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Profile: Richard Pettigrew (Bristol University)
  1. 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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  2. Richard Pettigrew (forthcoming). Reviewed Work(S): An Introduction to the Philosophy of Mathematics by Mark Colyvan. Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    Review by: Richard Pettigrew The Bulletin of Symbolic Logic, Volume 19, Issue 3, Page 396-397, September 2013.
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  3. Richard Pettigrew (2014). Accuracy, Risk, and the Principle of Indifference. Philosophy and Phenomenological Research 89 (1).
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  4. 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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  5. 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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  6. 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. Richard Pettigrew (2013). What Chance‐Credence Norms Should Not Be. Noûs 47 (3).
    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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  8. 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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  9. 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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  10. Richard Pettigrew, Evidence and Accuracy.
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  11. 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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  12. 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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  13. Richard Pettigrew, Epistemic Utility Arguments for Probabilism. Stanford Encyclopedia.
  14. 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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  15. 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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  16. 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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  17. Richard Pettigrew, Epistemic Utility Theory.
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  18. 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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  19. 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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  20. 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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  21. 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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  22. 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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  23. Richard Pettigrew (2008). 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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