About this topic
Summary Bayesian Reasoning includes issues related to: 1. the probabilistic logic of evidential support for hypotheses;  2. the logic of comparative belief, belief strengths, and belief updating as represented by classical probability functions; 3. the logic of decision as represented in terms of utilities, probabilities, and expected utility maximization, including ways in which this logic may represent comparative preferences among acts or states of affairs; 4. Bayesian probabilistic treatments of causal influence (e.g. via Bayes nets); 5. studies of relationships between human performance and models of reasoning and decision of a Bayesian kind (as described in 1-4 above).
Key works

Bayesian reasoning includes a wide variety of topics and issues. For introductory overviews of Bayesian confirmation theory and decision theory, among the best texts available are Skyrms 1966 and Hacking 2001; at a somewhat more advanced level Urbach & Howson 1993 is essential reading. Key sources for Bayesian probability and decision theory include Ramsey 1926Savage 1954Jeffrey 1965, and Joyce 1999. The classic treatment of Bayes nets is Pearl 1988Chater & Oaksford 2008 is an excellent collection of articles on Bayesian modeling of natural human reasoning. Also see the Stanford Encyclopedia of Philosophy (online, Zalta 2004) for helpful articles on various aspects of Bayesian reasoning: e.g. on Bayes' Theorem, Bayesian Epistemology, Inductive Logic, Decision Theory, etc.

Introductions Hájek 2007; Joyce 2008; Hawthorne 2011; Talbott 2008; Vineberg 2011; Weirich 2009; Hitchcock 2008.
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  1. A Strike Against a Striking Principle.Dan Baras - 2020 - Philosophical Studies 177 (6):1501-1514.
    Several authors believe that there are certain facts that are striking and cry out for explanation—for instance, a coin that is tossed many times and lands in the alternating sequence HTHTHTHTHTHT…. According to this view, we have prima facie reason to believe that such facts are not the result of chance. I call this view the striking principle. Based on this principle, some have argued for far-reaching conclusions, such as that our universe was created by intelligent design, that there are (...)
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  2. A New Probabilistic Explanation of the Modus Ponens–Modus Tollens Asymmetry.Stephan Hartmann, Benjamin Eva & Henrik Singmann - 2019 - In CogSci 2019 Proceedings. Montreal, Québec, Kanada: pp. 289–294.
    A consistent finding in research on conditional reasoning is that individuals are more likely to endorse the valid modus ponens (MP) inference than the equally valid modus tollens (MT) inference. This pattern holds for both abstract task and probabilistic task. The existing explanation for this phenomenon within a Bayesian framework (e.g., Oaksford & Chater, 2008) accounts for this asymmetry by assuming separate probability distributions for both MP and MT. We propose a novel explanation within a computational-level Bayesian account of reasoning (...)
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  3. Conditional Degree of Belief and Bayesian Inference.Jan Sprenger - 2020 - Philosophy of Science 87 (2):319-335.
    Why are conditional degrees of belief in an observation E, given a statistical hypothesis H, aligned with the objective probabilities expressed by H? After showing that standard replies are not satisfactory, I develop a suppositional analysis of conditional degree of belief, transferring Ramsey’s classical proposal to statistical inference. The analysis saves the alignment, explains the role of chance-credence coordination, and rebuts the charge of arbitrary assessment of evidence in Bayesian inference. Finally, I explore the implications of this analysis for Bayesian (...)
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  4. A Paradox of Evidential Equivalence.David Builes - 2020 - Mind 129 (513):113-127.
    Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...)
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  5. Literal Perceptual Inference.Alex Kiefer - 2017 - In Thomas Metzinger & Wanja Wiese (eds.), Philosophy and predictive processing. Frankfurt, Germany:
    In this paper, I argue that theories of perception that appeal to Helmholtz’s idea of unconscious inference (“Helmholtzian” theories) should be taken literally, i.e. that the inferences appealed to in such theories are inferences in the full sense of the term, as employed elsewhere in philosophy and in ordinary discourse. -/- In the course of the argument, I consider constraints on inference based on the idea that inference is a deliberate acton, and on the idea that inferences depend on the (...)
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  6. Evidence and Explanation in Cicero's On Divination.Frank Cabrera - forthcoming - Studies in History and Philosophy of Science Part A.
    In this paper, I examine Cicero’s oft-neglected De Divinatione, a dialogue investigating the legitimacy of the practice of divination. First, I offer a novel analysis of the main arguments for divination given by Quintus, highlighting the fact that he employs two logically distinct argument forms. Next, I turn to the first of the main arguments against divination given by Marcus. Here I show, with the help of modern probabilistic tools, that Marcus’ skeptical response is far from the decisive, proto-naturalistic assault (...)
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  7. Probabilism for Stochastic Theories.Jeremy Steeger - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 66:34–44.
    I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an assignment of chance values is possible if and only if it is given by a pure state on a given algebra, your estimates for chances avoid accuracy-dominance if and only if they are given by a state on that algebra. When your estimates avoid accuracy-dominance (roughly: when you cannot guarantee that other (...)
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  8. Time-Slice Rationality and Self-Locating Belief.David Builes - forthcoming - Philosophical Studies.
    The epistemology of self-locating belief concerns itself with how rational agents ought to respond to certain kinds of indexical information. I argue that those who endorse the thesis of Time-Slice Rationality ought to endorse a particular view about the epistemology of self-locating belief, according to which "essentially indexical" information is never evidentially relevant to non-indexical matters. I close by offering some independent motivations for endorsing Time-Slice Rationality in the context of the epistemology of self-locating belief.
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  9. The Epistemology of Disagreement: Why Not Bayesianism?Thomas Mulligan - forthcoming - Episteme.
    Disagreement is a ubiquitous feature of human life, and philosophers have dutifully attended to it. One important question related to disagreement is epistemological: How does a rational person change her beliefs (if at all) in light of disagreement from others? The typical methodology for answering this question is to endorse a steadfast or conciliatory disagreement norm (and not both) on a priori grounds and selected intuitive cases. In this paper, I argue that this methodology is misguided. Instead, a thoroughgoingly Bayesian (...)
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  10. Self‐Locating Evidence and the Metaphysics of Time.David Builes - 2019 - Philosophy and Phenomenological Research 99 (2):478-490.
    I argue that different views in the metaphysics of time make different observational predictions in both classical and relativistic cases. Because different views in the metaphysics of time differ over which facts are merely indexical facts, they make different observational predictions about certain self-locating propositions. I argue for this thesis by distinguishing the three main updating procedures that apply in cases of self-locating uncertainty, and I present a series of cases which cumulatively show that every one of these updating procedures (...)
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  11. Mary and Fátima: A Modest C-Inductive Argument for Catholicism.Tyler Dalton McNabb & Joseph Blado - forthcoming - Perichoresis.
    C-Inductive arguments are arguments that increase the probability of a hypothesis. This can be contrasted with what is called a P-Inductive argument. A P-inductive argument is an argument that shows the overall probability of a hypothesis to be more probable than not. In this paper, we put forth a C-inductive argument for the truth of the Catholic hypothesis (CH). Roughly, we take CH to be the hypothesis that the core creedal beliefs found within the Catholic Tradition are true. Specifically, we (...)
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  12. Kevin McCain and Ted Poston’s Best Explanations.Frank Cabrera - forthcoming - International Journal for the Study of Skepticism:1-10.
    I give a critical overview of the volume, focusing my attention on the chapters that deal with the explanationist response to skepticism.
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  13. Why is Bayesian Confirmation Theory Rarely Practiced?Robert W. P. Luk - 2019 - Science and Philosophy 7 (1):3-20.
    Bayesian confirmation theory is a leading theory to decide the confirmation/refutation of a hypothesis based on probability calculus. While it may be much discussed in philosophy of science, is it actually practiced in terms of hypothesis testing by scientists? Since the assignment of some of the probabilities in the theory is open to debate and the risk of making the wrong decision is unknown, many scientists do not use the theory in hypothesis testing. Instead, they use alternative statistical tests that (...)
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  14. Obligation, Permission, and Bayesian Orgulity.Michael Nielsen & Rush T. Stewart - 2019 - Ergo: An Open Access Journal of Philosophy 6.
    This essay has two aims. The first is to correct an increasingly popular way of misunderstanding Belot's Orgulity Argument. The Orgulity Argument charges Bayesianism with defect as a normative epistemology. For concreteness, our argument focuses on Cisewski et al.'s recent rejoinder to Belot. The conditions that underwrite their version of the argument are too strong and Belot does not endorse them on our reading. A more compelling version of the Orgulity Argument than Cisewski et al. present is available, however---a point (...)
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  15. Decision Theory with a Human Face. [REVIEW]David Strohmaier - 2019 - Philosophical Psychology 32 (3):432-435.
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  16. Biased Belief in the Bayesian Brain: A Deeper Look at the Evidence.Ben M. Tappin & Stephen Gadsby - 2019 - Consciousness and Cognition 68:107-114.
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  17. A Theory of Bayesian Groups.Franz Dietrich - 2019 - Noûs 53 (3):708-736.
    A group is often construed as one agent with its own probabilistic beliefs (credences), which are obtained by aggregating those of the individuals, for instance through averaging. In their celebrated “Groupthink”, Russell et al. (2015) require group credences to undergo Bayesian revision whenever new information is learnt, i.e., whenever individual credences undergo Bayesian revision based on this information. To obtain a fully Bayesian group, one should often extend this requirement to non-public or even private information (learnt by not all or (...)
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  18. A Defense of Belief-Credence Dualism.Elizabeth Jackson - 2018 - In João Luis Pereira Ourique (ed.), Proceedings of the Fifth Conference of the Brazilian Society of Analytic Philosophy. Pelotas, Brazil: pp. 77-78.
    I defend belief-credence dualism, the view that we have both beliefs and credences and both attitudes are equally fundamental. First, I explain belief, credence, and three views on their relationship. Then, I argue for dualism. I do so first by painting a picture of the mind on which belief and credence are two cognitive tools that we use for different purposes. Finally, I respond to two objections to dualism. I conclude that dualism is a promising view, and one that both (...)
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  19. String Theory, Non-Empirical Theory Assessment, and the Context of Pursuit.Frank Cabrera - 2018 - Synthese:1-29.
    In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical methods of theory assessment given (...)
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  20. The Perils of Parsimony.William Roche - 2018 - Journal of Philosophy 115 (9):485-505.
    It is widely thought in philosophy and elsewhere that parsimony is a theoretical virtue in that if T1 is more parsimonious than T2, then T1 is preferable to T2, other things being equal. This thesis admits of many distinct precisifications. I focus on a relatively weak precisification on which preferability is a matter of probability, and argue that it is false. This is problematic for various alternative precisifications, and even for Inference to the Best Explanation as standardly understood.
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  21. Intuition & Calibration.Jonathan M. Weinberg, Stephen Crowley, Chad Gonnerman, Ian Vandewalker & Stacey Swain - 2012 - Essays in Philosophy 13 (1):15.
    The practice of appealing to esoteric intuitions, long standard in analytic philosophy, has recently fallen on hard times. Various recent empirical results have suggested that philosophers are not currently able to distinguish good intuitions from bad. This paper evaluates one possible type of approach to this problematic methodological situation: calibration. Both critiquing and building on an argument from Robert Cummins, the paper explores what possible avenues may exist for the calibration of philosophical intuitions. It is argued that no good options (...)
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  22. The Objectivity of Subjective Bayesianism.Jan Sprenger - 2018 - European Journal for Philosophy of Science 8 (3):539-558.
    Subjective Bayesianism is a major school of uncertain reasoning and statistical inference. It is often criticized for a lack of objectivity: it opens the door to the influence of values and biases, evidence judgments can vary substantially between scientists, it is not suited for informing policy decisions. My paper rebuts these concerns by connecting the debates on scientific objectivity and statistical method. First, I show that the above concerns arise equally for standard frequentist inference with null hypothesis significance tests. Second, (...)
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  23. Being Realist About Bayes, and the Predictive Processing Theory of Mind.Matteo Colombo, Lee Elkin & Stephan Hartmann - forthcoming - British Journal for the Philosophy of Science.
    Some naturalistic philosophers of mind subscribing to the predictive processing theory of mind have adopted a realist attitude towards the results of Bayesian cognitive science. In this paper, we argue that this realist attitude is unwarranted. The Bayesian research program in cognitive science does not possess special epistemic virtues over alternative approaches for explaining mental phenomena involving uncertainty. In particular, the Bayesian approach is not simpler, more unifying, or more rational than alternatives. It is also contentious that the Bayesian approach (...)
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  24. Persistent Disagreement and Polarization in a Bayesian Setting.Michael Nielsen & Rush T. Stewart - forthcoming - British Journal for the Philosophy of Science:axy056.
    For two ideally rational agents, does learning a finite amount of shared evidence necessitate agreement? No. But does it at least guard against belief polarization, the case in which their opinions get further apart? No. OK, but are rational agents guaranteed to avoid polarization if they have access to an infinite, increasing stream of shared evidence? No.
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  25. De Se Beliefs and Centred Uncertainty.Silvia Milano - 2018 - Dissertation, London School of Economics and Political Science
    What kind of thing do you believe when you believe that you are in a certain place, that it is a certain time, and that you are a certain individual? What happens if you get lost, or lose track of the time? Can you ever be unsure of your own identity? These are the kind of questions considered in my thesis. Beliefs about where, when and who you are are what are called in the literature de se, or self-locating beliefs. (...)
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  26. Subjective Probability and its Dynamics.Alan Hajek & Julia Staffel - forthcoming - In Markus Knauff & Wolfgang Spohn (eds.), MIT Handbook of Rationality. MIT Press.
    This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research.
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  27. Content and Misrepresentation in Hierarchical Generative Models.Alex Kiefer & Jakob Hohwy - 2018 - Synthese 195 (6):2387-2415.
    In this paper, we consider how certain longstanding philosophical questions about mental representation may be answered on the assumption that cognitive and perceptual systems implement hierarchical generative models, such as those discussed within the prediction error minimization framework. We build on existing treatments of representation via structural resemblance, such as those in Gładziejewski :559–582, 2016) and Gładziejewski and Miłkowski, to argue for a representationalist interpretation of the PEM framework. We further motivate the proposed approach to content by arguing that it (...)
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  28. Why Do We Need to Employ Bayesian Statistics and How Can We Employ It in Studies of Moral Education?: With Practical Guidelines to Use JASP for Educators and Researchers.Hyemin Han - 2018 - Journal of Moral Education 47 (4):519-537.
    ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies can provide (...)
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  29. Hypothesis and Evidence in Psychoanalysis. Marshall Edelson.Michael Lavin - 1986 - Philosophy of Science 53 (2):300-302.
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  30. In Search of Good Probability Assessors: An Experimental Comparison of Elicitation Rules for Confidence Judgments.Guillaume Hollard, Sébastien Massoni & Jean-Christophe Vergnaud - 2016 - Theory and Decision 80 (3):363-387.
    In this paper, we use an experimental design to compare the performance of elicitation rules for subjective beliefs. Contrary to previous works in which elicited beliefs are compared to an objective benchmark, we consider a purely subjective belief framework. The performance of different elicitation rules is assessed according to the accuracy of stated beliefs in predicting success. We measure this accuracy using two main factors: calibration and discrimination. For each of them, we propose two statistical indexes and we compare the (...)
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  31. Probabilistic Metaphysics. [REVIEW]Brian Skyrms - 1987 - Philosophical Review 96 (3):447.
  32. Probabilistic Metaphysics. [REVIEW]Brian Skyrms - 1987 - Philosophical Review 96 (3):447.
  33. Inconsistency as a Touchstone for Coherence Measures.Mark Siebel & Michael Schippers - 2015 - Theoria : An International Journal for Theory, History and Fundations of Science 30 (1):11-41.
    The debate on probabilistic measures of coherence has focused on evaluating sets of consistent propositions. In this paper we draw attention to the largely neglected question of whether such measures concur with intuitions on test cases involving inconsistent propositions and whether they satisfy general adequacy constraints on coherence and inconsistency. While it turns out that, for the vast majority of measures in their original shape, this question must be answered in the negative, we show that it is possible to adapt (...)
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  34. Mayo & Spanos, Eds. 2009. Error and Inference.Christian Hennig - 2012 - Theoria : An International Journal for Theory, History and Fundations of Science 27 (2):245-247.
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  35. Bayesian Representation of a Prolonged Archaeological Debate.Efraim Wallach - 2018 - Synthese 195 (1):401-431.
    This article examines the effect of material evidence upon historiographic hypotheses. Through a series of successive Bayesian conditionalizations, I analyze the extended competition among several hypotheses that offered different accounts of the transition between the Bronze Age and the Iron Age in Palestine and in particular to the “emergence of Israel”. The model reconstructs, with low sensitivity to initial assumptions, the actual outcomes including a complete alteration of the scientific consensus. Several known issues of Bayesian confirmation, including the problem of (...)
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  36. Bayesian Decision Theory and Stochastic Independence.Philippe Mongin - 2017 - TARK 2017.
    Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not (...)
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  37. Mediated Confirmation.Tomoji Shogenji - 2017 - British Journal for the Philosophy of Science 68 (3):847-874.
    ABSTRACT This article aims to achieve two things: to identify the conditions for transitivity in probabilistic support in various settings, and to uncover the components and structure of the mediated probabilistic relation. It is shown that when the probabilistic relation between the two propositions, x and z, is mediated by multiple layers of partitions of propositions, the impact x has on z consists of the purely indirect impact, the purely bypass impact, and the mixed impact. It is also shown that (...)
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  38. X—Random Sampling and the Principles of Estimation.Peter Urbach - 1988 - Proceedings of the Aristotelian Society 89 (1):143-164.
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  39. A Bayesian Perspective on Constructing a Written Assessment of Probabilistic Clinical Reasoning in Experienced Clinicians.Clarence D. Kreiter - 2017 - Journal of Evaluation in Clinical Practice 23 (1):44-48.
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  40. Invariant Equivocation.Jürgen Landes & George Masterton - 2017 - Erkenntnis 82 (1):141-167.
    Objective Bayesians hold that degrees of belief ought to be chosen in the set of probability functions calibrated with one’s evidence. The particular choice of degrees of belief is via some objective, i.e., not agent-dependent, inference process that, in general, selects the most equivocal probabilities from among those compatible with one’s evidence. Maximising entropy is what drives these inference processes in recent works by Williamson and Masterton though they disagree as to what should have its entropy maximised. With regard to (...)
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  41. What is Logical About the Logical Interpretation of Probability?Torfehnezhad Parzhad - 2016 - Abstracta 9 (1).
    My goal, in this paper, is to critically assess the categorization of “interpretations of probability” as it appears in the literature. In some sources only Carnap’s treatment of probability is understood to be the best example of “logical” probability. This is surprisingly narrow and I will here suggest otherwise. In fact, I believe that certain forms of Baysianism should also be included in the logical camp.
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  42. R. B. Braithwaite on Probability and Induction.Henry E. Kyburg - 1958 - British Journal for the Philosophy of Science 9 (33):203.
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  43. Milne's Measure of Confirmation.Stephen Pollard - 1999 - Analysis 59 (4):335-338.
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  44. Likelihood: An Account of the Statistical Concept of Likelihood and Its Application to Scientific Inference. A. W. F. Edwards.Charles G. Morgan - 1974 - Philosophy of Science 41 (4):427-429.
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  45. Probability and the Logic of Rational Belief. Henry E. Kyburg, Jr.Wesley C. Salmon - 1967 - Philosophy of Science 34 (3):283-285.
  46. The Geometry of Opinion: Jeffrey Shifts and Linear Operators.Bas C. Van Fraassen - 1992 - Philosophy of Science 59 (2):163-175.
    Richard Jeffrey and Michael Goldstein have both introduced systematic approaches to the structure of opinion changes. For both approaches there are theorems which indicate great generality and width of scope. The main questions addressed here will be to what extent the basic forms of representation are intertranslatable, and how we can conceive of such programs in general.
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  47. Philosophy in the Laboratory: The Debate Over Evidence for E. J. Steele's Lamarckian Hypothesis.Mark Parascandola - 1995 - Studies in History and Philosophy of Science Part A 26 (3):469-492.
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  48. The Role of Probability Arguments in the History of Science.Friedel Weinert - 2010 - Studies in History and Philosophy of Science Part A 41 (1):95-104.
    The paper examines Wesley Salmon’s claim that the primary role of plausibility arguments in the history of science is to impose constraints on the prior probability of hypotheses. A detailed look at Copernicanism and Darwinism and, more briefly, Rutherford’s discovery of the atomic nucleus reveals a further and arguably more important role of plausibility arguments. It resides in the consideration of likelihoods, which state how likely a given hypothesis makes a given piece of evidence. In each case the likelihoods raise (...)
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  49. Bayesianism and Scientific Inference.Mary Hesse - 1975 - Studies in History and Philosophy of Science Part A 5 (4):367.
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  50. The Pre-Objective Reconsidered.Thomas N. Munson - 1959 - Review of Metaphysics 12 (4):624-632.
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