• Coherence1 for previsions of random variables with generalized betting; • Coherence2 for probability forecasts of events with Brier score penalty; • Coherence3 probability forecasts of events with various proper scoring rules.

Several axiom systems for preference among acts lead to a unique probability and a state-independent utility such that acts are ranked according to their expected utilities. These axioms have been used as a foundation for Bayesian decision theory and subjective probability calculus. In this article we note that the uniqueness of the probability is relative to the choice of whatcounts as a constant outcome. Although it is sometimes clear what should be considered constant, in many cases there are several possible (...) choices. Each choice can lead to a different "unique" probability and utility. By focusing attention on statedependent utilities, we determine conditions under which a truly unique probability and utility can be determined from an agent's expressed preferences among acts. Suppose that an agent's preference can be represented in terms of a probability P and a utility U.That is, the agent prefers one act to another iff the expected utility of that act is higher than that of the other. There are many other equivalent representations in terms of probabilities Q, which are mutually absolutely continuous with P, and state-dependent utilities V, which differ from U by possibly different positive affine transformations in each state of nature. We describe an example in which there are two different but equivalent state-independent utility representations for the same preference structure. They differ in which acts count as constants. The acts involve receiving different amounts of one or the other of two currencies, and the states are different exchange rates between the currencies. It is easy to see how it would not be possible for constant amounts of both currencies to have simultaneously constant values across the differentstates. Savage (1954, sec. 5.5) discovered a situation in which two seemingly equivalent preference structures are represented by different pairs of probability and utility. He attributed the phenomenon to the construction of a "small world." We show that the small world problem is just another example of two different, but equivalent, representations treating different actsas constants. Finally, we prove a theorem (similar to one of Karni 1985) that shows how to elicit a unique state-dependent utility and does not assume that there are prizes with constant value. To do this, we define a new hypothetical kind of act in which both the prize to be awarded and the state of nature are determined by an auxiliary experiment. (shrink)

The degree of incoherence, when previsions are not made in accordance with a probability measure, is measured by either of two rates at which an incoherent bookie can be made a sure loser. Each bet is considered as an investment from the points of view of both the bookie and a gambler who takes the bet. From each viewpoint, we define an amount invested (or escrowed) for each bet, and the sure loss of incoherent previsions is divided by the escrow (...) to determine the rate of incoherence. Potential applications include the treatment of arbitrage opportunities in financial markets and the degree of incoherence of classical statistical procedures. We illustrate the latter with the example of hypothesis testing at a fixed size. (shrink)

We investigate differences between a simple Dominance Principle applied to sums of fair prices for variables and dominance applied to sums of forecasts for variables scored by proper scoring rules. In particular, we consider differences when fair prices and forecasts correspond to finitely additive expectations and dominance is applied with infinitely many prices and/or forecasts.

It has long been known that the practice of testing all hypotheses at the same level , regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti’s “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure (...) to lose, so that we can distinguish slightly incoherent procedures from grossly incoherent ones. We present an analysis of testing a simple hypothesis against a simple alternative as a case‐study of how the method can work. (shrink)

It has long been known that the practice of testing all hypotheses at the same level , regardless of the distribution of the data, is not consistent with Bayesian expected utility maximization. According to de Finetti’s “Dutch Book” argument, procedures that are not consistent with expected utility maximization are incoherent and they lead to gambles that are sure to lose no matter what happens. In this paper, we use a method to measure the rate at which incoherent procedures are sure (...) to lose, so that we can distinguish slightly incoherent procedures from grossly incoherent ones. We present an analysis of testing a simple hypothesis against a simple alternative as a case‐study of how the method can work. (shrink)

Statistical decision theory, whether based on Bayesian principles or other concepts such as minimax or admissibility, relies on minimizing expected loss or maximizing expected utility. Loss and utility functions are generally treated as unit-less numerical measures of value for consequences. Here, we address the issue of the units in which loss and utility are settled and the implications that those units have on the rankings of potential decisions. When multiple currencies are available for paying the loss, one must take explicit (...) account of which currency is used as well as the exchange rates between the various available currencies. (shrink)

We give necessary and sufficient conditions for a scoring rule to be proper for a quantile if utility is linear, and the distribution is unrestricted. We also give results when the set of distributions is limited, for example, to distributions that have first moments.

We give an extension of de Finetti’s concept of coherence to unbounded random variables that allows for gambling in the presence of infinite previsions. We present a finitely additive extension of the Daniell integral to unbounded random variables that we believe has advantages over Lebesgue-style integrals in the finitely additive setting. We also give a general version of the Fundamental Theorem of Prevision to deal with conditional previsions and unbounded random variables.

uniquely into a convex combination of a countably additive probability and a purely finitely additive (PFA) one. The coefficient of the PFA probability..

We discuss several features of coherent choice functions—where the admissible options in a decision problem are exactly those that maximize expected utility for some probability/utility pair in fixed set S of probability/utility pairs. In this paper we consider, primarily, normal form decision problems under uncertainty—where only the probability component of S is indeterminate and utility for two privileged outcomes is determinate. Coherent choice distinguishes between each pair of sets of probabilities regardless the “shape” or “connectedness” of the sets of probabilities. (...) We axiomatize the theory of choice functions and show these axioms are necessary for coherence. The axioms are sufficient for coherence using a set of probability/almost-state-independent utility pairs. We give sufficient conditions when a choice function satisfying our axioms is represented by a set of probability/state-independent utility pairs with a common utility. (shrink)

This important collection of essays is a synthesis of foundational studies in Bayesian decision theory and statistics. An overarching topic of the collection is understanding how the norms for Bayesian decision making should apply in settings with more than one rational decision maker and then tracing out some of the consequences of this turn for Bayesian statistics. There are four principal themes to the collection: cooperative, non-sequential decisions; the representation and measurement of 'partially ordered' preferences; non-cooperative, sequential decisions; and pooling (...) rules and Bayesian dynamics for sets of probabilities. The volume will be particularly valuable to philosophers concerned with decision theory, probability, and statistics, statisticians, mathematicians, and economists. (shrink)

We review de Finetti’s two coherence criteria for determinate probabilities: coherence1defined in terms of previsions for a set of events that are undominated by the status quo – previsions immune to a sure-loss – and coherence2 defined in terms of forecasts for events undominated in Brier score by a rival forecast. We propose a criterion of IP-coherence2 based on a generalization of Brier score for IP-forecasts that uses 1-sided, lower and upper, probability forecasts. However, whereas Brier score is a strictly (...) proper scoring rule for eliciting determinate probabilities, we show that there is no real-valuedstrictly proper IP-score. Nonetheless, with respect to either of two decision rules – Γ-maximin or E-admissibility-+-Γ-maximin – we give a lexicographic strictly proper IP-scoring rule that is based on Brier score. (shrink)

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti and Dubins, subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-­additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our result, where we established that each finite but not countably additive probability has (...) conditional probabilities that fail to be conglomerable in some countable partition. (shrink)

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute these (...) claims by showing that the following three cannot simultaneously hold: (i) Coherent belief is reducible to rational preference, i.e. the generalized Dutch-Book argument fixes standards of coherence. (ii) Finitely additive probability is coherent. (iii) Admissible preference structures may be free of consequences, i.e. they may lack prizes whose values are robust against all contingencies. (shrink)

When real-valued utilities for outcomes are bounded, or when all variables are simple, it is consistent with expected utility to have preferences defined over probability distributions or lotteries. That is, under such circumstances two variables with a common probability distribution over outcomes – equivalent variables – occupy the same place in a preference ordering. However, if strict preference respects uniform, strict dominance in outcomes between variables, and if indifference between two variables entails indifference between their difference and the status quo, (...) then preferences over rich sets of unbounded variables, such as variables used in the St. Petersburg paradox, cannot preserve indifference between all pairs of equivalent variables. In such circumstances, preference is not a function only of probability and utility for outcomes. Then the preference ordering is not defined in terms of lotteries. (shrink)

When can a Bayesian investigator select an hypothesis H and design an experiment (or a sequence of experiments) to make certain that, given the experimental outcome(s), the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model (...) for the data but who holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an "improper" prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive. (shrink)

When can a Bayesian investigator select an hypothesis H and design an experiment to make certain that, given the experimental outcome, the posterior probability of H will be lower than its prior probability? We report an elementary result which establishes sufficient conditions under which this reasoning to a foregone conclusion cannot occur. Through an example, we discuss how this result extends to the perspective of an onlooker who agrees with the investigator about the statistical model for the data but who (...) holds a different prior probability for the statistical parameters of that model. We consider, specifically, one-sided and two-sided statistical hypotheses involving i.i.d. Normal data with conjugate priors. In a concluding section, using an "improper" prior, we illustrate how the preceding results depend upon the assumption that probability is countably additive. (shrink)

Experimenters sometimes insist that it is unwise to examine data before determining how to analyze them, as it creates the potential for biased results. I explore the rationale behind this methodological guideline from the standpoint of an error statistical theory of evidence, and I discuss a method of evaluating evidence in some contexts when this predesignation rule has been violated. I illustrate the problem of potential bias, and the method by which it may be addressed, with an example from the (...) search for the top quark. A point in favor of the error statistical theory is its ability, demonstrated here, to explicate such methodological problems and suggest solutions, within the framework of an objective theory of evidence. (shrink)

We extend de Finetti’s (1974) theory of coherence to apply also to unbounded random variables. We show that for random variables with mandated infinite prevision, such as for the St. Petersburg gamble, coherence precludes indifference between equivalent random quantities. That is, we demonstrate when the prevision of the difference between two such equivalent random variables must be positive. This result conflicts with the usual approach to theories of Subjective Expected Utility, where preference is defined over lotteries. In addition, we explore (...) similar results for unbounded variables when their previsions, though finite, exceed their expected values, as is permitted within de Finetti’s theory. In such cases, the decision maker’s coherent preferences over random quantities is not even a function of probability and utility. One upshot of these findings is to explain further the differences between Savage’s theory (1954), which requires bounded utility for non-simple acts, and de Finetti’s theory, which does not. And it raises a question whether there is a theory that fits between these two. (shrink)

Pi(AS) = Pi(A)Pi(S) for i = 1, 2. But the Linear Pool created a group opinion P3 with positive dependence. P3(A|S) > P3(A).

Part 1 Background on de Finetti’s twin criteria of coherence: Coherence1: 2-sided previsions free from dominance through a Book. Coherence2: Forecasts free from dominance under Brier (squared error) score. Part 2 IP theory based on a scoring rule.

Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Also we address Adam Elga’s rebuttal to Belot’s analysis, (...) which focuses attention on the role that the assumption of countable additivity plays in Belot’s criticisms. (shrink)

The Sleeping Beauty problem has spawned a debate between “thirders” and “halfers” who draw conflicting conclusions about Sleeping Beauty's credence that a coin lands heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. (...) We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the experiment. (shrink)

The Sleeping Beauty problem has spawned a debate between “Thirders” and “Halfers” who draw conflicting conclusions about Sleeping Beauty’s credence that a coin lands Heads. Our analysis is based on a probability model for what Sleeping Beauty knows at each time during the Experiment. We show that conflicting conclusions result from different modeling assumptions that each group makes. Our analysis uses a standard “Bayesian” account of rational belief with conditioning. No special handling is used for self-locating beliefs or centered propositions. (...) We also explore what fair prices Sleeping Beauty computes for gambles that she might be offered during the Experiment. (shrink)

In the longstanding foundational debate whether to require that probability is countably additive, in addition to being finitely additive, those who resist the added condition raise two concerns that we take up in this paper. (1) _Existence_: Settings where no countably additive probability exists though finitely additive probabilities do. (2) _Complete Additivity_: Where reasons for countable additivity don’t stop there. Those reasons entail complete additivity—the (measurable) union of probability 0 sets has probability 0, regardless the cardinality of that union. Then (...) probability distributions are discrete, not continuous. We use Easwaran’s (Easwaran, Thought 2:53–61, 2013) advocacy of the _Comparative_ principle to illustrate these two concerns. Easwaran supports countable additivity, both for numerical probabilities and for finer, qualitative probabilities, by defending a condition he calls the _Comparative_ principle [ \({\mathcal{C}}\) ]. For numerical probabilities, principle \({\mathcal{C}}\) contrasts pairs, P 1 and P 2, defined over a common partition \(\prod\) = {a _i_ : _i_ ∈ I} of measurable events. \({\mathcal{C}}\) requires that no P 1 may be pointwise dominated, i.e., no (finitely additive) probability P 2 exists such that for each _i_ ∈ I, P 2 (a _i_ ) > P 1 (a _i_ ). By design, the cardinality of \(\prod\) is not limited in \({\mathcal{C}}\), which Easwaran asserts is important when arguing that the principle does not require more, or less, than that probability is countably additive. We agree that a numerical probability P satisfies principle \({\mathcal{C}}\) in all partitions just in case P is countably additive. However, we show that for numerical probabilities, by considering the size of the algebra of events to which probability is applied, principle \({\mathcal{C}}\) is subject to each of the above concerns, (1) and (2). Also, Easwaran considers principle \({\mathcal{C}}\) with non-numerical, qualitative probabilities, where a qualitative probability may be finer than an almost agreeing numerical probability P. A qualitative probability is regular if possible events are strictly more likely than impossible events. Easwaran motivates and illustrates regular qualitative probabilities using a continuous, almost agreeing quantitative probability that is uniform on the unit interval. We make explicit the conditions for applying principle \({\mathcal{C}}\) with qualitative probabilities and show that \({\mathcal{C}}\) restricts regular qualitative probabilities to those whose almost agreeing quantitative probabilities are completely additive. For instance, Easwaran’s motivating example of a regular qualitative probability is precluded by principle \({\mathcal{C}}\). (shrink)

Consider two SEU Bayesian decision makers, Dick and Jane, who wish to form a cooperative partnership that will make decisions, constrained by the following two principles governing coherence and compromise.

Mark Jago presents an original philosophical account of meaningful thought: in particular, how it is meaningful to think about things that are impossible. We think about impossible things all the time. We can think about alchemists trying to turn base metal to gold, and about unfortunate mathematicians trying to square the circle. We may ponder whether God exists; and philosophers frequently debate whether properties, numbers, sets, moral and aesthetic qualities, and qualia exist. In many philosophical or mathematical debates, when (...) one side of the argument gets things wrong, it necessarily gets them wrong. As we consider both sides of one of these philosophical arguments, we will at some point think about something that’s impossible. Yet most philosophical accounts of meaning and content hold that we can’t meaningfully think or reason about the impossible. -/- In The Impossible, Jago argues that we often gain new information, new beliefs, and, sometimes, fresh knowledge through logic, mathematics, and philosophy. That is why logic, mathematics, and philosophy are useful. We therefore require accounts of knowledge and belief, of information and content, and of meaning which allow space for the impossible. Jago’s aim in this book is to provide such accounts. He gives a detailed analysis of the concept of hyperintensionality, whereby logically equivalent contents may be distinct, and develops a theory in terms of possible and impossible worlds. Along the way, he provides a theory of what those worlds are and how they feature in our analysis of normative epistemic concepts: knowledge, belief, information, and content. (shrink)

Nondescriptivist views in many areas of philosophy have long been associated with the commitment that in contrast to other domains of discourse, there are no propositions in their particular domain. For example, the ‘no truth conditions’ theory of conditionals1 is understood as the view that conditionals don’t express propositions, noncognitivist expressivism in metaethics is understood as advocating the view that there are not really moral propositions,2 and expressivism about epistemic modals is thought of as the view that there is no (...) such thing as the proposition that Jack might be at home, over and above the proposition that Jack is at home.3 Of course, it is nearly always acknowledged that advocates of a nondescriptivist theory need not deny that there are conditional, moral, or modal propositions ‘at the end of the day’ – for if they also endorse a deflationary reading of talk about propositions, as famously advocated by Simon Blackburn, then they can employ such deflationary talk just as much as the rest of us. They just don’t appeal to propositions to do any of the work in their theories. Rather, they ‘earn the right’ to talk about propositions.4 It is the aim of this paper to upset this way of thinking about the proper attitude of nondescriptivists toward propositions, and to advocate a more constructive and in some ways more radical alternative on behalf of the nondescriptivist. I will begin by introducing and developing a set of problems that are faced by any nondescriptivist theory which tries to do without propositions. All of these problems are easily solved by any view which postulates propositions across the board, but none of them are solved by merely deflationary talk about propositions – their most promising solutions require propositions to do real theoretical work, and therefore the problems themselves remind us of and illustrate some of the important reasons why it is worth positing propositions in the first place.. (shrink)

Gaining information can be modelled as a narrowing of epistemic space . Intuitively, becoming informed that such-and-such is the case rules out certain scenarios or would-be possibilities. Chalmers’s account of epistemic space treats it as a space of a priori possibility and so has trouble in dealing with the information which we intuitively feel can be gained from logical inference. I propose a more inclusive notion of epistemic space, based on Priest’s notion of open worlds yet which contains only those (...) epistemic scenarios which are not obviously impossible. Whether something is obvious is not always a determinate matter and so the resulting picture is of an epistemic space with fuzzy boundaries. (shrink)

I discuss three ways of responding to the logical omniscience problems faced by traditional ‘possible worlds’ epistemic logics. Two of these responses were put forward by Hintikka and the third by Cresswell; all three have been influential in the literature on epistemic logic. I show that both of Hintikka's responses fail and present some problems for Cresswell’s. Although Cresswell's approach can be amended to avoid certain unpalatable consequences, the resulting formal framework collapses to a sentential model of knowledge, which defenders (...) of the ‘possible worlds’ approach are frequently critical of. (shrink)

We argue that the interaction of biased media coverage and widespread employment of the recognition heuristic can produce epistemic injustices. First, we explain the recognition heuristic as studied by Gerd Gigerenzer and colleagues, highlighting how some of its components are largely external to, and outside the control of, the cognitive agent. We then connect the recognition heuristic with recent work on the hypotheses of embedded, extended, and scaffolded cognition, arguing that the recognition heuristic is best understood as an instance of (...) scaffolded cognition. In section three, we consider the double-edged sword of cognitive scaffolding. On the one hand, scaffolds can reduce the internal processing demands on cognitive agents while increasing their access to information. On the other hand, the use of scaffolding leaves cognitive agents increasingly vulnerable to forming false beliefs or failing to form beliefs at all about particular topics. With respect to the recognition heuristic, agents rely on third parties (such as the media) to report not just what’s true but also what’s important or valuable. This makes cognitive agents relying on these third parties vulnerable to two erroneous influences: 1) because they don’t recognize something, it isn’t important or valuable, and 2) because they do recognize something, it is important or valuable. Call the latter the Kardashian Inference and the former the Darfur Inference. In section four, we use Fricker’s (2007) concept of epistemic injustice to characterize the nature and harm of these false inferences, with special emphasis on the Darfur Inference. In section five, we use data-mining and an empirical study to show how Gigerenzer’s population estimation task is liable to produce Darfur Inferences. We conclude with some speculative remarks on more important Darfur Inferences, and how to avoid them by scaffolding better. One primary way to accomplish this it to shift the burden of embodying the virtue of epistemic justice from the hearer or consumer of media to the media themselves. (shrink)

This book offers a systematic framework for thinking about the relationship between language and technology and an argument for interweaving thinking about technology with thinking about language. The main claim of philosophy of technology—that technologies are not mere tools and artefacts not mere things, but crucially and significantly shape what we perceive, do, and are—is re-thought in a way that accounts for the role of language in human technological experiences and practices. Engaging with work by Wittgenstein, Heidegger, McLuhan, Searle, Ihde, (...) Latour, Ricoeur, and many others, the author critically responds to, and constructs a synthesis of, three "extreme", idealtype, untenable positions: only humans speak and neither language nor technologies speak, only language speaks and neither humans nor technologies speak, and only technology speaks and neither humans nor language speak. The construction of this synthesis goes hand in hand with a narrative about subjects and objects that become entangled and constitute one another. Using Words and Things thus draws in central discussions from other subdisciplines in philosophy, such as philosophy of language, epistemology, and metaphysics, to offer an original theory of the relationship between language and technology centered on use, performance, and narrative, and taking a transcendental turn. (shrink)

In this paper, I describe some of what I take to be the more interesting features of friendship, then explore the extent to which other virtues can be reconstructed as sharing those features. I use trustworthiness as my example throughout, but I think that other virtues such as generosity & gratitude, pride & respect, and the producer’s & consumer’s sense of humor can also be analyzed with this model. The aim of the paper is not to demonstrate that all moral (...) virtues are exactly like friendship in all important respects, but rather to articulate a fruitful model in which to explore the virtues. Section 2 explores the relational nature of friendship, drawing on Aristotle’s discussion of friendship in the Nicomachean Ethics. Section 3 catalogues four motivations for taking seriously the friendship model of virtue. Section 4 applies the friendship model in depth to the virtue of trustworthiness. (shrink)

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1,1 or H1,2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to 0.025 (...) when testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1,1 or H1,2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it refers to the familywise error rate. Hence, an inconsistent correction occurs when a researcher corrects their alpha level during multiple testing but does not make an inference about a union alternative hypothesis. In the present article, I discuss this inconsistent correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of inconsistent corrections from recent psychology studies. I conclude that inconsistent corrections represent a symptom of statisticism, and I call for a more nuanced inference-based approach to multiple testing corrections. (shrink)

Particularists in ethics emphasize that the normative is holistic, and invite us to infer with them that it therefore defies generalization. This has been supposed to present an obstacle to traditional moral theorizing, to have striking implications for moral epistemology and moral deliberation, and to rule out reductive theories of the normative, making it a bold and important thesis across the areas of normative theory, moral epistemology, moral psychology, and normative metaphysics. Though particularists emphasize the importance of the holism of (...) the normative, however, it is not something that they have been able to explain. In this paper I’ll show how to use a small number of simple and, I’ll argue, independently compelling assumptions in order to both predict and explain the holistic features of the normative with respect to the non-normative. The basic idea of the paper is simple. It is that normative claims are holistic because they are general, rather than because they defy generalization. (shrink)

From his earliest work on personal identity to his last on the value of truthfulness, the ideas and arguments of Bernard Williams - in the metaphysics of personhood, in the history of philosophy, but especially in ethics and moral psychology - have proved sometimes controversial, often influential, and always worth studying. This book provides a comprehensive account of Williams's many significant contributions to contemporary philosophy. Topics include personal identity, various critiques of moral theory, practical reasoning and moral motivation, truth and (...) objectivity, and the relevance of ancient Greece to modern life. It not only positions Williams among these important philosophical topics, but also with regard to the views of other philosophers, including prominent forerunners such as Hume and Nietzsche and contemporary thinkers such as, Nagel, McDowell, MacIntyre and Taylor. The fragmentary nature of Williams's work is addressed and recurring themes and connections within his work are brought to light. (shrink)

In this paper, I argue that there is a picture of how law works that most legal theorists are implicitly committed to and take to be common ground. This Standard Picture (SP, for short) is generally unacknowledged and unargued for. SP leads to a characteristic set of concerns and problems and yields a distinctive way of thinking about how law is supposed to operate. I suggest that the issue of whether SP is correct is a fundamental one for the philosophy (...) of law, more basic, for example, than the issue that divides legal positivists and anti-positivists, at least as the latter issue is ordinarily understood. The goals of the paper are fourfold: 1) to identify and articulate in some detail the Standard Picture; 2) to show that SP is widely held and has important consequences for other debates in the philosophy of law; 3) to show that SP leads to a serious theoretical problem; 4) to sketch an alternative picture that promises to avoid this problem. I emphasize the modesty of these goals in one respect. I make no claim to refute SP or to fully develop and defend an alternative picture. (shrink)

This article is a précis of Mark C. Murphy’s _Divine Holiness and Divine Action_ (Oxford University Press, 2021), which offers an account of God’s holiness and of the difference this view of God’s holiness should make to our understanding of divine action.