Jon Williamson University of Kent at Canterbury
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  • Faculty, University of Kent at Canterbury
  • PhD, King's College London, 1998.

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More up-to-date papers can be found at http://www.kent.ac.uk/secl/philosophy/jw/
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  1. Brendan Clarke, Donald Gillies, Phyllis Illari, Federica Russo & Jon Williamson (forthcoming). Mechanisms and the Evidence Hierarchy. Topoi:1-22.
    Evidence-based medicine (EBM) makes use of explicit procedures for grading evidence for causal claims. Normally, these procedures categorise evidence of correlation produced by statistical trials as better evidence for a causal claim than evidence of mechanisms produced by other methods. We argue, in contrast, that evidence of mechanisms needs to be viewed as complementary to, rather than inferior to, evidence of correlation. In this paper we first set out the case for treating evidence of mechanisms alongside evidence of correlation in (...)
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  2. Brendan Clarke, Bert Leuridan & Jon Williamson (2013). Modelling Mechanisms with Causal Cycles. Synthese:1-31.
    Mechanistic philosophy of science views a large part of scientific activity as engaged in modelling mechanisms. While science textbooks tend to offer qualitative models of mechanisms, there is increasing demand for models from which one can draw quantitative predictions and explanations. Casini et al. (Theoria 26(1):5–33, 2011) put forward the Recursive Bayesian Networks (RBN) formalism as well suited to this end. The RBN formalism is an extension of the standard Bayesian net formalism, an extension that allows for modelling the hierarchical (...)
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  3. Phyllis Illari & Jon Williamson (2013). In Defence of Activities. Journal for General Philosophy of Science 44 (1):69-83.
    In this paper, we examine what is to be said in defence of Machamer, Darden and Craver’s (MDC) controversial dualism about activities and entities (Machamer, Darden and Craver’s in Philos Sci 67:1–25, 2000). We explain why we believe the notion of an activity to be a novel, valuable one, and set about clearing away some initial objections that can lead to its being brushed aside unexamined. We argue that substantive debate about ontology can only be effective when desiderata for an (...)
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  4. Jon Williamson (2013). How Can Causal Explanations Explain? Erkenntnis 78 (2):257-275.
    The mechanistic and causal accounts of explanation are often conflated to yield a ‘causal-mechanical’ account. This paper prizes them apart and asks: if the mechanistic account is correct, how can causal explanations be explanatory? The answer to this question varies according to how causality itself is understood. It is argued that difference-making, mechanistic, dualist and inferentialist accounts of causality all struggle to yield explanatory causal explanations, but that an epistemic account of causality is more promising in this regard.
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  5. Jon Williamson (2013). How Uncertain Do We Need to Be? Erkenntnis:1-23.
    Expert probability forecasts can be useful for decision making (Sect. 1). But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty (Sect. 2). Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language (Sect. 3). But Bayesian epistemology comes in (...)
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  6. Jon Williamson (2013). Why Frequentists and Bayesians Need Each Other. Erkenntnis 78 (2):293-318.
    The orthodox view in statistics has it that frequentism and Bayesianism are diametrically opposed—two totally incompatible takes on the problem of statistical inference. This paper argues to the contrary that the two approaches are complementary and need to mesh if probabilistic reasoning is to be carried out correctly.
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  7. Phyllis Illari & Jon Williamson (2012). What is a Mechanism? Thinking About Mechanisms Across the Sciences. European Journal for Philosophy of Science 2 (1):119-135.
    After a decade of intense debate about mechanisms, there is still no consensus characterization. In this paper we argue for a characterization that applies widely to mechanisms across the sciences. We examine and defend our disagreements with the major current contenders for characterizations of mechanisms. Ultimately, we indicate that the major contenders can all sign up to our characterization.
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  8. Federica Russo & Jon Williamson (2012). EnviroGenomarkers: The Interplay Between Mechanisms and Difference Making in Establishing Causal Claims. Medicine Studies 3 (4):249-262.
    According to Russo and Williamson (Int Stud Philos Sci 21(2):157–170, 2007, Hist Philos Life Sci 33:389–396, 2011a, Philos Sci 1(1):47–69, 2011b), in order to establish a causal claim of the form, ‘C is a cause of E’, one typically needs evidence that there is an underlying mechanism between C and E as well as evidence that C makes a difference to E. This thesis has been used to argue that hierarchies of evidence, as championed by evidence-based movements, tend to give (...)
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  9. J. Williamson (2012). Calibration and Convexity: Response to Gregory Wheeler. British Journal for the Philosophy of Science 63 (4):851-857.
    This note responds to some criticisms of my recent book In Defence of Objective Bayesianism that were provided by Gregory Wheeler in his ‘Objective Bayesian Calibration and the Problem of Non-convex Evidence’.
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  10. J. Williamson (2012). Reliable Reasoning, by Gilbert Harman and Sanjeev Kulkarni. Mind 121 (484):1073-1076.
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  11. Lorenzo Casini, Phyllis Mckay Illari, Federica Russo & Jon Williamson (2011). Models for Prediction, Explanation and Control. Theoria 26 (1):5-33.
    The Recursive Bayesian Net (RBN) formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular (...)
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  12. George Darby & Jon Williamson (2011). Imaging Technology and the Philosophy of Causality. Philosophy and Technology 24 (2):115-136.
    Russo and Williamson (Int Stud Philos Sci 21(2):157–170, 2007) put forward the thesis that, at least in the health sciences, to establish the claim that C is a cause of E, one normally needs evidence of an underlying mechanism linking C and E as well as evidence that C makes a difference to E. This epistemological thesis poses a problem for most current analyses of causality which, in virtue of analysing causality in terms of just one of mechanisms or difference (...)
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  13. Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler & Jon Williamson (2011). Probabilistic Logics and Probabilistic Networks. Synthese Library.
    Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.
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  14. Phyllis McKay Illari, Federica Russo & Jon Williamson (eds.) (2011). Causality in the Sciences. Oxford University Press.
    The book tackles these questions as well as others concerning the use of causality in the sciences.
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  15. Phyllis McKay Illari, Federica Russo & Jon Williamson (2011). Why Look at Causality in the Sciences? In Phyllis McKay Illari, Federica Russo & Jon Williamson (eds.), Causality in the Sciences. Oup Oxford.
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  16. Phyllis McKay Illari & Jon Williamson (2011). Mechanisms Are Real and Local. In Phyllis McKay Illari, Federica Russo & Jon Williamson (eds.), Causality in the Sciences. Oup Oxford.
    Mechanisms have become much-discussed, yet there is still no consensus on how to characterise them. In this paper, we start with something everyone is agreed on – that mechanisms explain – and investigate what constraints this imposes on our metaphysics of mechanisms. We examine two widely shared premises about how to understand mechanistic explanation: (1) that mechanistic explanation offers a welcome alternative to traditional laws-based explanation and (2) that there are two senses of mechanistic explanation that we call ‘epistemic explanation’ (...)
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  17. Phyllis McKay Illari, Federica Russo & Jon Williamson (eds.) (2011). Causality in the Sciences. Oxford University Press.
    There is a need for integrated thinking about causality, probability and mechanisms in scientific methodology. Causality and probability are long-established central concepts in the sciences, with a corresponding philosophical literature examining their problems. On the other hand, the philosophical literature examining mechanisms is not long-established, and there is no clear idea of how mechanisms relate to causality and probability. But we need some idea if we are to understand causal inference in the sciences: a panoply of disciplines, ranging from epidemiology (...)
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  18. Federica Russo & Jon Williamson (2011). Epistemic Causality and Evidence-Based Medicine. History and Philosophy of the Life Sciences 33 (4).
    Causal claims in biomedical contexts are ubiquitous albeit they are not always made explicit. This paper addresses the question of what causal claims mean in the context of disease. It is argued that in medical contexts causality ought to be interpreted according to the epistemic theory. The epistemic theory offers an alternative to traditional accounts that cash out causation either in terms of “difference-making” relations or in terms of mechanisms. According to the epistemic approach, causal claims tell us about which (...)
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  19. Federica Russo & Jon Williamson (2011). Generic Versus Single-Case Causality: The Case of Autopsy. [REVIEW] European Journal for Philosophy of Science 1 (1):47-69.
    This paper addresses questions about how the levels of causality (generic and single-case causality) are related. One question is epistemological: can relationships at one level be evidence for relationships at the other level? We present three kinds of answer to this question, categorised according to whether inference is top-down, bottom-up, or the levels are independent. A second question is metaphysical: can relationships at one level be reduced to relationships at the other level? We present three kinds of answer to this (...)
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  20. Gregory Wheeler & Jon Williamson (2011). Evidential Probability and Objective Bayesian Epistemology. In Prasanta S. Bandyopadhyay & Malcolm Forster (eds.), Handbook of the Philosophy of Statistics. Elsevier.
    In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.
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  21. Jon Williamson (2011). An Objective Bayesian Account of Confirmation. In. In Dennis Dieks, Wenceslao Gonzalo, Thomas Uebel, Stephan Hartmann & Marcel Weber (eds.), Explanation, Prediction, and Confirmation. Springer. 53--81.
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  22. Jon Williamson (2011). Generic Versus Single-Case Causality: The Case of Autopsy. [REVIEW] European Journal for Philosophy of Science 1 (1):47-69.
    This paper addresses questions about how the levels of causality (generic and single-case causality) are related. One question is epistemological: can relationships at one level be evidence for relationships at the other level? We present three kinds of answer to this question, categorised according to whether inference is top-down, bottom-up, or the levels are independent. A second question is metaphysical: can relationships at one level be reduced to relationships at the other level? We present three kinds of answer to this (...)
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  23. Jon Williamson (2011). Imaging Technology and the Philosophy of Causality. Philosophy and Technology 24 (2):115-136.
    Russo and Williamson (Int Stud Philos Sci 21(2):157–170, 2007) put forward the thesis that, at least in the health sciences, to establish the claim that C is a cause of E, one normally needs evidence of an underlying mechanism linking C and E as well as evidence that C makes a difference to E. This epistemological thesis poses a problem for most current analyses of causality which, in virtue of analysing causality in terms of just one of mechanisms or difference (...)
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  24. Jon Williamson (2011). Models for Prediction, Explanation and Control: Recursive Bayesian Networks. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 26 (70):5-33.
    The Recursive Bayesian Net (RBN) formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular (...)
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  25. Jon Williamson (2011). Mechanistic Theories of Causality Part II. Philosophy Compass 6 (6):433-444.
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  26. Jon Williamson (2011). Mechanistic Theories of Causality Part I. Philosophy Compass 6 (6):421-432.
    Part I of this paper introduces a range of mechanistic theories of causality, including process theories and the complex-systems theories, and some of the problems they face. Part II argues that while there is a decisive case against a purely mechanistic analysis, a viable theory of causality must incorporate mechanisms as an ingredient, and describes one way of providing an analysis of causality which reaps the rewards of the mechanistic approach without succumbing to its pitfalls.
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  27. Jon Williamson (2011). Objective Bayesianism, Bayesian Conditionalisation and Voluntarism. Synthese 178 (1):67-85.
    Objective Bayesianism has been criticised on the grounds that objective Bayesian updating, which on a finite outcome space appeals to the maximum entropy principle, differs from Bayesian conditionalisation. The main task of this paper is to show that this objection backfires: the difference between the two forms of updating reflects negatively on Bayesian conditionalisation rather than on objective Bayesian updating. The paper also reviews some existing criticisms and justifications of conditionalisation, arguing in particular that the diachronic Dutch book justification fails (...)
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  28. Jon Williamson (2011). Teaching & Learning Guide For: Mechanistic Theories of Causality. Philosophy Compass 6 (6):445-447.
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  29. Phyllis McKay Illari & Jon Williamson (2010). Function and Organization: Comparing the Mechanisms of Protein Synthesis and Natural Selection. Studies in History and Philosophy of Science Part C 41 (3):279-291.
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  30. Jon Williamson (2010). B. De Finetti, Philosophical Lectures on Probability. [REVIEW] Philosophia Mathematica 18 (1):130-135.
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  31. Jon Williamson (2010). Explication. The Philosophers' Magazine 50 (50):114-115.
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  32. Jon Williamson (2010). Function and Organization: Comparing the Mechanisms of Protein Synthesis and Natural Selection. Studies in History and Philosophy of Science Part C 41 (3):279-291.
    In this paper, we compare the mechanisms of protein synthesis and natural selection. We identify three core elements of mechanistic explanation: functional individuation, hierarchical nestedness or decomposition, and organization. These are now well understood elements of mechanistic explanation in fields such as protein synthesis, and widely accepted in the mechanisms literature. But Skipper and Millstein have argued (2005) that natural selection is neither decomposable nor organized. This would mean that much of the current mechanisms literature does not apply to the (...)
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  33. Jon Williamson (2010). In Defence of Objective Bayesianism. OUP Oxford.
    How strongly should you believe the various propositions that you can express? -/- That is the key question facing Bayesian epistemology. Subjective Bayesians hold that it is largely (though not entirely) up to the agent as to which degrees of belief to adopt. Objective Bayesians, on the other hand, maintain that appropriate degrees of belief are largely (though not entirely) determined by the agent's evidence. This book states and defends a version of objective Bayesian epistemology. According to this version, objective (...)
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  34. Jon Williamson (2010). Bruno de Finetti. Philosophical Lectures on Probability. Collected, Edited, and Annotated by Alberto Mura. Translated by Hykel Hosni. Synthese Library; 340. [REVIEW] Philosophia Mathematica 18 (1):130-135.
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  35. Jon Williamson (2009). Probabilistic Theories. In Helen Beebee, Christopher Hitchcock & Peter Menzies (eds.), The Oxford Handbook of Causation. Oup Oxford.
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  36. Jon Williamson (2009). Probabilistic Theories of Causality. In Helen Beebee, Peter Menzies & Christopher Hitchcock (eds.), The Oxford Handbook of Causation. Oxford University Press. 185--212.
    This chapter provides an overview of a range of probabilistic theories of causality, including those of Reichenbach, Good and Suppes, and the contemporary causal net approach. It discusses two key problems for probabilistic accounts: counterexamples to these theories and their failure to account for the relationship between causality and mechanisms. It is argued that to overcome the problems, an epistemic theory of causality is required.
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  37. Jon Williamson (2009). Review: Response to Glymour. [REVIEW] British Journal for the Philosophy of Science 60 (4):857 - 860.
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  38. Jon Williamson (2009). Response to Glymour. [REVIEW] British Journal for the Philosophy of Science 60 (4):857-860.
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  39. Jan-Willem Romeijn, Jon Williamson, Gregory Wheeler & Rolf Haenni (2008). Possible Semantics for a Common Framework of Probabilistic Logics. In V. N. Huynh (ed.), International Workshop on Interval Probabilistic Uncertainty and Non-Classical Logics. Springer.
    In V. N. Huynh (ed.): Interval / Probabilistic Uncertainty and Non-Classical Logics, Advances in Soft Computing Series, Springer 2008, pp. 268-279. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
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  40. Gregory Wheeler, Jon Williamson, Jan-Willem Romeijn & Rolf Haenni (2008). Possible Semantics for a Common Framework of Probabilistic Logics. In V. N. Huynh (ed.), International Workshop on Interval Probabilistic Uncertainty and Non-Classical Logics. Springer.
    Summary. This paper proposes a common framework for various probabilistic logics. It consists of a set of uncertain premises with probabilities attached to them. This raises the question of the strength of a conclusion, but without imposing a particular semantics, no general solution is possible. The paper discusses several possible semantics by looking at it from the perspective of probabilistic argumentation.
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  41. Jon Williamson (2008). Objective Bayesianism with Predicate Languages. Synthese 163 (3):341 - 356.
    Objective Bayesian probability is often defined over rather simple domains, e.g., finite event spaces or propositional languages. This paper investigates the extension of objective Bayesianism to first-order logical languages. It is argued that the objective Bayesian should choose a probability function, from all those that satisfy constraints imposed by background knowledge, that is closest to a particular frequency-induced probability function which generalises the λ = 0 function of Carnap’s continuum of inductive methods.
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  42. Jon Williamson, Jan-Willem Romeijn, Rolf Haenni & Gregory Wheeler (2008). Logical Relations in a Statistical Problem. In Benedikt Lowe, Jan-Willem Romeijn & Eric Pacuit (eds.), Proceedings of the Foundations of the Formal Sciences VI: Reasoning about probabilities and probabilistic reasoning. College Publications.
    This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input. After an introduction to the framework as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The framework thus provides insight into the relations between these approaches, it (...)
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  43. Federica Russo & Jon Williamson (eds.) (2007). Causality and Probability in the Sciences.
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  44. Federica Russo & Jon Williamson (2007). Interpreting Causality in the Health Sciences. International Studies in the Philosophy of Science 21 (2):157 – 170.
    We argue that the health sciences make causal claims on the basis of evidence both of physical mechanisms, and of probabilistic dependencies. Consequently, an analysis of causality solely in terms of physical mechanisms or solely in terms of probabilistic relationships, does not do justice to the causal claims of these sciences. Yet there seems to be a single relation of cause in these sciences - pluralism about causality will not do either. Instead, we maintain, the health sciences require a theory (...)
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  45. Federica Russo & Jon Williamson (2007). Interpreting Probability in Causal Models for Cancer. In Federica Russo & Jon Williamson (eds.), Causality and Probability in the Sciences. 217--242.
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  46. Jon Williamson (2007). Interpreting Causality in the Health Sciences. International Studies in the Philosophy of Science 21 (2):157-170.
    We argue that the health sciences make causal claims on the basis of evidence both of physical mechanisms, and of probabilistic dependencies. Consequently, an analysis of causality solely in terms of physical mechanisms or solely in terms of probabilistic relationships, does not do justice to the causal claims of these sciences. Yet there seems to be a single relation of cause in these sciences?pluralism about causality will not do either. Instead, we maintain, the health sciences require a theory of causality (...)
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  47. Jon Williamson (2007). Inductive Influence. British Journal for the Philosophy of Science 58 (4):689 - 708.
    Objective Bayesianism has been criticised for not allowing learning from experience: it is claimed that an agent must give degree of belief ½ to the next raven being black, however many other black ravens have been observed. I argue that this objection can be overcome by appealing to objective Bayesian nets, a formalism for representing objective Bayesian degrees of belief. Under this account, previous observations exert an inductive influence on the next observation. I show how this approach can be used (...)
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  48. Matt Williams & Jon Williamson (2006). Combining Argumentation and Bayesian Nets for Breast Cancer Prognosis. Journal of Logic, Language and Information 15 (1-2):155-178.
    We present a new framework for combining logic with probability, and demonstrate the application of this framework to breast cancer prognosis. Background knowledge concerning breast cancer prognosis is represented using logical arguments. This background knowledge and a database are used to build a Bayesian net that captures the probabilistic relationships amongst the variables. Causal hypotheses gleaned from the Bayesian net in turn generate new arguments. The Bayesian net can be queried to help decide when one argument attacks another. The Bayesian (...)
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  49. J. Williamson (2006). From Bayesianism to the Epistemic View of Mathematics: Review of R. Jeffrey, Subjective Probability: The Real Thing. [REVIEW] Philosophia Mathematica 14 (3):365-369.
  50. Jon Williamson (2006). Combining Argumentation and Bayesian Nets for Breast Cancer Prognosis. Journal of Logic, Language and Information 15 (1-2):155-178.
    We present a new framework for combining logic with probability, and demonstrate the application of this framework to breast cancer prognosis. Background knowledge concerning breast cancer prognosis is represented using logical arguments. This background knowledge and a database are used to build a Bayesian net that captures the probabilistic relationships amongst the variables. Causal hypotheses gleaned from the Bayesian net in turn generate new arguments. The Bayesian net can be queried to help decide when one argument attacks another. The Bayesian (...)
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  51. Jon Williamson (2006). Combining Probability and Logic: Introduction. Journal of Logic, Language and Information 15 (1-2):1-3.
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  52. Jon Williamson (2006). Causal Pluralism Versus Epistemic Causality. Philosophica 77 (1):69-96.
    It is tempting to analyse causality in terms of just one of the indicators of causal relationships, e.g., mechanisms, probabilistic dependencies or independencies, counterfactual conditionals or agency considerations. While such an analysis will surely shed light on some aspect of our concept of cause, it will fail to capture the whole, rather multifarious, notion. So one might instead plump for pluralism: a different analysis for a different occasion. But we do not seem to have lots of different concepts of cause (...)
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  53. Jon Williamson (2006). Dispositional Versus Epistemic Causality. Minds and Machines 16 (3):259-276.
    I put forward several desiderata that a philosophical theory of causality should satisfy: it should account for the objectivity of causality, it should underpin formalisms for causal reasoning, it should admit a viable epistemology, it should be able to cope with the great variety of causal claims that are made, and it should be ontologically parsimonious. I argue that Nancy Cartwright’s dispositional account of causality goes part way towards meeting these criteria but is lacking in important respects. I go on (...)
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  54. Jon Williamson (2006). From Bayesianism to the Epistemic View of Mathematics: Review of R. Jeffrey, Subjective Probability: The Real Thing. [REVIEW] Philosophia Mathematica 14 (3):365-369.
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  55. Jon Williamson (2006). Introduction. Journal of Logic, Language and Information 15 (1-2):1-3.
    The need for a coherent answer to this question has become increasingly urgent in the past few years, particularly in the field of artificial intelligence. There, both logical and probabilistic techniques are routinely applied in an attempt to solve complex problems such as parsing natural language and determining the way proteins fold. The hope is that some combination of logic and probability will produce better solutions. After all, both natural language and protein molecules have some structure that admits logical representation (...)
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  56. Jon Williamson (2004). A Dynamic Interaction Between Machine Learning and the Philosophy of Science. Minds and Machines 14 (4):539-549.
    The relationship between machine learning and the philosophy of science can be classed as a dynamic interaction: a mutually beneficial connection between two autonomous fields that changes direction over time. I discuss the nature of this interaction and give a case study highlighting interactions between research on Bayesian networks in machine learning and research on causality and probability in the philosophy of science.
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  57. Jon Williamson (2004). Bayesian Nets and Causality: Philosophical and Computational Foundations. OUP Oxford.
    Bayesian nets are widely used in artificial intelligence as a calculus for causal reasoning, enabling machines to make predictions, perform diagnoses, take decisions and even to discover causal relationships. But many philosophers have criticised and ultimately rejected the central assumption on which such work is based - the Causal Markov Condition. So should Bayesian nets be abandoned? What explains their success in artificial intelligence? -/- This book argues that the Causal Markov Condition holds as a default rule: it often holds (...)
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  58. Jon Williamson (2003). Abduction, Reason, and Science: Processes of Discovery and Explanation. British Journal for the Philosophy of Science 54 (2):353-358.
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  59. Jon Williamson (2003). Bayesianism and Language Change. Journal of Logic, Language and Information 12 (1):53-97.
    Bayesian probability is normally defined over a fixed language or eventspace. But in practice language is susceptible to change, and thequestion naturally arises as to how Bayesian degrees of belief shouldchange as language changes. I argue here that this question poses aserious challenge to Bayesianism. The Bayesian may be able to meet thischallenge however, and I outline a practical method for changing degreesof belief over changes in finite propositional languages.
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  60. David Corfield & Jon Williamson (eds.) (2001). Foundations of Bayesianism. Kluwer Academic Publishers.
    The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the ...
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  61. Jon Williamson (2001). Foundations for Bayesian Networks. In. In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. 75--115.
    Bayesian networks may either be treated purely formally or be given an interpretation. I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches.
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  62. Jon Williamson & David Corfield (2001). Introduction: Bayesianism Into the 21st Century. In. In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. 1--16.
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  63. J. Williamson (1999). Countable Additivity and Subjective Probability. British Journal for the Philosophy of Science 50 (3):401-416.
    While there are several arguments on either side, it is far from clear as to whether or not countable additivity is an acceptable axiom of subjective probability. I focus here on de Finetti's central argument against countable additivity and provide a new Dutch book proof of the principle, To argue that if we accept the Dutch book foundations of subjective probability, countable additivity is an unavoidable constraint.
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  64. Jon Williamson, From Bayesian Epistemology to Inductive Logic.
    Inductive logic admits a variety of semantics (Haenni et al., 2011, Part 1). This paper develops semantics based on the norms of Bayesian epistemology (Williamson, 2010, Chapter 7). §1 introduces the semantics and then, in §2, the paper explores methods for drawing inferences in the resulting logic and compares the methods of this paper with the methods of Barnett and Paris (2008). §3 then evaluates this Bayesian inductive logic in the light of four traditional critiques of inductive logic, arguing (i) (...)
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  65. Jon Williamson, Probability Logic.
    Practical reasoning requires decision—making in the face of uncertainty. Xenelda has just left to go to work when she hears a burglar alarm. She doesn’t know whether it is hers but remembers that she left a window slightly open. Should she be worried? Her house may not be being burgled, since the wind or a power cut may have set the burglar alarm off, and even if it isn’t her alarm sounding she might conceivably be being burgled. Thus Xenelda can (...)
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  66. Jon Williamson, Recursive Bayesian Nets for Prediction, Explanation and Control in Cancer Science.
    this paper we argue that the formalism can also be applied to modelling the hierarchical structure of physical mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations are vital for prediction, explanation and control respectively, a recursive Bayesian net can be applied to all these tasks. We show how a Recursive Bayesian Net can be used to model mechanisms in cancer science. (...)
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  67. Jon Williamson, The Philosophy of Science and its Relation to Machine Learning.
    In this chapter I discuss connections between machine learning and the philosophy of science. First I consider the relationship between the two disciplines. There is a clear analogy between hypothesis choice in science and model selection in machine learning. While this analogy has been invoked to argue that the two disciplines are essentially doing the same thing and should merge, I maintain that the disciplines are distinct but related and that there is a dynamic interaction operating between the two: a (...)
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  68. Jon Williamson, Why Look at Causality in the Sciences? A Manifesto.
    This introduction to the volume begins with a manifesto that puts forward two theses: first, that the sciences are the best place to turn in order to understand causality; second, that scientifically-informed philosophical investigation can bring something to the sciences too. Next, the chapter goes through the various parts of the volume, drawing out relevant background and themes of the chapters in those parts. Finally, the chapter discusses the progeny of the papers and identifies some next steps for research into (...)
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  69. Jon Williamson & D. M. Gabbay, Recursive Causality in Bayesian Networks and Self-Fibring Networks.
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  70. Jon Williamson, Aggregating Judgements by Merging Evidence.
    The theory of belief revision and merging has recently been applied to judgement aggregation. In this paper I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a threestep strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the basis of this merged evidence (...)
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  71. Jon Williamson, A Note on Probabilistic Logics and Probabilistic Networks.
    ϕ1, . . . , ϕn |≈ ψ? Here ϕ1, . . . , ϕn, ψ are premisses of some formal language, such as a propositional language or a predicate language. |≈ is an entailment relation: the entailment holds if all models of the premisses also satisfy the conclusion, where the logic provides some suitable notion of ‘model’ and ‘satisfy’. Proof theory is normally invoked to answer a question of this form: one tries to prove the conclusion from the premisses (...)
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  72. Jon Williamson, Bayesian Nets and Causality.
    How should we reason with causal relationships? Much recent work on this question has been devoted to the theses (i) that Bayesian nets provide a calculus for causal reasoning and (ii) that we can learn causal relationships by the automated learning of Bayesian nets from observational data. The aim of this book is to..
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  73. Jon Williamson, Bayesian Networks for Logical Reasoning.
    By identifying and pursuing analogies between causal and logical influence I show how the Bayesian network formalism can be applied to reasoning about logical deductions.
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  74. Jon Williamson, Causality.
    This chapter addresses two questions: what are causal relationships? how can one discover causal relationships? I provide a survey of the principal answers given to these questions, followed by an introduction to my own view, epistemic causality, and then a comparison of epistemic causality with accounts provided by Judea Pearl and Huw Price.
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  75. Jon Williamson, Editorial.
    How is probability related to logic? Should probability and logic be combined? If so, how? Bayesianism tells us we ought to reason probabilistically. In that sense, probability theory is logic. How then does probability theory relate to classical logic and the various non-classical logics that also stake a claim on normative reasoning? Is probability theory to be preferred over other logics or vice versa? Is probability theory to be used in some situations, and the other logics in other situations? Or (...)
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  76. Jon Williamson, Epistemic Complexity From an Objective Bayesian Perspective.
    Evidence can be complex in various ways: e.g., it may exhibit structural complexity, containing information about causal, hierarchical or logical structure as well as empirical data, or it may exhibit combinatorial complexity, containing a complex combination of kinds of information. This paper examines evidential complexity from the point of view of Bayesian epistemology, asking: how should complex evidence impact on an agent’s degrees of belief? The paper presents a high-level overview of an objective Bayesian answer: it presents the objective Bayesian (...)
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  77. Jon Williamson, Evidential Probability, Objective Bayesianism, Non-Monotonicity and System P.
    This paper is a comparison of how first-order Kyburgian Evidential Probability (EP), second-order EP, and objective Bayesian epistemology compare as to the KLM system-P rules for consequence relations and the monotonic / non-monotonic divide.
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  78. Jon Williamson, Intervention, Underdetermination, and Theory Generation.
    We consider the use of intervention data for eliminating the underdetermination in statistical modelling, and for guiding extensions of the statistical models. The leading example is factor analysis, a major statistical tool in the social sciences. We first relate indeterminacy in factor analysis to the problem of underdetermination. Then we draw a parallel between factor analysis models and Bayesian networks with hidden nodes, which allows us to clarify the use of intervention data for dealing with indeterminacy. It will be shown (...)
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  79. Jon Williamson, Learning Causal Relationships.
    How ought we learn causal relationships? While Popper advocated a hypothetico-deductive logic of causal discovery, inductive accounts are currently in vogue. Many inductive approaches depend on the causal Markov condition as a fundamental assumption. This condition, I maintain, is not universally valid, though it is justifiable as a default assumption. In which case the results of the inductive causal learning procedure must be tested before they can be accepted. This yields a synthesis of the hypothetico-deductive and inductive accounts, which forms (...)
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  80. Jon Williamson, Maximising Entropy Efficiently.
    Recommended citation: . . Link¨ oping Electronic Articles in Computer and Information Science, Vol. 7(2002): nr 0. http://www.ep.liu.se/ea/cis/2002/00/. September 18, 2002. </div><div class="catsCon" id="ecats-con-WILMEE">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILMEE&proxyId=&u=http%3A%2F%2Fwww.kent.ac.uk%2Fsecl%2Fphilosophy%2Fjw%2F2002%2Fmaxenteffic.pdf" target='_blank' >Direct download</a> (<a href='/rec/WILMEE'>3 more</a>)  <div id="ml-WILMEE" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILMEE','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILMEE" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILMEE')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILMEE"></span></div></div></li> <li id='eWILMOB-2' onclick="ee('click','WILMOB-2')" onmouseover="ee('over','WILMOB-2')" onmouseout="ee('out','WILMOB-2')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILMOB-2"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Motivating Objective Bayesianism: From Empirical Constraints to Objective Probabilities.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">Kyburg goes half-way towards objective Bayesianism. He accepts that frequencies constrain rational belief to an interval but stops short of isolating an optimal degree of belief within this interval. I examine the case for going the whole hog. </div><div class="catsCon" id="ecats-con-WILMOB-2">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILMOB-2&proxyId=&u=http%3A%2F%2Fwww.kent.ac.uk%2Fsecl%2Fphilosophy%2Fjw%2F2005%2Fmotivating.pdf" target='_blank' >Direct download</a> (<a href='/rec/WILMOB-2'>2 more</a>)  <div id="ml-WILMOB-2" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILMOB-2','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILMOB-2" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILMOB-2')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILMOB-2"></span></div></div></li> <li id='eWILMTO-2' onclick="ee('click','WILMTO-2')" onmouseover="ee('over','WILMTO-2')" onmouseout="ee('out','WILMTO-2')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILMTO-2"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Mechanistic Theories of Causality.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">After introducing a range of mechanistic theories of causality and some of the problems they face, I argue that while there is a decisive case against a purely mechanistic analysis, a viable theory of causality must incorporate mechanisms as an ingredient. I describe one way of providing an analysis of causality which reaps the rewards of the mechanistic approach without succumbing to its pitfalls. </div><div class="catsCon" id="ecats-con-WILMTO-2">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILMTO-2&proxyId=&u=http%3A%2F%2Fwww.kent.ac.uk%2Fsecl%2Fphilosophy%2Fjw%2F2010%2FMechanisticCausality.pdf" target='_blank' >Direct download</a> (<a href='/rec/WILMTO-2'>3 more</a>)  <div id="ml-WILMTO-2" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILMTO-2','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILMTO-2" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILMTO-2')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILMTO-2"></span></div></div></li> <li id='eWILOBN' onclick="ee('click','WILOBN')" onmouseover="ee('over','WILOBN')" onmouseout="ee('out','WILOBN')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILOBN"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Objective Bayesian Nets.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">I present a formalism that combines two methodologies: objective Bayesianism and Bayesian nets. According to objective Bayesianism, an agent’s degrees of belief (i) ought to satisfy the axioms of probability, (ii) ought to satisfy constraints imposed by background knowledge, and (iii) should otherwise be as non-committal as possible (i.e. have maximum entropy). Bayesian nets offer an efficient way of representing and updating probability functions. An objective Bayesian net is a Bayesian net representation of the maximum entropy probability function. </div><div class="catsCon" id="ecats-con-WILOBN"><div><a class='catName' href='/browse/bayesian-reasoning-misc' rel='section'>Bayesian Reasoning, Misc</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> </div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILOBN&proxyId=&u=http%3A%2F%2Fwww.kent.ac.uk%2Fsecl%2Fphilosophy%2Fjw%2F2005%2Fobnets.pdf" target='_blank' >Direct download</a> (<a href='/rec/WILOBN'>2 more</a>)  <div id="ml-WILOBN" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILOBN','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILOBN" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILOBN')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILOBN"></span></div></div></li> <li id='eWILOBN-2' onclick="ee('click','WILOBN-2')" onmouseover="ee('over','WILOBN-2')" onmouseout="ee('out','WILOBN-2')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILOBN-2"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Objective Bayesian Nets for Systems Modelling and Prognosis in Breast Cancer.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">Cancer treatment decisions should be based on all available evidence. But this evidence is complex and varied: it includes not only the patient’s symptoms and expert knowledge of the relevant causal processes, but also clinical databases relating to past patients, databases of observations made at the molecular level, and evidence encapsulated in scientific papers and medical informatics systems. Objective Bayesian nets offer a principled path to knowledge integration, and we show in this chapter how they can be applied to integrate<span id="WILOBN-2-absexp"> (<span class="ll" onclick='$("WILOBN-2-abstract2").show();$("WILOBN-2-absexp").hide()'>...</span>)</span><span id="WILOBN-2-abstract2" style="display:none"> various kinds of evidence in the cancer domain. This is important from the systems biology perspective, which needs to integrate data that concern different levels of analysis, and is also important from the point of view of medical informatics. (<span class="ll" onclick='$("WILOBN-2-abstract2").hide();$("WILOBN-2-absexp").show();'>shrink</span>)</span></div><div class="catsCon" id="ecats-con-WILOBN-2"><div><a class='catName' href='/browse/bayesian-reasoning-misc' rel='section'>Bayesian Reasoning, Misc</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> </div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILOBN-2&proxyId=&u=http%3A%2F%2Fwww.kent.ac.uk%2Fsecl%2Fphilosophy%2Fjw%2F2006%2FObnetsPrognosis.pdf" target='_blank' >Direct download</a> (<a href='/rec/WILOBN-2'>2 more</a>)  <div id="ml-WILOBN-2" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILOBN-2','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILOBN-2" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILOBN-2')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILOBN-2"></span></div></div></li> <li id='eWILOBP' onclick="ee('click','WILOBP')" onmouseover="ee('over','WILOBP')" onmouseout="ee('out','WILOBP')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILOBP"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Objective Bayesian Probabilistic Logic.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets<span id="WILOBP-absexp"> (<span class="ll" onclick='$("WILOBP-abstract2").show();$("WILOBP-absexp").hide()'>...</span>)</span><span id="WILOBP-abstract2" style="display:none"> is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics. (<span class="ll" onclick='$("WILOBP-abstract2").hide();$("WILOBP-absexp").show();'>shrink</span>)</span></div><div class="catsCon" id="ecats-con-WILOBP"><div><a class='catName' href='/browse/bayesian-reasoning-misc' rel='section'>Bayesian Reasoning, Misc</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> </div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILOBP&proxyId=&u=http%3A%2F%2Fkar.kent.ac.uk%2F20878%2F" target='_blank' >Direct download</a> (<a href='/rec/WILOBP'>3 more</a>)  <div id="ml-WILOBP" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILOBP','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILOBP" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILOBP')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILOBP"></span></div></div></li> <li id='eWILPOP-3' onclick="ee('click','WILPOP-3')" onmouseover="ee('over','WILPOP-3')" onmouseout="ee('out','WILPOP-3')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILPOP-3"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Philosophies of Probability: Objective Bayesianism and its Challenges.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general. </div><div class="catsCon" id="ecats-con-WILPOP-3"><div><a class='catName' href='/browse/bayesian-reasoning-misc' rel='section'>Bayesian Reasoning, Misc</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> <div><a class='catName' href='/browse/logical-probability' rel='section'>Logical Probability</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> </div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILPOP-3&proxyId=&u=http%3A%2F%2Fwww.kent.ac.uk%2Fsecl%2Fphilosophy%2Fjw%2F2004%2Fphilprob.pdf" target='_blank' >Direct download</a>  <div id="ml-WILPOP-3" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILPOP-3','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILPOP-3" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILPOP-3')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILPOP-3"></span></div></div></li> <li id='eWILSIO' onclick="ee('click','WILSIO')" onmouseover="ee('over','WILSIO')" onmouseout="ee('out','WILSIO')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILSIO"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Special Issue on Combining Probability and Logic Introduction.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">This volume arose out of an international, interdisciplinary academic network on Probabilistic Logic and Probabilistic Networks involving four of us (Haenni, Romeijn, Wheeler and Williamson), called Progicnet and funded by the Leverhulme Trust from 2006–8. Many of the papers in this volume were presented at an associated conference, the Third Workshop on Combining Probability and Logic (Progic 2007), held at the University of Kent on 5–7 September 2007. The papers in this volume concern either the special focus on the connection<span id="WILSIO-absexp"> (<span class="ll" onclick='$("WILSIO-abstract2").show();$("WILSIO-absexp").hide()'>...</span>)</span><span id="WILSIO-abstract2" style="display:none"> between probabilistic logic and probabilistic networks or the more general question of the links between probability and logic. Here we introduce probabilistic logic, probabilistic networks, current and future directions of research and also the themes of the papers that follow. (<span class="ll" onclick='$("WILSIO-abstract2").hide();$("WILSIO-absexp").show();'>shrink</span>)</span></div><div class="catsCon" id="ecats-con-WILSIO"><div><a class='catName' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div></div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILSIO&proxyId=&u=http%3A%2F%2Fwww.kent.ac.uk%2Fsecl%2Fphilosophy%2Fjw%2F2007%2Fprogic_editorial.pdf" target='_blank' >Direct download</a>  <div id="ml-WILSIO" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILSIO','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILSIO" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILSIO')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILSIO"></span></div></div></li> <li id='eCLATET' onclick="ee('click','CLATET')" onmouseover="ee('over','CLATET')" onmouseout="ee('out','CLATET')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/CLATET"><span class='name'>Brendan Clarke</span>, <span class='name'>Donald Gillies</span>, <span class='name'>Phyllis Illari</span>, <span class='name'>Frederica Russo</span> & <span class='name'>Jon Williamson</span>, <span class='articleTitle'>The Evidence That Evidence-Based Medicine Omits.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">According to current hierarchies of evidence for EBM, evidence of correlation (e.g., from RCTs) is always more important than evidence of mechanisms when evaluating and establishing causal claims. We argue that evidence of mechanisms needs to be treated alongside evidence of correlation. This is for three reasons. First, correlation is always a fallible indicator of causation, subject in particular to the problem of confounding; evidence of mechanisms can in some cases be more important than evidence of correlation when assessing a<span id="CLATET-absexp"> (<span class="ll" onclick='$("CLATET-abstract2").show();$("CLATET-absexp").hide()'>...</span>)</span><span id="CLATET-abstract2" style="display:none"> causal claim. Second, evidence of mechanisms is often required in order to obtain evidence of correlation (for example, in order to set up and evaluate RCTs). Third, evidence of mechanisms is often required in order to generalise and apply causal claims. While the EBM movement has been enormously successful in making explicit and critically examining one aspect of our evidential practice, i.e., evidence of correlation, we wish to extend this line of work to make explicit and critically examine a second aspect of our evidential practices: evidence of mechanisms. (<span class="ll" onclick='$("CLATET-abstract2").hide();$("CLATET-absexp").show();'>shrink</span>)</span></div><div class="catsCon" id="ecats-con-CLATET">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=CLATET&proxyId=&u=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0091743512005452" target='_blank' >Direct download</a> (<a href='/rec/CLATET'>4 more</a>)  <div id="ml-CLATET" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('CLATET','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-CLATET" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('CLATET')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-CLATET"></span></div></div></li> <li id='eLANOBA' onclick="ee('click','LANOBA')" onmouseover="ee('over','LANOBA')" onmouseout="ee('out','LANOBA')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/LANOBA"><span class='name'>Jürgen Landes</span> & <span class='name'>Jon Williamson</span>, <span class='articleTitle'>Objective Bayesianism and the Maximum Entropy Principle.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective Bayesianism<span id="LANOBA-absexp"> (<span class="ll" onclick='$("LANOBA-abstract2").show();$("LANOBA-absexp").hide()'>...</span>)</span><span id="LANOBA-abstract2" style="display:none"> are usually justified in different ways. In this paper we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem. (<span class="ll" onclick='$("LANOBA-abstract2").hide();$("LANOBA-absexp").show();'>shrink</span>)</span></div><div class="catsCon" id="ecats-con-LANOBA"><div><a class='catName' href='/browse/conditionalization' rel='section'>Conditionalization</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> <div><a class='catName' href='/browse/indifference-principles' rel='section'>Indifference Principles</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> <div><a class='catName' href='/browse/updating-principles' rel='section'>Updating Principles</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> </div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=LANOBA&proxyId=&u=http%3A%2F%2Fkar.kent.ac.uk%2F35197%2F" target='_blank' >Direct download</a> (<a href='/rec/LANOBA'>4 more</a>)  <div id="ml-LANOBA" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('LANOBA','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-LANOBA" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('LANOBA')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-LANOBA"></span></div></div></li> <li id='eHAEPLA' onclick="ee('click','HAEPLA')" onmouseover="ee('over','HAEPLA')" onmouseout="ee('out','HAEPLA')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/HAEPLA"><span class='name'> Haenni, R.</span>, <span class='name'> Romeijn, J.-W.</span>, <span class='name'> Wheeler, G.</span> & <span class='name'> Williamson, J.</span>, <span class='articleTitle'>Probabilistic Logic and Probabilistic Networks.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">While in principle probabilistic logics might be applied to solve a range of problems, in practice they are rarely applied at present. This is perhaps because they seem disparate, complicated, and computationally intractable. However, we shall argue in this programmatic paper that several approaches to probabilistic logic into a simple unifying framework: logically complex evidence can be used to associate probability intervals or probabilities with sentences. </div><div class="catsCon" id="ecats-con-HAEPLA">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/apps/internet-group-chat.png"><div id="tr-HAEPLA" title="Translate to English" class="yui-skin-sam ldiv" style="cursor:pointer" onclick="translateEntry('HAEPLA')">Translate to English</div> | <img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=HAEPLA&proxyId=&u=http%3A%2F%2Fwww.rug.nl%2F" target='_blank' >Direct download</a> (<a href='/rec/HAEPLA'>2 more</a>)  <div id="ml-HAEPLA" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('HAEPLA','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-HAEPLA" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('HAEPLA')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-HAEPLA"></span></div></div></li> <li id='eROMIUA' onclick="ee('click','ROMIUA')" onmouseover="ee('over','ROMIUA')" onmouseout="ee('out','ROMIUA')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/ROMIUA"><span class='name'> Romeijn, J.-W.</span> & <span class='name'> Williamson, J.</span>, <span class='articleTitle'>Interventions, Underdetermination and Theory Generation.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">Investigation of the use of intervention data in estimating parameters in a Bayesian network. </div><div class="catsCon" id="ecats-con-ROMIUA"><div><a class='catName' href='/browse/bayesian-reasoning-misc' rel='section'>Bayesian Reasoning, Misc</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> </div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/apps/internet-group-chat.png"><div id="tr-ROMIUA" title="Translate to English" class="yui-skin-sam ldiv" style="cursor:pointer" onclick="translateEntry('ROMIUA')">Translate to English</div> | <img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=ROMIUA&proxyId=&u=http%3A%2F%2Fwww.rug.nl%2F" target='_blank' >Direct download</a> (<a href='/rec/ROMIUA'>5 more</a>)  <div id="ml-ROMIUA" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('ROMIUA','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-ROMIUA" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('ROMIUA')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-ROMIUA"></span></div></div></li> <li id='eWILPOP-7' onclick="ee('click','WILPOP-7')" onmouseover="ee('over','WILPOP-7')" onmouseout="ee('out','WILPOP-7')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILPOP-7"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Philosophies of Probability.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">This chapter presents an overview of the major interpretations of probability followed by an outline of the objective Bayesian interpretation and a discussion of the key challenges it faces. I discuss the ramifications of interpretations of probability and objective Bayesianism for the philosophy of mathematics in general. </div><div class="catsCon" id="ecats-con-WILPOP-7">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILPOP-7&proxyId=&u=http%3A%2F%2Fkar.kent.ac.uk%2F20892%2F" target='_blank' >Direct download</a>  <div id="ml-WILPOP-7" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILPOP-7','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILPOP-7" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILPOP-7')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILPOP-7"></span></div></div></li> <li id='eNAGOBN-2' onclick="ee('click','NAGOBN-2')" onmouseover="ee('over','NAGOBN-2')" onmouseout="ee('out','NAGOBN-2')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/NAGOBN-2"><span class='name'>Sylvia Nagl</span>, <span class='name'>Matthew Williams</span>, <span class='name'>Nadjet El-Mehidi</span>, <span class='name'>Vivek Patkar</span> & <span class='name'>Jon Williamson</span>, <span class='articleTitle'>Objective Bayesian Nets for Integrating Cancer Knowledge: A Systems Biology Approach.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">According to objective Bayesianism, an agent’s degrees of belief should be determined by a probability function, out of all those that satisfy constraints imposed by background knowledge, that maximises entropy. A Bayesian net offers a way of efficiently representing a probability function and efficiently drawing inferences from that function. An objective Bayesian net is a Bayesian net representation of the maximum entropy probability function. In this paper we apply the machinery of objective Bayesian nets to breast cancer prognosis. Background knowledge<span id="NAGOBN-2-absexp"> (<span class="ll" onclick='$("NAGOBN-2-abstract2").show();$("NAGOBN-2-absexp").hide()'>...</span>)</span><span id="NAGOBN-2-abstract2" style="display:none"> is diverse and comes from several different sources: a database of clinical data, a database of molecular data, and quantitative data from the literature. We show how an objective Bayesian net can be constructed from this background knowledge and how it can be applied to yield prognoses and aid translation of clinical knowledge to genomics research. (<span class="ll" onclick='$("NAGOBN-2-abstract2").hide();$("NAGOBN-2-absexp").show();'>shrink</span>)</span></div><div class="catsCon" id="ecats-con-NAGOBN-2"><div><a class='catName' href='/browse/bayesian-reasoning-misc' rel='section'>Bayesian Reasoning, Misc</a><span class='catIn'> in </span><a class='catArea' href='/browse/philosophy-of-probability' rel='section'>Philosophy of Probability</a></div> </div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=NAGOBN-2&proxyId=&u=http%3A%2F%2Fkar.kent.ac.uk%2F7448%2F" target='_blank' >Direct download</a>  <div id="ml-NAGOBN-2" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('NAGOBN-2','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-NAGOBN-2" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('NAGOBN-2')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-NAGOBN-2"></span></div></div></li> <li id='eWILFBT-4' onclick="ee('click','WILFBT-4')" onmouseover="ee('over','WILFBT-4')" onmouseout="ee('out','WILFBT-4')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILFBT-4"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>From Bayesianism to the Epistemic View of Mathematics: Remarks Motivated by Richard Jeffrey's 'Subjective Probability: The Real Thing'.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="catsCon" id="ecats-con-WILFBT-4">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILFBT-4&proxyId=&u=http%3A%2F%2Fkar.kent.ac.uk%2F7450%2F" target='_blank' >Direct download</a> (<a href='/rec/WILFBT-4'>2 more</a>)  <div id="ml-WILFBT-4" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILFBT-4','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILFBT-4" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILFBT-4')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILFBT-4"></span></div></div></li> <li id='eWILLMA-2' onclick="ee('click','WILLMA-2')" onmouseover="ee('over','WILLMA-2')" onmouseout="ee('out','WILLMA-2')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILLMA-2"><span class='name'>Jon Williamson</span>, <span class='articleTitle'>Lorenzo Magnani: Abduction, Reason and Science: Processes of Discovery and Explanation.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="catsCon" id="ecats-con-WILLMA-2">No categories</div><div class="options"><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/go-down.png"><a rel="nofollow" href="http://philpapers.org/go.pl?id=WILLMA-2&proxyId=&u=http%3A%2F%2Fkar.kent.ac.uk%2F7399%2F" target='_blank' >Direct download</a>  <div id="ml-WILLMA-2" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/places/folder.png"><span title="File in your personal bibliography" class="ll" onclick="showLists('WILLMA-2','')">My bibliography<img src="/philpapers/raw/subind.gif"></span>  <div id="la-WILLMA-2" title="Export to another format" class="yui-skin-sam ldiv"> </div><img class="texticon" src="/assets/raw/icons/tango-full/16x16/actions/document-save.png"><span class="ll" onclick="showExports('WILLMA-2')">Export citation<img src="/philpapers/raw/subind.gif"></span>  <span class="eMsg" id="msg-WILLMA-2"></span></div></div></li> <li id='eWILTBN-2' onclick="ee('click','WILTBN-2')" onmouseover="ee('over','WILTBN-2')" onmouseout="ee('out','WILTBN-2')" class='entry'><span class="citation"><a href="http://philpapers.org/rec/WILTBN-2"><span class='name'>Jon Williamson</span>, <span class='name'>Jung-Wook Bang</span> & <span class='name'>Raphael Chaleil</span>, <span class='articleTitle'>Two-Stage Bayesian Networks for Metabolic Network Prediction.</span></a><span class='pubInfo'></span></span><div class="extras"><div class="abstract">Metabolism is a set of chemical reactions, used by living organisms to process chemical compounds in order to take energy and eliminate toxic compounds, for example. Its processes are referred as metabolic pathways. Understanding metabolism is imperative to biology, toxicology and medicine, but the number and complexity of metabolic pathways makes this a difficult task. In our paper, we investigate the use of causal Bayesian networks to model the pathways of yeast saccharomyces cerevisiae metabolism: such a network can be used<span id="WILTBN-2-absexp"> (<span class="ll" onclick='$("WILTBN-2-abstract2").show();$("WILTBN-2-absexp").hide()'>...</span>)</span><span id="WILTBN-2-abstract2" style="display:none"> to draw predictions about the levels of metabolites and enzymes in a particular specimen. We propose a two-stage methodology for causal networks, as follows. First construct a causal network from the network of metabolic pathways. The viability of this causal network depends on the validity of the causal Markov condition. If this condition fails, however, the principle of the common cause motivates the addition of a new causal arrow or a new `hidden' common cause to the network (stage 2 of the model formation process). Algorithms for adding arrows or hidden nodes have been developed separately in a number of papers, and in this paper we combine them, showing how the resulting procedure can be applied to the metabolic pathway problem. Our general approach was tested on neural cell morphology data and demonstrated noticeable improvements in both prediction and network accuracy. 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