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Profile: Richard Pettigrew (Bristol University)
  1. Hannes Leitgeb & Richard Pettigrew (2010). An Objective Justification of Bayesianism I: Measuring Inaccuracy. 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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  2. Hannes Leitgeb & Richard Pettigrew (2010). An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy. 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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  3. Richard Pettigrew (2015). Transformative Experience and Decision Theory. 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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  4. Richard Pettigrew (2013). A New Epistemic Utility Argument for the Principal Principle. 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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  5. Richard Pettigrew (2012). Accuracy, Chance, and the Principal Principle. 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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  6.  48
    Richard Pettigrew (2013). Epistemic Utility and Norms for Credences. 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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  7. James Ladyman, Øystein Linnebo & Richard Pettigrew (2012). Identity and Discernibility in Philosophy and Logic. 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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  8. Øystein Linnebo & Richard Pettigrew (2011). Category Theory as an Autonomous Foundation. 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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  9.  21
    Richard Pettigrew (2016). The Population Ethics of Belief: In Search of an Epistemic Theory X. Noûs 50 (4).
    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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  10.  59
    Richard Pettigrew (2016). Accuracy, Risk, and the Principle of Indifference. 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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  11.  25
    Richard Pettigrew (2013). Accuracy and Evidence. 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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  12.  39
    Richard Pettigrew & Michael G. Titelbaum (2014). Deference Done Right. Philosophers' Imprint 14 (35):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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  13.  18
    Richard Pettigrew (2016). Transformative Experience, by L. A. Paul. Mind 125 (499):927-935.
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  14.  13
    Richard Pettigrew (2016). Jamesian Epistemology Formalised: An Explication of ‘the Will to Believe’. 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, credences. The latter part of the paper thus answers a question left open in Pettigrew.
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  15.  76
    Richard Pettigrew (2007). Platonism and Aristotelianism in Mathematics. 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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  16.  24
    Richard Pettigrew (2011). Epistemic Utility Arguments for Probabilism. Stanford Encyclopedia.
  17. Richard Pettigrew (2013). What Chance‐Credence Norms Should Not Be. 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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  18.  25
    Richard Pettigrew (2016). Risk, Rationality and Expected Utility Theory. 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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  19. Richard Pettigrew (2012). Indispensability Arguments and Instrumental Nominalism. 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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  20.  35
    Richard Pettigrew (2015). II—Pluralism About Belief States. 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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  21.  79
    Øystein Linnebo & Richard Pettigrew (2014). Two Types of Abstraction for Structuralism. 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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  22. Richard Pettigrew (2011). An Improper Introduction to Epistemic Utility Theory. In Henk de Regt, Samir Okasha & Stephan Hartmann (eds.), Proceedings of EPSA: Amsterdam '09. Springer 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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  23.  87
    Richard Pettigrew (2009). Aristotle on the Subject Matter of Geometry. 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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  24.  29
    Richard Pettigrew, Epistemic Utility Theory.
    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, and that she ought to update her belief function upon obtaining new (...)
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  25.  13
    Richard Pettigrew (forthcoming). Jamesian Epistemology Formalized: An Explication of 'The Will to Believe'. Episteme:1-16.
    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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  26. Richard Pettigrew (2010). The Foundations of Arithmetic in Finite Bounded Zermelo Set Theory. Cahiers du Centre de Logique 17:99-118.
    In this paper, I pursue such a logical foundation for arithmetic in a variant of Zermelo set theory that has axioms of subset separation only for quantifier-free formulae, and according to which all sets are Dedekind finite. In section 2, I describe this variant theory, which I call ZFin0. And in section 3, I sketch foundations for arithmetic in ZFin0 and prove that certain foundational propositions that are theorems of the standard Zermelian foundation for arithmetic are independent of ZFin0.<br><br>An equivalent (...)
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  27. Richard Pettigrew, Self-Locating Belief and the Goal of Accuracy.
    The goal of a partial belief is to be accurate, or close to the truth. By appealing to this norm, I seek norms for partial beliefs in self-locating and non-self-locating propositions. My aim is to find norms that are analogous to the Bayesian norms, which, I argue, only apply unproblematically to partial beliefs in non-self-locating propositions. I argue that the goal of a set of partial beliefs is to minimize the expected inaccuracy of those beliefs. However, in the self-locating framework, (...)
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  28.  14
    Richard Pettigrew (2016). John P. Burgess. Rigor and Structure. Oxford: Oxford University Press, 2015. ISBN: 978-0-19-872222-9 ; 978-0-19-103360-5 . Pp. Xii + 215. [REVIEW] Philosophia Mathematica 24 (1):129-136.
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  29.  19
    Richard Pettigrew (2015). Accuracy and the Belief-Credence Connection. Philosophers' Imprint 15 (16):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. Richard Pettigrew (2010). Modelling Uncertainty. Grazer Philosophische Studien 80 (1):308-316.
    Review essay on Huber, F. and C. Schmidt-Petri (eds.) Degrees of Belief (Springer).
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  31. Richard Pettigrew (2009). On Interpretations of Bounded Arithmetic and Bounded Set Theory. Notre Dame Journal of Formal Logic 50 (2):141-152.
    In 'On interpretations of arithmetic and set theory', Kaye and Wong proved the following result, which they considered to belong to the folklore of mathematical logic.

    THEOREM 1 The first-order theories of Peano arithmetic and Zermelo-Fraenkel set theory with the axiom of infinity negated are bi-interpretable.

    In this note, I describe a theory of sets that is bi-interpretable with the theory of bounded arithmetic IDelta0 + exp. Because of the weakness of this theory of sets, I cannot straightforwardly adapt Kaye and Wong's (...)
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  32. Denis M. Walsh, Leah Henderson, Noah D. Goodman, Joshua B. Tenenbaum, James F. Woodward, Hannes Leitgeb, Richard Pettigrew, Brad Weslake & John Kulvicki (2010). 1. Not a Sure Thing: Fitness, Probability, and Causation Not a Sure Thing: Fitness, Probability, and Causation (Pp. 147-171). [REVIEW] Philosophy of Science 77 (2).
     
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  33.  9
    Richard Pettigrew (2013). Reviewed Work(S): An Introduction to the Philosophy of Mathematics by Mark Colyvan. Association for Symbolic Logic: The Bulletin of Symbolic Logic 19 (3):396-397.
    Review by: Richard Pettigrew The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 396-397, September 2013.
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  34. Richard Pettigrew (2016). Accuracy and the Laws of Credence. 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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  35. Richard Pettigrew, Evidence and Accuracy.
     
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