•  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.
  •  92
    Risk writ large
    Philosophical Studies 174 (9): 2369-2384. 2017.
    Risk-weighted expected utility theory is motivated by small-world problems like the Allais paradox, but it is a grand-world theory by nature. And, at the grand-world level, its ability to handle the Allais paradox is dubious. The REU model described in Risk and Rationality turns out to be risk-seeking rather than risk-averse on one natural way of formulating the Allais gambles in the grand-world context. This result illustrates a general problem with the case for REU theory, we argue. There is a…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
  •  53
    No escape from Allais: reply to Buchak
    Philosophical Studies 177 (9): 2493-2500. 2020.
    In Risk and Rationality, Lara Buchak advertised REU theory as able to recover the modal preferences in the Allais paradox. But we pointed out that REU theory only applies in the “grand world” setting, where it actually struggles with the modal Allais preferences. Buchak offers two replies. Here we enumerate technical and philosophical problems they face.
  •  86
    Could've Thought Otherwise
    Philosophers' Imprint 20 (12). 2020.
    Evidence is univocal, not equivocal. Its implications don't depend on our beliefs or values, the evidence says what it says. But that doesn't mean there's no room for rational disagreement between people with the same evidence. Evaluating evidence is a lot like polling an electorate: getting an accurate reading requires a bit of luck, and even the best pollsters are bound to get slightly different results. So, even though evidence is univocal, rationality's requirements are not "unique." Underst…Read more
  •  202
    Belief in Psyontology
    Philosophers' Imprint 20 (11). 2020.
    Neither full belief nor partial belief is more fundamental, ontologically speaking. A survey of some relevant cognitive psychology supports a dualist ontology instead. Beliefs come in two kinds, categorical and graded, neither more fundamental than the other. In particular, the graded kind is no more fundamental. When we discuss belief in on/off terms, we are not speaking coarsely or informally about states that are ultimately credal.
  •  11
    Editorial
    Erkenntnis 70 (2): 133-134. 2009.
  •  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
  •  371
    Locating IBE in the Bayesian Framework
    Synthese 167 (1): 125-143. 2009.
    Inference to the Best Explanation (IBE) and Bayesianism are our two most prominent theories of scientific inference. Are they compatible? Van Fraassen famously argued that they are not, concluding that IBE must be wrong since Bayesianism is right. Writers since then, from both the Bayesian and explanationist camps, have usually considered van Fraassen’s argument to be misguided, and have plumped for the view that Bayesianism and IBE are actually compatible. I argue that van Fraassen’s argument i…Read more
  •  1209
    Clark and Shackel have recently argued that previous attempts to resolve the two-envelope paradox fail, and that we must look to symmetries of the relevant expected-value calculations for a solution. Clark and Shackel also argue for a novel solution to the peeking case, a variant of the two-envelope scenario in which you are allowed to look in your envelope before deciding whether or not to swap. Whatever the merits of these solutions, they go beyond accepted decision theory, even contradicting …Read more
  •  234
    Updating, Undermining, and Independence
    British Journal for the Philosophy of Science 66 (1): 121-159. 2015.
    Sometimes appearances provide epistemic support that gets undercut later. In an earlier paper I argued that standard Bayesian update rules are at odds with this phenomenon because they are ‘rigid’. Here I generalize and bolster that argument. I first show that the update rules of Dempster–Shafer theory and ranking theory are rigid too, hence also at odds with the defeasibility of appearances. I then rebut three Bayesian attempts to solve the problem. I conclude that defeasible appearances pose a…Read more
  •  252
    You've Come a Long Way, Bayesians
    Journal of Philosophical Logic 44 (6): 817-834. 2015.
    Forty years ago, Bayesian philosophers were just catching a new wave of technical innovation, ushering in an era of scoring rules, imprecise credences, and infinitesimal probabilities. Meanwhile, down the hall, Gettier’s 1963 paper [28] was shaping a literature with little obvious interest in the formal programs of Reichenbach, Hempel, and Carnap, or their successors like Jeffrey, Levi, Skyrms, van Fraassen, and Lewis. And how Bayesians might accommodate the discourses of full belief and knowled…Read more
  •  147
    An introduction to Dempster-Shafter Theory, from a lecture at the Northern Institute of Philosophy in 2010.
  •  109
    The preface paradox is a problem for everyone; you don’t need to be committed to any special epistemological theory to face the problem it raises. The problem of easy knowledge is supposed to be different in this respect. It is generally thought to arise only for those who believe there is such a thing as basic knowledge, i.e. knowledge acquired through a source that one does not know to be reliable or trustworthy. Because it is thought to arise only for those who believe in basic knowledge, the…Read more
  •  314
    Knowledge in Action
    Philosophers' Imprint 13. 2013.
    Recent proposals that frame norms of action in terms of knowledge have been challenged by Bayesian decision theorists. Bayesians object that knowledge-based norms conflict with the highly successful and established view that rational action is rooted in degrees of belief. I argue that the knowledge-based and Bayesian pictures are not as incompatible as these objectors have made out. Attending to the mechanisms of practical reasoning exposes space for both knowledge and degrees of belief to play …Read more
  •  77
    An introduction to the motivations and mechanics of John Pollock's theory of defeasible reasoning, from a lecture at the Northern Institute of Philosophy in 2010.
  •  228
    Commutativity or Holism? A Dilemma for Conditionalizers
    British Journal for the Philosophy of Science 60 (4): 793-812. 2009.
    Conditionalization and Jeffrey Conditionalization cannot simultaneously satisfy two widely held desiderata on rules for empirical learning. The first desideratum is confirmational holism, which says that the evidential import of an experience is always sensitive to our background assumptions. The second desideratum is commutativity, which says that the order in which one acquires evidence shouldn't affect what conclusions one draws, provided the same total evidence is gathered in the end. (Jeffr…Read more
  •  43
    Introducing Ergo
    with Franz Huber
    Ergo: An Open Access Journal of Philosophy 1. 2014.
  •  526
    Firing squads and fine-tuning: Sober on the design argument
    British Journal for the Philosophy of Science 56 (4): 809-821. 2005.
    Elliott Sober has recently argued that the cosmological design argument is unsound, since our observation of cosmic fine-tuning is subject to an observation selection effect (OSE). I argue that this view commits Sober to rejecting patently correct design inferences in more mundane scenarios. I show that Sober's view, that there are OSEs in those mundane cases, rests on a confusion about what information an agent ought to treat as background when evaluating likelihoods. Applying this analysis to …Read more
  •  515
    A Note on Design: What's Fine-tuning Got to Do With It?
    Analysis 70 (3): 431-438. 2010.
    We have known for a long time that there is complex, intelligent life. More recently we have discovered that the physics of our universe is fine-tuned so as to allow for the existence of such life. Call these two observations the Old Datum and the New Datum, respectively. Our question here is: once we know the Old Datum, does the New Datum provide additional evidence for the design hypothesis? I argue that it does not. Thus, there is an important sense in which the much-touted fine-tuning of phy…Read more
  •  704
    The argument from divine indifference
    Analysis 72 (4): 707-714. 2012.
    I argue that the rationale behind the fine-tuning argument for design is self-undermining, refuting the argument’s own premise that fine-tuning is to be expected given design. In (Weisberg 2010) I argued on informal grounds that this premise is unsupported. White (2011) countered that it can be derived from three plausible assumptions. But White’s third assumption is based on a fallacious rationale, and is even objectionable by the design theorist’s own lights. The argument that shows this, the …Read more
  •  53
    An introduction to the motivations and mechanics of upper and lower probabilities, from a lecture given at the Northern Institute of Philosophy in 2010.
  •  208
    Conditionalization, Reflection, and Self-Knowledge
    Philosophical Studies 135 (2): 179-197. 2007.
    Van Fraassen famously endorses the Principle of Reflection as a constraint on rational credence, and argues that Reflection is entailed by the more traditional principle of Conditionalization. He draws two morals from this alleged entailment. First, that Reflection can be regarded as an alternative to Conditionalization – a more lenient standard of rationality. And second, that commitment to Conditionalization can be turned into support for Reflection. Van Fraassen also argues that Reflection im…Read more
  •  1531
    Representation theorems and the foundations of decision theory
    Australasian Journal of Philosophy 89 (4). 2011.
    Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of repres…Read more
  •  8
    Offers a diagnosis of the easy knowledge problem, according to which easy knowledge is unjustified belief because the inferences that deliver easy knowledge feign evidential support that is not actually there. This diagnosis leads to a rejection of Closure. But, I argue, this rejection of Closure is more plausible than the traditional one endorsed by tracking theorists. I also argue that my diagnosis suggests a general plausibility argument against Closure, since a number of epistemic goods trad…Read more
  •  490
    Bootstrapping in General
    Philosophy and Phenomenological Research 81 (3): 525-548. 2010.
    The bootstrapping problem poses a general challenge, afflicting even strongly internalist theories. Even if one must always know that one’s source is reliable to gain knowledge from it, bootstrapping is still possible. I survey some solutions internalists might offer and defend the one I find most plausible: that bootstrapping involves an abuse of inductive reasoning akin to generalizing from a small or biased sample. I also argue that this solution is equally available to the reliabilist. The m…Read more
  •  346
    The Bootstrapping Problem
    Philosophy Compass 7 (9): 597-610. 2012.
    Bootstrapping is a suspicious form of reasoning that verifies a source's reliability by checking it against itself. Theories that endorse such reasoning face the bootstrapping problem. This article considers which theories face the problem, and surveys potential solutions. The initial focus is on theories like reliabilism and dogmatism, which allow one to gain knowledge from a source without knowing that it is reliable. But the discussion quickly turns to a more general version of the proble…Read more
  •  258
    Handbook of the History of Logic, vol. 10, eds. Dov Gabbay, Stephan Hartmann, and John Woods, forthcoming.