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  1. Non-Measurability, Imprecise Credences, and Imprecise Chances.Yoaav Isaacs, Alan Hájek & John Hawthorne - 2021 - Mind 131 (523):892-916.
    – We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...)
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  • Formal Methods.Richard Pettigrew - manuscript
    (This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...)
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  • The Selective Confirmation Answer to the Paradox of the Ravens.William Peden - 2019 - International Studies in the Philosophy of Science 32 (3-4):177-193.
    Philosophers such as Goodman, Scheffler and Glymour aim to answer the Paradox of the Ravens by distinguishing between confirmation simpliciter and selective confirmation. In the latter concept, the evidence both supports a hypothesis and undermines one of its "rivals". In this article, I argue that while selective confirmation does seem to be an important scientific notion, no attempt to formalise it thus far has managed to solve the Paradox of the Ravens.
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  • Conditional Probabilities.Kenny Easwaran - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198.
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  • Precise Credences.Michael Titelbaum - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 1-55.
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  • A weak symmetry condition for probabilistic measures of confirmation.Jakob Koscholke - 2018 - Philosophical Studies 175 (8):1927-1944.
    This paper presents a symmetry condition for probabilistic measures of confirmation which is weaker than commutativity symmetry, disconfirmation commutativity symmetry but also antisymmetry. It is based on the idea that for any value a probabilistic measure of confirmation can assign there is a corresponding case where degrees of confirmation are symmetric. It is shown that a number of prominent confirmation measures such as Carnap’s difference function, Rescher’s measure of confirmation, Gaifman’s confirmation rate and Mortimer’s inverted difference function do not satisfy (...)
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  • A fiction of long standing.Christian Dayé - 2016 - History of the Human Sciences 29 (4-5):35-58.
    There appears to be a widespread belief that the social sciences during the 1950s and 1960s can be characterized by an almost unquestioned faith in a positivist philosophy of science. In contrast, the article shows that even within the narrower segment of Cold War social science, positivism was not an unquestioned doctrine blindly followed by everybody, but that quite divergent views coexisted. The article analyses two ‘techniques of prospection’, the Delphi technique and political gaming, from the perspective of a comprehensive (...)
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  • Philosophy as conceptual engineering: Inductive logic in Rudolf Carnap's scientific philosophy.Christopher F. French - 2015 - Dissertation, University of British Columbia
    My dissertation explores the ways in which Rudolf Carnap sought to make philosophy scientific by further developing recent interpretive efforts to explain Carnap’s mature philosophical work as a form of engineering. It does this by looking in detail at his philosophical practice in his most sustained mature project, his work on pure and applied inductive logic. I, first, specify the sort of engineering Carnap is engaged in as involving an engineering design problem and then draw out the complications of design (...)
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  • Conditional Probability in the Light of Qualitative Belief Change.David C. Makinson - 2011 - Journal of Philosophical Logic 40 (2):121 - 153.
    We explore ways in which purely qualitative belief change in the AGM tradition throws light on options in the treatment of conditional probability. First, by helping see why it can be useful to go beyond the ratio rule defining conditional from one-place probability. Second, by clarifying what is at stake in different ways of doing that. Third, by suggesting novel forms of conditional probability corresponding to familiar variants of qualitative belief change, and conversely. Likewise, we explain how recent work on (...)
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  • Probabilistic Belief Contraction.Raghav Ramachandran, Arthur Ramer & Abhaya C. Nayak - 2012 - Minds and Machines 22 (4):325-351.
    Probabilistic belief contraction has been a much neglected topic in the field of probabilistic reasoning. This is due to the difficulty in establishing a reasonable reversal of the effect of Bayesian conditionalization on a probabilistic distribution. We show that indifferent contraction, a solution proposed by Ramer to this problem through a judicious use of the principle of maximum entropy, is a probabilistic version of a full meet contraction. We then propose variations of indifferent contraction, using both the Shannon entropy measure (...)
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  • Modus Ponens and Modus Tollens for Conditional Probabilities, and Updating on Uncertain Evidence.Jordan Howard Sobel - 2009 - Theory and Decision 66 (2):103 - 148.
    There are narrowest bounds for P(h) when P(e) = y and P(h/e) = x, which bounds collapse to x as y goes to 1. A theorem for these bounds -- bounds for probable modus ponens -- entails a principle for updating on possibly uncertain evidence subject to these bounds that is a generalization of the principle for updating by conditioning on certain evidence. This way of updating on possibly uncertain evidence is appropriate when updating by ’probability kinematics’ or ’Jeffrey-conditioning’ is, (...)
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  • Bayes' theorem.James Joyce - 2008 - Stanford Encyclopedia of Philosophy.
    Bayes' Theorem is a simple mathematical formula used for calculating conditional probabilities. It figures prominently in subjectivist or Bayesian approaches to epistemology, statistics, and inductive logic. Subjectivists, who maintain that rational belief is governed by the laws of probability, lean heavily on conditional probabilities in their theories of evidence and their models of empirical learning. Bayes' Theorem is central to these enterprises both because it simplifies the calculation of conditional probabilities and because it clarifies significant features of subjectivist position. Indeed, (...)
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  • Hempel's Raven paradox: A lacuna in the standard bayesian solution.Peter B. M. Vranas - 2004 - British Journal for the Philosophy of Science 55 (3):545-560.
    According to Hempel's paradox, evidence (E) that an object is a nonblack nonraven confirms the hypothesis (H) that every raven is black. According to the standard Bayesian solution, E does confirm H but only to a minute degree. This solution relies on the almost never explicitly defended assumption that the probability of H should not be affected by evidence that an object is nonblack. I argue that this assumption is implausible, and I propose a way out for Bayesians. Introduction Hempel's (...)
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  • (1 other version)How Bayesian Confirmation Theory Handles the Paradox of the Ravens.Branden Fitelson & James Hawthorne - 2010 - In Ellery Eells & James H. Fetzer (eds.), The Place of Probability in Science: In Honor of Ellery Eells (1953-2006). Springer. pp. 247--275.
    The Paradox of the Ravens (a.k.a,, The Paradox of Confirmation) is indeed an old chestnut. A great many things have been written and said about this paradox and its implications for the logic of evidential support. The first part of this paper will provide a brief survey of the early history of the paradox. This will include the original formulation of the paradox and the early responses of Hempel, Goodman, and Quine. The second part of the paper will describe attempts (...)
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  • The paradox of confirmation.Branden Fitelson - 2006 - Philosophy Compass 1 (1):95–113.
    Hempel first introduced the paradox of confirmation in (Hempel 1937). Since then, a very extensive literature on the paradox has evolved (Vranas 2004). Much of this literature can be seen as responding to Hempel’s subsequent discussions and analyses of the paradox in (Hempel 1945). Recently, it was noted that Hempel’s intuitive (and plausible) resolution of the paradox was inconsistent with his official theory of confirmation (Fitelson & Hawthorne 2006). In this article, we will try to explain how this inconsistency affects (...)
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  • Confirmation, paradoxes, and possible worlds.Shelley Stillwell - 1985 - British Journal for the Philosophy of Science 36 (1):19-52.
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  • Criteria for naturalness in conceptual spaces.Corina Strößner - 2022 - Synthese 200 (2):1-36.
    Conceptual spaces are a frequently applied framework for representing concepts. One of its central aims is to find criteria for what makes a concept natural. A prominent demand is that natural concepts cover convex regions in conceptual spaces. The first aim of this paper is to analyse the convexity thesis and the arguments that have been advanced in its favour or against it. Based on this, I argue that most supporting arguments focus on single-domain concepts (e.g., colours, smells, shapes). Unfortunately, (...)
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  • What is Probability?Patrick Maher - unknown
    In October 2009 I decided to stop doing philosophy. This meant, in particular, stopping work on the book that I was writing on the nature of probability. At that time, I had no intention of making my unfinished draft available to others. However, I recently noticed how many people are reading the lecture notes and articles on my web site. Since this draft book contains some important improvements on those materials, I decided to make it available to anyone who wants (...)
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  • (1 other version)The Place of Probability in Science: In Honor of Ellery Eells (1953-2006).Ellery Eells & James H. Fetzer (eds.) - 2010 - Springer.
    To clarify and illuminate the place of probability in science Ellery Eells and James H. Fetzer have brought together some of the most distinguished philosophers ...
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  • Jan Łukasiewicz’s program of the logicization of philosophy: its genesis, content and realizations.Anna Brożek - 2022 - Synthese 200 (3):1-24.
    In the paper, Jan Łukasiewicz’s program of the logicization of philosophy is presented and discussed. Łukasiewicz, known mostly for his invention of trivalent logic as well as his achievements in propositional calculus and metalogic, had always been concerned with the methodological condition of philosophy. He finally found “the measure of exactness” in mathematical logic. According to him, only the use of logical tools may provide philosophical investigations with an appropriate level of exactness. He expressed his views most firmly and directly (...)
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  • Non-bayesian foundations for statistical estimation, prediction, and the ravens example.Malcolm R. Forster - 1994 - Erkenntnis 40 (3):357 - 376.
    The paper provides a formal proof that efficient estimates of parameters, which vary as as little as possible when measurements are repeated, may be expected to provide more accurate predictions. The definition of predictive accuracy is motivated by the work of Akaike (1973). Surprisingly, the same explanation provides a novel solution for a well known problem for standard theories of scientific confirmation — the Ravens Paradox. This is significant in light of the fact that standard Bayesian analyses of the paradox (...)
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  • Der Rabe und der Bayesianist.Mark Siebel - 2004 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 35 (2):313-329.
    The Raven and the Bayesian. As an essential benefit of their probabilistic account of confirmation, Bayesians state that it provides a twofold solution to the ravens paradox. It is supposed to show that (i) the paradox’s conclusion is tenable because a white shoe only negligibly confirms the hypothesis that all ravens are black, and (ii) the paradox’s first premise is false anyway because a black raven can speak against the hypothesis. I argue that both proposals are not only unable to (...)
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  • Two envelopes.Jordan Howard Sobel - 1994 - Theory and Decision 36 (1):69-96.
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  • On the significance of conditional probabilities.Jordan Howard Sobel - 1996 - Synthese 109 (3):311 - 344.
    The orthodoxy that conditional probabilities reflect what are for a subject evidential bearings is seconded. This significance suggests that there should be principles equating rationally revised probabilities on new information with probabilities reached by conditionalizing on this information. Several principles, two of which are endorsed, are considered. A book is made against a violator of these, and it is argued that there must be something wrong with a person against whom such books can be made. Appendices comment on Popper-functions, elaborate (...)
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  • Janina Hosiasson-Lindenbaum on Analogical Reasoning: New Sources.Marta Sznajder - 2024 - Erkenntnis 89 (4):1349-1365.
    Janina Hosiasson-Lindenbaum is a known figure in philosophy of probability of the 1930s. A previously unpublished manuscript fills in the blanks in the full picture of her work on inductive reasoning by analogy, until now only accessible through a single publication. In this paper, I present Hosiasson’s work on analogical reasoning, bringing together her early publications that were never translated from Polish, and the recently discovered unpublished work. I then show how her late work relates to Rudolf Carnap’s approach to (...)
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  • The Raven Paradox Revisited in Terms of Random Variables.Bruno Carbonaro & Federica Vitale - 2013 - Erkenntnis 78 (4):763-795.
    The discussion about the Raven Paradox is ever-renewing: after nearly 70 years, many authors propose from time to time new solutions, and many authors state that these solutions are unsatisfactory. It is worthy to be carefully noted that though most arguments in favor or against the paradox are based on the notion of “probability” and on the application of Bayes’ law, not one of them makes use of the Kolmogorov axiomatic theory of probability and on the subsequent notion of “random (...)
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