Suppose that several individuals who have separately assessed prior probability distributions over a set of possible states of the world wish to pool their individual distributions into a single group distribution, while taking into account jointly perceived new evidence. They have the option of first updating their individual priors and then pooling the resulting posteriors or first pooling their priors and then updating the resulting group prior. If the pooling method that they employ is such that they arrive at the (...) same final distribution in both cases, the method is said to be externally Bayesian, a property first studied by Madansky . We show that a pooling method for discrete distributions is externally Bayesian if and only if it commutes with Jeffrey conditioning, parameterized in terms of certain ratios of new to old odds, as in Wagner , rather than in terms of the posterior probabilities of members of the disjoint family of events on which such conditioning originates. (shrink)

Jeffrey conditioning allows updating in Bayesian style when the evidence is uncertain. A weighted average, essentially, over classically updating on the alternatives. Unlike classical Bayesian conditioning, this allows learning to be unlearned.

A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...) just one individual), or to non-representable information (not representable by any event in the domain where credences are held). I pro- pose a taxonomy of six types of ‘group Bayesianism’. They differ in the information for which Bayesian revision of group credences is required: public representable information, private representable information, public non-representable information, etc. Six corre- sponding theorems establish how individual credences must (not) be aggregated to ensure group Bayesianism of any type, respectively. Aggregating through standard averaging is never permitted; instead, different forms of geometric averaging must be used. One theorem—that for public representable information—is essentially Russell et al.’s central result (with minor corrections). Another theorem—that for public non-representable information—fills a gap in the theory of externally Bayesian opinion pooling. (shrink)

We present a Bayesian analysis of the epistemology of analogue experiments with particular reference to Hawking radiation. Provided such experiments can be externally validated via universality arguments, we prove that they are confirmatory in Bayesian terms. We then provide a formal model for the scaling behaviour of the confirmation measure for multiple distinct realisations of the analogue system and isolate a generic saturation feature. Finally, we demonstrate that different potential analogue realisations could provide different levels of confirmation. Our results thus (...) provide a basis both to formalise the epistemic value of analogue experiments that have been conducted and to advise scientists as to the respective epistemic value of future analogue experiments. (shrink)

Hinge epistemology and Bayesianism are two prominent approaches in contemporary epistemology, but the relationship between these approaches has not been systematically studied. This paper formalizes the central commitments of hinge epistemology in a Bayesian framework and argues for the following two theses: (1) many of the types of claims that are treated as paradigmatic hinges in the hinge epistemology literature, such as the claim that there exists an external world of physical objects, are not capable of enabling rational inquiry, (...) even though this is typically regarded as a central property of hinges; (2) the standard Bayesian story of how rational inquiry proceeds is incorrect or at best incomplete. (shrink)

The data analyzed in this paper are part of the results described in Bueno et al. (2000). Three cytogenetics endpoints were analyzed in three populations of a species of wild rodent – Akodon montensis – living in an industrial, an agricultural, and a preservation area at the Itajaí Valley, State of Santa Catarina, Brazil. The polychromatic/normochromatic ratio, the mitotic index, and the frequency of micronucleated polychromatic erythrocites were used in an attempt to establish a genotoxic profile of each area. It (...) was assumed that the three populations were in the same conditions with respect to the influence of confounding factors such as animal age, health, nutrition status, presence of pathogens, and intra- and inter-populational genetic variability. Therefore, any differences found in the endpoints analyzed could be attributed to the external agents present in each area. The statistical models used in this paper are mixtures of negative-binomials and Poisson variables. The Poisson variables are used as approximations of binomials for rare events. The mixing distributions are beta densities. The statistical analyzes are under the bayesian perspective, as opposed to the frequentist ones often considered in the literature, as for instance in Bueno et al. (2000). (shrink)

This paper considers two novel Bayesian responses to a well-known skeptical paradox. The paradox consists of three intuitions: first, given appropriate sense experience, we have justification for accepting the relevant proposition about the external world; second, we have justification for expanding the body of accepted propositions through known entailment; third, we do not have justification for accepting that we are not disembodied souls in an immaterial world deceived by an evil demon. The first response we consider rejects the third (...) intuition and proposes an explanation of why we have a faulty intuition. The second response, which we favor, accommodates all three intuitions; it reconciles the first and the third intuition by the dual component model of justification, and defends the second intuition by distinguishing two principles of epistemic closure. (shrink)

We distinguish between literal and metaphorical applications of Bayesian models. When intended literally, an isomorphism exists between the elements of representation assumed by the rational analysis and the mechanism that implements the computation. Thus, observation of the implementation can externally validate assumptions underlying the rational analysis. In other applications, no such isomorphism exists, so it is not clear how the assumptions that allow a Bayesian model to fit data can be independently validated.

The terms nested sets, partitive frequencies, inside-outside view, and dual processes add little but confusion to our original analysis (Gigerenzer & Hoffrage 1995; 1999). The idea of nested set was introduced because of an oversight; it simply rephrases two of our equations. Representation in terms of chances, in contrast, is a novel contribution yet consistent with our computational analysis System 1.dual process theory” is: Unless the two processes are defined, this distinction can account post hoc for almost everything. In contrast, (...) an ecological view of cognition helps to explain how insight is elicited from the outside (the external representation of information) and, more generally, how cognitive strategies match with environmental structures. (shrink)

We resolve a useful formulation of the question how a statistician can coherently incorporate the information in a consulted expert’s probability assessment for an event into a personal posterior probability assertion. Using a framework that recognises the total information available as composed of units available only to each of them along with units available to both, we show: that a sufficient statistic for all the information available to both the expert and the statistician is the product of their odds ratios (...) in favour of the event; that the geometric mean of their two probabilities specifies a contour of pairs of assertions in the unit-square that yield the same posterior probability; that the information-combining function is parameterised by an unknown probability for the event conditioned only on the unspecified information common to both the statistician and the expert; and that an assessable mixing distribution over this unspecified probability allows an integrable mixture distribution to represent a computable posterior probability. The exact results allow the identification of the subclass of coherent probabilities that are externally Bayesian operators. This subclass is equivalent to the class of combining functions that honour the principles of uniformity and compromise. (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)

External world skeptics are typically opposed to admitting as evidence anything that goes beyond the purely phenomenal, and equally typically, they disown the use of rules of inference that might enable one to move from premises about the phenomenal alone to a conclusion about the external world. This seems to bar any a posteriori resolution of the skepticism debate. This paper argues that the situation is not quite so hopeless, and that an a posteriori resolution of the debate (...) becomes possible once it is recognized that the skeptic holds overly defensive and ill-motivated positions vis-à-vis both evidence and inference, and that more reasonable ones are available. In stating these more reasonable positions, as well as in showing how they make possible an a posteriori resolution of the skepticism debate, the paper draws on the machinery of Bayesian epistemology. (shrink)

We explore which types of probabilistic updating commute with convex IP pooling. Positive results are stated for Bayesian conditionalization, imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of externally Bayesian pooling operators due to Wagner :336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.

How are new Bayesian hypotheses generated within the framework of predictive processing? This explanatory framework purports to provide a unified, systematic explanation of cognition by appealing to Bayes rule and hierarchical Bayesian machinery alone. Given that the generation of new hypotheses is fundamental to Bayesian inference, the predictive processing framework faces an important challenge in this regard. By examining several cognitive‐level and neurobiological architecture‐inspired models of hypothesis generation, we argue that there is an essential difference between the two types of (...) models. Cognitive‐level models do not specify how they can be implemented in brains and include structures and assumptions that are external to the predictive processing framework. By contrast, neurobiological architecture‐inspired models, which aim to better resemble brain processes, fail to explain important capacities of cognition, such as categorization and few‐shot learning. The “scaling‐up” challenge for proponents of predictive processing is to explain the relationship between these two types of models using only the theoretical and conceptual machinery of Bayesian inference. (shrink)

Computational theories of vision typically rely on the analysis of two aspects of human visual function: (1) object and shape recognition (2) co-calibration of sensory measurements. Both these approaches are usually based on an inverse-optics model, where visual perception is viewed as a process of inference from a 2D retinal projection to a 3D percept within a Euclidean space schema. This paradigm has had great success in certain areas of vision science, but has been relatively less successful in understanding perceptual (...) representation, namely, the nature of the perceptual encoding. One of the drawbacks of inverse-optics approaches has been the difficulty in defining the constraints needed to make the inference computationally tractable (e.g. regularity assumptions, Bayesian priors, etc.). These constraints, thought to be learned assumptions about the nature of the physical and optical structures of the external world, have to be incorporated into any workable computational model in the inverse-optics paradigm. But inference models that employ an inverse optics plus structural assumptions approach inevitably result in a na. (shrink)

According to Bayesian orthodoxy, an agent should update---or at least should plan to update---her credences by conditionalization. Some have defended this claim by means of a diachronic Dutch book argument. They say: an agent who does not plan to update her credences by conditionalization is vulnerable (by her own lights) to a diachronic Dutch book, i.e., a sequence of bets which, when accepted, guarantee loss of utility. Here, I show that this argument is in tension with evidence externalism, i.e., the (...) view that an agent's evidence can entail non-trivial propositions about the external world. I argue that this tension casts doubt on the idea that diachronic Dutch books can be used to justify or vindicate updating plans. (shrink)

Sense of agency is a compelling but fragile experience that is augmented or attenuated by internal signals and by external cues. A disruption in SoA may characterise individual symptoms of mental illness such as delusions of control. Indeed, it has been argued that generic SoA disturbances may lie at the heart of delusions and hallucinations that characterise schizophrenia. A clearer understanding of how sensorimotor, perceptual and environmental cues complement, or compete with, each other in engendering SoA may prove valuable (...) in deepening our understanding the agency disruptions that characterise certain focal neurological disorders and mental illnesses. Here we examine the integration of SoA cues in health and illness, describing a simple framework of this integration based on Bayesian principles. We extend this to consider how alterations in cue integration may lead to aberrant experiences of agency. (shrink)

Medical ethics could be better understood if some basic theoretical aspects of practices in health care are analysed. By discussing the underlying ethical principles that govern medical practice, the student should also become familiar with the notion that medical ethics is much more than the external application of socially accepted moral standards. Professions in general and medicine in particular have internal values that command their moral virtuosity at the same time as their technical excellence. Three examples where clinical practice (...) can be clearly shown to require an ethical analysis are given: medical praxiology illustrates the motives, means and aims of physicians and patients; clinical decision-making as a practical syllogism that reaches prescriptive conclusions based on medical knowledge and the patient's wishes/intentions. Finally, diagnostics as an ethical bayesian approach is discussed, where the patient informedly decides the benefits and risks of further testing. (shrink)

Can the output of human cognition be predicted from the assumption that it is an optimal response to the information-processing demands of the environment? A methodology called rational analysis is described for deriving predictions about cognitive phenomena using optimization assumptions. The predictions flow from the statistical structure of the environment and not the assumed structure of the mind. Bayesian inference is used, assuming that people start with a weak prior model of the world which they integrate with experience to develop (...) stronger models of specific aspects of the world. Cognitive performance maximizes the difference between the expected gain and cost of mental effort. Memory performance can be predicted on the assumption that retrieval seeks a maximal trade-off between the probability of finding the relevant memories and the effort required to do so; in categorization performance there is a similar trade-off between accuracy in predicting object features and the cost of hypothesis formation; in casual inference the trade-off is between accuracy in predicting future events and the cost of hypothesis formation; and in problem solving it is between the probability of achieving goals and the cost of both external and mental problem-solving search. The implemention of these rational prescriptions in neurally plausible architecture is also discussed. (shrink)

When we perceive the external world, our brain has to deal with the incompleteness and uncertainty associated with sensory inputs, memory and prior knowledge. In theoretical neuroscience probabilistic approaches have received a growing interest recently, as they account for the ability to reason with incomplete knowledge and to efficiently describe perceptive and behavioral tasks. How can the probability distributions that need to be estimated in these models be represented and processed in the brain, in particular at the single cell (...) level? We consider the basic function carried out by photoreceptor cells which consists in detecting the presence or absence of light. We give a system-level understanding of the process of phototransduction based on a bayesian formalism: we show that the process of phototransduction is equivalent to a temporal probabilistic inference in a Hidden Markov Model (HMM), for estimating the presence or absence of light. Thus, the biochemical mechanisms of phototransduction underlie the estimation of the current state probability distribution of the presence of light. A classical descriptive model describes the interactions between the different molecular messengers, ions, enzymes and channel proteins occurring within the photoreceptor by a set of nonlinear coupled differential equations. In contrast, the probabilistic HMM model is described by a discrete recurrence equation. It appears that the binary HMM has a general solution in the case of constant input. This allows a detailed analysis of the dynamics of the system. The biochemical system and the HMM behave similarly under steady-state conditions. Consequently a formal equivalence can be found between the biochemical system and the HMM. Numerical simulations further extend the results to the dynamic case and to noisy input. All in all, we have derived a probabilistic model equivalent to a classical descriptive model of phototransduction, which has the additional advantage of assigning a function to phototransduction. The example of phototransduction shows how simple biochemical interactions underlie simple probabilistic inferences. (shrink)

An explanatory gap exists between physics and experience, raising the hard problem of consciousness: why are certain physical systems associated with an experience of an external world from an internal perspective? The living mirror theory holds that consciousness can be understood as arising from the computational interaction between a living system and its environment that is required for the organism's existence and survival. Maintaining a boundary that protects the system against destructive forces requires an interaction between the organism and (...) its outside world that can be cast in terms of Bayesian inference. The living mirror theory holds that this computational interaction results in statistical properties of the material world that are, in the absence of life, only implicit, becoming explicit in informational terms. This is held to give rise to the beliefs in qualities that constitute consciousness. Consciousness is therefore a necessary feature of all living systems as, in a world governed by the second law of thermodynamics, survival depends on the construction of beliefs regarding the potentially destructive forces in the outside world. From this perspective, consciousness is shown to be not a property of the brain in particular but instead to be a necessary feature of the life process itself. (shrink)

In this article, moving from being to becoming, we construe the ‘self’ as a dynamic process rather than as a static entity. To this end we draw on dialectics and Bayesian accounts of cognition. The former allows us to holistically consider the ‘self’ as the interplay between internalization and externalization and the latter to operationalize our suggestion formally. Internalization is considered here as the co-construction of bodily hierarchical models of the world and the organism, while externalization is taken as the (...) collective transformation of the world. We do not consider these processes as sequentially linked, but rather as a dialectic between the collective and the individual. This leads us to the suggestion of the self as a historical product of dialectical attunement across multiple time scales, from species evolution and culture to individual development and everyday learning. Subsequently, we describe concrete means for empirically testing our proposal in the form of two-person psychophysiology and multi-level analyses of intersubjectivity. Taken together, we suggest that a fine-grained analysis of social interaction might allow us to reconsider the ‘self’ beyond the static individual, i.e. how it emerges and manifests itself in social relations. Such an approach, we believe, could be relevant in multiple fields, from ethics and psychiatry to pedagogy and artificial intelligence. (shrink)

In this article, moving from being to becoming, we construe the ‘self’ as a dynamic process rather than as a static entity. To this end we draw on dialectics and Bayesian accounts of cognition. The former allows us to holistically consider the ‘self’ as the interplay between internalization and externalization and the latter to operationalize our suggestion formally. Internalization is considered here as the co-construction of bodily hierarchical models of the world and the organism, while externalization is taken as the (...) collective transformation of the world. We do not consider these processes as sequentially linked, but rather as a dialectic between the collective and the individual. This leads us to the suggestion of the self as a historical product of dialectical attunement across multiple time scales, from species evolution and culture to individual development and everyday learning. Subsequently, we describe concrete means for empirically testing our proposal in the form of two-person psychophysiology and multi-level analyses of intersubjectivity. Taken together, we suggest that a fine-grained analysis of social interaction might allow us to reconsider the ‘self’ beyond the static individual, i.e. how it emerges and manifests itself in social relations. Such an approach, we believe, could be relevant in multiple fields, from ethics and psychiatry to pedagogy and artificial intelligence. (shrink)

This study examines the job postings for open innovation (OI) specialists to determine a universal archetype of what competencies and tasks are requested from said professionals and their implications for corporate sustainability and responsibility. This research uses Bayesian statistics and latent Dirichlet allocation (LDA) topic modeling to measure multiple dimensions of the 341 sampled job postings. Our empirical findings unveil the pivotal role that OI specialists have in engaging with stakeholders and monitoring OI dynamics. Multiple dimensions are expected from OI (...) specialists, addressing a multitude of concerns, such as the environment and technologies. Moreover, this study underlines the need for OI specialists to comprehend both internal and external stakeholders' needs. This research contributes to the literature as follows. First, it underlines the value of topic modeling analysis in job profiling research. Second, it bridges existing knowledge gaps on OI specialists' competencies and roles with empirical evidence obtained from a global dataset. Third, it outlines the current market expectations and requirements for OI specialists, which is useful to both candidates and companies. (shrink)

The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on the same propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. The literature on judgment aggregation refers to such a problem as the \textit{discursive dilemma}. In this paper we assume that the decision which the group is trying to reach is factually right or wrong. Hence, we address the question of how good (...) the various approaches are at selecting the right conclusion. We focus on two approaches: distance-based procedures and a Bayesian analysis. They correspond to group-internal and group-external decision-making, respectively. We compare those methods in a probabilistic model, demonstrate the robustness of our results over various generalizations and discuss their applicability in different situations. The findings vindicate (i) that in judgment aggregation problems, reasons should carry higher weight than conclusions and (ii) that considering members of an advisory board to be highly competent is a better strategy than to underestimate their advice.". (shrink)

A focus on the conjunction of the contents of witness reports and on the coherence of their contents has had negative effects on the epistemic clarity of the Bayesian coherence literature. Whether or not increased coherence of witness reports is correlated with higher confirmation for some H depends upon the hypothesis in question and upon factors concerning the confirmation and independence of the reports, not directly on the positive relevance of the contents to each other. I suggest that Bayesians should (...) shift focus to “coherence for” an hypothesis – that is, to the definition and analysis of cumulative case arguments in which a body of evidence supports some hypothesis that is not restricted to the conjunction of the contents of reports. Such a shift of focus will be valuable for approaching issues such as the problem of the external world which have interested Bayesian coherentists all along. (shrink)

I offer an account of ad hocness that explains why the adoption of an ad hoc auxiliary is accompanied by the disconfirmation of a hypothesis H. H must be conjoined with an auxiliary a′, which is improbable antecedently given H, while ~H does not have this disability. This account renders it unnecessary to require, for identifying ad hocness, that either a′ or H have a posterior probability less than or equal to 0.5; there are also other reasons for abandoning that (...) condition. I distinguish between formal ad hocness, which is bad in the probabilistic sense that it results in disconfirmation of H, and argumentative ad hocness, which actually involves bad reasoning on the part of a subject. The latter is what I call “not counting the cost.” This distinction allows us to see why the 0.5 condition appeared attractive in the first place. The concept of not counting the cost also has implications for other areas of research, including both a Bayesian concept of unfalsifiability and the classic epistemological question of the problem of the external world. (shrink)

Probability kinematics is studied in detail within the framework of elementary probability theory. The merits and demerits of Jeffrey's and Field's models are discussed. In particular, the principle of maximum relative entropy and other principles are used in an epistemic justification of generalized conditionals. A representation of conditionals in terms of Bayesian conditionals is worked out in the framework of external kinematics.

Cephalopods are extraordinary molluscs equipped with vertebrate‐like intelligence and a unique buoyancy system for locomotion. A growing body of evidence from the fossil record, embryology and Bayesian molecular divergence estimations provides a comprehensive picture of their origins and evolution. Cephalopods evolved during the Cambrian (∼530 Ma) from a monoplacophoran‐like mollusc in which the conical, external shell was modified into a chambered buoyancy apparatus. During the mid‐Palaeozoic (∼416 Ma) cephalopods diverged into nautiloids and the presently dominant coleoids. Coleoids (i.e. squids, (...) cuttlefish and octopods) internalised their shells and, in the late Palaeozoic (∼276 Ma), diverged into Vampyropoda and the Decabrachia. This shell internalisation appears to be a unique evolutionary event. In contrast, the loss of a mineralised shell has occurred several times in distinct coleoid lineages. The general tendency of shell reduction reflects a trend towards active modes of life and much more complex behaviour. (shrink)

Causal reasoning is primarily concerned with what would happen to a system under external interventions. In particular, we are often interested in predicting the probability distribution of some random variables that would result if some other variables were forced to take certain values. One prominent approach to tackling this problem is based on causal Bayesian networks, using directed acyclic graphs as causal diagrams to relate post-intervention probabilities to pre-intervention probabilities that are estimable from observational data. However, such causal diagrams (...) are seldom fully testable given observational data. In consequence, many causal discovery algorithms based on data-mining can only output an equivalence class of causal diagrams. This paper is concerned with causal reasoning given an equivalence class of causal diagrams, represented by a ancestral graph. We present two main results. The first result extends Pearl 's celebrated do-calculus to the context of ancestral graphs. In the second result, we focus on a key component of Pearl's calculus---the property of invariance under interventions, and give stronger graphical conditions for this property than those implied by the first result. The second result also improves the earlier, similar results due to Spirtes et al. (shrink)

The Mystery Room problem is a close variant of the Mystery Bag scenario. It is argued here that dealing with this problem requires no revision of the Bayesian formalism, since there exists a solution to this problem in which indexicals or demonstratives play no essential role. The solution does require labels, which are internal to the probabilistic model. While there needs to be a connection between at least one label and one indexical or demonstrative, that connection is external to (...) the probabilistic model that is used to determine the relevant conditional probability; hence, it does not complicate the update procedure. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.4 (2001) 592-594 [Access article in PDF] John Earman. Hume's Abject Failure: The Argument Against Miracles. New York: Oxford University Press, 2000. Pp. xi + 217. Cloth, $39.95. Paper, $21.95. As his uncompromising title announces, John Earman considers Hume's famous account of miracles in the Enquiry Concerning Human Understanding to be an "abject failure." More than this, the author judges Hume's well-known arguments (...) to have failed in multiple ways. As he states in the opening paragraph: "It is not simply that Hume's [End Page 592] essay does not achieve its goals, but that his goals are ambiguous and confused." Hume's deliberations on this topic, Earman further contends, are unoriginal, and where original, insubstantial. Further, the logic of the position expressed in the essay "reveals the weakness and poverty of Hume's own account of induction and probabilistic reasoning." Finally, "the essay represents the kind of overreaching that gives philosophy a bad name." While there are occasional hints in the book that the author is himself not completely immune to this latter tendency, for the most part these bluntly stated objections to the famous essay are well supported. This book is a comprehensive and persuasive demolition of Hume's much vaunted claims about the credibility of miracle reports, and it issues a serious challenge to standard readings.Hume's Abject Failure is divided into two parts, the first of which takes the form of an analysis and critique of Hume's arguments. This eighty-page section is followed by another hundred pages of primary materials, mostly eighteenth-century, which address issues related to Hume's essay. It is clear from the format of the book that Earman intends to take seriously the intellectual context in which Hume's arguments first appeared. This a most welcome development. Many treatments of Hume's "Of Miracles" tend to be profoundly ahistorical. What becomes immediately apparent from a consideration of this context is the startling unoriginality of Hume's chief argument. The principle that uniform experience overrides testimony to the occurrence of a miracle was aired long before Hume claimed it as his own, although it can be conceded that in Hume's hands it took on a particularly persuasive form.More importantly, however, this is an argument which does not work. Earman claims that Hume would have been aware of this had he availed himself of the developing science of probability, and in particular Thomas Bayes's pioneering attempts to quantify degrees of belief and credibility. Hume's probabilistic arguments, even on the most charitable interpretation, simply fail the test of a Bayesian analysis, and a number of Earman's chapters forcefully demonstrate this. Having exposed the dubious nature of the argument based on competing testimony, Earman goes on to makes good his claim about the inadequacy of Hume's view of induction, showing how it would rule out not merely miracle testimony, but many empirical claims of the kind typically made in the sciences.It is perhaps a little unfair to charge Hume with having articulated a flawed argument the limitations of which only become obvious with the application of a sophisticated calculus unavailable to him. There is no evidence that Hume ever read Bayes. Earman points out that Richard Price, in his 1767 critique of the argument, drew Hume's attention to the possibility of a Bayesian approach, but Hume was apparently reluctant to incorporate quantification into subsequent editions of the Essay. Whether this amounts to a major failing on Hume's part is debatable. It is also worth noting that at times Earman seems to blur the contemporary distinction between "internal" and "external evidences" (miracles were instances of the latter). This distinction is important for understanding why Hume did not adopt the subjective notions of "miracle" of Locke and the Newtonians, and also why in section two of the Essay he deploys the 'contrary miracles' argument. There is also the puzzle as to how so acute a philosophical mind as Hume's could in this instance have... (shrink)

본고는 딥러닝의 이미지 인식 원리와 유아의 이미지 인식 원리를 종합하면서, 이미지-개념 학습을 위한 새로운 교수학습모델, 즉 “베이지안 구조구성주의 교수학습모델”(Bayesian Structure-constructivist Teaching-learning Model: BSTM)을 제안한다. 달리 말하면, 기계학습 원리와 인간학습 원리를 비교함으로써 얻게 되는 시너지 효과를 바탕으로, 유아들의 이미지-개념 학습을 위한 새로운 교수 모델을 구성하는 것을 목표로 한다. 이런 맥락에서 본고는 전체적으로 3가지 차원에서 논의된다. 첫째, 아동의 이미지 학습에 대한 역사적 중요 이론인 “대상 전체론적 가설”, “분류학적 가설”, “배타적 가설”, “기본 수준 범주 가설” 등을 역사 비판적 관점에서 검토한다. 둘째, 컴퓨터 공학에서 (...) 전개된 머신러닝의 이미지 학습 원리 및 그 구조의 역사적 변형들에 대해서 비판적으로 분석하면서, 특히 딥러닝의 교육 인식론적 의미를 도출한다. 셋째, 선행하는 논의들을 토대로 이미지와 개념을 연결시키는 학습, 즉 단어학습을 위한 필자의 고유한 이론인 구조구성주의 개념교수모델을 제안한다. 이때 필자는 피아제의 명제논리학적 학습 가설, 즉 논리-수학적 구조를 중시하는 기존의 피아제 학파의 학습 가설과 최근의 베이지안 학습 이론에서 강조된 확률론적 추론 가설, 특히 “교육학적 추론 가설”을 동시에 포함할 수 있는 교수학습모델의 구조 및 주요 지향점들을 제안한다. (shrink)

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it (...) does not re- place it or aim at replacing it. (shrink)

Learning is fundamentally about action, enabling the successful navigation of a changing and uncertain environment. The experience of pain is central to this process, indicating the need for a change in action so as to mitigate potential threat to bodily integrity. This review considers the application of Bayesian models of learning in pain that inherently accommodate uncertainty and action, which, we shall propose are essential in understanding learning in both acute and persistent cases of pain.

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this (...) significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework. (shrink)

Mathematicians often speak of conjectures as being confirmed by evidence that falls short of proof. For their own conjectures, evidence justifies further work in looking for a proof. Those conjectures of mathematics that have long resisted proof, such as the Riemann hypothesis, have had to be considered in terms of the evidence for and against them. In recent decades, massive increases in computer power have permitted the gathering of huge amounts of numerical evidence, both for conjectures in pure mathematics and (...) for the behavior of complex applied mathematical models and statistical algorithms. Mathematics has therefore become (among other things) an experimental science (though that has not diminished the importance of proof in the traditional style). We examine how the evaluation of evidence for conjectures works in mathematical practice. We explain the (objective) Bayesian view of probability, which gives a theoretical framework for unifying evidence evaluation in science and law as well as in mathematics. Numerical evidence in mathematics is related to the problem of induction; the occurrence of straightforward inductive reasoning in the purely logical material of pure mathematics casts light on the nature of induction as well as of mathematical reasoning. (shrink)

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...) covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle. (shrink)

How should we reason in science? Jan Sprenger and Stephan Hartmann offer a refreshing take on classical topics in philosophy of science, using a single key concept to explain and to elucidate manifold aspects of scientific reasoning. They present good arguments and good inferences as being characterized by their effect on our rational degrees of belief. Refuting the view that there is no place for subjective attitudes in 'objective science', Sprenger and Hartmann explain the value of convincing evidence in terms (...) of a cycle of variations on the theme of representing rational degrees of belief by means of subjective probabilities (and changing them by Bayesian conditionalization). In doing so, they integrate Bayesian inference—the leading theory of rationality in social science—with the practice of 21st century science. Bayesian Philosophy of Science thereby shows how modeling such attitudes improves our understanding of causes, explanations, confirming evidence, and scientific models in general. It combines a scientifically minded and mathematically sophisticated approach with conceptual analysis and attention to methodological problems of modern science, especially in statistical inference, and is therefore a valuable resource for philosophers and scientific practitioners. (shrink)

Bayesian reverse-engineering is a research strategy for developing three-level explanations of behavior and cognition. Starting from a computational-level analysis of behavior and cognition as optimal probabilistic inference, Bayesian reverse-engineers apply numerous tweaks and heuristics to formulate testable hypotheses at the algorithmic and implementational levels. In so doing, they exploit recent technological advances in Bayesian artificial intelligence, machine learning, and statistics, but also consider established principles from cognitive psychology and neuroscience. Although these tweaks and heuristics are highly pragmatic in character and (...) are often deployed unsystematically, Bayesian reverse-engineering avoids several important worries that have been raised about the explanatory credentials of Bayesian cognitive science: the worry that the lower levels of analysis are being ignored altogether; the challenge that the mathematical models being developed are unfalsifiable; and the charge that the terms ‘optimal’ and ‘rational’ have lost their customary normative force. But while Bayesian reverse-engineering is therefore a viable and productive research strategy, it is also no fool-proof recipe for explanatory success. (shrink)

The prominence of Bayesian modeling of cognition has increased recently largely because of mathematical advances in specifying and deriving predictions from complex probabilistic models. Much of this research aims to demonstrate that cognitive behavior can be explained from rational principles alone, without recourse to psychological or neurological processes and representations. We note commonalities between this rational approach and other movements in psychology – namely, Behaviorism and evolutionary psychology – that set aside mechanistic explanations or make use of optimality assumptions. Through (...) these comparisons, we identify a number of challenges that limit the rational program's potential contribution to psychological theory. Specifically, rational Bayesian models are significantly unconstrained, both because they are uninformed by a wide range of process-level data and because their assumptions about the environment are generally not grounded in empirical measurement. The psychological implications of most Bayesian models are also unclear. Bayesian inference itself is conceptually trivial, but strong assumptions are often embedded in the hypothesis sets and the approximation algorithms used to derive model predictions, without a clear delineation between psychological commitments and implementational details. Comparing multiple Bayesian models of the same task is rare, as is the realization that many Bayesian models recapitulate existing (mechanistic level) theories. Despite the expressive power of current Bayesian models, we argue they must be developed in conjunction with mechanistic considerations to offer substantive explanations of cognition. We lay out several means for such an integration, which take into account the representations on which Bayesian inference operates, as well as the algorithms and heuristics that carry it out. We argue this unification will better facilitate lasting contributions to psychological theory, avoiding the pitfalls that have plagued previous theoretical movements. (shrink)

Probabilistic models have much to offer to philosophy. We continually receive information from a variety of sources: from our senses, from witnesses, from scientific instruments. When considering whether we should believe this information, we assess whether the sources are independent, how reliable they are, and how plausible and coherent the information is. Bovens and Hartmann provide a systematic Bayesian account of these features of reasoning. Simple Bayesian Networks allow us to model alternative assumptions about the nature of the information sources. (...) Measurement of the coherence of information is a controversial matter: arguably, the more coherent a set of information is, the more confident we may be that its content is true, other things being equal. The authors offer a new treatment of coherence which respects this claim and shows its relevance to scientific theory choice. Bovens and Hartmann apply this methodology to a wide range of much discussed issues regarding evidence, testimony, scientific theories, and voting. Bayesian Epistemology is an essential tool for anyone working on probabilistic methods in philosophy, and has broad implications for many other disciplines. (shrink)

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language‐learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners’ input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized learning biases. The test case is an experiment (Culbertson, Smolensky, & Legendre, 2012) targeting the learning of word‐order patterns in the nominal domain. The model identifies internal biases of (...) the experimental participants, providing evidence that learners impose (possibly arbitrary) properties on the grammars they learn, potentially resulting in the cross‐linguistic regularities known as typological universals. Learners exposed to mixtures of artificial grammars tended to shift those mixtures in certain ways rather than others; the model reveals how learners’ inferences are systematically affected by specific prior biases. These biases are in line with a typological generalization—Greenberg's Universal 18—which bans a particular word‐order pattern relating nouns, adjectives, and numerals. (shrink)

The posthumous publication, in 1763, of Thomas Bayes’ “Essay Towards Solving a Problem in the Doctrine of Chances” inaugurated a revolution in the understanding of the confirmation of scientific hypotheses—two hundred years later. Such a long period of neglect, followed by such a sweeping revival, ensured that it was the inhabitants of the latter half of the twentieth century above all who determined what it was to take a “Bayesian approach” to scientific reasoning.

Any theory of confirmation must answer the following question: what is the purpose of its conception of confirmation for scientific inquiry? In this article, we argue that no Bayesian conception of confirmation can be used for its primary intended purpose, which we take to be making a claim about how worthy of belief various hypotheses are. Then we consider a different use to which Bayesian confirmation might be put, namely, determining the epistemic value of experimental outcomes, and thus to decide (...) which experiments to carry out. Interestingly, Bayesian confirmation theorists rule out that confirmation be used for this purpose. We conclude that Bayesian confirmation is a means with no end. 1 Introduction2 Bayesian Confirmation Theory3 Bayesian Confirmation and Belief4 Confirmation and the Value of Experiments5 Conclusion. (shrink)

Bayesian reasoning has been applied formally to statistical inference, machine learning and analysing scientific method. Here I apply it informally to more common forms of inference, namely natural language arguments. I analyse a variety of traditional fallacies, deductive, inductive and causal, and find more merit in them than is generally acknowledged. Bayesian principles provide a framework for understanding ordinary arguments which is well worth developing.

Many Bayesians such as White and Silins have argued that Moorean reasoning is defective because it is a case where probabilistic support fails to transmit across the relevant entailment. In this paper, I argue against their claim. On the Bayesian argument, a skeptical hypothesis is that you are a brain in a vat that appears to have hands. To disclose the defect in Moorean reasoning, the Bayesian argument is supposed to show that its appearing to you as if you have (...) hands does not increase the probability of a non-skeptical hypothesis such that you are not a brain in a vat. But what their argument really shows is rather a trivial fact that acquiring theses handlike experiences eliminates the possibility of not having these experiences, and so your having these experiences lowers the probability of the disjunctive claim that you are not a brain in a vat or it does not appear as if you have hands. Along these lines, I argue that what the Bayesian proof establishes has nothing to do with the defect in Moorean reasoning. (shrink)