This paper discusses the finite version of the two envelope paradox. (That is, we treat the paradox against the background assumption that there is only a finite amount of money in the world.).

There is a trade-off between specificity and accuracy in existing models of belief. Descriptions of agents in the tripartite model, which recognizes only three doxastic attitudes—belief, disbelief, and suspension of judgment—are typically accurate, but not sufficiently specific. The orthodox Bayesian model, which requires real-valued credences, is perfectly specific, but often inaccurate: we often lack precise credences. I argue, first, that a popular attempt to fix the Bayesian model by using sets of functions is also inaccurate, since it requires us to (...) have interval-valued credences with perfectly precise endpoints. We can see this problem as analogous to the problem of higher order vagueness. Ultimately, I argue, the only way to avoid these problems is to endorse Insurmountable Unclassifiability. This principle has some surprising and radical consequences. For example, it entails that the trade-off between accuracy and specificity is in-principle unavoidable: sometimes it is simply impossible to characterize an agent’s doxastic state in a way that is both fully accurate and maximally specific. What we can do, however, is improve on both the tripartite and existing Bayesian models. I construct a new model of belief—the minimal model—that allows us to characterize agents with much greater specificity than the tripartite model, and yet which remains, unlike existing Bayesian models, perfectly accurate. (shrink)

Cooperative relations steeped in honesty and good faith are a necessity for any viable society. This is especially relevant to the police institution because the police are entrusted to promote justice and security. Despite the necessity of societal honesty and good faith, the police institution has embraced deception, dishonesty, and bad faith as tools of the trade for providing security. In fact, it seems that providing security is impossible without using deception and dishonesty during interrogations, undercover operations, pretextual detentions, and (...) other common scenarios. This presents a paradox related to the erosion of public faith in the police institution and the weakening of the police's legitimacy. -/- The book seeks to solve this puzzle by showing that many of our assumptions about policing and security are unjustified. Specifically, they are unjustified in the way many of our assumptions about security were unjustified after the 9/11 terrorist attacks, when state institutions embraced a variety of brutal rules and tactics in pursuit of perceived security enhancements. The police are likewise unjustified in their pursuit of many supposed security enhancements that rely on proactive deception, dishonesty, and bad faith. -/- There are compelling reasons to think that the police's widespread use of proactive deception and dishonesty is inconsistent with fundamental norms of political morality regarding fraud and the rule of law. Although there are times and places for such tactics in policing, those times and places should be much more limited than current practices suggest. (shrink)

At the core of republican thought, on Philip Pettit’s account, lies the conception of freedom as non-domination, as opposed to freedom as noninterference in the liberal sense. I revisit the distinction between liberal and republican freedom and argue that republican freedom incorporates a particular rule-of-law requirement, whereas liberal freedom does not. Liberals may also endorse such a requirement, but not as part of their conception of freedom itself. I offer a formal analysis of this rule-of-law requirement and compare liberal and (...) republican freedom on its basis. While I agree with Pettit that republican freedom has broader implications than liberal freedom, I conclude that we face a trade-off between two dimensions of freedom (scope and robustness) and that it is harder for republicans to solve that trade-off than it is for liberals. Key Words: freedom • republicanism • liberalism • noninterference • non-domination • rule of law • robustness • liberal paradox. (shrink)

Political theorists have offered many accounts of collective decision-making under pluralism. I discuss a key dimension on which such accounts differ: the importance assigned not only to the choices made but also to the reasons underlying those choices. On that dimension, different accounts lie in between two extremes. The ‘minimal liberal account’ holds that collective decisions should be made only on practical actions or policies and that underlying reasons should be kept private. The ‘comprehensive deliberative account’ stresses the importance of (...) giving reasons for collective decisions, where such reasons should also be collectively decided. I compare these two accounts on the basis of a formal model developed in the growing literature on the ‘discursive dilemma’ and ‘judgment aggregation’ and address several questions: What is the trade-off between the (minimal liberal) demand for reaching agreement on outcomes and the (comprehensive deliberative) demand for reason-giving? How large should the ‘sphere of public reason’ be? When do the decision procedures suggested by the two accounts agree and when not? How good are these procedures at truthtracking on factual matters? What strategic incentives do they generate for decision-makers? My discussion identifies what is at stake in the choice between minimal liberal and comprehensive deliberative accounts of collective decisionmaking, and sheds light not only on these two ideal-typical accounts themselves, but also on many characteristics that intermediate accounts share with them. (shrink)

The Black antislavery theorist Quobna Ottobah Cugoano (c.1757–c.1791) is increasingly recognized as a noteworthy figure in the history of philosophy. Born in present-day Ghana, Cugoano was enslaved at the age of 13 and shipped to Grenada, before being taken onwards to England, where the 1772 Somerset court ruling in effect freed him. His Thoughts and Sentiments on the Evil of Slavery [1787/1791] broke new ground by demanding the immediate end of the slave-trade and of slavery itself, without any compensation to (...) slaveholders. Notwithstanding this, Cugoano endorsed the legitimacy of penal enslavement on principled grounds – like many other abolitionists writing in late eighteenth-century Britain. “Every free community might keep slaves, or criminal prisoners in bondage” – and even sell them. Amidst the growing literature exploring Cugoano’s abolitionism, his paradoxical justification of penal slavery has bewildered commentators. Far from an offhand inconsistency, I argue that this justification is deeply embedded within his moral and legal philosophy; constraining his antislavery arguments while simultaneously serving retaliatory aims. His two-pronged principle of just punishment – the lex talionis (‘eye for an eye, bondage for bondage’) as tempered by mercy – sometimes demands penally enslaving colonial slaveholders and slave-traders in turn. Throughout, I compare Cugoano’s justification of penal enslavement with those of other early modern philosophers, especially Locke and Kant. This helps me position Cugoano within the history of philosophy, thus making his views more accessible to a wider philosophical audience. It also indicates just how deeply theories of punishment shaped philosophical thinking about penal bondage in the period. (shrink)

Peter Singer’s famous and influential article is criticised in three main ways that can be considered libertarian, although many non-libertarians could also accept them: 1) the relevant moral principle is more plausibly about upholding an implicit contract rather than globalising a moral intuition that had local evolutionary origins; 2) its principle of the immorality of not stopping bad things is paradoxical, as it overlooks the converse aspect that would be the positive morality of not starting bad things and also thereby (...) conceptually eliminates innocence; and 3) free markets—especially international free trade—have been cogently explained to be the real solution to the global “major evils” of “poverty” and “pollution”, while “overpopulation” does not exist in free-market frameworks; hence charity is a relatively minor alleviant to the problem of insufficiently free markets. There are also various subsidiary arguments throughout. (shrink)

This paper explores the possibility that Hobbesian jurisprudence is best understood as a ‘third way’ in legal theory, irreducible to classical natural law or legal positivism. I sketch two potential ‘third theories’ of law -- legal pragmatism and legal dualism -- and argue that, when considered in its broadest sense, Leviathan is best viewed as an example of legal pragmatism. I consider whether this legal pragmatist interpretation can be sustained in the examination of Leviathan’s treatment of civil law, and argue (...) that the pragmatic interpretation can only be successful if we can resolve two textual issues in that chapter. First, while Hobbes argues that law entails the existence of public (sharable) reasons, he does not adequately defend the view that the sovereign is the unique authority over such reasons in all cases, especially as far as they concern known collective emergencies. Second, Hobbes both affirms and denies that a sovereign can fail to do justice, which is paradoxical. Both problems are best resolved by legal pragmatism, though the second problem resists a fully satisfying resolution. The upshot is that, although Leviathan ought to be regarded as an episode of legal pragmatism, there are trade-offs on every reading. (shrink)

This Article aims to demonstrate that the WTO jurisprudence on science-related trade disputes has become imbued with a specific vision of science that has prevented any possible application of the precautionary principle. This situation is due both to the WTO’s specific dispute settlement procedures and to the substantive nature of precautionary measures. Indeed, such measures’ foundation on “insufficient scientific evidence” dramatically undermines the probative value of science in WTO adjudication and creates a seeming contradiction: The system requires defendants to provide (...) legal evidence of the absence of sufficient scientific evidence. The reasoning of the Panel on the EC–Biotech case was riddled with this apparent paradox. For the first time, the US–Continued Suspension case has opened a gateway to address this fundamental issue. (shrink)

Palawan is a land of promise, and of paradox. On maps, it appears on the edge of the Philippines, isolated. Indeed, it is a kind of last frontier. Its population remained tiny for centuries, the government offering homestead land in the 1950s practically for free to attract migrants from outside. The Palawan State University was established by law in 1965, but did not become operational until 1972. A commercial airport did not exist until the 1980s, and for many years, (...) flights were limited. Yet Palawan is one of the oldest sites of human habitation in the Philippines with the famous Tabon Cave human fossils. The oldest bone fragment here has been dated to be about 47,000 years. We know, too, that trade with China goes back several centuries. Today, Palawan seems to be making up for lost time with new commercial investments pouring in at breakneck speed. In particular, outsiders have rediscovered its potentials around logging, mining, fisheries, and tourism. This has caused concern among individuals and civil society organizations who want sustainable development, and see the commercial developments mainly as extractive, not just of natural resources but of the human. There’s very cheap labor available. And when potential investors marvel about cheap land, they’re actually talking about displacing earlier settlers, including indigenous people, from their lands. A subtle but still insidious aspect of the exploitation of human resources is a transformation of the very concept of human development. Using the rhetoric of modernity, residents in Palawan are reorienting the way they view themselves as well as their families and friends. The value of a human being now hinges on how they look, and the desired appearance is defined from the outside, as we see in this anthology of research reports coming from the Chemical Youth project of the University of Amsterdam and the University of the Philippines Diliman. We read about the importance of fair skin as a projection of cleanliness, of high social status (meaning someone not engaged in manual labor and therefore not exposed to the sun). We read of how “femininity” is defined around body contours, and cosmetics, and how hormones are used by male-to-female transgenders. We go beyond the visual, reading about the importance of controlling or enhancing body odors among tour guides, who interestingly are especially concerned about the bad odor management of their foreign customers, using car perfumes to keep their work manageable and we learn how difficult it is for security guards to stay alert during their long shifts. Energy drinks and cigarettes help them perform their duties. All these transformations through what the French philosopher and historian Michel Foucault has called “technologies of the self” are as paradoxical as Palawan. On the surface, the products—which are technologies—seem to be mainly in the realm of the self but are, in reality, pushed, through marketing, from the outside, in contexts of inequality and exploitative labour relations. Personal aspirations are not personal but are for predefined standards of modernity, related to work-related demands and expectations. The self must be made presentable to the tourist, to the customers in malls, and to those who may threaten the properties that young people protect. It is not surprising that these transformations become problematic for the “self.” The skin whiteners, the hormones, the body deodorants, and the energy drinks are expensive and can distort budgetary priorities. The money for tonic drinks, for example, could well go into more nutritious food. The tragedy, too, many of the products used are of doubtful safety and efficacy. Even the energy drinks have much too high levels of caffeine that can cause cardiac palpitations. Cosmetics and the skin whiteners imported from China and unregistered with the Food and Drug Administration may contain toxic chemicals like mercury. But even registered skin whiteners can be problematic, their so-called “skin-whitening effect” coming about because they take away the upper layers of the skin, leaving behind a red glow (seen as “whitening”) which is actually inflammation. The whitened skin fails to protect against the sun, leading to adverse effects such as black spots. Ultimately though, the problems come with the very definition of the self. As the reports show, young people use the chemicals with some ambivalence, knowing how expensive they are and experiencing some of the undesirable side effects. There is, too, doubt about whether what they’re doing is indeed “good,” captured by how IP women will put on cosmetics only when they’re away from home and about to go to work. The cosmetics have to be removed before they return home because they are not socially acceptable. The research reports are not for Palawan alone. It must make us more critical and discerning as we revisit concepts of development and exploitation, modernity and tradition, self and community. The chemicals, in many ways, are like the products used in precolonial barter trade. For the Chinese, the beeswax and the sea cucumbers, for the inhabitants of Palawan the ceramics, represented faraway lands. To have those products gave prestige. Today, the skin whiteners and tonic drinks and other chemicals described in this anthology represent modernity with promises of not just of a more attractive self, but of better jobs, a better life. We are proud to have worked with the Palawan State University, and the people of Palawan, to gather powerful narratives that will now challenge the outside, the purveyors of modernity, to be more critical and discerning, the chemicals now to be seen not just as stuff applied to the biological body, but as powerful shapers of social bodies. (shrink)

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

The World Trade Organization (WTO) is a multilateral trade organization that, at least partially, governs trade relations between its member states. The WTO (2011a) proclaims that its “overriding objective is to help trade flow smoothly, freely, fairly and predictably.” The WTO is a “treaty-based” organization – it has been constituted through an agreed, legally binding treaty made up of more than 30 articles, along with additional commitments by some members in specific areas. At present, 153 states are members of the (...) WTO, which collectively make up over 97 percent of all trade worldwide (WTO 2011b). Together, the WTO treaty specifies the rights and obligations of its member states. To become a member of the WTO, a state must treat the agreement as a “single undertaking.” Members cannot choose à la carte which agreements – for example, regarding tariffs, or trade in services or intellectual property – they want to accede to and which they do not. Instead, they must take on the obligations of the agreement in toto. The WTO is one of the most consequential governance institutions in the world, a lodestar of political debate about globalization (see globalization), attracting increased interest from moral and political philosophers in recent years (James 2006; Moellendorf 2005; Risse 2007; Brock 2009). (shrink)

Abstract:Trust is important for a variety of social relationships. Trust facilitates trade, which increases prosperity and induces us to interact with people of different backgrounds on terms that benefit all parties. Trade promotes trustworthiness, which enables us to form meaningful as well as mutually beneficial relationships. In what follows, I argue that when we erect institutions that enhance trust and reward people who are worthy of trust, we create the conditions for a certain kind of moral progress.

On the traditional relationalist conception of singular thought, a thought has singular content when it is based on an ‘information relation’ to its object. Recent work rejects relationalism and suggests singular thoughts are distinguished from descriptive thoughts by their inferential role: only thoughts with singular content can be employed in ‘direct’ inferences, or inferences that ‘trade on identity’. Firstly this view is insufficiently clear, because it conflates two distinct ideas—one about a kind of inference, the other a kind of process (...) that grounds inferences—under the title, ‘trading on identity’. Secondly, this leaves us without a notion that can be used as an alternative to relationalism about singular thought. The first notion is no more applicable to singular than to descriptive thought. The second may help us better understand singular thought, but does so, not by replacing the view that singular thoughts are information-based, but by helping us understand the nature of information-based thought. (shrink)

We argue that deliberative decision-making that is inclusive, transparent and accountable can contribute to more trustworthy and legitimate decisions on difficult ethical questions and political trade-offs during the pandemic and beyond.

The discrepancy between individual women and the stereotypes attributed to the group as a ‎whole has become progressively greater and more explicit over the course of history. The stereotypes remain the same age-old ‎allegations whilst the ‎developments in the occupations of women and the traits they have opportunity to express have increased the distance between women and those ascribed traits. Stereotypes’ abstention from revision in light of contrary evidence constitutes an epistemic paradox for it entails conflict between the stereotypical (...) knowledge and empirical evidence, as well as between the stereotypical knowledge and other empirical knowledges. This paradox of stubbornness also raises the question as to the epistemic source of stereotypes. For, people at young ages encounter evidence which should have formed a more complex knowledge regarding women rather than the pervasive stereotypical knowledge. It is this extremity of absurdness of stereotypes regarding women that is utile to understanding stereotypes as a whole. The epistemic paradox that is engrained in all stereotypes is exposed uncompromisingly by this group. The paradox cannot be dismissed with excuses of having a small basis of evidence, such as may be said regarding other social groups with which one may have had minimal or no contact. Thus, stereotypes of women provide a limit case to understanding the epistemology of this paradoxical form of knowledge. The traits and epistemic phenomena which render stereotypes epistemically puzzling and intriguing is the relationship between knowledges. Stereotypical knowledge regarding women as a group conflict with one’s experience-founded knowledges of particular women, deeming the corporate body of knowledge incoherent. Quine’s theory of knowledge, with its holistic empirical approach endorsing conceptual schemes, provides fertile ground for this analysis. The novelty in his account is his establishment of the criteria of coherency, which shifts the focal point of epistemic inquiry away from the adequacy of individual knowledges with empirical evidence to the intra-knowledge relationships themselves. In his empiricism, Quine rather examines the interactions between knowledges and the overarching coherence of the body of knowledge as a holistic unit. Quine creates place in his account for mechanism which provide for the epistemic incongruences of stubbornness and conflict found between stereotypical knowledges and empirical evidence. These very mechanisms are what this paper requests to examine. Quine, ultimately, formulates knowledge as a collectively held fabric consisting of relations and of posits – socially constructed mechanisms which are empirically-irreducible and implemented pragmatically for the organisation of empirical evidence. According to Quine, the fabric formation is a conceptual scheme sourced in social heritage. People are bestowed with an eclectic framework of ‎knowledge to pragmatically merge between an inherited, collective conceptual scheme and the personally experienced empirical evidence. This paper will delve into Quine’s fabric of knowledge, its relations, and inner-mechanisms. The finding of stereotypes to be an age-old posit entrenched pragmatically – thus stubbornly – in the collective conceptual scheme, will explain the epistemic paradoxes they entail and offer insight to their revision in light of empiric reality and its women. (shrink)

The paradox of pain refers to the idea that the folk concept of pain is paradoxical, treating pains as simultaneously mental states and bodily states. By taking a close look at our pain terms, this paper argues that there is no paradox of pain. The air of paradox dissolves once we recognize that pain terms are polysemous and that there are two separate but related concepts of pain rather than one.

Can agents rationally inquire into things that they know? On my view, the answer is yes. Call this view the Compatibility Thesis. One challenge to this thesis is to explain why assertions like “I know that p, but I’m wondering whether p” sound odd, if not Moore-Paradoxical. In response to this challenge, I argue that we can reject one or both premises that give rise to it. First, we can deny that inquiry requires interrogative attitudes. Second, we can deny the (...) ignorance norm, on which agents are not permitted to both know and have interrogative attitudes, such as wondering. I argue that there are compelling reasons to deny the former and reasons to question the latter. Both options pave the way for further work on further inquiry. (shrink)

If I were to say, “Agnes does not know that it is raining, but it is,” this seems like a perfectly coherent way of describing Agnes’s epistemic position. If I were to add, “And I don’t know if it is, either,” this seems quite strange. In this chapter, we shall look at some statements that seem, in some sense, contradictory, even though it seems that these statements can express propositions that are contingently true or false. Moore thought it was paradoxical (...) that statements that can express true propositions or contingently false propositions should nevertheless seem absurd like this. If we can account for the absurdity, we shall solve Moore’s Paradox. In this chapter, we shall look at Moore’s proposals and more recent discussions of Moorean absurd thought and speech. (shrink)

Supererogatory acts—good deeds “beyond the call of duty”—are a part of moral common sense, but conceptually puzzling. I propose a unified solution to three of the most infamous puzzles: the classic Paradox of Supererogation (if it’s so good, why isn’t it just obligatory?), Horton’s All or Nothing Problem, and Kamm’s Intransitivity Paradox. I conclude that supererogation makes sense if, and only if, the grounds of rightness are multi-dimensional and comparative.

I aim at dissolving Kripke's dogmatism paradox by arguing that, with respect to any particular proposition p which is known by a subject A, it is not irrational for A to ignore all evidence against p. Along the way, I offer a definition of 'A is dogmatic with respect to p', and make a distinction between an objective and a subjective sense of 'should' in the statement 'A should ignore all the evidence against p'. For the most part, I (...) deal with Kripke's original version of the paradox, wherein the subject wishes, above all else, to avoid losing her true belief or gaining a false one; in the final section I investigate the possibility of having a paradox for a subject who values knowledge above anything else. (shrink)

This article begins by distinguishing between two approaches to egalitarian trade justice – the explicative approach and the applicative approach – and notes that the former has been used to defend conclusions that are less strongly egalitarian than those defended by advocates of the latter. The article then engages with the primary explicative account of trade egalitarianism – that offered by Aaron James – and argues that its egalitarian conclusions are unduly minimalistic. The aim of the article is not to (...) criticize the explicative approach, but rather to show that the arguments and commitments of its best-known defender – James – either fail to rule out, or in fact positively support, more robustly egalitarian conclusions. (shrink)

I propose a revision of Cantor’s account of set size that understands comparisons of set size fundamentally in terms of surjections rather than injections. This revised account is equivalent to Cantor's account if the Axiom of Choice is true, but its consequences differ from those of Cantor’s if the Axiom of Choice is false. I argue that the revised account is an intuitive generalization of Cantor’s account, blocks paradoxes—most notably, that a set can be partitioned into a set that is (...) bigger than it—that can arise from Cantor’s account if the Axiom of Choice is false, illuminates the debate over whether the Axiom of Choice is true, is a mathematically fruitful alternative to Cantor’s account, and sheds philosophical light on one of the oldest unsolved problems in set theory. (shrink)

Thomas Kroedel argues that the lottery paradox can be solved by identifying epistemic justification with epistemic permissibility rather than epistemic obligation. According to his permissibility solution, we are permitted to believe of each lottery ticket that it will lose, but since permissions do not agglomerate, it does not follow that we are permitted to have all of these beliefs together, and therefore it also does not follow that we are permitted to believe that all tickets will lose. I present (...) two objections to this solution. First, even if justification itself amounts to no more than epistemic permissibility, the lottery paradox recurs at the level of doxastic obligations unless one adopts an extremely permissive view about suspension of belief that is in tension with our practice of doxastic criticism. Second, even if there are no obligations to believe lottery propositions, the permissibility solution fails because epistemic permissions typically agglomerate, and the lottery case provides no exception to this rule. (shrink)

This paper presents and motivates a new philosophical and logical approach to truth and semantic paradox. It begins from an inferentialist, and particularly bilateralist, theory of meaning---one which takes meaning to be constituted by assertibility and deniability conditions---and shows how the usual multiple-conclusion sequent calculus for classical logic can be given an inferentialist motivation, leaving classical model theory as of only derivative importance. The paper then uses this theory of meaning to present and motivate a logical system---ST---that conservatively extends (...) classical logic with a fully transparent truth predicate. This system is shown to allow for classical reasoning over the full (truth-involving) vocabulary, but to be non-transitive. Some special cases where transitivity does hold are outlined. ST is also shown to give rise to a familiar sort of model for non-classical logics: Kripke fixed points on the Strong Kleene valuation scheme. Finally, to give a theory of paradoxical sentences, a distinction is drawn between two varieties of assertion and two varieties of denial. On one variety, paradoxical sentences cannot be either asserted or denied; on the other, they must be both asserted and denied. The target theory is compared favourably to more familiar related systems, and some objections are considered. (shrink)

In this essay I defend a solution to a skeptical paradox. The paradox I focus on concerns epistemic justification (rather than knowledge), and skeptical scenarios that entail that most of our ordinary beliefs about the external world are false. This familiar skeptical paradox hinges on a “closure” principle. The solution is to restrict closure, despite its first appearing as a fully general principle, so that it can no longer give rise to the paradox. This has some (...) extra advantages. First, it suggests a general strategy that provides solutions to other versions of the paradox, not just those that depend on closure. Second, it clarifies the relation between the paradox and other kinds of skeptical problem. (shrink)

There is growing concern that decision-making informed by machine learning (ML) algorithms may unfairly discriminate based on personal demographic attributes, such as race and gender. Scholars have responded by introducing numerous mathematical definitions of fairness to test the algorithm, many of which are in conflict with one another. However, these reductionist representations of fairness often bear little resemblance to real-life fairness considerations, which in practice are highly contextual. Moreover, fairness metrics tend to be implemented in narrow and targeted toolkits that (...) are difficult to integrate into an algorithm’s broader ethical assessment. In this paper, we derive lessons from ethical philosophy and welfare economics as they relate to the contextual factors relevant for fairness. In particular we highlight the debate around acceptability of particular inequalities and the inextricable links between fairness, welfare and autonomy. We propose Key Ethics Indicators (KEIs) as a way towards providing a more holistic understanding of whether or not an algorithm is aligned to the decision-maker’s ethical values. (shrink)

According to Aristotle if a universal proposition (for example: “All men are white”) is true, its contrary proposition (“All men are not white”) must be false; and, according to Aristotle, if a universal proposition (for example: “All men are white”) is true, its contradictory proposition (“Not all men are white”) must be false. I agree with what Aristotle wrote about universal propositions, but there are universal propositions which have no contrary proposition and have no contradictory proposition. The proposition X “All (...) the propositions that contradict this proposition are true” does not have the contrary proposition and does not have the contradictory proposition. In fact: FEX “All the propositions that contradict this proposition are not true” has a different subject: the subject of the proposition X is constituted by all the propositions that contradict the proposition X; by contrast, the subject of the proposition FEX is constituted by all the propositions that contradict the proposition FEX. And FOX “Not all the propositions that contradict this proposition are true” has a different subject: the subject of the proposition X is constituted by the propositions that contradict the proposition X; by contrast, the subject of the proposition FOX is constituted by the propositions that contradict the proposition FOX. According to Aristotle, a singular proposition (in his example: "Socrates is white") which is true must have its negative proposition ("Socrates is not white") which is false. I agree with Aristotle, but there are singular propositions which do not have the corresponding negative proposition. The proposition (or, rather, the pseudo-proposition) L “This same statement is not true” does not have the negative proposition because the proposition FNL “This same statement is true” has a different subject from the subject of the proposition L: the subject of the proposition L is the proposition L; by contrast, the subject of the proposition FNL is the proposition FNL. L and FNL cannot have the same subject. By contrast, the proposition M “This mount is entirely in Swiss territory” and the proposition NM “This mount is not entirely in Swiss territory” can have the same subject (for example, the Mount Eiger): in case the subject of the proposition M and the subject of the proposition NM is the same, M and NM are opposite propositions, NM is the negative proposition of M. By contrast, the proposition (or, rather, the pseudo-proposition) L "This same statement is not true" cannot have the corresponding negative proposition because FNL "This same statement is true" has a different subject: the subject of L is L ; by contrast, the subject of FNL is FNL. Then the paper continues by analyzing some variants of the liar’s paradox: L1 “The statement L1 is not true”; the so-called liar cycle; and the so-called Yablo’s paradox. (shrink)

I distinguish paradoxes and hypodoxes among the conundrums of time travel. I introduce ‘hypodoxes’ as a term for seemingly consistent conundrums that seem to be related to various paradoxes, as the Truth-teller is related to the Liar. In this article, I briefly compare paradoxes and hypodoxes of time travel with Liar paradoxes and Truth-teller hypodoxes. I also discuss Lewis’ treatment of time travel paradoxes, which I characterise as a Laissez Faire theory of time travel. Time travel paradoxes are impossible according (...) to Laissez Faire theories, while it seems hypodoxes are possible. (shrink)

In recent years it has often been claimed that policies such as subsidies paid to domestic producers by affluent countries and tariffs on goods produced by foreign producers in poorer countries violate important moral requirements because they do severe harm to poor people, even kill them. Such claims involve an empirical aspect—such policies are on balance very bad for the global poor—and a philosophical aspect—that the causal influence of these policies can fairly be characterized as doing severe harm and killing. (...) In this essay, we examine the philosophical aspect of this issue. We conclude that these policies do not do harm to the poor, but rather enable harm to them in various ways, and explore the moral implications of this fact. (shrink)

Philosophers have long argued that duties to oneself are paradoxical, as they seem to entail an incoherent power to release oneself from obligations. I argue that self-release is possible, both as a matter of deontic logic and of metaethics.

It is widely accepted that there is what has been called a non-hypocrisy norm on the appropriateness of moral blame; roughly, one has standing to blame only if one is not guilty of the very offence one seeks to criticize. Our acceptance of this norm is embodied in the common retort to criticism, “Who are you to blame me?”. But there is a paradox lurking behind this commonplace norm. If it is always inappropriate for x to blame y for (...) a wrong that x has committed, then all cases in which x blames x (i.e. cases of self-blame) are rendered inappropriate. But it seems to be ethical common-sense that we are often, sadly, in position (indeed, excellent, privileged position) to blame ourselves for our own moral failings. And thus we have a paradox: a conflict between the inappropriateness of hypocritical blame, and the appropriateness of self-blame. We consider several ways of resolving the paradox, and contend none is as defensible as a position that simply accepts it: we should never blame ourselves. In defending this startling position, we defend a crucial distinction between self-blame and guilt. (shrink)

We begin by showing that every theory of the value of uncertain prospects must have one of three unpalatable properties. _Reckless_ theories recommend giving up a sure thing, no matter how good, for an arbitrarily tiny chance of enormous gain; _timid_ theories permit passing up an arbitrarily large potential gain to prevent a tiny increase in risk; _non-transitive_ theories deny the principle that, if A is better than B and B is better than C, then A must be better than (...) C. Having set up this trilemma, we study its horns. Non-transitivity has been much discussed; we focus on drawing out the costs and benefits of recklessness and timidity when it comes to axiology, decision theory, and normative uncertainty. (shrink)

This paper gives a definition of self-reference on the basis of the dependence relation given by Leitgeb (2005), and the dependence digraph by Beringer & Schindler (2015). Unlike the usual discussion about self-reference of paradoxes centering around Yablo's paradox and its variants, I focus on the paradoxes of finitary characteristic, which are given again by use of Leitgeb's dependence relation. They are called 'locally finite paradoxes', satisfying that any sentence in these paradoxes can depend on finitely many sentences. I (...) prove that all locally finite paradoxes are self-referential in the sense that there is a directed cycle in their dependence digraphs. This paper also studies the 'circularity dependence' of paradoxes, which was introduced by Hsiung (2014). I prove that the locally finite paradoxes have circularity dependence in the sense that they are paradoxical only in the digraph containing a proper cycle. The proofs of the two results are based directly on König's infinity lemma. In contrast, this paper also shows that Yablo's paradox and its nested variant are non-self-referential, and neither McGee's paradox nor the omega-cycle liar paradox has circularity dependence. (shrink)

This paper is concerned with the paradox of decrease. Its aim is to defend the answer to this puzzle that was propounded by its originator, namely, the Stoic philosopher Chrysippus. The main trouble with this answer to the paradox is that it has the seemingly problematic implication that a material thing could perish due merely to extrinsic change. It follows that in order to defend Chrysippus’ answer to the paradox, one has to explain how it could be (...) that Theon is destroyed by the amputation without changing intrinsically. In this paper, I shall answer this challenge by appealing to the broadly Aristotelian idea that at least some of the proper parts of a material substance are ontologically dependent on that substance. I will also appeal to this idea in order to offer a new solution to the structurally similar paradox of increase. In this way, we will end up with a unified solution to two structurally similar paradoxes. (shrink)

Counterfactuals are somewhat tolerant. Had Socrates been at least six feet tall, he need not have been exactly six feet tall. He might have been a little taller—he might have been six one or six two. But while he might have been a little taller, there are limits to how tall he would have been. Had he been at least six feet tall, he would not have been more than a hundred feet tall, for example. Counterfactuals are not just tolerant, (...) then, but bounded. This paper presents a surprising paradox: If counterfactuals are tolerant and bounded, then we can prove a flat contradiction using natural rules of inference. Something has to go then. But what? (shrink)

Paradoxes have played an important role both in philosophy and in mathematics and paradox resolution is an important topic in both fields. Paradox resolution is deeply important because if such resolution cannot be achieved, we are threatened with the charge of debilitating irrationality. This is supposed to be the case for the following reason. Paradoxes consist of jointly contradictory sets of statements that are individually plausible or believable. These facts about paradoxes then give rise to a deeply troubling (...) epistemic problem. Specifically, if one believes all of the constitutive propositions that make up a paradox, then one is apparently committed to belief in every proposition. This is the result of the principle of classical logical known as ex contradictione (sequitur) quodlibetthat anything and everything follows from a contradiction, and the plausible idea that belief is closed under logical or material implication (i.e. the epistemic closure principle). But, it is manifestly and profoundly irrational to believe every proposition and so the presence of even one contradiction in one’s doxa appears to result in what seems to be total irrationality. This problem is the problem of paradox-induced explosion. In this paper it will be argued that in many cases this problem can plausibly be avoided in a purely epistemic manner, without having either to resort to non-classical logics for belief (e.g. paraconsistent logics) or to the denial of the standard closure principle for beliefs. The manner in which this result can be achieved depends on drawing an important distinction between the propositional attitude of belief and the weaker attitude of acceptance such that paradox constituting propositions are accepted but not believed. Paradox-induced explosion is then avoided by noting that while belief may well be closed under material implication or even under logical implication, these sorts of weaker commitments are not subject to closure principles of those sorts. So, this possibility provides us with a less radical way to deal with the existence of paradoxes and it preserves the idea that intelligent agents can actually entertain paradoxes. (shrink)

This paper presents two challenges faced by many initiatives that try to diversify undergraduate philosophy curricula, both intellectually and demographically. Trade-offs involve making difficult decisions to prioritise some values over others (like gender diversity over cultural diversity). Backfires involve unintended consequences contrary to the aims and values of diversity initiatives, including ones that compromise more general philosophical values. I discuss two specific backfire risks, involving the critical and political dimensions of teaching philosophy. Some general practical advice is offered along the (...) way. (shrink)

I present a paradoxical combination of desires. I show why it's paradoxical, and consider ways of responding. The paradox saddles us with an unappealing trilemma: either we reject the possibility of the case by placing surprising restrictions on what we can desire, or we deny plausibly constitutive principles linking desires to the conditions under which they are satisfied, or we revise some bit of classical logic. I argue that denying the possibility of the case is unmotivated on any reasonable (...) way of thinking about mental content, and rejecting those desire-satisfaction principles leads to revenge paradoxes. So the best response is a non-classical one, according to which certain desires are neither determinately satisfied nor determinately not satisfied. Thus, theorizing about paradoxical propositional attitudes helps constrain the space of possibilities for adequate solutions to semantic paradoxes more generally. (shrink)

The present work outlines a logical and philosophical conception of propositions in relation to a group of puzzles that arise by quantifying over them: the Russell-Myhill paradox, the Prior-Kaplan paradox, and Prior's Theorem. I begin by motivating an interpretation of Russell-Myhill as depending on aboutness, which constrains the notion of propositional identity. I discuss two formalizations of of the paradox, showing that it does not depend on the syntax of propositional variables. I then extend to propositions a (...) modal predicative response to the paradoxes articulated by an abstraction principle for propositions. On this conception, propositions are “shadows” of the sentences that express them. Modal operators are used to uncover the implicit relation of dependence that characterizes propositions that are about propositions. The benefits of this approach are shown by application to other intensional puzzles. The resulting view is an alternative to the plenitudinous metaphysics of impredicative comprehension principles. (shrink)

Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned (...) with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion. (shrink)

Illusionism is the view that conscious experience is some sort of introspective illusion. According to illusionism, there is no conscious experience, but it merely seems like there is conscious experience. This would suggest that much phenomenological enquiry, including work on phenomenological psychopathology, rests on a mistake. Some philosophers have argued that illusionism is obviously false, because seeming is itself an experiential state, and so necessarily presupposes the reality of conscious experience. In response, the illusionist could suggest that the relevant sort (...) of seeming here is not an experiential state, but is a cognitive state, such as a judgement or a belief, which is fully amenable to a physical or functionalist analysis. Herein, I argue that this response is unsuccessful and fails to undermine the reality of conscious experience. Nonetheless, the response does raise the problem of how a judgement or belief about the character of a conscious experience, even if it is true, can be justified if the conscious experience has no causal role in the formation of the judgement or belief. This is not a new problem, but is a reiteration of an old problem that is known in the philosophy of mind literature as the paradox of phenomenal judgement. I consider how the paradox of phenomenal judgement can be resolved and how the judgement or belief about conscious experience can be justified with appeal to the notion of acquaintance. (shrink)

Most paradoxes of self-reference have a dual or ‘hypodox’. The Liar paradox (Lr = ‘Lr is false’) has the Truth-Teller (Tt = ‘Tt is true’). Russell’s paradox, which involves the set of sets that are not self-membered, has a dual involving the set of sets which are self-membered, etc. It is widely believed that these duals are not paradoxical or at least not as paradoxical as the paradoxes of which they are duals. In this paper, I argue that (...) some paradox’s duals or hypodoxes are as paradoxical as the paradoxes of which they are duals, and that they raise neglected and interestingly different problems. I first focus on Richard’s paradox (arguably the simplest case of a paradoxical dual), showing both that its dual is as paradoxical as Richard’s paradox itself, and that the classical, Richard-Poincaré solution to the latter does not generalize to the former in any obvious way. I then argue that my argument applies mutatis mutandis to other paradoxes of self-reference as well, the dual of the Liar (the Truth-Teller) proving paradoxical. (shrink)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. (...) While there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

This article offers a characterization of what I call multiple-models juxtaposition, a strategy for managing trade-offs among modeling desiderata. MMJ displays models of distinct phenomena to...

The lottery paradox involves a set of judgments that are individually easy, when we think intuitively, but ultimately hard to reconcile with each other, when we think reflectively. Empirical work on the natural representation of probability shows that a range of interestingly different intuitive and reflective processes are deployed when we think about possible outcomes in different contexts. Understanding the shifts in our natural ways of thinking can reduce the sense that the lottery paradox reveals something problematic about (...) our concept of knowledge. However, examining these shifts also raises interesting questions about how we ought to be thinking about possible outcomes in the first place. (shrink)