for science, and for culture. He would also change his mind considerably about their religion. [End Page 117]Perhaps the most significant change—and one that would later play a large role in his legal battle with the Capuchins for control of the Tibetan mission—concerned the knowledge that Tibetans had of the Holy Trinity, the central Christian mystery that God is Father, Son, and Holy Spirit. In what follows, I would like to explore Ippolito Desideri's explanation of the Holy Trinity, especially in the Ke ri se ste aṇ kyi chos lugs kyi snying po (The Essence of Christian Doctrine). I will briefly situate Desideri's account of Tibetans' knowledge of the Trinity in the general historical and theological context of the early modern missions, outline his various attempts to explain this central Christian mystery in Tibetan, and offer some tentative speculations on the Jesuit's motives for choosing certain Tibetan terms. I hope this discussion of Desideri's treatment of the Holy Trinity might contribute to Christian theologians and Buddhist philosophers who are engaged in interreligious dialogue and assist them in their reflections about how best to translate their respective faiths in such dialogue. Desideri's translations are not always perspicacious—as we shall see—but they are instructive, especially to the extent that they show us the issues that must be considered when anyone wishes to translate the basic terms of his own religion into an alien language. With this difficulty in mind, we might also consider the inadequacy of all language, human or angelic, when confronted with the mystery of God's infinite transcendence.Ippolito Desideri in ContextBefore addressing Desideri's translations, I would like to point out that the description of Tibetan religion... (shrink)

We report two issues concerning diverging sets of Bayesian (conditional) probabilities-divergence of "posteriors"-that can result with increasing evidence. Consider a set P of probabilities typically, but not always, based on a set of Bayesian "priors." Fix E, an event of interest, and X, a random variable to be observed. With respect to P, when the set of conditional probabilities for E, given X, strictly contains the set of unconditional probabilities for E, for each possible outcome X = x, (...) call this phenomenon dilation of the set of probabilities (Seidenfeld and Wasserman 1993). Thus, dilation contrasts with the asymptotic merging of posterior probabilities reported by Savage (1954) and by Blackwell and Dubins (1962). (1) In a wide variety of models for Robust Bayesian inference the extent to which X dilates E is related to a model specific index of how far key elements of P are from a distribution that makes X and E independent. (2) At a fixed confidence level, (1-α), Classical interval estimates A n for, e.g., a Normal mean θ have length O(n -1/2 ) (for sample size n). Of course, the confidence level correctly reports the (prior) probability that θ ∈ A n ,P(A n )=1-α , independent of the prior for θ . However, as shown by Pericchi and Walley (1991), if an ε -contamination class is used for the prior on the parameter θ , there is asymptotic (posterior) dilation for the A n , given the data. If, however, the intervals A ′ n are chosen with length $O(\sqrt{\log (\text{n})/\text{n})}$ , then there is no asymptotic dilation. We discuss the asymptotic rates of dilation for ClassClassical and Bayesian interval estimates and relate these to Bayesian hypothesis testing. (shrink)

According to one theory, the brain is a sophisticated hypothesis tester: perception is Bayesian unconscious inference where the brain actively uses predictions to test, and then refine, models about what the causes of its sensory input might be. The brain’s task is simply continually to minimise prediction error. This theory, which is getting increasingly popular, holds great explanatory promise for a number of central areas of research at the intersection of philosophy and cognitive neuroscience. I show how the (...) theory can help us understand striking phenomena at three cognitive levels: vision, sensory integration, and belief. First, I illustrate central aspects of the theory by showing how it provides a nice explanation of why binocular rivalry occurs. Then I suggest how the theory may explain the role of the unified sense of self in rubber hand and full body illusions driven by visuotactile conflict. Finally, I show how it provides an approach to delusion formation that is consistent with one-deficit accounts of monothematic delusions. (shrink)

Complex constraints like conditionals ('If A, then B') and probabilistic constraints ('The probability that A is p') pose problems for Bayesian theories of learning. Since these propositions do not express constraints on outcomes, agents cannot simply conditionalize on the new information. Furthermore, a natural extension of conditionalization, relative information minimization, leads to many counterintuitive predictions, evidenced by the sundowners problem and the Judy Benjamin problem. Building on the notion of a `paradigm shift' and empirical research in psychology and economics, (...) I argue that the model of hypothesis testing can explain how people learn complex, theory-laden propositions like conditionals and probability constraints. Theories are formalized as probability distributions over a set of possible outcomes and theory change is triggered by a constraint which is incompatible with the initial theory. This leads agents to consult a higher order probability function, or a 'prior over priors,' to choose the most likely alternative theory which satisfies the constraint. The hypothesis testing model is applied to three examples: learning a simple probabilistic constraint involving coin bias, the sundowners problem for conditional learning, and the Judy Benjamin problem for learning conditional probability constraints. (shrink)

The study tests the hypothesis that conditional probability judgments can be influenced by causal links between the target event and the evidence even when the statistical relations among variables are held constant. Three experiments varied the causal structure relating three variables and found that (a) the target event was perceived as more probable when it was linked to evidence by a causal chain than when both variables shared a common cause; (b) predictive chains in which evidence is a cause (...) of the hypothesis gave rise to higher judgments than diagnostic chains in which evidence is an effect of the hypothesis; and (c) direct chains gave rise to higher judgments than indirect chains. A Bayesian learning model was applied to our data but failed to explain them. An explanation-based hypothesis stating that statistical information will affect judgments only to the extent that it changes beliefs about causal structure is consistent with the results. (shrink)

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually (...) endorsed by practicing experimentalists. (shrink)

This article examines the methodology of a core branch of contemporary political theory or philosophy: “analytic” political theory. After distinguishing political theory from related fields, such as political science, moral philosophy, and legal theory, the article discusses the analysis of political concepts. It then turns to the notions of principles and theories, as distinct from concepts, and reviews the methods of assessing such principles and theories, for the purpose of justifying or criticizing them. Finally, it looks at a recent debate (...) on how abstract and idealized political theory should be, and assesses the significance of disagreement in political theory. The discussion is carried out from an angle inspired by the philosophy of science. (shrink)

Event segmentation theory posits that people segment continuous experience into discrete events and that event boundaries occur when there are large transient increases in prediction error. Here, we set out to test this theory in the context of story listening, by using a deep learning language model (GPT‐2) to compute the predicted probability distribution of the next word, at each point in the story. For three stories, we used the probability distributions generated by GPT‐2 to compute the time series of (...) prediction error. We also asked participants to listen to these stories while marking event boundaries. We used regression models to relate the GPT‐2 measures to the human segmentation data. We found that event boundaries are associated with transient increases in Bayesian surprise but not with a simpler measure of prediction error (surprisal) that tracks, for each word in the story, how strongly that word was predicted at the previous time point. These results support the hypothesis that prediction error serves as a control mechanism governing event segmentation and point to important differences between operational definitions of prediction error. (shrink)

Review of Jaynes, Probability Theory: The Logic of Science; Marrison, The Fundamentals of Risk Management; and Hastie, Tibshirani and Friedman, The Elements of Statistical Learning. A standard view of probability and statistics centers on distributions and hypothesis testing. To solve a real problem, say in the spread of disease, one chooses a “model”, a distribution or process that is believed from tradition or intuition to be appropriate to the class of problems in question. One uses data to estimate the (...) parameters of the model, and then delivers the resulting exactly specified model to the customer for use in prediction and classification. As a gateway to these mysteries, the combinatorics of dice and coins are recommended; the energetic youth who invest heavily in the calculation of relative frequencies will be inclined to protect their investment through faith in the frequentist philosophy that probabilities are all really relative frequencies. Those with a taste for foundational questions are referred to measure theory, an excursion from which few return. That picture, standardised by Fisher and Neyman in the 1930s, has proved in many ways remarkably serviceable. It is especially reasonable where it is known that the data are generated by a physical process that conforms to the model. It is not so useful where the data is a large and little understood mess, as is typical in, for example, insurance data being investigated for fraud. Nor is it suitable where one has several speculations about possible models and wishes to compare them, or.. (shrink)

The appeal to expert opinion is an argument form that uses the verdict of an expert to support a position or hypothesis. A previous scheme-based treatment of the argument form is formalized within a Bayesian network that is able to capture the critical aspects of the argument form, including the central considerations of the expert's expertise and trustworthiness. We propose this as an appropriate normative framework for the argument form, enabling the development and testing of quantitative predictions as (...) to how people evaluate this argument, suggesting that such an approach might be beneficial to argumentation research generally. We subsequently present two experiments as an example of the potential for future research in this vein, demonstrating that participants' quantitative ratings of the convincingness of a proposition that has been supported with an appeal to expert opinion were broadly consistent with the predictions of the Bayesian model. (shrink)

Professor Meehl [2] has pointed out a very significant problem in the methodology of psychological research, indicating that statistical tests of psychological hypotheses against a null hypothesis are loaded in favor of eventual success at rejecting the null hypothesis. In my opinion this is not, however, a contrast between physics and psychology, but rather between the method of parameter estimation and that of the null hypothesis in the tradition of Fisher. A physicist could use the null (...) class='Hi'>hypothesis method as well as the psychologist. The fact that he doesn't is probably related to the more advanced state of his measurement techniques and theoretical constructs. (shrink)

Human risk (the risk of people doing things they shouldn't, or not doing things they should') is the largest single risk facing all organisations -- when things go wrong, there's always a human component, either causing the problem or making it worse. Collectively, companies spend billions trying to manage human risk via functions like Compliance, InfoSec, Risk, Audit, Legal, Human Resources and Internal Comms -- it is people in these functions, as well as those tasked with managing people, that is (...) the target audience for the book. Technology exacerbates the problem by providing each of us with weapons of mass destruction' from a human risk perspective -- even the most junior employee can cause huge damage via their keyboard, either in the work environment or via their personal social media account -- and by taking over basic, repetitive tasks, which mean people are spending more time in human risk sensitive' activities. Traditional approaches to mitigating human risk rely heavily on the idealised presumption that because people are employed, they can simply be told what to do -- this works well in safety-critical environments, where the black & white' parameters of desired outcomes are easy to predict, but is much harder when it comes to grey', less codifiable, areas like ethics which are often difficult to monitor until it's too late and rely on employees being positively engaged. If we want to mitigate the risks posed by human decision-making, then we need to base our approach on an understanding of how humans actually make decisions, which is where Behavioural Science -- a discipline based on academic research and field-tested on real' humans by advertisers, governments and transport authorities -- can help achieve better outcomes. This book is designed to help all those involved in managing human risk to achieve compliance' with a small -- in other words, getting their desired outcome -- and explores how organisations can get the best out of their people by designing frameworks that work with, rather than against, the grain of human thinking. Readers will learn to challenge their existing presumptions about managing human risk and discover practical techniques and examples they can deploy in their work environment. (shrink)

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

Dahlman analyzes the case with a version of Bayes’ rule that can handle dependencies. He claims that his method can help a fact finder avoid various kinds of bias in probabilistic reasoning, and he identifies occurrences of these biases in the analyzed decision. While a mathematical analysis may give a false impression of objectivity to fact finders, Dahlman claims as a benefit that it forces to make assumptions explicit, which can then be scrutinized.

In quantity discrimination tasks, adults, infants and animals have been sometimes observed to process number only after all continuous variables, such as area or density, have been controlled for. This has been taken as evidence that processing number may be more cognitively demanding than processing continuous variables. We tested this hypothesis by training mosquitofish to discriminate two items from three in three different conditions. In one condition, continuous variables were controlled while numerical information was available; in another, the number (...) was kept constant and information relating to continuous variables was available; in the third condition, stimuli differed for both number and continuous quantities. Fish learned to discriminate more quickly when both number and continuous information were available compared to when they could use continuous information only or number only; there was no difference in the learning rate between the two latter conditions. Our results do not support the hypothesis that processing numbers imposes a higher cognitive load than processing continuous variables. Rather, they suggest that availability of multiple information sources may facilitate discrimination learning. (shrink)

Suppose several individuals (e.g., experts on a panel) each assign probabilities to some events. How can these individual probability assignments be aggregated into a single collective probability assignment? This article reviews several proposed solutions to this problem. We focus on three salient proposals: linear pooling (the weighted or unweighted linear averaging of probabilities), geometric pooling (the weighted or unweighted geometric averaging of probabilities), and multiplicative pooling (where probabilities are multiplied rather than averaged). We present axiomatic characterisations of each class of (...) pooling functions (most of them classic, but one new) and argue that linear pooling can be justified procedurally, but not epistemically, while the other two pooling methods can be justified epistemically. The choice between them, in turn, depends on whether the individuals' probability assignments are based on shared information or on private information. We conclude by mentioning a number of other pooling methods. (shrink)

The debate about the nature of the representational format of concepts seems to have reached an impasse. The debate faces two fundamental problems. Firstly, amodalists (i.e., those who argue that concepts are represented by amodal symbols) and modalists (i.e., those who see concepts as involving crucially representations including sensorimotor information) claim that the same empirical evidence is compatible with their views. Secondly, there is no shared understanding of what a modal or amodal format amounts to. Both camps recognize that the (...) two formats play essential roles in higher cognition, leading to an increasing number of hybrid proposals. In this paper, I argue that the existence of those fundamental problems should make us suspicious about a modal/amodal dichotomy. Also, I suggest that hybrid approaches, as they currently stand, do not provide suitable solutions to the impasse. Instead, we should overcome the dichotomy and treat the modal/amodal distinction as a graded phenomenon. I illustrate this hypothesis with an example of a cognitive-computational model of concepts based on the Predictive Processing framework. (shrink)

Majority cycling and related social choice paradoxes are often thought to threaten the meaningfulness of democracy. But deliberation can prevent majority cycles – not by inducing unanimity, which is unrealistic, but by bringing preferences closer to single-peakedness. We present the first empirical test of this hypothesis, using data from Deliberative Polls. Comparing preferences before and after deliberation, we find increases in proximity to single-peakedness. The increases are greater for lower versus higher salience issues and for individuals who seem to (...) have deliberated more versus less effectively. They are not merely a byproduct of increased substantive agreement. Our results both refine and support the idea that deliberation, by increasing proximity to single-peakedness, provides an escape from the problem of majority cycling. (shrink)

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

Predictive processing, an increasingly popular paradigm in cognitive sciences, has focused primarily on giving accounts of perception, motor control and a host of psychological phenomena, including consciousness. But higher cognitive processes, like conceptual thought, language, and logic, have received only limited attention to date and PP still stands disconnected from a huge body of research in those areas. In this thesis, I aim to address this gap and I attempt to go some way towards developing and defending a cognitive-computational approach (...) to higher cognition within the predictive processing paradigm. To test its explanatory potential, I apply it to a range of linguistic and conceptual phenomena. I proceed in three steps. First, I lay out an account of concepts and suggest how concepts are represented, how they can be context-sensitively processed, and how the apparent diversity of formats arise. Secondly, I propose how paradigmatic higher cognitive competencies, like language and logical reasoning, could fit into the PP picture. Thirdly, I apply the PP account of concepts and language to a range of linguistic-conceptual phenomena as test cases, namely: metaphor, the semantic paradox (specifically the Liar Paradox) and copredication. Finally, I discuss some challenges and objections to the PP framework as applied to higher cognition and in general. (shrink)

Road traffic carnages are global concerns and seemingly on the rise in Ghana. Several risk factors have been studied as associated with road traffic fatalities. However, inadequate road traffic fatality data and inconsistent probability outcomes for RTF remain major challenges. The objective of this study was to illustrate and estimate probability models that can predict road traffic fatalities. We relied on 66,159 recorded casualties who were involved in road traffic accidents in Ghana from 2015 to 2019. Three generalized linear models, (...) namely, logistic regression, probit regression, and linear probability model, were used for the analysis. We found that gender and age groups have significant effects in predicting the probability of road traffic fatality for all three models. Through a likelihood ratio test, however, it was determined that the logit regression model produced consistent probabilities of traffic fatalities which are very close to the actual probability values across the age groups and gender, compared to the other two models. Thus, we recommend intensified campaign for the use of seat belts in vehicles, targeted at the aged and male users of road transport, to reduce the possibility of death in any RTA. (shrink)

I disagree with several of Chow's traditional descriptions and justifications of null hypothesis testing: (1) accepting the null hypothesis whenever p > .05; (2) random sampling from a population; (3) the frequentist interpretation of probability; (4) having the null hypothesis generate both a probability distribution and a complement of the desired conclusion; (5) assuming that researchers must fix their sample size before performing their study.

Background:To date, most research on aggression in mental disorders focused on active-aggressive behavior and found self-directed and other-directed active aggression to be a symptom and risk-factor of psychopathology. On the other hand, passive-aggressive behavior has been investigated less frequently and only in research on psychodynamic defense mechanisms, personality disorders, and dysfunctional self-control processes. This small number of studies primarily reflects a lack of a reliable and valid clinical assessment of passive-aggressive behavior. To address this gap, we developed the Test of (...) Passive Aggression (TPA), a 24-item self-rating scale for the assessment of self-directed and other-directed passive-aggressive behavior.Method:Study 1 examined the internal consistency and factorial validity of the TPA in an inpatient sample (N= 307). Study 2 investigated the retest-reliability, internal consistency, and construct validity (active aggression, personality traits, impulsivity) of the TPA in a student sample (N= 180).Results:In line with our hypothesis, Exploratory Structural Equation Modeling revealed an acceptable to good fit of a bi-factorial structure of the TPA (Chi-square-df-ratio= 1.98;RMSR= 0.05, fit.off = 0.96). Both TPA scales showed good to excellent internal consistency (α= 0.83–0.90) and 4-week retest-reliability (rtt= 0.86). Correlations with well-established aggression scales, measures of personality, and impulsivity support discriminant and convergent validity of the TPA.Conclusions:The TPA is a reliable and valid instrument for the assessment of self-directed and other-directed passive-aggressive behavior. (shrink)

The distribution of matter in our universe is strikingly time asymmetric. Most famously, the Second Law of Thermodynamics says that entropy tends to increase toward the future but not toward the past. But what explains this time-asymmetric distribution of matter? In this paper, I explore the idea that time itself has a direction by drawing from recent work on grounding and metaphysical fundamentality. I will argue that positing such a direction of time, in addition to time-asymmetric boundary conditions, enables a (...) better explanation of the thermodynamic asymmetry than is available otherwise. (shrink)

Schurz (Synthese 164:201–234, 2008) proposed a justification of creative abduction on the basis of the Reichenbachian principle of the common cause. In this paper we take up the idea of combining creative abduction with causal principles and model instances of successful creative abduction within a Bayes net framework. We identify necessary conditions for such inferences and investigate their unificatory power. We also sketch several interesting applications of modeling creative abduction Bayesian style. In particular, we discuss use-novel predictions, confirmation, and (...) the problem of underdetermination in the context of abductive inferences. (shrink)

How can collective decisions be made among individuals with conflicting preferences or judgments? Arrow’s impossibility theorem and other social-choice-theoretic results suggest that, for many collective decision problems, there are no attractive democratic solutions. In response, deliberative democrats argue that group deliberation makes collective decisions more tractable. How can deliberation accomplish this? In this paper, I explore the distinction between two different types of agreement and discuss how they can facilitate collective decision making. Deliberative democrats have traditionally defended the hypothesis (...) that group deliberation generates consensus on what decision option should be chosen: "substantive agreement". But substantive agreement is not only empirically unrealistic, but also logically unnecessary for meaningful collective decision making. An alternative, less demanding hypothesis is that, under certain conditions, group deliberation generates consensus on how a decision problem should be conceptualized: "meta-agreement". I assess the latter hypothesis, explain how it can be empirically tested, and cite some evidence consistent with it. My discussion addresses two contexts of democratic decision making: preference aggregation and judgment aggregation. (shrink)

ABSTRACT Average utilitarianism and several related axiologies, when paired with the standard expectational theory of decision-making under risk and with reasonable empirical credences, can find their practical prescriptions overwhelmingly determined by the minuscule probability that the agent assigns to solipsism—that is, to the hypothesis that there is only one welfare subject in the world, namely, herself. This either (i) constitutes a reductio of these axiologies, (ii) suggests that they require bespoke decision theories, or (iii) furnishes an unexpected argument for (...) ethical egoism. (shrink)

The gravitational influence of Jupiter on Saturn produces, among other things, non-negligible changes in the eccentricity of Saturn that affect the magnitude of error of Ptolemaic astronomy. The value that Ptolemy obtained for the eccentricity of Saturn is a good approximation of the real eccentricity—including the perturbation of Jupiter—that Saturn had during the time of Ptolemy's planetary observations or a bit earlier. Therefore, it seems more probable that the observations used for obtaining the eccentricity of Saturn were done near Ptolemy’s (...) time, and rather unlikely earlier than the first century AD. Even if this is not quite a demonstration that Ptolemy used observations of his own, my argument increases its probability and practically discards the idea that Ptolemy borrowed values or observations from astronomers further back than the first century AD, such as Hipparchus or the Babylonians. (shrink)