Accelerating Turing machines have attracted much attention in the last decade or so. They have been described as “the work-horse of hypercomputation” (Potgieter and Rosinger 2010: 853). But do they really compute beyond the “Turing limit”—e.g., compute the halting function? We argue that the answer depends on what you mean by an accelerating Turing machine, on what you mean by computation, and even on what you mean by a Turing machine. We show first that in the current literature the term (...) “accelerating Turing machine” is used to refer to two very different species of accelerating machine, which we call end-stage-in and end-stage-out machines, respectively. We argue that end-stage-in accelerating machines are not Turing machines at all. We then present two differing conceptions of computation, the internal and the external, and introduce the notion of an epistemic embedding of a computation. We argue that no accelerating Turing machine computes the halting function in the internal sense. Finally, we distinguish between two very different conceptions of the Turing machine, the purist conception and the realist conception; and we argue that Turing himself was no subscriber to the purist conception. We conclude that under the realist conception, but not under the purist conception, an accelerating Turing machine is able to compute the halting function in the external sense. We adopt a relatively informal approach throughout, since we take the key issues to be philosophical rather than mathematical. (shrink)

This paper extends a stochastic theory for buffer fill distribution for multiple “on‘ and “off‘ sources to a mobile environment. Queue fill distribution is described by a set of differential equations assuming sources alternate asynchronously between exponentially distributed periods in “on‘ and “off‘ states. This paper includes the probabilities that mobile sources have links to a given queue. The sources represent mobile user nodes, and the queue represents the capacity of a switch. This paper presents a method of analysis which (...) uses mobile parameters such as speed, call rates per unit area, cell area, and call duration and determines queue fill distribution at the ATM cell level. The analytic results are compared with simulation results. (shrink)

Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly (...) addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary. (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.

With the advent of modern technology, the way society handles and performs monetary transactions has changed tremendously. The world is moving swiftly towards the digital arena. The use of Automated Teller Machine cards has led to a “cash-less society” and has fostered digital payments and purchases. In addition to this, the trust and reliance of the society upon these small pieces of plastic, having numbers engraved upon them, has increased immensely over the last two decades. In the past few years, (...) the number of ATM fraud cases has increased exponentially. With the money of the people shifting towards the digital platform, ATM skimming has become a problem that has eventually led to a global outcry. The present review discusses the serious repercussions of ATM card cloning and the associated privacy, ethical and legal concerns. The preventive measures which need to be taken and adopted by the government authorities to mitigate the problem have also been discussed. (shrink)

The author believes that large‐scale rationality on the part of the interpretant is essential to his interpretability, and therefore, in his view, to her having a mind. How, then are cases of irrationality, such as akrasia or self‐deception, judged by the interpretant's own standards, possible? He proposes that, in order to resolve the apparent paradoxes, one must distinguish between accepting a contradictory proposition and accepting separately each of two contradictory propositions, which are held apart, which in turn requires to conceive (...) of the mind as containing a number of semi‐independent structures of interlocking beliefs, desires, emotions, memories, and other mental states. (shrink)

I argue that on very weak assumptions about truth (in particular, that there are coherent norms governing the use of "true"), there is a proposition absolutely inexpressible with conventional language, or something very close. I argue for this claim "constructively": I use a variant of the Berry Paradox to reveal a particular thought for my readership to entertain that very strongly resists conventional expression. I gauge the severity of this expressive limitation within a taxonomy of expressive failures, and argue (...) that despite its strength there is nothing incoherent about admitting its existence. The argument forms part of a project of clarifying precisely what trade-offs are required to secure the kinds of expressive power truth theorists typically want, in the process showing that the admission of very strong expressive limitations may ultimately prove to be the lesser of two evils. (shrink)

By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.

A commitment to truth requires that you are open to receiving new evidence, even if that evidence contradicts your current beliefs. You should be open to changing your mind. However, this truism gives rise to the paradox of empathy. The paradox arises with the possibility of mental corruption through transformative change, and has consequences for how we should understand tolerance, disagreement, and the ability to have an open mind. I close with a discussion of how understanding this (...) class='Hi'>paradox provides a new explanation for a certain kind of standoff between the believer and the skeptic with regard to religious belief. (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)

Paradoxes are arguments that lead from apparently true premises, via apparently uncontroversial reasoning, to a false or even contradictory conclusion. Paradoxes threaten our basic understanding of central concepts such as space, time, motion, infinity, truth, knowledge, and belief. In this volume Roy T Cook provides a sophisticated, yet accessible and entertaining, introduction to the study of paradoxes, one that includes a detailed examination of a wide variety of paradoxes. The book is organized around four important types of paradox: the (...) semantic paradoxes involving truth, the set-theoretic paradoxes involving arbitrary collections of objects, the Soritical paradoxes involving vague concepts, and the epistemic paradoxes involving knowledge and belief. In each of these cases, Cook frames the discussion in terms of four different approaches one might take towards solving such paradoxes. Each chapter concludes with a number of exercises that illustrate the philosophical arguments and logical concepts involved in the paradoxes. _Paradoxes_ is the ideal introduction to the topic and will be a valuable resource for scholars and students in a wide variety of disciplines who wish to understand the important role that paradoxes have played, and continue to play, in contemporary philosophy. (shrink)

This book will examine paradoxes in diverse areas of thought: philosophy, mathematics, physics, economics, political science, psychology, computer science, logic, statistics, linguistics, law, etc. Though the treatment of each paradox is rigorous, the book will be written accessibly with a lighthearted and humorous tone so as to keep the reader engaged. Each chapter will focus on a single paradox, structured roughly like so: 1. A question is asked in the context of a story. As an answer, the (...) class='Hi'>paradox is presented (which often results in an aha moment). The historical background of the paradox is recounted. 2. The dénouement explains how the paradox is resolved or why there is no resolution. 3. The chapter ends with further remarks, usually contemporary real-world examples or applications of said paradox. Some examples of the paradoxes covered are the Axiom of Choice (Mathematics), Monty Hall Problem (Statistics), Morgenbesser's Paradox (Linguistics), Tea Leaves Paradox (Physics), The Ultimatum Game (Economics), and The Chicken or Egg Question (Evolution). (shrink)

Paradoxes are poems of science and philosophy that collectively allow us to address broad multidisciplinary issues within a microcosm. A true paradox is a source of creativity and a concise expression that delivers a profound idea and provokes a wild and endless imagination. The study of paradoxes leads to ultimate clarity and, at the same time, indisputably challenges your mind. Paradoxes in Scientific Inference analyzes paradoxes from many different perspectives: statistics, mathematics, philosophy, science, artificial intelligence, and more. The book (...) elaborates on findings and reaches new and exciting conclusions. It challenges your knowledge, intuition, and conventional wisdom, compelling you to adjust your way of thinking. Ultimately, you will learn effective scientific inference through studying the paradoxes. (shrink)

Ataxia‐telangiectasia (A‐T) is a pleiotropic recessive disorder characterized cerebellar ataxia, immunodeficiency, specific developmental defects, profound predisposition to cancer and acute radiosensitivity. Functional inactivation of single gene product, ATM, accounts for this compound phenotype. We suggest that ATM acts as a sensor of reactive oxygen species and/or oxidative damage cellular macromolecules, including DNA. In turn, ATM induces signalling through multiple pathways, thereby coordinating acute phase stress responses with cell cycle checkpoint control and repair of oxidative damage. Absence of ATM is proposed (...) to limit the repair of insidious oxidative damage that can occur under normal physiological conditions, ultimately leading to apoptosis of particularly sensitive cells, such as neurons and thymocytes. (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)

The Paradox of Intellectual Property in Capitalism is an innovative book that comprehensively discusses and analyses intellectual property under capitalistic social conditions and relations. It not only addresses some historical developments of intellectual property but also brings to the fore the very notion of what knowledge is, knowledge creation, and knowledge production and appropriation within a Marxist framework. Nonetheless, the adopted approach pays heed to multiple fields of knowledge, providing rich discussions that facilitate the understanding of actual social totality (...) in which capitalism, knowledge production and appropriation, and the struggles of appropriation mutually reinforce each other, although not devoid of antagonisms and contradictions. In light of contemporary capitalism, the transformations that social property relations are undergoing must be scrutinised – such as those brought about by the development of digitalisation and the convergence between big pharma and tech giants. What are the conditions of intellectual property creation today? What theoretical assumptions does it make? Under what social relations is intellectual property produced? Throughout, the emphasis is not on individual cases or symptoms but on the overarching logic: the logic of capitalism as revealed in intellectual property. (shrink)

What is a paradox? -- Knowing and believing -- Vagueness and identity -- Logic and truth -- Mathematical paradoxes -- Probability paradoxes -- Space and time -- Impossibilities -- Deciding and acting -- Index of philosophers.

Dans un langage accessible, 150 notions sont ici élucidées par l'épreuve de leur propre paradoxe. D'Absolu à Volonté, en passant par Conscience et Tabou, Plaisir et Droit, Cosmos et Substance, ce dictionnaire offre une introduction inédite à la philosophie et un remarquable approfondissement de son exercice."--Back cover.

The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to (...) argue against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. The result has also been used to draw more general lessons about the limits of human knowledge. Still others have taken the proof to be fallacious, since it collapses an apparently moderate brand of anti-realism into an obviously implausible and naive idealism. (shrink)

In the early modern period, ignorance was commonly perceived as a sin, a flaw, a defect, and even a threat to religion and the social order. Yet praises of ignorance were also expressed in the same context. Reclaiming the long-lasting legacy of medieval doctrines of ignorance and taking a comparative perspective, Sandrine Parageau tells the history of the apparently counter-intuitive moral, cognitive and epistemological virtues attributed to ignorance in the long seventeenth century (1580s-1700) in England and in France. With close (...) textual analysis of hitherto neglected sources and a reassessment of canonical philosophical works by Montaigne, Bacon, Descartes, Locke, and others, Parageau specifically examines the role of ignorance in the production of knowledge, identifying three common virtues of ignorance as a mode of wisdom, a principle of knowledge, and an epistemological instrument, in philosophical and theological works. How could an essentially negative notion be turned into something profitable and even desirable? Taken in the context of Renaissance humanism, the Reformation and the "Scientific Revolution" - which all called for a redefinition and reaffirmation of knowledge - ignorance, Parageau finds, was not dismissed in the early modern quest for renewed ways of thinking and knowing. On the contrary, it was assimilated into the philosophical and scientific discourses of the time. The rehabilitation of ignorance emerged as a paradoxical cornerstone of the nascent modern science. (shrink)

This book unites the worlds of physics and depth psychology through analysis of carefully selected existing and new dream materials. Their interpretation by Matthews provides fertile ground for the unifying of the extreme opposites of psyche and matter and forms a continuation of the deep dialogue between acclaimed psychologist Carl Jung and Nobel physicist Wolfgang Pauli. What emerges is an individuation process where inner and outer worlds are intertwined through a succession of dream images, culminating with that of the ring (...) i, the mathematical function at the heart of quantum physics. This mysterious function unites wave and particle and symbolically carries the quality of paradox. The occurrence of the ring i in Pauli's and the author's dreams suggests paradox is a necessary psychological state to experience a living union between psyche and matter. Analysis of accompanying materials further indicates the arising of a new world view where inner and outer, mind and matter, may again be seen as a unified whole. This book is an engaging read for academics and researchers in the field of Jungian psychology and will appeal to those interested in the novel application of quantum physics to philosophy, psychology and spirituality. (shrink)

Modern societies depend on a growing production of scientific knowledge, which is based on the functional differentiation of science into still more specialised scientific disciplines and subdisciplines. This is the basis for the paradox of scientific expertise: The growth of science leads to a fragmentation of scientific expertise. To resolve this paradox, the present paper investigates three hypotheses: 1) All scientific knowledge is perspectival. 2) The perspectival structure of science leads to specific forms of knowledge asymmetries. 3) Such (...) perspectival knowledge asymmetries must be handled through second order perspectives. We substantiate these hypotheses on the basis of a perspectivist philosophy of science grounded in Peircean semiotics and autopoietic systems theory. Perspectival knowledge asymmetries are an unavoidable and necessary part of the growth of scientific knowledge, and more awareness of this fact can help avoid blind and futile struggles between scientific perspectives, and direct efforts toward more appropriate ways of handling these fundamental knowledge asymmetries. Concretely, we show how different kinds of scientific knowledge, expertise, disagreement and learning can be correlated to the perspectival structure of science, and propose how polyocular communication based on observations of the observations made by specialised perspectives can be used to handle such perspectival knowledge asymmetries. This can help overcome the observed problems in carrying out cross-disciplinary research and in the collective use of different kinds of scientific expertise, and thereby make society better able to solve complex, real-world problems. (shrink)

For centuries, the Sorites Paradox has spurred philosophers to think and argue about the problem of vagueness. This volume offers a guide to the paradox which is both an accessible survey and an exposition of the state of the art, with a chapter-by-chapter presentation of all of the main solutions to the paradox and of all its main areas of influence. Each chapter offers a gentle introduction to its topic, gradually building up to a final discussion of (...) some open problems. Students will find a comprehensive guide to the fundamentals of the paradox, together with lucid explanations of the challenges it continues to raise. Researchers will find exciting new ideas and debates on the paradox. (shrink)

A paradox can be defined as an unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Many paradoxes raise serious philosophical problems, and they are associated with crises of thought and revolutionary advances. The expanded and revised third edition of this intriguing book considers a range of knotty paradoxes including Zeno's paradoxical claim that the runner can never overtake the tortoise, a new chapter on paradoxes about morals, paradoxes about belief, and hardest of all, paradoxes about truth. (...) The discussion uses a minimum of technicality but also grapples with complicated and difficult considerations, and is accompanied by helpful questions designed to engage the reader with the arguments. The result is not only an explanation of paradoxes but also an excellent introduction to philosophical thinking. (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.

This discusses the kind of paradox that has since become known as "the forced march sorites", here called "the transition question". The question is whether this is really a new kind of paradox, or the familiar sorites in unfamiliar garb. The author argues that resources adequate to deal with ordinary sorites are sufficient to deal with the transition question, and tentatively proposes an affirmative answer.

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)

This chapter contains sections titled: Appendix: Analysis of the Wind‐Powered Boat.

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)

_Paradoxes from A to Z, Third edition_ is the essential guide to paradoxes, and takes the reader on a lively tour of puzzles that have taxed thinkers from Zeno to Galileo, and Lewis Carroll to Bertrand Russell. Michael Clark uncovers an array of conundrums, such as Achilles and the Tortoise, Theseus’ Ship, and the Prisoner’s Dilemma, taking in subjects as diverse as knowledge, science, art and politics. Clark discusses each paradox in non-technical terms, considering its significance and looking at (...) likely solutions. This third edition is revised throughout, and adds nine new paradoxes that have important bearings in areas such as law, logic, ethics and probability. Paradoxes from A to Z, Third edition is an ideal starting point for those interested not just in philosophical puzzles and conundrums, but anyone seeking to hone their thinking skills. (shrink)

The Paradox of Transgression in Games looks at transgressive games as an aesthetic experience, tackling how players respond to game content that shocks, disturbs, and distresses, and how contemporary video games can evoke intense emotional reactions. The book delves into the commercial success of many controversial videogames: although such games may appear shocking for the observing bystander, playing them is experienced as deeply rewarding for the player. Drawing on qualitative player studies and approaches from media aesthetics theory, the book (...) challenges the perception of games as innocent entertainment, and examines the range of emotional, moral, and intellectual experiences of players. As they explore what players consider transgressive, the authors ask whether there is something about the gameplay situation that works to mitigate the sense of transgression, stressing gameplay as an aesthetic experience. Anchoring the aesthetic game experience both in play studies as well as in aesthetic theory, this book will be an essential resource for scholars and students of game studies, aesthetics, media studies, philosophy of art, and emotions. (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)

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The (...) view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (shrink)

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The (...) view that a statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (shrink)