We present a puzzle about knowledge, probability and conditionals. We show that in certain cases some basic and plausible principles governing our reasoning come into conflict. In particular, we show that there is a simple argument that a person may be in a position to know a conditional the consequent of which has a low probability conditional on its antecedent, contra Adams’ Thesis. We suggest that the puzzle motivates a very strong restriction on the inference of a conditional from a (...) disjunction. (shrink)

We explore consequences of the view that to know a proposition your rational credence in the proposition must exceed a certain threshold. In other words, to know something you must have evidence that makes rational a high credence in it. We relate such a threshold view to Dorr et al.’s :277–287, 2014) argument against the principle they call fair coins: “If you know a coin won’t land tails, then you know it won’t be flipped.” They argue for rejecting fair coins (...) because it leads to a pervasive skepticism about knowledge of the future. We argue that the threshold view of evidence and knowledge gives independent grounds to reject fair coins. (shrink)

We argue that definite noun phrases give rise to uniqueness inferences characterized by a pattern we call definiteness projection. Definiteness projection says that the uniqueness inference of a definite projects out unless there is an indefinite antecedent in a position that filters presuppositions. We argue that definiteness projection poses a serious puzzle for e-type theories of (in)definites; on such theories, indefinites should filter existence presuppositions but not uniqueness presuppositions. We argue that definiteness projection also poses challenges for dynamic approaches, which (...) have trouble generating uniqueness inferences and predicting some filtering behavior, though unlike the challenge for e-type theories, these challenges have mostly been noted in the literature, albeit in a piecemeal way. Our central aim, however, is not to argue for or against a particular view, but rather to formulate and motivate a generalization about definiteness which any adequate theory must account for. (shrink)

Two recent and influential papers, van Rooij 2007 and Lassiter 2012, propose solutions to the proviso problem that make central use of related notions of independence—qualitative in the first case, probabilistic in the second. We argue here that, if these solutions are to work, they must incorporate an implicit assumption about presupposition accommodation, namely that accommodation does not interfere with existing qualitative or probabilistic independencies. We show, however, that this assumption is implausible, as updating beliefs with conditional information does not (...) in general preserve independencies. We conclude that the approach taken by van Rooij and Lassiter does not succeed in resolving the proviso problem. (shrink)

We offer two arguments against the halving repose to Sleeping Beauty. First, we show that halving violates the Epistemological Sure-Thing Principle, which we argue is a necessary constraint on any reasonable probability assignment. The constraint is that if hypothetically on C you assign to A the same probability you assign to A hypothetical on not-C, you must assign that probability to A simpliciter. Epistemically, it's a sure thing for you that A has this probability. Second, we show that halving violates (...) solid statistical reasoning (or draws absurdly irrelevant distinctions). (shrink)

We show that each of three natural sets of assumptions about the conditional entails necessitarianism: that anything possible is necessary.

Moral debunking arguments are meant to show that, by realist lights, moral beliefs are not explained by moral facts, which in turn is meant to show that they lack some significant counterfactual connection to the moral facts (e.g., safety, sensitivity, reliability). The dominant, “minimalist” response to the arguments—sometimes defended under the heading of “third-factors” or “pre-established harmonies”—involves affirming that moral beliefs enjoy the relevant counterfactual connection while granting that these beliefs are not explained by the moral facts. We show that (...) the minimalist gambit rests on a controversial thesis about epistemic priority: that explanatory concessions derive their epistemic import from what they reveal about counterfactual connections. We then challenge this epistemic priority thesis, which undermines the minimalist response to debunking arguments (in ethics and elsewhere). (shrink)

Public discussions of political and social issues are often characterized by deep and persistent polarization. In social psychology, it’s standard to treat belief polarization as the product of epistemic irrationality. In contrast, we argue that the persistent disagreement that grounds political and social polarization can be produced by epistemically rational agents, when those agents have limited cognitive resources. Using an agent-based model of group deliberation, we show that groups of deliberating agents using coherence-based strategies for managing their limited resources tend (...) to polarize into different subgroups. We argue that using that strategy is epistemically rational for limited agents. So even though group polarization looks like it must be the product of human irrationality, polarization can be the result of fully rational deliberation with natural human limitations. (shrink)

Popular discussions of faith often assume that having faith is a form of believing on insufficient evidence and that having faith is therefore in some way rationally defective. Here I offer a characterization of action-centered faith and show that action-centered faith can be both epistemically and practically rational even under a wide variety of subpar evidential circumstances.

A normative reason for a person to? is a consideration which favours?ing. A motivating reason is a reason for which or on the basis of which a person?s. This paper explores a connection between normative and motivating reasons. More specifically, it explores the idea that there are second-order normative reasons to? for or on the basis of certain first-order normative reasons. In this paper, I challenge the view that there are second-order reasons so understood. I then show that prominent views (...) in contemporary epistemology are committed to the existence of second-order reasons, specifically, views about the epistemic norms governing practical reasoning and about the role of higher-order evidence. If there are no second-order reasons, those views are mistaken. (shrink)

It is commonly said that some standards, such as morality, are ‘normatively authoritative’ in a way that other standards, such as etiquette, are not; standards like etiquette are said to be ‘not really normative’. Skeptics deny the very possibility of normative authority, and take claims like ‘etiquette is not really normative’ to be either empty or confused. I offer a different route to defeat skeptics about authority: instead of focusing on what makes standards like morality special, we should focus on (...) what makes standards like etiquette ‘not really normative’. I defend a fictionalist theory on which etiquette is ‘not really normative’ in roughly the same way that Sherlock is ‘not really a detective’, and show that fictionalism about some normative standards helps us explain the possibility of normative authority. (shrink)

This paper explores various subtleties in our ordinary thought and talk about normative reasons—subtleties which, if taken seriously, have various upshots, both substantive and methodological. I focus on two subtleties in particular. The first concerns the use of reason (in its normative sense) as both a count noun and as a mass noun, and the second concerns the context-sensitivity of normative reasons-claims. The more carefully we look at the language of reasons, I argue, the clearer its limitations and liabilities become. (...) The cumulative upshot is that although talk of reasons is intelligible and useful for the purposes of communication, we should be wary of placing much weight on it when engaging in substantive normative inquiry. By way of illustration, I consider some potential pitfalls of taking our talk of reasons too seriously, explaining how careful attention to the language of reasons undermines the main argument for moral particularism, Mark Schroeder’s recent defense of Humeanism about practical reasons, and the “reasons-first” program in metanormativity. (shrink)

Conversational exculpature is a pragmatic process whereby information is subtracted from, rather than added to, what the speaker literally says. This pragmatic content subtraction explains why we can say “Rob is six feet tall” without implying that Rob is between 5'0.99" and 6'0.01" tall, and why we can say “Ellen has a hat like the one Sherlock Holmes always wears” without implying Holmes exists or has a hat. This article presents a simple formalism for understanding this pragmatic mechanism, specifying how, (...) in context, the result of such subtractions is determined. And it shows how the resulting theory of conversational exculpature accounts for a varied range of linguistic phenomena. A distinctive feature of the approach is the crucial role played by the question under discussion in determining the result of a given exculpature. (shrink)

There has been much debate over whether to accept the claim that meaning is normative. One obstacle to making progress in that debate is that it is not always clear what the claim amounts to. In this paper, I try to resolve a dispute between those who advance the claim concerning how it should be understood. More specifically, I critically examine two competing conceptions of the normativity of meaning, rejecting one and defending the other. Though the paper aims to settle (...) a dispute among proponents of the claim that meaning is normative, it should be of interest to those who challenge it. After all, before one takes aim, one’s target needs to be in clear view. (shrink)

Value pluralists believe in multiple dimensions of value. What does betterness along a dimension have to do with being better overall? Any systematic answer begins with the Strong Pareto principle: one thing is overall better than another if it is better along one dimension and at least as good along all others. We defend Strong Pareto from recent counterexamples and use our discussion to develop a novel view of dimensions of value, one which puts Strong Pareto on firmer footing. We (...) conclude by defending Dimensionalism, the hypothesis that overall value relations are determined solely by how things compare along value dimensions. These are first steps towards a more systematic value pluralism. (shrink)

A standing challenge in the theory of counterfactuals is to solve the “deviation problem”. Consider ordinary counterfactuals involving an antecedent concerning a difference from the actual course of events at a particular time, and a consequent concerning, at least in part, what happens at a later time. In the possible worlds framework, the problem is often put in terms of which are the relevant antecedent worlds. Desiderata for the solution include that the relevant antecedent worlds be governed by the actual (...) laws of nature with no miracles; that the past in those worlds before the antecedent time matches the actual past; that the account is compatible with determinism, and that many of our ordinary counterfactual judgments are correct, and would be correct even given determinism. Many theorists have compromised on one or more of these desiderata, but this paper presents an account employing impossible worlds that satisfies them all. (shrink)

Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. -/- Once we have a (...) sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of "if... then...". This paper argues that the closest-worlds approach outlined in Nolan 1997 offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related "contraction conditionals". (shrink)

The U.S. election in November 2016 raised and amplified doubts about first-past-the-post (“plurality rule”) electoral systems. Arguments against plurality rule and for alternatives like preferential voting tend to be consequentialist: it is argued that systems like preferential voting produce different, better outcomes. After briefly noting why the consequentialist case against plurality rule is more complex and contentious than it first appears, I offer an expressive alternative: plurality rule produces actual or apparent dilemmas for voters in ways that are morally objectionable, (...) and avoidable under preferential voting systems. This expressive case against plurality rule is both simpler and more ecumenical than its consequentialist counterpart, and it provides strong reasons to prefer alternatives to plurality rule. Moreover, it suggests a distinct way of evaluating different alternatives like preferential voting. (shrink)

Recent advances in the Super Linguistics of pictures have laid the Super Semantic foundation for modelling the phenomena of narrative sequencing and co-reference in pictorial and mixed linguistic-pictorial discourses. We take up the question of how one arrives at the pragmatic interpretations of such discourses. In particular, we offer an analysis of: (i) the discourse composition problem: how to represent the joint meaning of a multi-picture discourse, (ii) observed differences in narrative sequencing in prima facie equivalent linguistic vs pictorial discourses, (...) and (iii) the phenomenon of co-referencing across pictures. We extend Segmented Discourse Representation Theory to spell out a formal Super Pragmatics that applies to linguistic, pictorial and mixed discourses, while respecting the particular ‘genius’ of either medium and computing their distinctive pragmatic interpretations. (shrink)

While those who take a "structuralist" approach to racial justice issues are right to call attention to the importance of social practices, laws, etc., they sometimes go too far by suggesting that antiracist efforts ought to focus on changing unjust social systems rather than changing individuals’ minds. We argue that while the “either/or” thinking implied by this framing is intuitive and pervasive, it is misleading and self-undermining. We instead advocate for a “both/and” approach to antiracist moral education that explicitly teaches (...) how social structures influence ideas about race and how ideas about race shape, sustain, and transform social structures. Ideally, antiracist moral education will help people see how social change and moral progress depend on the symbiotic relations between individuals and structures. We articulate a conception of “structure-facing virtue” that exemplifies this hybrid approach to illuminate the pivotal role moral education plays in the fight for racial justice. (shrink)

The last two decades have seen a surge of support for normative quietism: most notably, from Dworkin, Nagel, Parfit and Scanlon. Detractors like Enoch and McPherson object that quietism is incompatible with realism about normativity. The resulting debate has stagnated somewhat. In this paper I explore and defend a more promising way of developing that objection: I’ll argue that if normative quietism is true, we can create reasons out of thin air, so normative realists must reject normative quietism.

It is intuitive that circumstantial ignorance, even when culpable, can mitigate blameworthiness for morally wrong behavior. In this paper I suggest an explanation of why this is so. The explanation offered is that an agent’s degree of blameworthiness for some action depends at least in part upon the quality of will expressed in that action, and that an agent’s level of awareness when performing a morally wrong action can make a difference to the quality of will that is expressed in (...) it. This explanation makes use of Holly Smith’s distinction between benighting and benighted actions as well as a notion developed here called “capture.”. (shrink)

The expressivist advances a view about how we explain the meaning of a fragment of language, such as claims about what we morally ought to do. Critics evaluate expressivism on those terms. This is a serious mistake. We don’t just use that fragment of language in isolation. We make claims about what we morally, legally, rationally, and prudentially ought to do. To account for this linguistic phenomenon, the expressivist owes us an account not just of each fragment of language, but (...) of how they weave together into a broader tapestry. I argue that expressivists face a dilemma in doing so: either they fail to explain the univocality of terms like 'ought', or they fail to explain when normative statements are and aren't inconsistent. (shrink)

We argue that generic generalizations about racial groups are pernicious in what they communicate (both to members of that racial group and to members of other racial groups), and may be central to the construction of social categories like racial groups. We then consider how we should change and challenge uses of generic generalizations about racial groups.

In this paper, I outline a heuristic for thinking about the relation between explanation and understanding that can be used to capture various levels of “intimacy”, between them. I argue that the level of complexity in the structure of explanation is inversely proportional to the level of intimacy between explanation and understanding, i.e. the more complexity the less intimacy. I further argue that the level of complexity in the structure of explanation also affects the explanatory depth in a similar way (...) to intimacy between explanation and understanding, i.e. the less complexity the greater explanatory depth and vice versa. (shrink)

What do normative terms like “obligation” mean in legal contexts? On one view, which H.L.A. Hart may have endorsed, “obligation” is ambiguous in moral and legal contexts. On another, which is dominant in jurisprudence, “obligation” has a distinctively moralized meaning in legal contexts. On a third view, which is often endorsed in philosophy of language, “obligation” has a generic meaning in moral and legal con- texts. After making the nature of and disagreements between these views precise, I show how linguistic (...) data militates against both rivals to the generic meaning view, and argue that this has significant implications for jurisprudence. (shrink)

Mandatory minimum sentencing provisions have been a feature of the U.S. justice system since 1790. But they have expanded considerably under the war on drugs, and their use has expanded considerably under the Trump Administration; some states are also poised to expand drug-related mandatory minimums further in efforts to fight the current opioid epidemic. In this paper I outline and evaluate three prominent arguments for and against the use of mandatory minimums in the war on drugs—they appeal, respectively, to proportionality, (...) consistency, and efficiency. I ultimately defend the view that the use of mandatory minimums in the war on drugs is unjust. -/- . (shrink)

This essay introduces the transcription and translation of Paul Feyerabend's "Der Begriff der Verständlichkeit in der modernen Physik" [The concept of intelligibility in modern physics] (1948), which is an early essay written by Paul Feyerabend in 1948 on the topic of intelligibility (Verständlichkeit) and visualizability (Anschaulichkeit) of physical theories. The existence of such essay was likely. It is listed in his bibliography as his first publication. Yet the content of the essay was unknown, as no original or copy is extant (...) in Feyerabend's Nachlass and no known published version was available to the community—until now. The essay has both historical and philosophical interest: it is, as far as our current knowledge goes, Feyerabend's earliest extant publication. It documents Feyerabend's philosophical interest as a physicist-to-be, in what he himself called his “positivist” phase; and it gives a rare if fragmentary insight into the early discussions of the ‘Third Vienna Circle’ and, more generally, the philosophical culture of discussion in Vienna. (shrink)

Jason Brennan and Peter Jaworski reject expressive objections to markets on the grounds that market symbolism is culturally contingent, and contingent cultural symbols are less important than the benefits markets offer. I grant and, but I deny that these points suffice as grounds to dismiss expressive critiques of markets. For many plausible expressive critiques of markets are not symbolic critiques at all. Rather, they are critiques grounded in the idea that some market transactions embody morally inappropriate normative stances toward the (...) goods or services on offer. (shrink)

This chapter provides an introduction to possible worlds semantics in both logic and the philosophy of language, including a discussion of some of the advantages and challenges for possible worlds semantics.

Throughout the 20th century, market capitalism was defended on parallel grounds. First, it promotes freedom by enabling individuals to exploit their own property and labor-power; second, it facilitates an efficient allocation and use of resources. Recently, however, both defenses have begun to unravel—as capitalism has moved into its “platform” phase. Today, the pursuit of allocative efficiency, bolstered by pervasive data surveillance, often undermines individual freedom rather than promoting it. And more fundamentally, the very idea that markets are necessary to achieve (...) allocative efficiency has come under strain. Even supposing, for argument’s sake, that the claim was true in the early 20th century when von Mises and Hayek pioneered it, advances in computing have rekindled the old “socialist calculation” debate. And this time around, markets—as information technology—are unlikely to have the upper hand. -/- All of this, we argue, raises an important set of governance questions regarding the political economy of the future. We focus on two: How much should our economic system prioritize freedom, and to what extent should it rely on markets? The arc of platform capitalism bends, increasingly, toward a system that neither prioritizes freedom nor relies on markets. And the dominant critical response, exemplified by Shoshana Zuboff’s work, has been to call for a restoration of market capitalism. Longer term, however, we believe it would be more productive to think about how “postmarket” economic arrangements might promote freedom—or better yet, autonomy—even more effectively than markets, and to determine the practical steps necessary to realize that possibility. (shrink)

The Alcibiades I concludes with an arresting image of an eye that sees itself by looking into another eye. Using the dialogue as a whole, I offer a detailed interpretation of this image and I discuss its implications for the question of self-knowledge. The Alcibiades I reveals both what self-knowledge is (knowledge of soul in its particularity and its universality) and how we are to seek it (by way of philosophical dialogue). This makes the pursuit of self-knowledge an inescapably social (...) pursuit. Yet as Socrates cautions us, our ability to gain self-knowledge—and indeed his very account of what it is—are limited. The dialogue is thus challenging us to take the inquiry further, thereby displaying the very matter being discussed. (shrink)

Many philosophers reject the view that well-being over a lifetime is simply an aggregation of well-being at every moment of one's life, and thus they reject theories of well-being like hedonism and concurrentist desire satisfactionism. They raise concerns that such a view misses the importance of the relationships between moments in a person's life or the role narratives play in a person's well-being. In this article, we develop an atomist meta-theory of well-being, according to which the prudential value of a (...) life depends solely on the prudential value of each moment of that life. This is a general account of momentary well-being that can capture different features of well-being that standard atomistic accounts fail to capture, thus allowing for the possibility of an atomism that is compatible with a variety of well-being theories. Contrary to many criticisms leveled against momentary well-being, this well-being atomism captures all of the important features of well-being. (shrink)

Take “legal reality” to be the part of reality that actual legal thought and talk is dis- tinctively about, such as legal institutions, legal obligations, and legal norms. Our goal is to explore whether legal reality is disunified. To illustrate the issue, consider the possibility that an important metaphysical thesis such as positivism is true of one part of legal reality (legal institutions), but not another (legal norms). We offer two arguments that suggest that legal reality is disunified: one concerns (...) the heteroge- neity of different entities that are part of legal reality; the other concerns variation within legal thought and talk. We then show that taking the possibility of the disunity of legal reality seriously has important upshots for how we think about the positivist and antipositivist traditions, the debate between them, and their relation to other parts of legal theory, such as critical legal theory and legal realism. (shrink)

Textual entailment is a relationship that obtains between fragments of text when one fragment in some sense implies the other fragment. The automation of textual entailment recognition supports a wide variety of text-based tasks, including information retrieval, information extraction, question answering, text summarization, and machine translation. Much ingenuity has been devoted to developing algorithms for identifying textual entailments, but relatively little to saying what textual entailment actually is. This article is a review of the logical and philosophical issues involved in (...) providing an adequate definition of textual entailment. We show that many natural definitions of textual entailment are refuted by counterexamples, including the most widely cited definition of Dagan et al. We then articulate and defend the following revised definition: T textually entails H = df typically, a human reading T would be justified in inferring the proposition expressed by H from the proposition expressed by T. We also show that textual entailment is context-sensitive, nontransitive, and nonmonotonic. (shrink)

Pascal’s wager has received the attention of philosophers for centuries. Most of its criticisms arise from how the wager is often framed. We present Pascal’s wager three ways: in isolation from any further apologetic arguments, as leading toward a regimen intended to produce belief, and finally embedded in a larger apology that includes evidence for Christianity. We find that none of the common objections apply when the wager is presented as part of Pascal’s larger project. Pascal’s wager is a successful (...) argument in its proper place. However, the most interesting features of our first two presentations of the wager turn out to be either irrelevant or missing from our reading: infinite utility and the relativity of evidence. The successful wager is a boring wager. Still, this study shows us how the wager might profitably be incorporated into different apologetic contexts and why it often can’t. (shrink)

Analyzing the position of two philosophers whose views are recognizably divergent, W. O. Quine and M. Dummett, we intend to support a striking point of agreement between them: the idea that our logical principles constitute our principles about what there is, and therefore, that logic is metaphysics.

Knows-knows principles in epistemology say that if you know some proposition, then you are in a position to know that you know it. This paper examines the viability of analogous principles in ethics, which I call ought-ought principles. Several epistemologists have recently offered new defences of KK principles and of other related principles, and there has recently been an increased interest in examining analogies between ethics and epistemology, and so it seems natural to examine whether defences of KK and related (...) principles carry over to OO principles. In this paper, I introduce two OO principles, and I show how some arguments in favour of KK carry over to them. Then I show how these OO principles can be used to shed light on a much-discussed case in ethics, that of Professor Procrastinate. (shrink)

In this chapter we explain what experimental philosophy of science is, how it relates to the philosophy of science, and STS more broadly, and what sorts of contributions is can make to ongoing research in the philosophy of science.

Our concern in this paper lies with a common argument from racial discrimination to realism about races: some people are discriminated against for being members of a particular race (i.e., racial discrimination exists), so some people must be members of that race (i.e., races exist). Error theorists have long responded that we can explain racial discrimination in terms of racial attitudes alone, so we need not explain it in terms of race itself. But to date there has been little detailed (...) discussion of whether it is better to explain racial discrimination in terms of race or in terms of racial attitudes alone. Our goal is to offer a novel and detailed argument in defense of explaining racial discrimination in terms of racial attitudes alone, by attending to the neglected phenomenon of misperception discrimination, which involves differential treatment due to misperceived race. We argue that the discriminatory action in misperception cases must be explained in the same way as cases where (according to the realist) the victim’s race is accurately perceived. Thus, the victim’s actual race cannot provide the best explanation. The main upshot of our argument is that explanatory arguments from racial discrimination to realism about race fail. (shrink)

This review article provides a new perspective on the ethics of green nudging. We advance a new model for assessing the ethical permissibility of green nudges (GNs). On this model, which provides normative guidance for policymakers, a GN is ethically permissible when the intervention is (1) efficacious, (2) cost-effective, and (3) the advantages of the GN (i.e. reducing the environmental harm) are not outweighed by countervailing costs/harms (i.e. for nudgees). While traditional ethical objections to nudges (paternalism, etc.) remain potential normative (...) costs associated with GNs, any such costs must be weighed against the injunction to reduce environmental harm to third parties. (shrink)

My central claim in this paper is that Kierkegaard’s Fear and Trembling is governed by the basic aim to articulate a real dilemma, and to elicit its proper recognition as such. I begin by indicating how Kierkegaard’s works are shaped in general by this aim, and what the aim involves. I then show how the dilemmaticstructure of Fear and Trembling is obscured in a recent dispute between Michelle Kosch and John Lippitt regarding the basic aims and upshot of the book. (...) Finally, I consider two critical questions: Why does Kierkegaard present his dilemmatic reasoning in the form of a “dialectical lyric”? And why does he write a book that aims only to articulate a dilemma, and not also to resolve it? (shrink)

Many Christian theodicists believe that God's creating us with the capacity to love Him and each other justifies, in large part, God's permitting evil. For example, after reminding us that, according to Christian doctrine, the supreme good for human beings is to enter into a reciprocal love relationship with God, Vincent Brummer recently wrote: In creating human persons in order to love them, God necessarily assumes vulnerability in relation to them. In fact, in this relation, he becomes even more vulnerable (...) than we do, since he cannot count on the steadfastness of our love the way we can count on his steadfastness.... If God did not grant us the ability to sin and cause affliction to him and to one another, we would not have the kind of free and autonomous existence necessary to enter into a relation of love with God and with one another.... Far from contradicting the value which the free will defence places upon the freedom and responsibility of human persons, the idea of a loving God necessarily entails it. In this way we can see that the free will defence is based on the love of God rather than on the supposed intrinsic value of human freedom and responsibility.1 And Peter van Inwagen recently put the same point this way. (shrink)