•  434
    Autonomy for Changing Selves
    In Ben Colburn (ed.), The Routledge Handbook of Autonomy, Routledge. 2023.
    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 for our theorising about rational choice, and these have been discussed at length. In §2 and…Read more
  •  398
    Accuracy, Chance, and the Principal Principle
    Philosophical Review 121 (2): 241-275. 2012.
    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 Prin…Read more
  •  390
    In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epis…Read more
  •  350
    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 follo…Read more
  •  344
    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 tha…Read more
  •  344
    Accuracy, Risk, and the Principle of Indifference
    Philosophy and Phenomenological Research 92 (1): 35-59. 2016.
    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 very restrictive answer. It demands that such…Read more
  •  327
    We often learn the opinions of others without hearing the evidence on which they're based. The orthodox Bayesian response is to treat the reported opinion as evidence itself and update on it by conditionalizing. But sometimes this isn't feasible. In these situations, a simpler way of combining one's existing opinion with opinions reported by others would be useful, especially if it yields the same results as conditionalization. We will show that one method---upco, also known as multiplicative po…Read more
  •  324
    What Chance‐Credence Norms Should Not Be
    Noûs 47 (3): 177-196. 2013.
    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…Read more
  •  265
    In this paper, I ask three questions of the liberal. In each, I fill in philosophical detail around a certain sort of complaint raised in current public debates about their position. In the first, I probe the limits of the liberal's tolerance for civil disobedience; in the second, I ask how the liberal can adjudicate the most divisive moral disputes of the age; and, in the third, I suggest the liberal faces a problem when there is substantial disagreement about the boundaries of the rational and…Read more
  •  262
    Indispensability arguments and instrumental nominalism
    Review of Symbolic Logic 5 (4): 687-709. 2012.
    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 argumen…Read more
  •  237
    An Improper Introduction to Epistemic utility theory
    In Henk de Regt, Samir Okasha & Stephan Hartmann (eds.), Proceedings of EPSA: Amsterdam '09, Springer. pp. 287--301. 2011.
    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 new…Read more
  •  232
    Two types of abstraction for structuralism
    Philosophical Quarterly 64 (255): 267-283. 2014.
    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’…Read more
  •  223
    The foundations of arithmetic in finite bounded Zermelo set theory
    Cahiers du Centre de Logique 17 99-118. 2010.
    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.<…Read more
  •  215
    Epistemic decision theorists aim to justify Bayesian norms by arguing that these norms further the goal of epistemic accuracy—having beliefs that are as close as possible to the truth. The standard defense of Probabilism appeals to accuracy dominance: for every belief state that violates the probability calculus, there is some probabilistic belief state that is more accurate, come what may. The standard defense of Conditionalization, on the other hand, appeals to expected accuracy: before the ev…Read more
  •  213
    Deference Done Right
    Philosophers' Imprint 14 1-19. 2014.
    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 a…Read more
  •  197
    My aim in this paper is to identify the wrong that is done in all cases of testimonial injustice, if there is one. Miranda Fricker (2007) proposes one account of this distinctive wrong, and Gaile Pohlhaus Jr. (2014) offers another. I think neither works. Nor does an account based on giving due respect to the testifier's epistemic competence. Nor does an account based on exposing the testifier to substantial risk of harm. Rachel Fraser (2023) describes a further account, and the proposal I favour…Read more
  •  187
    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 answers a question left …Read more
  •  179
    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 to a qu…Read more
  •  178
    The Dutch Book Arguments
    Cambridge University Press. 2020.
    (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 a measure of…Read more
  •  163
    Risk, rationality and expected utility theory
    Canadian Journal of Philosophy 45 (5-6): 798-826. 2015.
    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 the…Read more
  •  162
    On interpretations of bounded arithmetic and bounded set theory
    Notre Dame Journal of Formal Logic 50 (2): 141-152. 2009.
    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 straightforw…



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  •  159
    Many welfarists wish to assign to each possible state of the world a numerical value that measures something like its moral goodness. How are we to determine this quantity? This paper proposes a contractualist approach: a legitimate measure of moral goodness is one that could be justified to each member of the population in question. How do we justify a measure of moral goodness to each individual? Each individual recognises the measure of moral goodness must be a compromise between the differen…Read more
  •  158
    Platonism and aristotelianism in mathematics
    Philosophia Mathematica 16 (3): 310-332. 2008.
    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 test that…Read more
  •  155
    Aristotle on the subject matter of geometry
    Phronesis 54 (3): 239-260. 2009.
    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 passages …Read more
  •  154
    Epistemic Utility and Norms for Credences
    Philosophy Compass 8 (10): 897-908. 2013.
    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-the…Read more
  •  150
    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 evidence by c…Read more
  •  142
    Modelling Uncertainty
    Grazer Philosophische Studien 80 (1): 308-316. 2010.
    Review essay on Huber, F. and C. Schmidt-Petri (eds.) Degrees of Belief (Springer).
  •  135
    Adaptive preferences give rise to puzzles in ethics, political philosophy, decision theory, and the theory of action. Like our other preferences, adaptive preferences lead us to make choices, take action, and give consent. In 'False Consciousness for Liberals', recently published in The Philosophical Review, David Enoch (2020) proposes a criterion by which to identify when these choices, actions, and acts of consent are less than fully autonomous; that is, when they suffer from what Natalie Stol…Read more
  •  117
    The Principal Principle does not imply the Principle of Indifference
    British Journal for the Philosophy of Science. 2017.
    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 …Read more
  •  115
    Accuracy and the Laws of Credence
    Oxford University Press UK. 2016.
    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…Read more