Recent interest in the external validity of prediction models has produced many methods for finding predictive distributions that are invariant to dataset shifts and can be used for prediction in new, unseen environments. However, these methods consider different types of shifts and have been developed under disparate frameworks, making it difficult to theoretically analyze how solutions differ with respect to stability and accuracy. Taking a causal graphical view, we use a flexible graphical representation to express various types of dataset shifts. (...) Given a known graph of the data generating process, we show that all invariant distributions correspond to a causal hierarchy of graphical operators, which disable the edges in the graph that are responsible for the shifts. The hierarchy provides a common theoretical underpinning for understanding when and how stability to shifts can be achieved, and in what ways stable distributions can differ. We use it to establish conditions for minimax optimal performance across environments, and derive new algorithms that find optimal stable distributions. By using this new perspective, we empirically demonstrate that that there is a tradeoff between minimax and average performance. (shrink)

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent, (...) whereas propositions express beliefs that are persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave. (shrink)

Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left early. This article compares two proposed Bayes net theories as models of people's understanding of counterfactuals. Experiments 1-3 show that neither theory makes correct predictions about backtracking counterfactuals (in which the event of the if-clause (...) occurs after the event of the then-clause), and Experiment 4 shows the same is true of forward counterfactuals. An amended version of one of the approaches, however, can provide a more accurate account of these data. (shrink)

For nearly as long as the word “correlation” has been part of statistical parlance, students have been warned that correlation does not prove causation, and that only experimental studies, e.g., randomized clinical trials, can establish the existence of a causal relationship. Over the last few decades, somewhat of a consensus has emerged between statisticians, computer scientists, and philosophers on how to represent causal claims and connect them to probabilistic relations. One strand of this work studies the conditions under which evidence (...) accumulated from non-experimental (observational) studies can be used to infer a causal relationship. In this paper, I compare the typical conditions required to infer that one variable is a direct cause of another in observational and experimental studies. I argue that they are essentially the same. (shrink)

This commentary gives a personal perspective on modeling and modeling developments in cognitive science, starting in the 1950s, but focusing on the author’s personal views of modeling since training in the late 1960s, and particularly focusing on advances since the official founding of the Cognitive Science Society. The range and variety of modeling approaches in use today are remarkable, and for many, bewildering. Yet to come to anything approaching adequate insights into the infinitely complex fields of mind, brain, and intelligent (...) systems, an extremely wide array of modeling approaches is vital and necessary. (shrink)

Cartwright (Synthese 121(1/2):3–27, 1999a; The dappled world, Cambridge University Press, Cambridge, 1999b) attacked the view that causal relations conform to the Markov condition by providing a counterexample in which a common cause does not screen off its effects: the prominent chemical factory. In this paper we suggest a new way to handle counterexamples to Markov causation such as the chemical factory. We argue that Cartwright’s as well as similar scenarios feature a certain kind of non-causal dependence that kicks in once (...) the common cause occurs. We then develop a representation of this specific kind of non-causal dependence that allows for modeling the problematic scenarios in such a way that the Markov condition is not violated anymore. (shrink)

A theory of categorization is presented in which knowledge of causal relationships between category features is represented in terms of asymmetric and probabilistic causal mechanisms. According to causal‐model theory, objects are classified as category members to the extent they are likely to have been generated or produced by those mechanisms. The empirical results confirmed that participants rated exemplars good category members to the extent their features manifested the expectations that causal knowledge induces, such as correlations between feature pairs that are (...) directly connected by causal relationships. These expectations also included sensitivity to higher‐order feature interactions that emerge from the asymmetries inherent in causal relationships. Quantitative fits of causal‐model theory were superior to those obtained with extensions to traditional similarity‐based models that represent causal knowledge either as higher‐order relational features or “prior exemplars” stored in memory. (shrink)

A central question in cognitive research concerns how new properties are generalized to categories. This article introduces a model of how generalizations involve a process of causal inference in which people estimate the likely presence of the new property in individual category exemplars and then the prevalence of the property among all category members. Evidence in favor of this causal‐based generalization (CBG) view included effects of an existing feature’s base rate (Experiment 1), the direction of the causal relations (Experiments 2 (...) and 4), the number of those relations (Experiment 3), and the distribution of features among category members (Experiments 4 and 5). The results provided no support for an alternative view that generalizations are promoted by the centrality of the to‐be‐generalized feature. However, there was evidence that a minority of participants based their judgments on simpler associative reasoning processes. (shrink)

We present a multiscale integrationist interpretation of the boundaries of cognitive systems, using the Markov blanket formalism of the variational free energy principle. This interpretation is intended as a corrective for the philosophical debate over internalist and externalist interpretations of cognitive boundaries; we stake out a compromise position. We first survey key principles of new radical views of cognition. We then describe an internalist interpretation premised on the Markov blanket formalism. Having reviewed these accounts, we develop our positive multiscale account. (...) We argue that the statistical seclusion of internal from external states of the system—entailed by the existence of a Markov boundary—can coexist happily with the multiscale integration of the system through its dynamics. Our approach does not privilege any given boundary, nor does it argue that all boundaries are equally prescient. We argue that the relevant boundaries of cognition depend on the level being characterised and the explanatory interests that guide investigation. We approach the issue of how and where to draw the boundaries of cognitive systems through a multiscale ontology of cognitive systems, which offers a multidisciplinary research heuristic for cognitive science. (shrink)

It is a widespread intuition that the coherence of independent reports provides a powerful reason to believe that the reports are true. Formal results by Huemer, M. 1997. “Probability and Coherence Justification.” Southern Journal of Philosophy 35: 463–72, Olsson, E. 2002. “What is the Problem of Coherence and Truth?” Journal of Philosophy XCIX : 246–72, Olsson, E. 2005. Against Coherence: Truth, Probability, and Justification. Oxford University Press., Bovens, L., and S. Hartmann. 2003. Bayesian Epistemology. Oxford University Press, prove that, under (...) certain conditions, coherence cannot increase the probability of the target claim. These formal results, known as ‘the impossibility theorems’ have been widely discussed in the literature. They are taken to have significant epistemic upshot. In particular, they are taken to show that reports must first individually confirm the target claim before the coherence of multiple reports offers any positive confirmation. In this paper, I dispute this epistemic interpretation. The impossibility theorems are consistent with the idea that the coherence of independent reports provides a powerful reason to believe that the reports are true even if the reports do not individually confirm prior to coherence. Once we see that the formal discoveries do not have this implication, we can recover a model of coherence justification consistent with Bayesianism and these results. This paper, thus, seeks to turn the tide of the negative findings for coherence reasoning by defending coherence as a unique source of confirmation. (shrink)

Two notions from philosophical logic and linguistics are brought together and applied to the psychological study of defeasible conditional reasoning. The distinction between disabling conditions and alternative causes is shown to be a special case of Pollock’s (1987) distinction between ‘rebutting’ and ‘undercutting’ defeaters. ‘Inferential’ conditionals are shown to come in two varieties, one that is sensitive to rebutters, the other to undercutters. It is thus predicted and demonstrated in two experiments that the type of inferential conditional used as the (...) major premise of conditional arguments can reverse the heretofore classic, distinctive effects of defeaters. (shrink)

This paper reviews the psychological investigation of reasoning with conditionals, putting an emphasis on recent work. In the first part, a few methodological remarks are presented. In the second part, the main theories of deductive reasoning (mental rules, mental models, and the probabilistic approach) are considered in turn; their content is summarised and the semantics they assume for if and the way they explain formal conditional reasoning are discussed, in particular in the light of experimental work on the probability of (...) conditionals. The last part presents the recent shift of interest towards the study of conditional reasoning in context, that is, with large knowledge bases and uncertain premises. (shrink)

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q& R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability (...) calculus for prob(P/Q& R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q& R) 1 A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of "probable probabilities" that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, andprob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application. (shrink)

Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.

In artificial intelligence (AI), a number of criticisms were raised against the use of probability for dealing with uncertainty. All these criticisms, except what in this article we call the non-adequacy claim, have been eventually confuted. The non-adequacy claim is an exception because, unlike the other criticisms, it is exquisitely philosophical and, possibly for this reason, it was not discussed in the technical literature. A lack of clarity and understanding of this claim had a major impact on AI. Indeed, mostly (...) leaning on this claim, some scientists developed an alternative research direction and, as a result, the AI community split in two schools: a probabilistic and an alternative one. In this article, we argue that the non-adequacy claim has a strongly metaphysical character and, as such, should not be accepted as a conclusive argument against the adequacy of probability. (shrink)

The dispute over the continuity of life and mind. Arguments for cognitivism: The purpose of this paper is to discuss the position of non-cognitivism on the issue of the so-called dispute over the continuity / discontinuity of life and mind. In discussing the views of Michael Kirchhoff and Tom Froese, I will point out some difficulties related to their position. Next, I will formulate three arguments in favor of the cognitive alternative, emphasizing the need to resort to semantic information in (...) explaining these phenomena. According to noncognitivist position, there is a continuity in the life-mind line, which can be justified by referring to the concept of Shannon’s syntactic information. Opponents of this thesis, i.e. supporters of cognitivism, claim that the explanation of cognition requires the use of other tools than those used to explanation of life, because, first, the notion of syntactic information does not exhaust the complexity of these phenomena, and, second, the non-cognitive position raises many problems and ambiguities. According to cognitivists, when explaining life and mind, one should refer to the concept of semantic information that is rejected by noncognitivists. In the Conclusion I will analyze the ambiguities and assumptions related to the thesis about the continuity or discontinuity between life and cognitive processes. (shrink)

The background target of the research going into the present article is to forge an intellectual alliance between, on the one hand, active inference and the free-energy principle (FEP), and on the other, Charles S. Peirce’s theory of semiotics and pragmatism. In the present paper, the focus is on the allegiance between the nomenclatures of active and abductive inferences as the proper place to begin reaching at that wider target. The paper outlines the key conceptual elements involved in a naturalistic (...) rendering of Peirce’s late semiotic and logical notion of abductive reasoning. The target is a cognitive-biological model of abduction which preserves the functional integrity of an organism and fulfils the existential imperative for living beings’ evidence of existence. Such a model is an adaptation of Peirce’s late logical schema of abduction proposed in his largely unpublished works during the early 20th century. The proposed model is argued to be a feasible sketch also of recent breakthroughs in computational (sensu Bayesian) cognitive science. (shrink)

It is often assumed that cognitive science is built upon folk psychology, and that challenges to folk psychology are therefore challenges to cognitive science itself. We argue that, in practice, cognitive science and folk psychology treat entirely non-overlapping domains: cognitive science considers aspects of mental life which do not depend on general knowledge, whereas folk psychology considers aspects of mental life which do depend on general knowledge. We back up our argument on theoretical grounds, and also illustrate the separation between (...) cognitive scientific and folk psychological phenomena in a number of cognitive domains. We consider the methodological and theoretical significance of our arguments for cognitive science research. (shrink)

We discuss O&C's probabilistic approach from a probability logical point of view. Specifically, we comment on subjective probability, the indispensability of logic, the Ramsey test, the consequence relation, human nonmonotonic reasoning, intervals, generalized quantifiers, and rational analysis.

Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference should be drawn. It is the type of conclusion we draw in the ordinary world and ordinary situations in which we find ourselves. Formally speaking, ‘nonmonotonic reasoning’ refers to argumentation in (...) which one uses certain information to reach a conclusion, but where it is possible that adding some further information to those very same premises could make one want to retract the original conclusion. It is easily seen that the informal notion of default reasoning manifests a type of nonmonotonic reasoning. Generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged existence of “exceptional instances” of the class. In the absence of explicit information that an object is one of the exceptions we are enjoined to apply the default statement to the object. But further information may later tell us that the object is in fact one of the exceptions. So this is one of the points where nonmonotonicity resides in default reasoning. (shrink)

What is the relation between coherence and truth? This paper rejects numerous answers to this question, including the following: truth is coherence; coherence is irrelevant to truth; coherence always leads to truth; coherence leads to probability, which leads to truth. I will argue that coherence of the right kind leads to at least approximate truth. The right kind is explanatory coherence, where explanation consists in describing mechanisms. We can judge that a scientific theory is progressively approximating the truth if it (...) is increasing its explanatory coherence in two key respects: broadening by explaining more phenomena and deepening by investigating layers of mechanisms. I sketch an explanation of why deepening is a good epistemic strategy and discuss the prospect of deepening knowledge in the social sciences and everyday life. (shrink)

We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical Ramsey-Adams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994; Gärdenfors, 1993).'Expectation' is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form (...) of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of non-monotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability. (shrink)

Trust is a natural mechanism by which an autonomous party, an agent, can deal with the inherent uncertainty regarding the behaviours of other parties and the uncertainty in the information it shares with those parties. Trust is thus crucial in any decentralised system. This paper builds on recent efforts to use argumentation to reason about trust. Specifically, a set of schemes is provided, and abstract patterns of reasoning that apply in multiple situations geared towards trust. Schemes are described in which (...) one agent, A, can establish arguments for trusting another agent, B, directly, as well as schemes that A can use to construct arguments for trusting C, where C is trusted by B. For both sets of schemes, a set of critical questions is offered that identify the situations in which these schemes can fail. (shrink)

The causal nature of evolution is one of the central topics in the philosophy of biology. The issue concerns whether equations used in evolutionary genetics point to some causal processes or purely phenomenological patterns. To address this question the present article builds well-defined causal models that underlie standard equations in evolutionary genetics. These models are based on minimal and biologically plausible hypotheses about selection and reproduction, and generate statistics to predict evolutionary changes. The causal reconstruction of the evolutionary principles shows (...) adaptive evolution as a genuine causal process, where fitness and selection are both causes of evolution. 1 Introduction2 The Philosophical Puzzle3 Causal Models4 Causal Foundations of Evolutionary Genetics4.1 Univariate quantitative genetics model4.1.1 The causal graph4.1.2 Structural equations4.1.3 Deriving evolutionary transition functions4.2 One-locus population genetics model5 Evolution as a Causal Process5.1 Selection as a causal process5.2 Causes of evolutionary change6 Conclusion. (shrink)

The causal nature of evolution is one of the central topics in the philosophy of biology. The issue concerns whether equations used in evolutionary genetics point to some causal processes or purely phenomenological patterns. To address this question the present article builds well-defined causal models that underlie standard equations in evolutionary genetics. These models are based on minimal and biologically plausible hypotheses about selection and reproduction, and generate statistics to predict evolutionary changes. The causal reconstruction of the evolutionary principles shows (...) adaptive evolution as a genuine causal process, where fitness and selection are both causes of evolution. 1 Introduction2 The Philosophical Puzzle3 Causal Models4 Causal Foundations of Evolutionary Genetics4.1 Univariate quantitative genetics model4.1.1 The causal graph4.1.2 Structural equations4.1.3 Deriving evolutionary transition functions4.2 One-locus population genetics model5 Evolution as a Causal Process5.1 Selection as a causal process5.2 Causes of evolutionary change6 Conclusion. (shrink)

We advance a model of human probability judgment and apply it to the design of an extrapolation algorithm. Such an algorithm examines a person's judgment about the likelihood of various statements and is then able to predict the same person's judgments about new statements. The algorithm is tested against judgments produced by thirty undergraduates asked to assign probabilities to statements about mammals.

The paper sets out the challenges facing the Police in respect of the detection and prevention of the volume crime of burglary. A discussion of data mining and decision support technologies that have the potential to address these issues is undertaken and illustrated with reference the authors’ work with three Police Services. The focus is upon the use of “soft” forensic evidence which refers to modus operandi and the temporal and geographical features of the crime, rather than “hard” evidence such (...) as DNA or fingerprint evidence. Three objectives underpin this paper. First, given the continuing expansion of forensic computing and its role in the emergent discipline of Crime Science, it is timely to present a review of existing methodologies and research. Second, it is important to extract some practical lessons concerning the application of computer science within this forensic domain. Finally, from the lessons to date, a set of conclusions will be advanced, including the need for multidisciplinary input to guide further developments in the design of such systems. The objectives are achieved by first considering the task performed by the intended systems users. The discussion proceeds by identifying the portions of these tasks for which automation would be both beneficial and feasible. The knowledge discovery from databases process is then described, starting with an examination of the data that police collect and the reasons for storing it. The discussion progresses to the development of crime matching and predictive knowledge which are operationalised in decision support software. The paper concludes by arguing that computer science technologies which can support criminal investigations are wide ranging and include geographical information systems displays, clustering and link analysis algorithms and the more complex use of data mining technology for profiling crimes or offenders and matching and predicting crimes. We also argue that knowledge from disciplines such as forensic psychology, criminology and statistics are essential to the efficient design of operationally valid systems. (shrink)

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

According to Aristotle, humans are the rational animal. The borderline between rationality and irrationality is fundamental to many aspects of human life including the law, mental health, and language interpretation. But what is it to be rational? One answer, deeply embedded in the Western intellectual tradition since ancient Greece, is that rationality concerns reasoning according to the rules of logic – the formal theory that specifies the inferential connections that hold with certainty between propositions. Piaget viewed logical reasoning as defining (...) the end-point of cognitive development; and contemporary psychology of reasoning has focussed on comparing human reasoning against logical standards. (shrink)

This paper addresses the apparent mismatch between the normative and descriptive literatures in the cognitive science of conditional reasoning. Descriptive psychological theories still regard material implication as the normative theory of the conditional. However, over the last 20 years in the philosophy of language and logic the idea that material implication can account for everyday indicative conditionals has been subject to severe criticism. The majority view is now apparently in favour of a subjective conditional probability interpretation. A comparative model fitting (...) exercise is presented that shows that a conditional probability model can explain as much of the data on abstract indicative conditional reasoning tasks as psychological theories that supplement material implication with various rationally unjustified processing assumptions. Consequently, when people are asked to solve laboratory reasoning tasks, they can be seen as simply generalising their everyday probabilistic reasoning strategies to this novel context. (shrink)

This paper expounds that besides the well-known spatio-temporal problem there is a causal problem of entanglement: even when one neglects spatio-temporal constraints, the peculiar statistics of EPR/B experiment is inconsistent with usual principles of causal explanation as stated by the theory of causal Bayes nets. The conflict amounts to a dilemma that either there are uncaused correlations or there are caused independences . I argue that the central ideas of causal explanations can be saved if one accepts the latter horn (...) and explains the unfaithful independences by a stable fine-tuning of the causal parameters. (shrink)

Current psychological research on causal inference is dominated by two basic approaches: the covariation approach and the mechanism approach. This article reviews these two approaches, evaluates the contributions and limitations of each approach, and suggests how these approaches might be integrated into a more comprehensive framework. Covariation theorists assume that cognizers infer causal relations from conditional probabilities computed over samples of multiple events, but they do not provide an adequate account of how cognizers constrain their search for candidate causes and (...) relevant evidence. Mechanism theorists assume that cognizers use their knowledge of potential mechanisms to infer the causes of individual events, but they do not account for the origins of this kind of knowledge. Theorists might integrate these approaches into a framework that overcomes these limitations by (1) examining important relations between cognizers' beliefs about the nature of causality, the logic of causal inference, and the processes cognizers use to make causal inferences, and (2) providing a more complete account of cognizers' conceptions of causality and the origins of those conceptions. (shrink)

Bayesian models of legal arguments generally aim to produce a single integrated model, combining each of the legal arguments under consideration. This combined approach implicitly assumes that variables and their relationships can be represented without any contradiction or misalignment, and in a way that makes sense with respect to the competing argument narratives. This paper describes a novel approach to compare and ‘average’ Bayesian models of legal arguments that have been built independently and with no attempt to make them consistent (...) in terms of variables, causal assumptions or parameterization. The approach involves assessing whether competing models of legal arguments are explained or predict facts uncovered before or during the trial process. Those models that are more heavily disconfirmed by the facts are given lower weight, as model plausibility measures, in the Bayesian model comparison and averaging framework adopted. In this way a plurality of arguments is allowed yet a single judgement based on all arguments is possible and rational. (shrink)

Causal analysis in the social sciences takes advantage of a variety of methods and of a multi-fold source of information and evidence. This pluralistic methodology and source of information raises the question of whether we should accordingly have a pluralistic metaphysics and epistemology. This paper focuses on epistemology and argues that a pluralistic methodology and evidence don’t entail a pluralistic epistemology. It will be shown that causal models employ a single rationale of testing, based on the notion of variation. Further, (...) I shall argue that this monistic epistemology is also involved in alternative philosophical theories of causation. (shrink)

The paper introduces, compares and contrasts formal models of source reliability proposed in the epistemology literature, in particular the prominent models of Bovens and Hartmann and Olsson :127–143, 2011). All are Bayesian models seeking to provide normative guidance, yet they differ subtly in assumptions and resulting behavior. Models are evaluated both on conceptual grounds and through simulations, and the relationship between models is clarified. The simulations both show surprising similarities and highlight relevant differences between these models. Most importantly, however, our (...) evaluations reveal that important normative concerns arguably remain unresolved. The philosophical implications of this for testimony are discussed. (shrink)

Richard Jeffrey developed the formula for probability kinematics with the intent that it would show that strong foundations are epistemologically unnecessary. But the reasons that support strong foundationalism are considerations of dynamics rather than kinematics. The strong foundationalist is concerned with the origin of epistemic force; showing how epistemic force is propagated therefore cannot undermine his position. The weakness of personalism is evident in the difficulty the personalist has in giving a principled answer to the question of when the conditions (...) for the application of the kinematic formula—the rigidity of the posteriors—are fulfilled, a problem made intractable by the personalist commitment to treating changes in intermediate probability as unexplained surds. Because the strong foundationalist admits changes in the intermediate probability of propositions only when there is some change in the foundations, he can avail himself of ananswer to the problem of the rigidity of the posteriors which the personalist cannot regard as complete. While probability kinematics does not make certain foundations unnecessary, the possession of certain foundations also does not make the probability kinematics formula superfluous. The formula allowsus to model the indirect routes by which the foundations influence various non-foundational propositions in the probability distribution. (shrink)

The phenomenon of mutual support presents a specific challenge to the foundationalist epistemologist: Is it possible to model mutual support accurately without using circles of evidential support? We argue that the appearance of loops of support arises from a failure to distinguish different synchronic lines of evidential force. The ban on loops should be clarified to exclude loops within any such line, and basing should be understood as taking place within lines of evidence. Uncertain propositions involved in mutual support relations (...) are conduits to each other of independent evidence originating ultimately in the foundations. We examine several putative examples of benign loops of support and show that, given the distinctions noted, they can be accurately modeled in a foundationalist fashion. We define an evidential "tangle," a relation among three propositions that appears to require a loop for modeling, and prove that all such tangles are trivial in a sense that precludes modeling them with an evidential circle. (shrink)

The principle of the common cause demands that every pair of causally independent but statistically correlated events should be the effect of a common cause. This demand is often supplemented with the requirement that said cause should screen-off the two events from each other. This paper introduces a new probabilistic model for common causes, which generalises this requirement to include sets of distinct but non-disjoint causes. It is demonstrated that the model hereby proposed satisfies the explanatory function generally attributed to (...) common causes and an existential proof is offered. Finally, the model is compared to other known structures intended to perform a similar function, such as Reichenbachian Common Cause Systems and Bayesian Networks. (shrink)

The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when conditioning on the action of some underlying common cause. The extended interpretation of the principle, by contrast, urges that common causes should be called for in order to explain positive deviations between the estimated correlation of two events and the expected value of their correlation. (...) The aim of this paper is to provide the extended reading of the principle with a general probabilistic model, capturing the simultaneous action of a system of multiple common causes. To this end, two distinct models are elaborated, and the necessary and sufficient conditions for their existence are determined. (shrink)