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Logical Foundations of Probability

Mind 62 (245):86-99 (1950)

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  1. On Ratio Measures of Confirmation: Critical Remarks on Zalabardo’s Argument for the Likelihood-Ratio Measure.Valeriano Iranzo & Ignacio Martínez de Lejarza - 2013 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 44 (1):193-200.
    There are different Bayesian measures to calculate the degree of confirmation of a hypothesis H in respect of a particular piece of evidence E. Zalabardo (Analysis 69:630–635, 2009) is a recent attempt to defend the likelihood-ratio measure (LR) against the probability-ratio measure (PR). The main disagreement between LR and PR concerns their sensitivity to prior probabilities. Zalabardo invokes intuitive plausibility as the appropriate criterion for choosing between them. Furthermore, he claims that it favours the ordering of pairs evidence/hypothesis generated by (...)
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  • Probing the quantitative–qualitative divide in probabilistic reasoning.Duligur Ibeling, Thomas Icard, Krzysztof Mierzewski & Milan Mossé - forthcoming - Annals of Pure and Applied Logic.
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  • A logic for arguing about probabilities in measure teams.Tapani Hyttinen, Gianluca Paolini & Jouko Väänänen - 2017 - Archive for Mathematical Logic 56 (5-6):475-489.
    We use sets of assignments, a.k.a. teams, and measures on them to define probabilities of first-order formulas in given data. We then axiomatise first-order properties of such probabilities and prove a completeness theorem for our axiomatisation. We use the Hardy–Weinberg Principle of biology and the Bell’s Inequalities of quantum physics as examples.
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  • Merging of opinions and probability kinematics.Simon M. Huttegger - 2015 - Review of Symbolic Logic 8 (4):611-648.
    We explore the question of whether sustained rational disagreement is possible from a broadly Bayesian perspective. The setting is one where agents update on the same information, with special consideration being given to the case of uncertain information. The classical merging of opinions theorem of Blackwell and Dubins shows when updated beliefs come and stay closer for Bayesian conditioning. We extend this result to a type of Jeffrey conditioning where agents update on evidence that is uncertain but solid. However, merging (...)
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  • Analogical Predictive Probabilities.Simon M. Huttegger - 2019 - Mind 128 (509):1-37.
    It is well known that Rudolf Carnap’s original system of inductive logic failed to provide an adequate account of analogical reasoning. Since this problem was identified, there has been no shortage of proposals for how to incorporate analogy into inductive inference. Most alternatives to Carnap’s system, unlike his original one, have not been derived from first principles; this makes it to some extent unclear what the epistemic situations are to which they apply. This paper derives a new analogical inductive logic (...)
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  • Epistemic inconsistency and categorical coherence: a study of probabilistic measures of coherence.Michael Hughes - 2017 - Synthese 194 (8):3153-3185.
    Is logical consistency required for a set of beliefs or propositions to be categorically coherent? An affirmative answer is often assumed by mainstream epistemologists, and yet it is unclear why. Cases like the lottery and the preface call into question the assumption that beliefs must be consistent in order to be epistemically rational. And thus it is natural to wonder why all inconsistent sets of propositions are incoherent. On the other hand, Easwaran and Fitelson have shown that particular kinds of (...)
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  • Serious theories and skeptical theories: Why you are probably not a brain in a vat.Michael Huemer - 2016 - Philosophical Studies 173 (4):1031-1052.
    Skeptical hypotheses such as the brain-in-a-vat hypothesis provide extremely poor explanations for our sensory experiences. Because these scenarios accommodate virtually any possible set of evidence, the probability of any given set of evidence on the skeptical scenario is near zero; hence, on Bayesian grounds, the scenario is not well supported by the evidence. By contrast, serious theories make reasonably specific predictions about the evidence and are then well supported when these predictions are satisfied.
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  • What Is the Point of Confirmation?Franz Huber - 2005 - Philosophy of Science 72 (5):1146-1159.
    Philosophically, one of the most important questions in the enterprise termed confirmation theory is this: Why should one stick to well confirmed theories rather than to any other theories? This paper discusses the answers to this question one gets from absolute and incremental Bayesian confirmation theory. According to absolute confirmation, one should accept ''absolutely well confirmed'' theories, because absolute confirmation takes one to true theories. An examination of two popular measures of incremental confirmation suggests the view that one should stick (...)
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  • The Logic of Theory Assessment.Franz Huber - 2007 - Journal of Philosophical Logic 36 (5):511-538.
    This paper starts by indicating the analysis of Hempel's conditions of adequacy for any relation of confirmation (Hempel, 1945) as presented in Huber (submitted). There I argue contra Carnap (1962, Section 87) that Hempel felt the need for two concepts of confirmation: one aiming at plausible theories and another aiming at informative theories. However, he also realized that these two concepts are conflicting, and he gave up the concept of confirmation aiming at informative theories. The main part of the paper (...)
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  • On the justification of deduction and induction.Franz Huber - 2017 - European Journal for Philosophy of Science 7 (3):507-534.
    The thesis of this paper is that we can justify induction deductively relative to one end, and deduction inductively relative to a different end. I will begin by presenting a contemporary variant of Hume ’s argument for the thesis that we cannot justify the principle of induction. Then I will criticize the responses the resulting problem of induction has received by Carnap and Goodman, as well as praise Reichenbach ’s approach. Some of these authors compare induction to deduction. Haack compares (...)
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  • Hempel’s logic of confirmation.Franz Huber - 2008 - Philosophical Studies 139 (2):181-189.
    This paper presents a new analysis of C.G. Hempel’s conditions of adequacy for any relation of confirmation [Hempel C. G. (1945). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press, pp. 3–51.], differing from the one Carnap gave in §87 of his [1962. Logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.]. Hempel, it is argued, felt the need for two concepts of confirmation: one aiming at true hypotheses and another (...)
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  • Assessing theories, Bayes style.Franz Huber - 2008 - Synthese 161 (1):89-118.
    The problem addressed in this paper is “the main epistemic problem concerning science”, viz. “the explication of how we compare and evaluate theories [...] in the light of the available evidence” (van Fraassen, BC, 1983, Theory comparison and relevant Evidence. In J. Earman (Ed.), Testing scientific theories (pp. 27–42). Minneapolis: University of Minnesota Press). Sections 1– 3 contain the general plausibility-informativeness theory of theory assessment. In a nutshell, the message is (1) that there are two values a theory should exhibit: (...)
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  • The rule of succession, inductive logic, and probability logic.Colin Howson - 1975 - British Journal for the Philosophy of Science 26 (3):187-198.
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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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  • Must the logical probability of laws be zero?C. Howson - 1973 - British Journal for the Philosophy of Science 24 (2):153-163.
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  • Philosophical Analysis: The Concept Grounding View.Joachim Horvath - 2017 - Philosophy and Phenomenological Research 97 (3):724-750.
    Philosophical analysis was the central preoccupation of 20th-century analytic philosophy. In the contemporary methodological debate, however, it faces a number of pressing external and internal challenges. While external challenges, like those from experimental philosophy or semantic externalism, have been extensively discussed, internal challenges to philosophical analysis have received much less attention. One especially vexing internal challenge is that the success conditions of philosophical analysis are deeply unclear. According to the standard textbook view, a philosophical analysis aims at a strict biconditional (...)
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  • Carnap's inductive probabilities as a contribution to decision theory.Joachim Hornung - 1980 - Theoretical Medicine and Bioethics 1 (3):325-367.
    Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a (...)
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  • Why Metaethics Needs Empirical Moral Psychology.Jeroen Hopster & Michael Klenk - 2020 - Critica 52 (155):27-54.
    What is the significance of empirical moral psychology for metaethics? In this article we take up Michael Ruse’s evolutionary debunking argument against moral realism and reassess it in the context of the empirical state of the art. Ruse’s argument depends on the phenomenological presumption that people generally experience morality as objective. We demonstrate how recent experimental findings challenge this widely-shared armchair presumption and conclude that Ruse’s argument fails. We situate this finding in the recent debate about Carnapian explication and argue (...)
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  • Intuitions and Conceptual Analysis in Wittgensteinian Pragmatism.David Hommen & Frauke Albersmeier - 2019 - History of Philosophy & Logical Analysis 22 (1):72-91.
    The nature of intuitions remains a contested issue in philosophy. Yet, intuitions are frequently cited in philosophical work, featuring most prominently in conceptual analysis, the philosophical method par excellence. In this paper, we approach the question about the nature of intuitions based on a pragmatist, namely, Wittgensteinian account of concepts. To Wittgenstein, intuitions are just immediate ‘reactions’ to certain cognitive tasks. His view provides a distinct alternative to identifying intuitions with either doxastic states or quasi-perceptual experiences. We discuss its implications (...)
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  • Non-zero probabilities for universal generalizations.Ruurik Holm - 2013 - Synthese 190 (18):4001-4007.
    This article discusses the classical problem of zero probability of universal generalizations in Rudolf Carnap’s inductive logic. A correction rule for updating the inductive method on the basis of evidence will be presented. It will be shown that this rule has the effect that infinite streams of uniform evidence assume a non-zero limit probability. Since Carnap’s inductive logic is based on finite domains of individuals, the probability of the corresponding universal quantification changes accordingly. This implies that universal generalizations can receive (...)
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  • Unnaturalised Racial Naturalism.Adam Hochman - 2014 - Studies in History and Philosophy of Science Part C: Studies in History and Philosophy of Biological and Biomedical Sciences 46 (1):79-87.
    Quayshawn Spencer (2014) misunderstands my treatment of racial naturalism. I argued that racial naturalism must entail a strong claim, such as “races are subspecies”, if it is to be a substantive position that contrasts with anti-realism about biological race. My recognition that not all race naturalists make such a strong claim is evident throughout the article Spencer reviews (Hochman, 2013a). Spencer seems to agree with me that there are no human subspecies, and he endorses a weaker form of racial naturalism. (...)
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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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  • Degrees of commensurability and the repugnant conclusion.Alan Hájek & Wlodek Rabinowicz - 2021 - Noûs 56 (4):897-919.
    Two objects of valuation are said to be incommensurable if neither is better than the other, nor are they equally good. This negative, coarse-grained characterization fails to capture the nuanced structure of incommensurability. We argue that our evaluative resources are far richer than orthodoxy recognizes. We model value comparisons with the corresponding class of permissible preference orderings. Then, making use of our model, we introduce a potentially infinite set of degrees of approximation to better, worse, and equally good, which we (...)
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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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  • Events and times: a case study in means-ends metaphysics.Christopher Hitchcock - 2012 - Philosophical Studies 160 (1):79-96.
    There is a tradition, tracing back to Kant, of recasting metaphysical questions as questions about the utility of a conceptual scheme, linguistic framework, or methodological rule for achieving some particular end. Following in this tradition, I propose a ‘means-ends metaphysics ’, in which one rigorously demonstrates the suitability of some conceptual framework for achieving a specified goal. I illustrate this approach using a debate about the nature of events. Specifically, the question is whether the time at which an event occurs (...)
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  • Suppositions, Presuppositions, and Ontology.Ian Hinckfuss - 1993 - Canadian Journal of Philosophy 23 (4):595 - 618.
    It has been widely accepted in the past and it remains accepted in many quarters even now, that an ontologically economical position is to be rejected if the corresponding Platonic or otherwise ontologically prodigal discourse cannot be translated, paraphrased or otherwise ‘reduced’ to discourse exhibiting a more economical ontology. Such an attitude is often accompanied by the claim that the prodigal ontology explains some important truthsandthe demand that the nominalist or fictionalist or economicalist provide an alternative explanation for those truths (...)
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  • Philosophy of science (Wissenschaftstheorie) in Finland.Jaakko Hintikka - 1970 - Zeitschrift Für Allgemeine Wissenschaftstheorie 1 (1):119-132.
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  • Philosophy of science (wissenschaftstheorie) in finland.Jaakko Hintikka - 1970 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 1 (1):119-132.
    Summary A survey of recent work in the philosophy of science in Finland, with a bibliography. The main sources of influence emphasized are Eino Kaila (1890–1958) and G. H. von Wright (b. 1916). The main topics covered are: induction and probability; information and explanation; the acceptance and application of theories; the role of auxiliary (theoretical) terms; measurement; general methodology of social and behavioral sciences; finalistic explanation; methodology of sociology and history.
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  • Responsible AI Through Conceptual Engineering.Johannes Himmelreich & Sebastian Köhler - 2022 - Philosophy and Technology 35 (3):1-30.
    The advent of intelligent artificial systems has sparked a dispute about the question of who is responsible when such a system causes a harmful outcome. This paper champions the idea that this dispute should be approached as a conceptual engineering problem. Towards this claim, the paper first argues that the dispute about the responsibility gap problem is in part a conceptual dispute about the content of responsibility and related concepts. The paper then argues that the way forward is to evaluate (...)
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  • The Counterpart Principle of Analogical Support by Structural Similarity.Alexandra Hill & Jeffrey Bruce Paris - 2014 - Erkenntnis 79 (S6):1-16.
    We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures.
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  • Non‐Humean theories of natural necessity.Tyler Hildebrand - 2020 - Philosophy Compass 15 (5):e12662.
    Non‐Humean theories of natural necessity invoke modally‐laden primitives to explain why nature exhibits lawlike regularities. However, they vary in the primitives they posit and in their subsequent accounts of laws of nature and related phenomena (including natural properties, natural kinds, causation, counterfactuals, and the like). This article provides a taxonomy of non‐Humean theories, discusses influential arguments for and against them, and describes some ways in which differences in goals and methods can motivate different versions of non‐Humeanism (and, for that matter, (...)
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  • The dialectics of infinitism and coherentism: inferential justification versus holism and coherence.Frederik Herzberg - 2014 - Synthese 191 (4):701-723.
    This paper formally explores the common ground between mild versions of epistemological coherentism and infinitism; it proposes—and argues for—a hybrid, coherentist–infinitist account of epistemic justification. First, the epistemological regress argument and its relation to the classical taxonomy regarding epistemic justification—of foundationalism, infinitism and coherentism—is reviewed. We then recall recent results proving that an influential argument against infinite regresses of justification, which alleges their incoherence on account of probabilistic inconsistency, cannot be maintained. Furthermore, we prove that the Principle of Inferential Justification (...)
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  • Thick Concepts in Economics: The Case of Becker and Murphy’s Theory of Rational Addiction.Catherine Herfeld & Charles Djordjevic - 2021 - Philosophy of the Social Sciences 51 (4):371-399.
    In this paper, we examine the viability of avoiding value judgments encoded in thick concepts when these concepts are used in economic theories. We focus on what implications the use of such thick concepts might have for the tenability of the fact/value dichotomy in economics. Thick concepts have an evaluative and a descriptive component. Our suggestion is that despite attempts to rid thick concepts of their evaluative component, economists are often not successful. We focus on the strategy of explication to (...)
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  • How strong is the argument from inductive risk?Tobias Henschen - 2021 - European Journal for Philosophy of Science 11 (3):1-23.
    The argument from inductive risk, as developed by Rudner and others, famously concludes that the scientist qua scientist makes value judgments. The paper aims to show that trust in the soundness of the argument is overrated – that philosophers who endorse its conclusion fail to refute two of the most important objections that have been raised to its soundness: Jeffrey’s objection that the genuine task of the scientist is to assign probabilities to hypotheses, and Levi’s objection that the argument is (...)
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  • Carnap and de finetti on bets and the probability of singular events: The dutch book argument reconsidered.Klaus Heilig - 1978 - British Journal for the Philosophy of Science 29 (4):325-346.
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  • A defense of objectivism about evidential support.Brian Hedden - 2015 - Canadian Journal of Philosophy 45 (5):716-743.
    Objectivism about evidential support is the thesis that facts about the degree to which a body of evidence supports a hypothesis are objective rather than depending on subjective factors like one’s own language or epistemic values. Objectivism about evidential support is key to defending a synchronic, time-slice-centric conception of epistemic rationality, on which what you ought to believe at a time depends only on what evidence you have at that time, and not on how you were at previous times. Here, (...)
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  • Probability in Wittgenstein's Tractatus.Clare Hay - 2021 - Philosophical Investigations 45 (2):130-145.
    Philosophical Investigations, Volume 45, Issue 2, Page 130-145, April 2022.
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  • Logic and probability theory versus canons of rationality.Gilbert Harman - 1983 - Behavioral and Brain Sciences 6 (2):251-251.
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  • Kyburg on practical certainty.Willam L. Harper - 1983 - Behavioral and Brain Sciences 6 (2):251-252.
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  • Confirmation and adequacy conditions.Marsha Hanen - 1971 - Philosophy of Science 38 (3):361-368.
    Several standard conditions of adequacy for confirmation are considered and a conclusion of B. Skyrms regarding the converse-consequence condition is shown to be mistaken. Widely accepted conditions such as the entailment condition and the special consequence condition are shown to be open to counterexample, and confusion about these conditions is traced to confusion about the difference between two kinds of confirmation concepts--concepts of firmness and concepts of increase in firmness. The importance of concepts of the latter sort is stressed. Finally, (...)
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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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  • Stop Talking about Fake News!Joshua Habgood-Coote - 2019 - Inquiry: An Interdisciplinary Journal of Philosophy 62 (9-10):1033-1065.
    Since 2016, there has been an explosion of academic work and journalism that fixes its subject matter using the terms ‘fake news’ and ‘post-truth’. In this paper, I argue that this terminology is not up to scratch, and that academics and journalists ought to completely stop using the terms ‘fake news’ and ‘post-truth’. I set out three arguments for abandonment. First, that ‘fake news’ and ‘post-truth’ do not have stable public meanings, entailing that they are either nonsense, context-sensitive, or contested. (...)
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  • On Logic in the Law: "Something, but not All".Susan Haack - 2007 - Ratio Juris 20 (1):1-31.
    In 1880, when Oliver Wendell Holmes (later to be a Justice of the U.S. Supreme Court) criticized the logical theology of law articulated by Christopher Columbus Langdell (the first Dean of Harvard Law School), neither Holmes nor Langdell was aware of the revolution in logic that had begun, the year before, with Frege's Begriffsschrift. But there is an important element of truth in Holmes's insistence that a legal system cannot be adequately understood as a system of axioms and corollaries; and (...)
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  • Über den Grad der Bewährung naturwissenschaftlicher Hypothesen.O. -J. Grüsser - 1983 - Zeitschrift Für Allgemeine Wissenschaftstheorie 14 (2):273-291.
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  • Über den Grad der bewährung naturwissenschaftlicher hypothesen.O. -J. Grüsser - 1983 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 14 (2):273-291.
    The formulae advanced by Popper to calculate the degree of corroboration C of a scientific hypothesis are unsatisfactory in that the probability values required in the computation are often not available. An attempt is made to define a quantitative measure B* in the place of C in which only countable empirical values would be used. This condition is fulfilled in two basic formulae and eq. ), which could be applied to calculate the degree of corroboration. When m successful falsifications of (...)
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  • Is the method of bold conjectures and attempted refutations justifiably the method of science?Adolf Grünbaum - 1976 - British Journal for the Philosophy of Science 27 (2):105-136.
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  • Wrongful ways to raise the epistemic standard.Jumbly Grindrod - 2020 - Episteme (3):1-15.
    This paper is concerned with identifying and accounting for cases where the epistemic standard is raised inappropriately. The first section is concerned with identifying a notion of a variable epistemic standard that is neutral regarding a range of theoretical issues. The second section argues that the possibility the epistemic standard could be raised in some epistemic inappropriate way warrants further investigation. The third section outlines and provides a partial explanation of such a case: one in which a climate change denier (...)
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  • Evolution, Dysfunction, and Disease: A Reappraisal.Paul E. Griffiths & John Matthewson - 2018 - British Journal for the Philosophy of Science 69 (2):301-327.
    Some ‘naturalist’ accounts of disease employ a biostatistical account of dysfunction, whilst others use a ‘selected effect’ account. Several recent authors have argued that the biostatistical account offers the best hope for a naturalist account of disease. We show that the selected effect account survives the criticisms levelled by these authors relatively unscathed, and has significant advantages over the BST. Moreover, unlike the BST, it has a strong theoretical rationale and can provide substantive reasons to decide difficult cases. This is (...)
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  • A Typology of Conceptual Explications.Dirk Greimann - 2012 - Disputatio 4 (34):645-670.
    Greimann-Dirk_A-typology-of-conceptual-explications.
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  • Induction and knowledge-what.Peter Gärdenfors & Andreas Stephens - 2017 - European Journal for Philosophy of Science 8 (3):1-21.
    Within analytic philosophy, induction has been seen as a problem concerning inferences that have been analysed as relations between sentences. In this article, we argue that induction does not primarily concern relations between sentences, but between properties and categories. We outline a new approach to induction that is based on two theses. The first thesis is epistemological. We submit that there is not only knowledge-how and knowledge-that, but also knowledge-what. Knowledge-what concerns relations between properties and categories and we argue that (...)
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