We begin with a prepositional languageLpcontaining conjunction (Λ), a class of sentence names {Sα}αϵA, and a falsity predicateF. We (only) allow unrestricted infinite conjunctions, i.e., given any non-empty class of sentence names {Sβ}βϵB,is a well-formed formula (we will useWFFto denote the set of well-formed formulae).The language, as it stands, is unproblematic. Whether various paradoxes are produced depends on which names are assigned to which sentences. What is needed is a denotation function:For example, theLPsentence “F(S1)” (i.e.,Λ{F(S1)}), combined with a denotation functionδsuch (...) thatδ(S1)“F(S1)”, provides the (or, in this context, a)Liar Paradox.To give a more interesting example,Yablo's Paradox[4] can be reconstructed within this framework.Yablo's Paradoxconsists of an ω-sequence of sentences {Sk}kϵωwhere, for eachnϵω:WithinLPan equivalent construction can be obtained using infinite conjunction in place of universal quantification - the sentence names are {Si}iϵωand the denotation function is given by:We can express this in more familiar terms as:etc. (shrink)

Global ignorance about Africa continues to sustain inappropriate global interventions to resolve public health crises, often with disastrous consequences. To explain why this continues to happen, I marshal two theorems that predict basic statistical properties, called ‘the doctrinal paradox’ and ‘the discursive dilemma’, which underlie scientific consensus formation and evidence-based decision making on a global scale. These mathematical results illuminate the epistemic and material injustices committed by the protocols of medical research conducted at the highest level of global knowledge (...) production in the service of international humanitarian aid for Africans. These social choice theorems reveal that a global scientific consensus projecting claims and proposing policies about Africa’s disease burden is likely to yield a low degree of reliability, in that the probability of its accuracy is less than chance. The solution to this anomaly is to remove from the global scientific agenda the statistically unrealisable demand of satisfying too many multinational corporate and foreign governments’ priorities as equally entitled to benefit from the knowledge produced to improve Africa’s public health sector. Instead, foreign funding targeted to support medical science and policy in Africa should be directed by those specialists in situ who are most familiar with their own national health challenges and potential solutions, rather than relying upon foreign decision makers to interpret Africa’s emergency public health care needs. Keywords Doctrinal paradox, discursive dilemma, scientific consensus, epistemic trust, global health ethics, group agency. (shrink)

Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently (...) there is no valid reason not to give preference to the derived accounts over the accounts from which they come. (shrink)

This paper presents a model for the structure of universal frameworks in logic, mathematics, and physics that are closed to logical conclusion by the mechanism of paradox across a dualism of elements. The prohibition takes different forms defined by the framework of observation inherent to the structure. Forms include either prohibition to conclusion on the logical relationship of internal elements or prohibition to conclusion based on the existence of an element not included in the framework of a first element. (...) The model is applied to logical arguments in philosophy, mathematics, and physics and is initially a geometrical analysis of quantum theory and its application in experiment. Conclusion from the analysis is extended to give insight into the complexity of infinities above the two-dimensional boundary of the model. (shrink)

Humberstone has shown that if some set of agents is collectively omniscient (every true proposition is known by at least one agent) then one of them alone must be omniscient. The result is paradoxical as it seems possible for a set of agents to partition resources whereby at the level of the whole community they enjoy eventual omniscience. The Humberstone paradox only requires the assumption that knowledge distributes over conjunction and as such can be viewed as a reductio against (...) the universal validity of that principle. A new route to this paradox is presented which does not require the distribution principle, building on earlier work of Jago and Williamson on Fitch’s paradox. The result relies on an axiom strictly weaker than one necessary for the Jago-Fitch variant. It is shown that the same reasoning behind the variant form of Humberstone’s paradox can recover Bigelow’s results in action theory in a way that is immune to an objection brought against it by Guigon and Humberstone. (shrink)

A probability function is non-conglomerable just in case there is some proposition E and partition \ of the space of possible outcomes such that the probability of E conditional on any member of \ is bounded by two values yet the unconditional probability of E is not bounded by those values. The paradox of non-conglomerability is the counterintuitive—and controversial—claim that a rational agent’s subjective probability function can be non-conglomerable. In this paper, I present a qualitative analogue of the (...) class='Hi'>paradox. I show that, under antecedently plausible assumptions, an analogue of the paradox arises for rational comparative confidence. As I show, the qualitative paradox raises its own distinctive set of philosophical issues. (shrink)

This article seeks to answer why there are two different versions of Meno’s Paradox. I argue that the dilemma contained in Socrates’s version is a pre-existing puzzle, familiar to both Meno and Socrates before their discussion. The two versions of the paradox are thus different because Meno’s version is a mistaken attempt to remember the puzzle contained in Socrates’s version. Although Meno’s version is a mistaken attempt to state Socrates’s version, it is a philosophically richer puzzle that makes (...) three interesting points about inquiry and recognition. After arguing that Socrates’s version is unsound and that Meno’s version is an attempt to recollect or remember it, I analyze Meno’s version in detail. In closing, I consider the relationship between the notion of recognition, which figures prominently in Meno’s version, and the theory of recollection, suggesting that the latter may have arisen as an attempt to explain the origin of moral intuitions. (shrink)

McTaggart’s argument for the unreality of time, first published in 1908, set the agenda for 20th-century philosophy of time. Yet there is very little agreement on what it actually says—nobody agrees with the conclusion, but still everybody finds something important in it. This book presents the first critical overview of the last century of debate on what is popularly called "McTaggart’s Paradox". Scholars have long assumed that McTaggart’s argument stands alone and does not rely on any contentious ontological principles. (...) The author demonstrates that these assumptions are incorrect—McTaggart himself explicitly claimed his argument to be dependent on the ontological principles that form the basis of his idealist metaphysics. The result is that scholars have proceeded to understand the argument on the basis of their own metaphysical assumptions, duly arriving at very different interpretations. This book offers an alternative reading of McTaggart’s argument, and at the same time explains why other commentators arrive at their mutually incompatible interpretations. It will be of interest to students and scholars with an interest in the philosophy of time and other areas of contemporary metaphysics. (shrink)

Paradox Lost covers ten of philosophy’s most fascinating paradoxes, in which seemingly compelling reasoning leads to absurd conclusions. The following paradoxes are included: The Liar Paradox, in which a sentence says of itself that it is false. Is the sentence true or false? The Sorites Paradox, in which we imagine removing grains of sand one at a time from a heap of sand. Is there a particular grain whose removal converts the heap to a non-heap? The Puzzle (...) of the Self-Torturer, in which a series of seemingly rational choices has us accepting a life of excruciating pain, in exchange for millions of dollars. Newcomb’s Problem, in which we seemingly maximize our expected profit by taking an unknown sum of money, rather than taking the same sum plus $1000. The Surprise Quiz Paradox, in which a professor finds that it is impossible to give a surprise quiz on any particular day of the week... but also that if this is so, then a surprise quiz can be given on any day. The Two Envelope Paradox, in which we are asked to choose between two indistinguishable envelopes, and it is seemingly shown that each envelope is preferable to the other. The Ravens Paradox, in which observing a purple shoe provides evidence that all ravens are black. The Shooting Room Paradox, in which a deadly game kills 90% of all who play, yet each individual’s survival turns on the flip of a fair coin. Each paradox is clearly described, common mistakes are explored, and a clear, logical solution offered. Paradox Lost will appeal to professional philosophers, students of philosophy, and all who love intellectual puzzles. (shrink)

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)

Deontological moral theories may forbid a particular action in certain circumstances even though performing it would result in fewer actions of the forbidden type. This is the paradox of deontology, and the first two sections of the essay explicate this paradox and criticize some ways in which deontologists have responded to it. Thereafter, however, I come to the assistance of the deontologist. The third and fourth sections discuss the conditions that must be met before this paradox poses (...) a genuine problem and the likelihood of those conditions being satisfied. Then, with a nod to rule utilitarianism, I show that the deontologist has an important, albeit pragmatic line of rebuttal, which in conjunction with other considerations raised in the essay can assist nonconsequentialists to disarm the paradox of deontology. (shrink)

Whether we're buying a pair of jeans, ordering a cup of coffee, selecting a long-distance carrier, applying to college, choosing a doctor, or setting up a 401(k), everyday decisions ; both big and small ; have become increasingly complex due to the overwhelming abundance of choice with which we are presented. As Americans, we assume that more choice means better options and greater satisfaction. But beware of excessive choice: choice overload can make you question the decisions you make before you (...) even make them, it can set you up for unrealistically high expectations, and it can make you blame yourself for any and all failures. In the long run, this can lead to decision-making paralysis, anxiety, and perpetual stress. And, in a culture that tells us that there is no excuse for falling short of perfection when your options are limitless, too much choice can lead to clinical depression. In The Paradox of Choice, Barry Schwartz explains at what point choice ; the hallmark of individual freedom and self-determination that we so cherish ; becomes detrimental to our psychological and emotional well-being. In accessible, engaging, and anecdotal prose, Schwartz shows how the dramatic explosion in choice ; from the mundane to the profound challenges of balancing career, family, and individual needs ; has paradoxically become a problem instead of a solution. Schwartz also shows how our obsession with choice encourages us to seek that which makes us feel worse. By synthesizing current research in the social sciences, Schwartz makes the counter intuitive case that eliminating choices can greatly reduce the stress, anxiety, and busyness of our lives. He offers eleven practical steps on how to limit choices to a manageable number, have the discipline to focus on those that are important and ignore the rest, and ultimately derive greater satisfaction from the choices you have to make."--provided by publisher. (shrink)

This paper attempts to show that contextualism cannot adequately handle all versions of ‘The Lottery Paradox.” Although the application of contextualist rules is meant to vindicate the intuitive distinction between cases of knowledge and non-knowledge, it fails to do so when applied to certain versions of “The Lottery Paradox.” In making my argument, I first briefly explain why this issue should be of central importance for contextualism. I then review Lewis’ contextualism before offering my argument that the lottery (...) paradox persists on all contextualist accounts. Although I argue that the contextualist does not fare well, hope nevertheless remains. For, on Lewis’ behalf, I offer what I take to be the best solution for the contextualist and argue that once this solution is adopted, contextualism will be in a better position to handle the lottery paradox than any other substantive epistemological theory. (shrink)

Do victims of moral wrongdoing have moral grounds to complain if they have freely committed a similar wrongdoing in the past? This question explores the connection between the moral standing of complainers and their previous deeds. According to Saul Smilansky two equally justifiable competing views create an antinomy with respect to the said question. In this article I present two arguments that attempt to undermine Smilansky's alleged paradox, presenting it as no more than a resolvable moral conflict. My first (...) argument attempts to resolve the conflict in cases where the complaining wrongdoers have already been sanctioned for their past transgression. My second argument challenges the validity of the alleged paradox, based on an alternative explanation of the seemingly paradoxical moral results. (shrink)

A notable feature of paradox is recognition that seemingly contradictory terms are inextricably intertwined and interrelated—holding out the hope that something new can be learned from the cognitive tension contained within. Aram has characterized the central concern of the business and society field as the paradox of interdependent relations. Our study argues that this and related paradoxes can be addressed by engaging with others and trying to gain shared insight via an interactive, developmental, exploratory sensemaking process that can (...) inform the governance of stakeholder networks. We advocate multistakeholder learning dialogues (MSLDs) as a means for both scholars and practitioners to construct meanings that can guide joint efforts to cope with messy problems that help shape complex, paradoxical relationships within stakeholder networks. (shrink)

An argument against Parfit's view (in his chapter of Reasons and Persons on five mistakes in moral mathematics) that, rather than maximizing the difference one makes as an individual, one should join that group whose members together make the most positive difference in cases involving imperceptible benefits. It is shown how Parfit's defence of this view has the problematic implication either (1) that each outcome is less beneficial than itself or (2) that "less beneficial than" is not transitive.

Questioning reality -- The hair of the dog -- Good/bad -- Resistance and the side effect -- Putting resistance on the couch -- Modern medicine : a health report -- Psychotherapeutic paradox -- Loops -- Dialectics -- Paradox within the home -- The staying-with-it principle -- Immunization and immunotherapy -- A little poison is good for you -- The strange obsession of Dr. Hahnemann -- From gods to genes -- RPM -- Such stuff as dreams -- The attack (...) of the evil things -- Becoming well. (shrink)

This paper resolves a paradox concerning colour constancy. On the one hand, our intuitive, pre-theoretical concept holds that colour constancy involves invariance in the perceived colours of surfaces under changes in illumination. On the other, there is a robust scientific consensus that colour constancy can persist in cerebral achromatopsia, a profound impairment in the ability to perceive colours. The first stage of the solution advocates pluralism about our colour constancy capacities. The second details the close relationship between colour constancy (...) and contrast. The third argues that achromatopsics retain a basic type of colour constancy associated with invariants in contrast processing. The fourth suggests that one person-level, conscious upshot of such processing is the visual awareness of chromatic contrasts ‘at’ the edges of surfaces, implicating the ‘colour for form’ perceptual function. This primitive type of constancy sheds new light on our most basic perceptual capacities, which mark the lower borders of representational mind. (shrink)

The doctrine that whatever could exist does exist leads to a proliferation of possibly concrete objects given certain principles of recombination. If, for example, there could have been a large infinite number of concrete objects, then there is at least the same number of possibly concrete objects in existence. And further cardinality considerations point to a tension between the preceding doctrine and the Cantorian conception of the absolutely infinite. This paper develops a parallel problem for a variety of possible worlds (...) accounts of modality which eschew the commitment to a plethora of possibly concrete objects. Moreover, the difficulty is importantly different from more familiar threats of paradox exemplified by certain descendants of Russell's paradox of propositions and Kaplan's paradox. (shrink)

In approaching Ch. 4 of Saving Truth from Paradox, it might be helpful first to revisit Curry’s original paper, and to revisit Lukasiewicz too, to provide more of the scenesetting that Field doesn’t himself fill in. So in §1 I’ll say something about Curry, in §2 we’ll look at what Lukasiewicz was up to in his original three-valued logic, and in §3 we’ll look at the move from a three-valued to a many-valued Lukasiewicz logic. In §4, I move on (...) to announce a theorem by H´. (shrink)

It is raining but you don’t believe that it is raining. Imagine silently accepting this claim. Then you believe both that it is raining and that you don’t believe that it is raining. This would be an ‘absurd’ thing to believe,yet what you believe might be true. Itmight be raining, while at the same time, you are completely ignorant of the state of the weather. But how can it be absurd of you to believe something about yourself that might be (...) true of you? This is Moore’s paradox as it occurs in thought. Solving the paradox consists in explaining why such beliefs are absurd. I give a survey of some of the main explanations. I largely deal with explanations of the absurdity of ‘omissive’ beliefs with contents of the form p & I don’t believe that p and of ‘commissive beliefs’ with contents of the form p & I believe that not-p as well as beliefs with contents of the form p & I don’t know that p. (shrink)

The concept of medical necessity is often used to explain or justify certain decisions—for example, which treatments should be allowed under certain conditions—as though it had an obvious, agreed-upon meaning as well as an inherent normative force. In introducing this special issue of Clinical Ethics on medical necessity, we argue that the term, as used in various discourses, generally lacks a definition that is clear, non-circular, conceptually plausible, and fit for purpose. We propose that future work on this concept should (...) address three main questions: what medical necessity is (i.e., what makes something medically necessary, as opposed to something else); what the concept does (what ‘work’ is it doing when invoked in different settings); and what should follow, normatively, from the fact that something is indeed medically necessary (on some plausible conception). (shrink)

Resolving Bertrand’s probability paradox.

Roy T Cook examines the Yablo paradox--a paradoxical, infinite sequence of sentences, each of which entails the falsity of all others that follow it. He focuses on questions of characterization, circularity, and generalizability, and pays special attention to the idea that it provides us with a semantic paradox that involves no circularity.

Modern epistemology has run into several paradoxes in its efforts to explain how knowledge acquisition can be both socially based and still able to determine objective facts about the world. In this important book, Richmond Campbell attempts to dispel some of these paradoxes, to show how they are ultimately just "illusions of paradox," by developing ideas central to two of the most promising currents in epistemology: feminist epistemology and naturalized epistemology. Campbell's aim is to construct a coherent theory of (...) knowing that is feminist and "naturalized." Illusions of Paradox will be valuable for students and scholars of epistemology and women's studies. (shrink)

Sometimes people desire that their lives go badly, take pleasure in their lives going badly, or believe that their lives are going badly. As a result, some popular theories of welfare are paradoxical. I show that no attempt to defend those theories from the paradox fully succeeds.

Classical particles of the same kind are distinguishable: they can be labeled by their positions and follow different trajectories. This distinguishability affects the number of ways W a macrostate can be realized on the micro-level, and via S=k ln W this leads to a non-extensive expression for the entropy. This result is generally considered wrong because of its inconsistency with thermodynamics. It is sometimes concluded from this inconsistency, notoriously illustrated by the Gibbs paradox, that identical particles must be treated (...) as indistinguishable after all; and even that quantum mechanics is indispensable for making sense of this. In this article we argue, by contrast, that the classical statistics of distinguishable particles and the resulting non-extensive entropy function are perfectly all-right both from a theoretical and an experimental perspective. We remove the inconsistency with thermodynamics by pointing out that the entropy concept in statistical mechanics is not completely identical to the thermodynamical one. Finally, we observe that even identical quantum particles are in some cases distinguishable; and conclude that quantum mechanics is irrelevant to the Gibbs paradox. (shrink)

Bodily pain strikes many philosophers as deeply paradoxical. The issue is that pains seem to bear both physical characteristics, such as a location in the body, and mental characteristics, such being mind-dependent. In this paper I clarify and address this alleged paradox of pain. I begin by showing how a further assumption, Objectivism, the thesis that what one feels in one’s body when one is in pain is something mind-independent, is necessary for the generation of the paradox. Consequently, (...) the paradox can be avoided if one rejects this idea. However, doing so raises its own difficulties, for it is not obvious how anything can possess all of the features we typically associate with bodily pain. To address this puzzle and finally put the paradox of pain to rest, I develop the Embodied View, a novel metaphysical account on which pains are constitutively mind-dependent features of parts of a subject’s body. (shrink)