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The theory of probability

Berkeley,: University of California Press (1949)

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  1. Testimony, induction and folk psychology.Jack Lyons - 1997 - Australasian Journal of Philosophy 75 (2):163 – 178.
    An influential argument for anti-reductionism about testimony, due to CAJ Coady, fails, because it assumes that an inductive global defense of testimony would proceed along effectively behaviorist lines. If we take seriously our wealth of non-testimonially justified folk psychological beliefs, the prospects for inductivism and reductionism look much better.
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  • Introduction: Machine learning as philosophy of science.Kevin B. Korb - 2004 - Minds and Machines 14 (4):433-440.
    I consider three aspects in which machine learning and philosophy of science can illuminate each other: methodology, inductive simplicity and theoretical terms. I examine the relations between the two subjects and conclude by claiming these relations to be very close.
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  • In search of the philosopher's stone: Remarks on Humphreys and Freedman's critique of causal discovery.Kevin B. Korb & Chris S. Wallace - 1997 - British Journal for the Philosophy of Science 48 (4):543-553.
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  • The speed-optimality of Reichenbach's straight rule of induction.Cory F. Juhl - 1994 - British Journal for the Philosophy of Science 45 (3):857-863.
    Hans Reichenbach made a bold and original attempt to ‘vindicate’ induction. He proposed a rule, the ‘straight rule’ of induction, which would guarantee inductive success if any rule of induction would. A central problem facing his attempt to vindicate the straight rule is that too many other rules are just as good as the straight rule if our only constraint on what counts as ‘success’ for an inductive rule is that it is ‘asymptotic’, i.e. that it converges in the limit (...)
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  • Theories of probability.Colin Howson - 1995 - British Journal for the Philosophy of Science 46 (1):1-32.
    My title is intended to recall Terence Fine's excellent survey, Theories of Probability [1973]. I shall consider some developments that have occurred in the intervening years, and try to place some of the theories he discussed in what is now a slightly longer perspective. Completeness is not something one can reasonably hope to achieve in a journal article, and any selection is bound to reflect a view of what is salient. In a subject as prone to dispute as this, there (...)
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  • The reference class problem is your problem too.Alan Hájek - 2007 - Synthese 156 (3):563--585.
    The reference class problem arises when we want to assign a probability to a proposition (or sentence, or event) X, which may be classified in various ways, yet its probability can change depending on how it is classified. The problem is usually regarded as one specifically for the frequentist interpretation of probability and is often considered fatal to it. I argue that versions of the classical, logical, propensity and subjectivist interpretations also fall prey to their own variants of the reference (...)
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  • Twenty-one arguments against propensity analyses of probability.Antony Eagle - 2004 - Erkenntnis 60 (3):371–416.
    I argue that any broadly dispositional analysis of probability will either fail to give an adequate explication of probability, or else will fail to provide an explication that can be gainfully employed elsewhere (for instance, in empirical science or in the regulation of credence). The diversity and number of arguments suggests that there is little prospect of any successful analysis along these lines.
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  • The difference between selection and drift: A reply to Millstein. [REVIEW]Robert N. Brandon - 2005 - Biology and Philosophy 20 (1):153-170.
    Millstein [Bio. Philos. 17 (2002) 33] correctly identies a serious problem with the view that natural selection and random drift are not conceptually distinct. She offers a solution to this problem purely in terms of differences between the processes of selection and drift. I show that this solution does not work, that it leaves the vast majority of real biological cases uncategorized. However, I do think there is a solution to the problem she raises, and I offer it here. My (...)
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  • The frame problem: An AI fairy tale. [REVIEW]Kevin B. Korb - 1998 - Minds and Machines 8 (3):317-351.
    I analyze the frame problem and its relation to other epistemological problems for artificial intelligence, such as the problem of induction, the qualification problem and the "general" AI problem. I dispute the claim that extensions to logic (default logic and circumscriptive logic) will ever offer a viable way out of the problem. In the discussion it will become clear that the original frame problem is really a fairy tale: as originally presented, and as tools for its solution are circumscribed by (...)
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  • Belief, Knowledge and Practical Matters.Jie Gao - 2024 - Hangzhou: Zhejiang University Press.
    This book takes purism about knowledge as the default position and defends it from the challenges of pragmatic encroachment. The book is divided into two parts, a negative and a positive one. The negative part critically examines existing purist strategies in response to pragmatic encroachment. The positive part provides a new theory of how practical factors can systematically influence our confidence and explores some implications of such influence.
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  • Triviality and the logic of restricted quantification.Nate Charlow - 2022 - Synthese 200 (4):1-21.
    This paper clarifies the relationship between the Triviality Results for the conditional and the Restrictor Theory of the conditional. On the understanding of Triviality proposed here, it is implausible—pace many proponents of the Restrictor Theory—that Triviality rests on a syntactic error. As argued here, Triviality arises from simply mistaking the feature a claim has when that claim is logically unacceptable for the feature a claim has when that claim is unsatisfiable. Triviality rests on a semantic confusion—one which some semantic theories, (...)
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  • God et al—World-Making as Collaborative Improvisation: New Metaphors for Open Theists.Mark Steen - 2022 - In K. J. Clark and J. Koperski (ed.), Abrahamic Reflections on Randomness and Providence. pp. 311-338.
    The Abrahamic traditions regard God as the world’s author. But what kind of author? A novelist? A playwright? Perhaps a composer of classical music? I will argue that it is best to regard God as like an improvisational play director or the leader of a jazz ensemble. Each determines the broad melodic contours or coarse-grained plot beforehand, while allowing their musicians or actors, and chance, to fill in the more fine-grained details. This analogy allows us to regard God as the (...)
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  • Direct inference and probabilistic accounts of induction.Jon Williamson - 2023 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 54 (3):451-472.
    Schurz (2019, ch. 4) argues that probabilistic accounts of induction fail. In particular, he criticises probabilistic accounts of induction that appeal to direct inference principles, including subjective Bayesian approaches (e.g., Howson 2000) and objective Bayesian approaches (see, e.g., Williamson 2017). In this paper, I argue that Schurz’ preferred direct inference principle, namely Reichenbach’s Principle of the Narrowest Reference Class, faces formidable problems in a standard probabilistic setting. Furthermore, the main alternative direct inference principle, Lewis’ Principal Principle, is also hard to (...)
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  • Dynamic probability and the problem of initial conditions.Michael Strevens - 2021 - Synthese 199 (5-6):14617-14639.
    Dynamic approaches to understanding probability in the non-fundamental sciences turn on certain properties of physical processes that are apt to produce “probabilistically patterned” outcomes. The dynamic properties on their own, however, seem not quite sufficient to explain the patterns; in addition, some sort of assumption about initial conditions must be made, an assumption that itself typically takes a probabilistic form. How should such a posit be understood? That is the problem of initial conditions. Reichenbach, in his doctoral dissertation, floated a (...)
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  • No Double-Halfer Embarrassment: A Reply to Titelbaum.Joel Pust - 2023 - Analytic Philosophy 64 (3):346-354.
    “Double-halfers” think that throughout the Sleeping Beauty Scenario, Beauty ought to maintain a credence of 1/2 in the proposition that the fair coin toss governing the experimental protocol comes up heads. Titelbaum (2012) introduces a novel variation on the standard scenario, one involving an additional coin toss, and claims that the double-halfer is committed to the absurd and embarrassing result that Beauty’s credence in an indexical proposition concerning the outcome of a future fair coin toss is not 1/2. I argue (...)
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  • Reichenbach, Russell and scientific realism.Christopher Pincock - 2021 - Synthese 199 (3-4):8485-8506.
    This paper considers how to best relate the competing accounts of scientific knowledge that Russell and Reichenbach proposed in the 1930s and 1940s. At the heart of their disagreements are two different accounts of how to best combine a theory of knowledge with scientific realism. Reichenbach argued that a broadly empiricist epistemology should be based on decisions. These decisions or “posits” informed Reichenbach’s defense of induction and a corresponding conception of what knowledge required. Russell maintained that a scientific realist must (...)
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  • Human Induction in Machine Learning: A Survey of the Nexus.Petr Spelda & Vit Stritecky - forthcoming - ACM Computing Surveys.
    As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...)
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  • Epistemic Projects, Indispensability, and the Structure of Modal Thought.Felipe Morales Carbonell - 2020 - Res Philosophica 97 (4):611-638.
    I argue that modal epistemology should pay more attention to questions about the structure and function of modal thought. We can treat these questions from synchronic and diachronic angles. From a synchronic perspective, I consider whether a general argument for the epistemic support of modal though can be made on the basis of modal thoughs’s indispensability for what Enoch and Schechter (2008) call rationally required epistemic projects. After formulating the argument, I defend it from various objections. I also examine the (...)
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  • Belief, Credence and Statistical Evidence.Davide Fassio & Jie Gao - 2020 - Theoria 86 (4):500-527.
    According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational credence. (...)
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  • Moral Obligation and Epistemic Risk.Zoe Johnson King & Boris Babic - 2020 - Oxford Studies in Normative Ethics 10:81-105.
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  • The trouble with standards of proof.Zoë A. Johnson King - 2020 - Synthese 199 (1-2):141-159.
    The “beyond a reasonable doubt” standard of proof, currently used in criminal trials, is notoriously vague and undermotivated. This paper discusses two popular strategies for justifying our choice of a particular precise interpretation of the standard: the “ratio-to-standard strategy” identifies a desired ratio of trial outcomes and then argues that a certain standard is the one that we can expect to produce our desired ratio, while the “utilities-to-standard strategy” identifies utilities for trial outcomes and then argues that a certain standard (...)
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  • Objectivity and the Method of Arbitrary Functions.Chloé de Canson - 2022 - British Journal for the Philosophy of Science 73 (3):663-684.
    There is widespread excitement in the literature about the method of arbitrary functions: many take it to show that it is from the dynamics of systems that the objectivity of probabilities emerge. In this paper, I differentiate three ways in which a probability function might be objective, and I argue that the method of arbitrary functions cannot help us show that dynamics objectivise probabilities in any of these senses.
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  • Feature selection methods for solving the reference class problem.James Franklin - 2010 - Columbia Law Review Sidebar 110:12-23.
    Probabilistic inference from frequencies, such as "Most Quakers are pacifists; Nixon is a Quaker, so probably Nixon is a pacifist" suffer from the problem that an individual is typically a member of many "reference classes" (such as Quakers, Republicans, Californians, etc) in which the frequency of the target attribute varies. How to choose the best class or combine the information? The article argues that the problem can be solved by the feature selection methods used in contemporary Big Data science: the (...)
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  • Abduction − the context of discovery + underdetermination = inference to the best explanation.Mousa Mohammadian - 2021 - Synthese 198 (5):4205-4228.
    The relationship between Peircean abduction and the modern notion of Inference to the Best Explanation is a matter of dispute. Some philosophers, such as Harman :88–95, 1965) and Lipton, claim that abduction and IBE are virtually the same. Others, however, hold that they are quite different :503, 1998; Minnameier in Erkenntnis 60:75–105, 2004) and there is no link between them :419–442, 2009). In this paper, I argue that neither of these views is correct. I show that abduction and IBE have (...)
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  • No Free Lunch Theorem, Inductive Skepticism, and the Optimality of Meta-induction.Gerhard Schurz - 2017 - Philosophy of Science 84 (5):825-839.
    The no free lunch theorem is a radicalized version of Hume’s induction skepticism. It asserts that relative to a uniform probability distribution over all possible worlds, all computable prediction algorithms—whether ‘clever’ inductive or ‘stupid’ guessing methods —have the same expected predictive success. This theorem seems to be in conflict with results about meta-induction. According to these results, certain meta-inductive prediction strategies may dominate other methods in their predictive success. In this article this conflict is analyzed and dissolved, by means of (...)
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  • Grounding Reichenbach’s Pragmatic Vindication of Induction.Michael J. Shaffer - 2017 - Polish Journal of Philosophy 11 (1):43-55.
    This paper has three interdependent aims. The first is to make Reichenbach’s views on induction and probabilities clearer, especially as they pertain to his pragmatic justification of induction. The second aim is to show how his view of pragmatic justification arises out of his commitment to extensional empiricism and moots the possibility of a non-pragmatic justification of induction. Finally, and most importantly, a formal decision-theoretic account of Reichenbach’s pragmatic justification is offered in terms both of the minimax principle and the (...)
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  • Direct Inference from Imprecise Frequencies.Paul D. Thorn - 2017 - In Michela Massimi, Jan-Willem Romeijn & Gerhard Schurz (eds.), EPSA15 Selected Papers: The 5th conference of the European Philosophy of Science Association in Düsseldorf. Cham: Springer. pp. 347-358.
    It is well known that there are, at least, two sorts of cases where one should not prefer a direct inference based on a narrower reference class, in particular: cases where the narrower reference class is gerrymandered, and cases where one lacks an evidential basis for forming a precise-valued frequency judgment for the narrower reference class. I here propose (1) that the preceding exceptions exhaust the circumstances where one should not prefer direct inference based on a narrower reference class, and (...)
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  • Selection in a Complex World: Deriving Causality from Stable Equilibrium.Hugh Desmond - 2018 - Erkenntnis 83 (2):265-286.
    It is an ongoing controversy whether natural selection is a cause of population change, or a mere statistical description of how individual births and deaths accumulate. In this paper I restate the problem in terms of the reference class problem, and propose how the structure of stable equilibrium can provide a solution in continuity with biological practice. Insofar natural selection can be understood as a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in a modification of the Newtonian-force analogy, (...)
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  • Can the Behavioral Sciences Self-correct? A Social Epistemic Study.Felipe Romero - 2016 - Studies in History and Philosophy of Science Part A 60 (C):55-69.
    Advocates of the self-corrective thesis argue that scientific method will refute false theories and find closer approximations to the truth in the long run. I discuss a contemporary interpretation of this thesis in terms of frequentist statistics in the context of the behavioral sciences. First, I identify experimental replications and systematic aggregation of evidence (meta-analysis) as the self-corrective mechanism. Then, I present a computer simulation study of scientific communities that implement this mechanism to argue that frequentist statistics may converge upon (...)
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  • Fifteen Arguments Against Hypothetical Frequentism.Alan Hájek - 2009 - Erkenntnis 70 (2):211-235.
    This is the sequel to my “Fifteen Arguments Against Finite Frequentism” ( Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A ’s among the B ’s would be p if there were an infinite sequence of B ’s. I offer fifteen arguments against this analysis. I (...)
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  • Preuves intuitionnistes touchant la première philosophie.Joseph Vidal-Rosset - 2013 - In . Les Cahiers D'Ithaque.
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  • 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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  • The Propensity Interpretation of Probability: A Re-evaluation.Joseph Berkovitz - 2015 - Erkenntnis 80 (S3):629-711.
    Single-case and long-run propensity theories are among the main objective interpretations of probability. There have been various objections to these theories, e.g. that it is difficult to explain why propensities should satisfy the probability axioms and, worse, that propensities are at odds with these axioms, that the explication of propensities is circular and accordingly not informative, and that single-case propensities are metaphysical and accordingly non-scientific. We consider various propensity theories of probability and their prospects in light of these objections. We (...)
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  • On Law and Reason.Aleksander Peczenik - 1989 - Dordrecht, Netherland: Springer Verlag.
    a This is an outline of a coherence theory of law. Its basic ideas are: reasonable support and weighing of reasons. All the rest is commentary.a (TM) These words at the beginning of the preface of this book perfectly indicate what On Law and Reason is about. It is a theory about the nature of the law which emphasises the role of reason in the law and which refuses to limit the role of reason to the application of deductive logic. (...)
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  • On the classification of diseases.Benjamin Smart - 2014 - Theoretical Medicine and Bioethics 35 (4):251-269.
    Identifying the necessary and sufficient conditions for individuating and classifying diseases is a matter of great importance in the fields of law, ethics, epidemiology, and of course, medicine. In this paper, I first propose a means of achieving this goal, ensuring that no two distinct disease-types could correctly be ascribed to the same disease-token. I then posit a metaphysical ontology of diseases—that is, I give an account of what a disease is. This is essential to providing the most effective means (...)
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  • Feminist Philosophy of Science.Lynn Hankinson Nelson - 2002 - In Peter K. Machamer & Michael Silberstein (eds.), The Blackwell guide to the philosophy of science. Malden, Mass.: Blackwell. pp. 312–331.
    This chapter contains sections titled: Highlights of Past Literature Current Work Future Work.
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  • In philosophical defence of Bayesian rationality.Jon Dorling - 1983 - Behavioral and Brain Sciences 6 (2):249-250.
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  • Psychological objectives for logical theories.J. St B. T. Evans - 1983 - Behavioral and Brain Sciences 6 (2):250-250.
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  • Kyburg on practical certainty.Willam L. Harper - 1983 - Behavioral and Brain Sciences 6 (2):251-252.
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  • Normative theories of rationality: Occam's razor, Procrustes' bed?Lola L. Lopes - 1983 - Behavioral and Brain Sciences 6 (2):255-256.
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  • Confirming confirmation bias.P. Pollard - 1983 - Behavioral and Brain Sciences 6 (2):258-259.
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  • Inductive Justification and Discovery. On Hans Reichenbach’s Foundation of the Autonomy of the Philosophy of Science.Gregor Schiemann - 2002 - In Schickore J. & Steinle F. (eds.), Revisiting Discovery and Justification. Max-Planck-Institut. pp. 23-39.
    I would like to assume that Reichenbach's distinction of Justification and Discovery lives on, and to seek arguments in his texts that would justify their relevance in this field. The persuasive force of these arguments transcends the contingent circumstances apart from which their genesis and local transmission cannot be made understandable. I shall begin by characterizing the context distinction as employed by Reichenbach in "Experience and Prediction" to differentiate between epistemology and science (1). Following Thomas Nickles and Kevin T. Kelly, (...)
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  • The new Tweety puzzle: arguments against monistic Bayesian approaches in epistemology and cognitive science.Matthias Unterhuber & Gerhard Schurz - 2013 - Synthese 190 (8):1407-1435.
    In this paper we discuss the new Tweety puzzle. The original Tweety puzzle was addressed by approaches in non-monotonic logic, which aim to adequately represent the Tweety case, namely that Tweety is a penguin and, thus, an exceptional bird, which cannot fly, although in general birds can fly. The new Tweety puzzle is intended as a challenge for probabilistic theories of epistemic states. In the first part of the paper we argue against monistic Bayesians, who assume that epistemic states can (...)
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  • Two Problems of Direct Inference.Paul D. Thorn - 2012 - Erkenntnis 76 (3):299-318.
    The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...)
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  • Probabilistic Logics and Probabilistic Networks.Rolf Haenni, Jan-Willem Romeijn, Gregory Wheeler & Jon Williamson - 2010 - Dordrecht, Netherland: Synthese Library. Edited by Gregory Wheeler, Rolf Haenni, Jan-Willem Romeijn & and Jon Williamson.
    Additionally, the text shows how to develop computationally feasible methods to mesh with this framework.
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  • Chance versus Randomness.Antony Eagle - 2010 - Stanford Encyclopedia of Philosophy.
    This article explores the connection between objective chance and the randomness of a sequence of outcomes. Discussion is focussed around the claim that something happens by chance iff it is random. This claim is subject to many objections. Attempts to save it by providing alternative theories of chance and randomness, involving indeterminism, unpredictability, and reductionism about chance, are canvassed. The article is largely expository, with particular attention being paid to the details of algorithmic randomness, a topic relatively unfamiliar to philosophers.
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  • Entropy - A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford, GB: Oxford University Press. pp. 115-142.
    Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...)
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  • After Popper, Kuhn and Feyerabend: Recent Issues in Theories of Scientific Method.Robert Nola & Howard Sankey (eds.) - 2000 - Boston: Kluwer Academic Publishers.
    Some think that issues to do with scientific method are last century's stale debate; Popper was an advocate of methodology, but Kuhn, Feyerabend, and others are alleged to have brought the debate about its status to an end. The papers in this volume show that issues in methodology are still very much alive. Some of the papers reinvestigate issues in the debate over methodology, while others set out new ways in which the debate has developed in the last decade. The (...)
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  • Social mechanisms and causal inference.Daniel Steel - 2004 - Philosophy of the Social Sciences 34 (1):55-78.
    Several authors have claimed that mechanisms play a vital role in distinguishing between causation and mere correlation in the social sciences. Such claims are sometimes interpreted to mean that without mechanisms, causal inference in social science is impossible. The author agrees with critics of this proposition but explains how the account of how mechanisms aid causal inference can be interpreted in a way that does not depend on it. Nevertheless, he shows that this more charitable version of the account is (...)
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  • Causality and causal modelling in the social sciences.Federica Russo - 2009 - Springer, Dordrecht.
    The anti-causal prophecies of last century have been disproved. Causality is neither a ‘relic of a bygone’ nor ‘another fetish of modern science’; it still occupies a large part of the current debate in philosophy and the sciences. This investigation into causal modelling presents the rationale of causality, i.e. the notion that guides causal reasoning in causal modelling. It is argued that causal models are regimented by a rationale of variation, nor of regularity neither invariance, thus breaking down the dominant (...)
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