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Richard Pettigrew [69]Richard G. Pettigrew [4]
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Richard Pettigrew
Bristol University
  1.  64
    Accuracy and the Laws of Credence.Richard Pettigrew - 2016 - Oxford University Press UK.
    Richard Pettigrew offers an extended investigation into a particular way of justifying the rational principles that govern our credences. The main principles that he justifies are the central tenets of Bayesian epistemology, though many other related principles are discussed along the way. Pettigrew looks to decision theory in order to ground his argument. He treats an agent's credences as if they were a choice she makes between different options, gives an account of the purely epistemic utility enjoyed by different sets (...)
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  2. An Accuracy‐Dominance Argument for Conditionalization.R. A. Briggs & Richard Pettigrew - forthcoming - Noûs.
  3. Accuracy, Risk, and the Principle of Indifference.Richard G. Pettigrew - 2016 - Philosophy and Phenomenological Research 92 (1):35-59.
    In Bayesian epistemology, the problem of the priors is this: How should we set our credences (or degrees of belief) in the absence of evidence? That is, how should we set our prior or initial credences, the credences with which we begin our credal life? David Lewis liked to call an agent at the beginning of her credal journey a superbaby. The problem of the priors asks for the norms that govern these superbabies. -/- The Principle of Indifference gives a (...)
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  4. An Objective Justification of Bayesianism I: Measuring Inaccuracy.Hannes Leitgeb & Richard Pettigrew - 2010 - Philosophy of Science 77 (2):201-235.
    One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its sequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In this paper, we make this norm mathematically precise in various ways. We describe three epistemic dilemmas that an agent might face if she attempts (...)
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  5. An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy.Hannes Leitgeb & Richard Pettigrew - 2010 - Philosophy of Science 77 (2):236-272.
    One of the fundamental problems of epistemology is to say when the evidence in an agent’s possession justifies the beliefs she holds. In this paper and its prequel, we defend the Bayesian solution to this problem by appealing to the following fundamental norm: Accuracy An epistemic agent ought to minimize the inaccuracy of her partial beliefs. In the prequel, we made this norm mathematically precise; in this paper, we derive its consequences. We show that the two core tenets of Bayesianism (...)
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  6. Transformative Experience and Decision Theory.Richard Pettigrew - 2015 - Philosophy and Phenomenological Research 91 (3):766-774.
    This paper is part of a book symposium for L. A. Paul (2014) Transformative Experience (OUP).
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  7. Accuracy, Chance, and the Principal Principle.Richard Pettigrew - 2012 - Philosophical Review 121 (2):241-275.
    In ‘A Non-Pragmatic Vindication of Probabilism’, Jim Joyce attempts to ‘depragmatize’ de Finetti’s prevision argument for the claim that our partial beliefs ought to satisfy the axioms of probability calculus. In this paper, I adapt Joyce’s argument to give a non-pragmatic vindication of various versions of David Lewis’ Principal Principle, such as the version based on Isaac Levi's account of admissibility, Michael Thau and Ned Hall's New Principle, and Jenann Ismael's Generalized Principal Principle. Joyce enumerates properties that must be had (...)
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  8. A New Epistemic Utility Argument for the Principal Principle.Richard G. Pettigrew - 2013 - Episteme 10 (1):19-35.
    Jim Joyce has presented an argument for Probabilism based on considerations of epistemic utility [Joyce, 1998]. In a recent paper, I adapted this argument to give an argument for Probablism and the Principal Principle based on similar considerations [Pettigrew, 2012]. Joyce’s argument assumes that a credence in a true proposition is better the closer it is to maximal credence, whilst a credence in a false proposition is better the closer it is to minimal credence. By contrast, my argument in that (...)
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  9. On the Accuracy of Group Credences.Richard Pettigrew - 2020 - Oxford Studies in Epistemology 6.
    to appear in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6 We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And (...)
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  10. What is conditionalization, and why should we do it?Richard Pettigrew - 2020 - Philosophical Studies 177 (11):3427-3463.
    Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...)
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  11. Choosing for Changing Selves.Richard Pettigrew - 2019 - Oxford, UK: Oxford University Press.
    What we value, like, endorse, want, and prefer changes over the course of our lives. Richard Pettigrew presents a theory of rational decision making for agents who recognise that their values will change over time and whose decisions will affect those future times.
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  12.  88
    The Dutch Book Arguments.Richard Pettigrew - 2020 - Cambridge, UK: Cambridge University Press.
    (This is for the series Elements of Decision Theory published by Cambridge University Press and edited by Martin Peterson) -/- Our beliefs come in degrees. I believe some things more strongly than I believe others. I believe very strongly that global temperatures will continue to rise during the coming century; I believe slightly less strongly that the European Union will still exist in 2029; and I believe much less strongly that Cardiff is east of Edinburgh. My credence in something is (...)
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  13. Epistemic Utility and Norms for Credences.Richard Pettigrew - 2013 - Philosophy Compass 8 (10):897-908.
    Beliefs come in different strengths. An agent's credence in a proposition is a measure of the strength of her belief in that proposition. Various norms for credences have been proposed. Traditionally, philosophers have tried to argue for these norms by showing that any agent who violates them will be lead by her credences to make bad decisions. In this article, we survey a new strategy for justifying these norms. The strategy begins by identifying an epistemic utility function and a decision-theoretic (...)
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  14. Identity and Discernibility in Philosophy and Logic.James Ladyman, Øystein Linnebo & Richard Pettigrew - 2012 - Review of Symbolic Logic 5 (1):162-186.
    Questions about the relation between identity and discernibility are important both in philosophy and in model theory. We show how a philosophical question about identity and dis- cernibility can be ‘factorized’ into a philosophical question about the adequacy of a formal language to the description of the world, and a mathematical question about discernibility in this language. We provide formal definitions of various notions of discernibility and offer a complete classification of their logical relations. Some new and surprising facts are (...)
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  15. Two Types of Abstraction for Structuralism.Øystein Linnebo & Richard Pettigrew - 2014 - Philosophical Quarterly 64 (255):267-283.
    If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such ‘foreign’ properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction meant to purge mathematical objects of all ‘foreign’ properties. One form is inspired by Frege; the other (...)
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  16. Risk, Rationality and Expected Utility Theory.Richard Pettigrew - 2015 - Canadian Journal of Philosophy 45 (5-6):798-826.
    There are decision problems where the preferences that seem rational to many people cannot be accommodated within orthodox decision theory in the natural way. In response, a number of alternatives to the orthodoxy have been proposed. In this paper, I offer an argument against those alternatives and in favour of the orthodoxy. I focus on preferences that seem to encode sensitivity to risk. And I focus on the alternative to the orthodoxy proposed by Lara Buchak’s risk-weighted expected utility theory. I (...)
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  17.  63
    Accuracy and Evidence.Richard Pettigrew - 2013 - Dialectica 67 (4):579-596.
    In “A Nonpragmatic Vindication of Probabilism”, Jim Joyce argues that our credences should obey the axioms of the probability calculus by showing that, if they don't, there will be alternative credences that are guaranteed to be more accurate than ours. But it seems that accuracy is not the only goal of credences: there is also the goal of matching one's credences to one's evidence. I will consider four ways in which we might make this latter goal precise: on the first, (...)
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  18. Jamesian Epistemology Formalised: An Explication of ‘the Will to Believe’.Richard Pettigrew - 2016 - Episteme 13 (3):253-268.
    Famously, William James held that there are two commandments that govern our epistemic life: Believe truth! Shun error! In this paper, I give a formal account of James' claim using the tools of epistemic utility theory. I begin by giving the account for categorical doxastic states – that is, full belief, full disbelief, and suspension of judgment. Then I will show how the account plays out for graded doxastic states – that is, credences. The latter part of the paper thus (...)
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  19. Epistemic Utility and the Normativity of Logic.Richard Pettigrew - 2017 - Logos and Episteme 8 (4):455-492.
    How does logic relate to rational belief? Is logic normative for belief, as some say? What, if anything, do facts about logical consequence tell us about norms of doxastic rationality? In this paper, we consider a range of putative logic-rationality bridge principles. These purport to relate facts about logical consequence to norms that govern the rationality of our beliefs and credences. To investigate these principles, we deploy a novel approach, namely, epistemic utility theory. That is, we assume that doxastic attitudes (...)
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  20. The Population Ethics of Belief: In Search of an Epistemic Theory X.Richard Pettigrew - 2018 - Noûs 52 (2):336-372.
    Consider Phoebe and Daphne. Phoebe has credences in 1 million propositions. Daphne, on the other hand, has credences in all of these propositions, but she's also got credences in 999 million other propositions. Phoebe's credences are all very accurate. Each of Daphne's credences, in contrast, are not very accurate at all; each is a little more accurate than it is inaccurate, but not by much. Whose doxastic state is better, Phoebe's or Daphne's? It is clear that this question is analogous (...)
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  21. Category Theory as an Autonomous Foundation.Øystein Linnebo & Richard Pettigrew - 2011 - Philosophia Mathematica 19 (3):227-254.
    Does category theory provide a foundation for mathematics that is autonomous with respect to the orthodox foundation in a set theory such as ZFC? We distinguish three types of autonomy: logical, conceptual, and justificatory. Focusing on a categorical theory of sets, we argue that a strong case can be made for its logical and conceptual autonomy. Its justificatory autonomy turns on whether the objects of a foundation for mathematics should be specified only up to isomorphism, as is customary in other (...)
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  22.  19
    On the Accuracy of Group Credences.Richard Pettigrew - 2019 - In Oxford Studies in Epistemology Vol.6. Oxford University Press.
  23. Illness as Transformative Experience.Havi Carel, Richard Pettigrew & Ian James Kidd - 2017 - The Lancet 388:1152-1153..
    We propose that certain forms of chronic illness can be transformative experiences, in the sense described by L.A. Paul.
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  24. Logical Ignorance and Logical Learning.Richard G. Pettigrew - forthcoming - Synthese:1-30.
    According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Ian Hacking (1967), I develop a version of Bayesianism that permits logical ignorance. This includes an account of the synchronic norms that govern a logically ignorant individual at any given time, (...)
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  25.  21
    The Principal Principle Does Not Imply the Principle of Indifference.Richard Pettigrew - 2020 - British Journal for the Philosophy of Science 71 (2):605-619.
    In a recent paper in this journal, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson argue that the principal principle entails the principle of indifference. In this article, I argue that it does not. Lewis’s version of the principal principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW base their argument on certain intuitions concerning when one proposition is admissible for another: Conditions 1 and 2. There are two ways of reading their (...)
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  26.  17
    On the Accuracy of Group Credences.Richard Pettigrew - 2019 - Oxford Studies in Epistemology 6.
    We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...)
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  27.  91
    II—Pluralism About Belief States.Richard Pettigrew - 2015 - Aristotelian Society Supplementary Volume 89 (1):187-204.
    With his Humean thesis on belief, Leitgeb seeks to say how beliefs and credences ought to interact with one another. To argue for this thesis, he enumerates the roles beliefs must play and the properties they must have if they are to play them, together with norms that beliefs and credences intuitively must satisfy. He then argues that beliefs can play these roles and satisfy these norms if, and only if, they are related to credences in the way set out (...)
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  28.  65
    Epistemic Utility Arguments for Probabilism.Richard Pettigrew - 2011 - Stanford Encyclopedia.
  29.  25
    Accuracy and the Credence-Belief Connection.Richard Pettigrew - 2015 - Philosophers' Imprint 15:1-20.
    Probabilism says an agent is rational only if her credences are probabilistic. This paper is concerned with the so-called Accuracy Dominance Argument for Probabilism. This argument begins with the claim that the sole fundamental source of epistemic value for a credence is its accuracy. It then shows that, however we measure accuracy, any non-probabilistic credences are accuracy-dominated: that is, there are alternative credences that are guaranteed to be more accurate than them. It follows that non-probabilistic credences are irrational. In this (...)
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  30. On the Expected Utility Objection to the Dutch Book Argument for Probabilism.Richard Pettigrew - 2021 - Noûs (1):23-38.
    The Dutch Book Argument for Probabilism assumes Ramsey's Thesis (RT), which purports to determine the prices an agent is rationally required to pay for a bet. Recently, a new objection to Ramsey's Thesis has emerged (Hedden 2013, Wronski & Godziszewski 2017, Wronski 2018)--I call this the Expected Utility Objection. According to this objection, it is Maximise Subjective Expected Utility (MSEU) that determines the prices an agent is required to pay for a bet, and this often disagrees with Ramsey's Thesis. I (...)
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  31.  85
    The Principal Principle Does Not Imply the Principle of Indifference.Richard Pettigrew - 2017 - British Journal for the Philosophy of Science:axx060.
    In a recent paper in this journal, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson argue that the principal principle entails the principle of indifference. In this paper, I argue that it does not. Lewis’s version of the principal principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW base their argument on certain intuitions concerning when one proposition is admissible for another: Conditions 1 and 2. There are two ways of reading their (...)
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  32. Platonism and Aristotelianism in Mathematics.Richard Pettigrew - 2008 - Philosophia Mathematica 16 (3):310-332.
    Philosophers of mathematics agree that the only interpretation of arithmetic that takes that discourse at 'face value' is one on which the expressions 'N', '0', '1', '+', and 'x' are treated as proper names. I argue that the interpretation on which these expressions are treated as akin to free variables has an equal claim to be the default interpretation of arithmetic. I show that no purely syntactic test can distinguish proper names from free variables, and I observe that any semantic (...)
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  33. What is Justified Credence?Richard Pettigrew - 2021 - Episteme 18 (1):16-30.
    In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...)
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  34. Deference Done Right.Richard Pettigrew & Michael G. Titelbaum - 2014 - Philosophers' Imprint 14:1-19.
    There are many kinds of epistemic experts to which we might wish to defer in setting our credences. These include: highly rational agents, objective chances, our own future credences, our own current credences, and evidential probabilities. But exactly what constraint does a deference requirement place on an agent's credences? In this paper we consider three answers, inspired by three principles that have been proposed for deference to objective chances. We consider how these options fare when applied to the other kinds (...)
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  35. The Open Handbook of Formal Epistemology.Richard Pettigrew & Jonathan Weisberg (eds.) - 2019 - PhilPapers Foundation.
    In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluctuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. Then, we (...)
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  36.  61
    Transformative Experience, by L. A. Paul.Richard Pettigrew - 2016 - Mind 125 (499):927-935.
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  37. Indispensability Arguments and Instrumental Nominalism.Richard Pettigrew - 2012 - Review of Symbolic Logic 5 (4):687-709.
    In the philosophy of mathematics, indispensability arguments aim to show that we are justified in believing that abstract mathematical objects exist. I wish to defend a particular objection to such arguments that has become increasingly popular recently. It is called instrumental nominalism. I consider the recent versions of this view and conclude that it has yet to be given an adequate formulation. I provide such a formulation and show that it can be used to answer the indispensability arguments. -/- There (...)
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  38. What Chance‐Credence Norms Should Not Be.Richard G. Pettigrew - 2013 - Noûs 47 (3):177-196.
    A chance-credence norm states how an agent's credences in propositions concerning objective chances ought to relate to her credences in other propositions. The most famous such norm is the Principal Principle (PP), due to David Lewis. However, Lewis noticed that PP is too strong when combined with many accounts of chance that attempt to reduce chance facts to non-modal facts. Those who defend such accounts of chance have offered two alternative chance-credence norms: the first is Hall's and Thau's New Principle (...)
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  39.  19
    Aggregating Incoherent Agents Who Disagree.Richard Pettigrew - unknown
    In this paper, we explore how we should aggregate the degrees of belief of a group of agents to give a single coherent set of degrees of belief, when at least some of those agents might be probabilistically incoherent. There are a number of ways of aggregating degrees of belief, and there are a number of ways of fixing incoherent degrees of belief. When we have picked one of each, should we aggregate first and then fix, or fix first and (...)
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  40.  40
    What We Talk About When We Talk About Numbers.Richard Pettigrew - 2018 - Annals of Pure and Applied Logic 169 (12):1437-1456.
    In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.
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  41. An Improper Introduction to Epistemic Utility Theory.Richard Pettigrew - 2011 - In Henk de Regt, Samir Okasha & Stephan Hartmann (eds.), Proceedings of EPSA: Amsterdam '09. Springer. pp. 287--301.
    Beliefs come in different strengths. What are the norms that govern these strengths of belief? Let an agent's belief function at a particular time be the function that assigns, to each of the propositions about which she has an opinion, the strength of her belief in that proposition at that time. Traditionally, philosophers have claimed that an agent's belief function at any time ought to be a probability function (Probabilism), and that she ought to update her belief function upon obtaining (...)
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  42. Aristotle on the Subject Matter of Geometry.Richard Pettigrew - 2009 - Phronesis 54 (3):239-260.
    I offer a new interpretation of Aristotle's philosophy of geometry, which he presents in greatest detail in Metaphysics M 3. On my interpretation, Aristotle holds that the points, lines, planes, and solids of geometry belong to the sensible realm, but not in a straightforward way. Rather, by considering Aristotle's second attempt to solve Zeno's Runner Paradox in Book VIII of the Physics , I explain how such objects exist in the sensibles in a special way. I conclude by considering the (...)
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  43.  28
    Précis and Replies to Contributors for Book Symposium on Accuracy and the Laws of Credence.Richard Pettigrew - 2017 - Episteme 14 (1):1-30.
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  44.  57
    Accuracy and the Belief-Credence Connection.Richard Pettigrew - 2015 - Philosophers' Imprint 15:1-20.
    Probabilism says an agent is rational only if her credences are probabilistic. This paper is concerned with the so-called Accuracy Dominance Argument for Probabilism. This argument begins with the claim that the sole fundamental source of epistemic value for a credence is its accuracy. It then shows that, however we measure accuracy, any non-probabilistic credences are accuracy-dominated: that is, there are alternative credences that are guaranteed to be more accurate than them. It follows that non-probabilistic credences are irrational. In this (...)
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  45.  45
    Internalism, Externalism, and the KK Principle.Alexander Bird & Richard Pettigrew - 2019 - Erkenntnis:1-20.
    This paper examines the relationship between the KK principle and the epistemological theses of externalism and internalism. In particular we examine arguments from Okasha :80–86, 2013) and Greco :169–197, 2014) which deny that we can derive the denial of the KK principle from externalism.
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  46. Accuracy-First Epistemology Without Additivity.Richard Pettigrew - forthcoming - Philosophy of Science.
    Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.
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  47.  88
    Autonomy for Changing Selves.Richard Pettigrew - manuscript
    For the Routledge Handbook of Autonomy (edited by Ben Colburn) -/- Our values change. What we value, want, desire, prefer, and how much; for nearly everyone, these will be different at different times in their life. These changes can be gradual or abrupt; they can be long-lasting or short-lived; and they can be induced by forces outside yourself or they can come from within or they can have no specific catalyst at all. Such preference change raises a number of questions (...)
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  48.  36
    A note on deterministic updating and van Fraassen’s symmetry argument for conditionalization.Richard Pettigrew - 2021 - Philosophical Studies 178 (2):665-673.
    In a recent paper, Pettigrew argues that the pragmatic and epistemic arguments for Bayesian updating are based on an unwarranted assumption, which he calls deterministic updating, and which says that your updating plan should be deterministic. In that paper, Pettigrew did not consider whether the symmetry arguments due to Hughes and van Fraassen make the same assumption Scientific inquiry in philosophical perspective. University Press of America, Lanham, pp. 183–223, 1987). In this note, I show that they do.
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  49. Bayesian Updating When What You Learn Might Be False.Richard Pettigrew - forthcoming - Erkenntnis:1-16.
    Michael Rescorla (2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever you take yourself to learn something with certainty, it's true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla's new argument by giving a very general Dutch Book argument that applies to many cases of updating (...)
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  50. Dutch Book Arguments.Richard Pettigrew - 2020 - Cambridge University Press.
    Our beliefs come in degrees. I'm 70% confident it will rain tomorrow, and 0.001% sure my lottery ticket will win. What's more, we think these degrees of belief should abide by certain principles if they are to be rational. For instance, you shouldn't believe that a person's taller than 6ft more strongly than you believe that they're taller than 5ft, since the former entails the latter. In Dutch Book arguments, we try to establish the principles of rationality for degrees of (...)
     
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