The sharpest corner of the cutting edge of recent epistemology is to be found in Richard Pettigrew’s Accuracy and the Laws of Credence. In this fine book Pettigrew argues that a certain kind of accuracy-based value monism entails that rational credence manifests a host of features emphasized by anti-externalists in epistemology. Specifically, he demonstrates how a particular version of accuracy-based value monism—to be discussed at length below—when placed with some not implausible views about how epistemic value and rationality (...) relate to one another, ensures that rational credence manifests many of the structural properties emphasized by those who give evidence pride of place in the theory of rationality. A major goal of Pettigrew’s book, then, is to make clear how accuracy-based value monism fits together with the phenomena used by those who argue against accuracy-based externalism.2 2. (shrink)

Summary of Transformative Experience by L.A. Paul and replies to symposiasts. Discussion of undefined values, preference change, authenticity, experiential value, collective minds, mind control.

Leitgeb and Pettigrew argue that (1) agents should minimize the expected inaccuracy of their beliefs and (2) inaccuracy should be measured via the Brier score. They show that in certain diachronic cases, these claims require an alternative to Jeffrey Conditionalization. I claim that this alternative is an irrational updating procedure and that the Brier score, and quadratic scoring rules generally, should be rejected as legitimate measures of inaccuracy.

I have claimed that risk-weighted expected utility maximizers are rational, and that their preferences cannot be captured by expected utility theory. Richard Pettigrew and Rachael Briggs have recently challenged these claims. Both authors argue that only EU-maximizers are rational. In addition, Pettigrew argues that the preferences of REU-maximizers can indeed be captured by EU theory, and Briggs argues that REU-maximizers lose a valuable tool for simplifying their decision problems. I hold that their arguments do not succeed and that (...) my original claims still stand. However, their arguments do highlight some costs of REU theory. (shrink)

Pettigrew offers new axiomatic constraints on legitimate measures of inaccuracy. His axiom called ‘Decomposition’ stipulates that legitimate measures of inaccuracy evaluate a credence function in part based on its level of calibration at a world. I argue that if calibration is valuable, as Pettigrew claims, then this fact is an explanandum for accuracy-rst epistemologists, not an explanans, for three reasons. First, the intuitive case for the importance of calibration isn’t as strong as Pettigrew believes. Second, calibration is (...) a perniciously global property that both contravenes Pettigrew’s own views about the nature of credence functions themselves and undercuts the achievements and ambitions of accuracy-rst epistemology. Finally, Decomposition introduces a new kind of value compatible with but separate from accuracy-proper in violation of Pettigrew’s alethic monism. introduction. (shrink)

Richard Pettigrew has recently advanced a justification of the Principle of Indifference on the basis of a principle that he calls “cognitive conservatism,” or “extreme epistemic conservatism.” However, the credences based on the Principle of Indifference, as Pettigrew formulates it, violate another desideratum, namely, that learning from experience be possible. If it is accepted that learning from experience should be possible, this provides grounds for rejecting cognitive conservatism. Another set of criteria considered by Pettigrew, which involves a (...) weighted mean of worst-case and best-case accuracy, affords some learning, but not the sort that one would expect. This raises the question of whether accuracy-based considerations can be adapted to justify credence functions that permit induction. (shrink)

Richard Pettigrew has recently advanced a justification of the Principle of Indifference on the basis of a principle that he calls “cognitive conservatism,” or “extreme epistemic conservatism.” However, the credences based on the Principle of Indifference, as Pettigrew formulates it, violate another desideratum, namely, that learning from experience be possible. If it is accepted that learning from experience should be possible, this provides grounds for rejecting cognitive conservatism. Another set of criteria considered by Pettigrew, which involves a (...) weighted mean of worst-case and best-case accuracy, affords some learning, but not the sort that one would expect. This raises the question of whether accuracy-based considerations can be adapted to justify credence functions that permit induction. (shrink)

Øystein Linnebo and Richard Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this article, we argue that the structuralist thesis, (...) even when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds. 1Introduction 2The Structuralist Thesis 3LP-Structuralism 4Purity 5A Formal Framework for Structural Abstraction 6Fundamental Relations 7The Structuralist Thesis Vindicated 8Conclusion. (shrink)

In a recent paper, Pettigrew reports a generalization of the celebrated accuracy-dominance theorem due to Predd et al., but Pettigrew’s proof is incorrect. I will explain the mistakes and provide a correct proof.

Øystein Linnebo and Richard Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They argue that their theory of abstract structures proves a consistent version of the structuralist thesis that positions in abstract structures only have structural properties. They do this by defining a subset of the properties of positions in structures, so-called fundamental properties, and argue that all fundamental properties of positions are structural. In this paper, we argue that the structuralist thesis, (...) even when restricted to fundamental properties, does not follow from the theory of structures that Linnebo and Pettigrew have developed. To make their account work, we propose a formal framework in terms of Kripke models that makes structural abstraction precise. The formal framework allows us to articulate a revised definition of fundamental properties, understood as intensional properties. Based on this revised definition, we show that the restricted version of the structuralist thesis holds. (shrink)

Linnebo and Pettigrew have recently developed a version of non-eliminative mathematical structuralism based on Fregean abstraction principles. They recognize that this version of structuralism is vulnerable to the well-known problem of non-rigid structures. This paper offers a solution to the problem for this version of structuralism. The solution involves expanding the languages used to describe mathematical structures. We then argue that this solution is philosophically acceptable to those who endorse mathematical structuralism based on Fregean abstraction principles.

Linnebo and Pettigrew present some objections to category theory as an autonomous foundation. They do a commendable job making clear several distinct senses of ‘autonomous’ as it occurs in the phrase ‘autonomous foundation’. Unfortunately, their paper seems to treat the ‘categorist’ perspective rather unfairly. Several infelicities of this sort were addressed by McLarty. In this note I address yet another apparent infelicity.

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew, and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we (...) should be careful to distinguish diachronic update principles from related synchronic principles for conditional probability. (shrink)

Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true of (...) the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)

Linnebo and Pettigrew's critique in this journal of categorical foundations well emphasizes that the particulars of various categorical foundations matter, and that mathematical practice must be a major consideration. But several categorists named by the authors as proposing categorical foundations do not propose foundations, notably Awodey, and the article's description of current textbook practice seems inaccurate. They say that categorical foundations have justificatory autonomy if and only if mathematics can be justified simply by its practice. Do they seriously believe (...) philosophers may be able to justify some currently unpractised mathematics better than current practice justifies itself? (shrink)

Epistemic decision theory produces arguments with both normative and mathematical premises. I begin by arguing that philosophers should care about whether the mathematical premises (1) are true, (2) are strong, and (3) admit simple proofs. I then discuss a theorem that Briggs and Pettigrew (2020) use as a premise in a novel accuracy-dominance argument for conditionalization. I argue that the theorem and its proof can be improved in a number of ways. First, I present a counterexample that shows that (...) one of the theorem’s claims is false. As a result of this, Briggs and Pettigrew’s argument for conditionalization is unsound. I go on to explore how a sound accuracy-dominance argument for conditionalization might be recovered. In the course of doing this, I prove two new theorems that correct and strengthen the result reported by Briggs and Pettigrew. I show how my results can be combined with various normative premises to produce sound arguments for conditionalization. I also show that my results can be used to support normative conclusions that are stronger than the one that Briggs and Pettigrew’s argument supports. Finally, I show that Briggs and Pettigrew’s proofs can be simplified considerably. (shrink)

In Accuracy and the Laws of Credence Richard Pettigrew assumes a particular view of belief, which states that people don't have any other doxastic states besides credences. This is in tension with the popular position that people have both credences and outright beliefs. Pettigrew claims that such a dual view of belief is incompatible with the accuracy-first approach. I argue in this paper that it is not. This is good news for Pettigrew, since it broadens the appeal (...) of his framework. (shrink)

This paper highlights the role of Lewis’ Principal Principle and certain auxiliary conditions on admissibility as serving to explicate normal informal standards of what is reasonable. These considerations motivate the presuppositions of the argument that the Principal Principle implies the Principle of Indifference, put forward by Hawthorne et al.. They also suggest a line of response to recent criticisms of that argument, due to Pettigrew and Titelbaum and Hart, 621–632, 2020). The paper also shows that related concerns of Hart (...) and Titelbaum, 252–262, 2015) do not undermine the argument of Hawthorne et al.. (shrink)

There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Pettigrew 2016). However, this equivalence has been established only when the set of propositions on which credence functions are defined is finite. In this paper, I establish connections between accuracy dominance and coherence when credence functions are defined on an infinite set of propositions. In particular, I establish the necessary results to extend the classic (...) accuracy argument for probabilism to certain classes of infinite sets of propositions including countably infinite partitions. (shrink)

In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a structure is not to be (...) accounted for by anything other than the structure itself and that (ii) mathematical practice provides evidence for this view. We want to thank Leon Horsten, Jeff Ketland, Øystein Linnebo, John Mayberry, Richard Pettigrew, and Philip Welch for valuable comments on drafts of this paper. We are especially grateful to Fraser MacBride for correcting our interpretation of two of his papers and for other helpful comments. CiteULike Connotea Del.icio.us What's this? (shrink)

According to Paul (Transformative experience, 1st edn, Oxford University Press, 2014), transformative experiences pose a challenge to decision theory since their value cannot be anticipated. Building on Pettigrew’s (in: Lambert, Schwenkler (eds) Becoming someone new: essays on transformative experience, choice, and change, Oxford University Press, pp 100–121, 2020) redescription, this paper presents a new approach to how and when transformative decisions can nevertheless be made rationally. Thanks to fundamental higher-order facts that apply to any kind of experience, an agent (...) always at least knows the general shape of the utility space. This in combination with the knowledge about the non-transformative alternative in the choice set can enable rational decision-making despite the presence of a transformative experience. For example, this paper’s approach provides novel arguments for why gender transition (cf. McKinnon in Res Philosophica 92(2):419–440, 2015) or staying childfree (cf. Barnes in Philos Phenomenol Res 91(3):775–786, 2015) can be rational. (shrink)

Some of the most interesting recent work in formal epistemology has focused on developing accuracy-based approaches to justifying Bayesian norms. These approaches are interesting not only because they offer new ways to justify these norms, but because they potentially offer a way to justify all of these norms by appeal to a single, attractive epistemic goal: having accurate beliefs. Recently, Easwaran & Fitelson (2012) have raised worries regarding whether such “all-accuracy” or “purely alethic” approaches can accommodate and justify evidential Bayesian (...) norms. In response, proponents of purely alethic approaches, such as Pettigrew (2013b) and Joyce (2016), have argued that scoring rule arguments provide us with compatible and purely alethic justifications for the traditional Bayesian norms, including evidential norms. In this paper I raise several challenges to this claim. First, I argue that many of the justifications these scoring rule arguments provide are not compatible. Second, I raise worries for the claim that these scoring rule arguments provide purely alethic justifications. Third, I turn to assess the more general question of whether purely alethic justifications for evidential norms are even possible, and argue that, without making some contentious assumptions, they are not. Fourth, I raise some further worries for the possibility of providing purely alethic justifications for content-sensitive evidential norms, like the Principal Principle. (shrink)

Laurie Paul has recently argued that transformative experiences pose a problem for decision theory. According to Paul, agents facing transformative experiences do not possess the states required for decision theory to formulate its prescriptions. Agents facing transformative experiences are impoverished relative to their decision problems, and decision theory doesn’t know what to do with impoverished agents. Richard Pettigrew takes Paul’s challenge seriously. He grants that decision theory cannot handle decision problems involving transformative experiences. To deal with the problems posed (...) by transformative experiences, Pettigrew proposes two alterations to decision theory. The first alteration is meant to handle the problem posed by epistemically transformative experiences, and the second alteration is meant to handle the problem posed by personally transformative experiences. I argue that Pettigrew’s proposed alterations are untenable. Pettigrew’s novel decision theory faces both formal and philosophical problems. It is doubtful that Pettigrew can formulate the sort of decision theory he wants, and further doubtful that he should want such a decision theory in the first place. Moreover, the issues with Pettigrew’s proposed alterations help reveal issues with Paul’s initial challenge to decision theory. I suggest that transformative experiences should not be taken to pose a problem for decision theory, but should instead be taken to pose a topic for ethics. (shrink)

Formal and social epistemologists have devoted significant attention to the question of how to aggregate the credences of a group of agents who disagree about the probabilities of events. Moss and Pettigrew argue that group credences can be a linear mean of the credences of each individual in the group. By contrast, I argue that if the epistemic value of a credence function is determined solely by its accuracy, then we should, where possible, aggregate the underlying statistical models that (...) individuals use to generate their credence functions, using “stacking” techniques from statistics and machine learning first developed by Wolpert. (shrink)

Since Elga published his “Self-locating belief and the Sleeping Beauty problem,” there has been an intense debate about which credence between 1/2 and 1/3 Beauty should assign to (H) the coin’s landing heads, when she is awakened on Monday. The Halfers claim that she ought to assign 1/2 to H at that moment. The Thirders argue that she ought to assign 1/3 to H then. Meanwhile, Pettigrew defended a new chance-credence coordination principle, called the “Evidential Temporal Principle” (ETP), in (...) a recent edition of his book. In this paper, I provide a novel argument against the Halfer view and a partial defense of the Thirder view, respectively based on ETP. In addition, I generalize ETP to what I call the “Evidential Centered Principle,” which links one’s credences in centered propositions with their objective chances. (shrink)

Review of Richard Pettigrew, Choosing for Changing Selves.

Based on an analysis of ten popular introductions to social psychology, we will show that Karl Popper's philosophy of ‘critical rationalism’ so far has had little to no traceable influence on the epistemology and practice of social psychology. If Popper is quoted or mentioned in the textbooks at all, the guiding principle of ‘falsificationism’ is reduced to a mere ‘falsifiability’ and some central elements of critical rationalism are left out – those that are incompatible with positivism and inductivism. Echoing earlier (...) attempts to introduce Popper to social psychology by Paul Meehl and Tom Pettigrew, we will argue that a discussing Popper's ideas in more depth could help social psychology to move forward in view of the ‘crisis of confidence’ that has emerged recently in view of the ‘Stapel affair’ and the reports of failures to replicate social psychological experiments in high-powered replication attempts. (shrink)

I argue that three arguments for conditionalization -- the Diachronic Dutch Book, the expected-accuracy maximization argument from Greaves and Wallace, and the accuracy-dominance argument from Briggs and Pettigrew -- can all be improved by narrowing their focus. I suggest alternative, targeted arguments which better identify the flaw involved in non-conditionalizing updates.

One of the main goals of Bayesian epistemology is to justify the rational norms credence functions ought to obey. Accuracy arguments attempt to justify these norms from the assumption that the source of value for credences relevant to their epistemic status is their accuracy. This assumption and some standard decision-theoretic principles are used to argue for norms like Probabilism, the thesis that an agent’s credence function is rational only if it obeys the probability axioms. We introduce an example that shows (...) that the accuracy arguments for Probabilism given by Joyce and Pettigrew fail, and that Probabilism in fact turns out to be false given Pettigrew’s way of conceiving of the goal of having accurate credences. Finally, we use our discussion of Pettigrew’s framework to draw an important general lesson about normative theorizing that relies on the positing of ideal agents. (shrink)

This paper aims to provide a novel response on behalf of Process Reliabilism to the Swamping Problem. Unlike previous responses, the present response does not involve conditional probabilities (as Goldman and Olsson do), it does not appeal to permissivism or attitudes towards epistemic risk (as Pettigrew does), it will not depend on the generality of the problem (as Carter and Jarvis do) and it does not embrace either evidentialism or evidence monism (as Bjelde does). Instead it appeals to the (...) modal properties of those beliefs formed through reliable process-types. What is more, the argument is generalizable: while I will frame my conclusion in Process Reliabilist terms, it should be of interest to anyone who is a truth monist regarding epistemic value. (shrink)

ABSTRACTInAccuracy and the Laws of Credence, Richard Pettigrew gives several decision-theoretic arguments for formal requirements on rational credence. Pettigrew's arguments build on a central notion of epistemic value, but employ different decision rules. These comments explore how our choice of decision rule might matter, and discuss one of Pettigrew's arguments in detail: his argument for the Principle of Indifference, which relies on Maximin.

This is a discussion of Richard Pettigrew's book "Accuracy and the Laws of Credence". I target Pettigrew's application of the accuracy framework to derive chance-credence principles. My principal contention is that Pettigrew's preferred version of the argument might in one sense be circular and, moreover, that Pettigrew's premises have content that go beyond that of standard chance-credence principles.

Risk is inherent to many, if not all, transformative decisions. The risk of regret, of turning into a person you presently consider to be morally objectionable, or of value change are all risks of choosing to transform. This aspect of transformative decision-making has thus far been ignored, but carries important consequences to those wishing to defend decision theory from the challenge posed by transformative decision-making. I contend that a problem lies in a common method used to cardinalise utilities – the (...) von Neumann and Morgenstern (vNM) method – which measures an agent's utility function over sure outcomes. I argue that the risks involved in transformative experiences are constitutively valuable, and hence their value cannot be accurately measured by the vNM method. In Section 1, I outline what transformative experiences are and the problem they pose to decision theory. In Section 2, I outline Pettigrew's (2019, Choosing for Changing Selves) decision-theoretic response, and in Section 3, I present the case for thinking that risks can carry value. In Section 4, I argue for the claim that at least some transformative experiences involve constitutive risk. I argue that this causes a problem for decision-theoretic responses within the vNM framework in Section 5. (shrink)