•  2807
    The Open Handbook of Formal Epistemology (edited book)
    PhilPapers Foundation. 2019.
    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, w…Read more
  •  1608
    Choosing for Changing Selves
    Oxford University Press. 2019.
    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.
  •  1442
    Transformative Experience and Decision Theory
    Philosophy and Phenomenological Research 91 (3): 766-774. 2015.
    This paper is part of a book symposium for L. A. Paul (2014) Transformative Experience (OUP).
  •  1226
    Radical epistemology, structural explanations, and epistemic weaponry
    Philosophical Studies 179 (1): 289-304. 2021.
    When is a belief justified? There are three families of arguments we typically use to support different accounts of justification: arguments from our intuitive responses to vignettes that involve the concept; arguments from the theoretical role we would like the concept to play in epistemology; and arguments from the practical, moral, and political uses to which we wish to put the concept. I focus particularly on the third sort, and specifically on arguments of this sort offered by Clayton Littl…Read more
  •  1135
    (This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ra…Read more
  •  1119
    Epistemologists who study credences have a well-developed account of how you should change them when you learn new evidence; that is, when your body of evidence grows. What's more, they boast a diverse range of epistemic and pragmatic arguments that support that account. But they do not have a satisfactory account of when and how you should change your credences when you become aware of possibilities and propositions you have not entertained before; that is, when your awareness grows. In this pa…Read more
  •  1091
    Longtermism is the view that the most urgent global priorities, and those to which we should devote the largest portion of our resources, are those that focus on (i) ensuring a long future for humanity, and perhaps sentient or intelligent life more generally, and (ii) improving the quality of the lives that inhabit that long future. While it is by no means the only one, the argument most commonly given for this conclusion is that these interventions have greater expected goodness per unit of res…Read more
  •  1021
    Geometric Pooling: A User's Guide
    British Journal for the Philosophy of Science. forthcoming.
    Much of our information comes to us indirectly, in the form of conclusions others have drawn from evidence they gathered. When we hear these conclusions, how can we modify our own opinions so as to gain the benefit of their evidence? In this paper we study the method known as geometric pooling. We consider two arguments in its favour, raising several objections to one, and proposing an amendment to the other.
  •  1015
    On the Accuracy of Group Credences
    Oxford Studies in Epistemology 6. 2019.
    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 group in question? According to the cre…Read more
  •  954
    What is justified credence?
    Episteme 18 (1): 16-30. 2021.
    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 ri…Read more
  •  949
    Epistemic Risk and the Demands of Rationality
    Oxford University Press. 2022.
    How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility theory, and it…Read more
  •  927
    A decision theory is self-recommending if, when you ask it which decision theory you should use, it considers itself to be among the permissible options. I show that many alternatives to expected utility theory are not self-recommending, and I argue that this tells against them.
  •  761
    What we talk about when we talk about numbers
    Annals of Pure and Applied Logic 169 (12): 1437-1456. 2018.
    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…Read more
  •  753
    Logical ignorance and logical learning
    Synthese 198 (10): 9991-10020. 2021.
    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 Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that gove…Read more
  •  748
    What is conditionalization, and why should we do it?
    Philosophical Studies 177 (11): 3427-3463. 2020.
    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 de…Read more
  •  719
    Nudging for changing selves
    Synthese 201 (1): 1-21. 2023.
    When is it legitimate for a government to ‘nudge’ its citizens, in the sense described by Thaler and Sunstein (2008)? In their original work on the topic, Thaler and Sunstein developed the _‘as judged by themselves’ (or AJBT) test_ to answer this question (Thaler and Sunstein 2008, p. 5). In a recent paper, Paul and Sunstein (2019) raised a concern about this test: it often seems to give the wrong answer in cases in which we are nudged to make a decision that leads to what Paul calls a _personal…Read more
  •  717
    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'…Read more
  •  686
    In the first half of this paper, I argue that group belief ascriptions are highly ambiguous. What's more, in many cases, neither the available contextual factors nor known pragmatic considerations are sufficient to allow the audience to identify which of the many possible meanings is intended. In the second half, I argue that this ambiguity often has bad consequences when a group belief ascription is heard and taken as testimony. And indeed it has these consequences even when the ascription is t…Read more
  •  671
    Accuracy-First Epistemology Without Additivity
    Philosophy of Science 89 (1): 128-151. 2022.
    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.
  •  636
    to appear in Lambert, E. and J. Schwenkler (eds.) Transformative Experience (OUP) L. A. Paul (2014, 2015) argues that the possibility of epistemically transformative experiences poses serious and novel problems for the orthodox theory of rational choice, namely, expected utility theory — I call her argument the Utility Ignorance Objection. In a pair of earlier papers, I responded to Paul’s challenge (Pettigrew 2015, 2016), and a number of other philosophers have responded in similar ways (Doughe…Read more
  •  633
    There are many reasons we might want to take the opinions of various individuals and pool them to give the opinions of the group they constitute. If all the individuals in the group have probabilistic opinions about the same propositions, there is a host of pooling functions we might deploy, such as linear or geometric pooling. However, there are also cases where different members of the group assign probabilities to different sets of propositions, which might overlap a lot, a little, or not at …Read more
  •  625
    In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.
  •  620
    Veritism, Epistemic Risk, and the Swamping Problem
    Australasian Journal of Philosophy 97 (4): 761-774. 2019.
    Veritism says that the fundamental source of epistemic value for a doxastic state is the extent to which it represents the world correctly: that is, its fundamental epistemic value is deter...
  •  587
    Epistemic Utility and the Normativity of Logic
    Logos and Episteme 8 (4): 455-492. 2017.
    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 a…Read more
  •  586
    Category theory as an autonomous foundation
    Philosophia Mathematica 19 (3): 227-254. 2011.
    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 …Read more
  •  580
    Identity and discernibility in philosophy and logic
    Review of Symbolic Logic 5 (1): 162-186. 2012.
    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 logica…Read more
  •  493
    Consequences of Calibration
    British Journal for the Philosophy of Science 14. forthcoming.
    Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improv…Read more
  •  486
    Effective altruists (EAs) seek to persuade the globally wealthy to donate a proportion of their income to do good, and specifically to donate it to those charit.
  •  480
    Bayesian updating when what you learn might be false
    Erkenntnis 88 (1): 309-324. 2023.
    Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is 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 m…Read more
  •  458
    An Objective Justification of Bayesianism I: Measuring Inaccuracy
    Philosophy of Science 77 (2): 201-235. 2010.
    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 to f…Read more