An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature (...) and practice of mathematics. Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau’s Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor. Readers will gain not only a bird’s-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape. (shrink)

Humanity stands at a precipice. -/- Our species could survive for millions of generations — enough time to end disease, poverty, and injustice; to reach new heights of flourishing. But this vast future is at risk. With the advent of nuclear weapons, humanity entered a new age, gaining the power to destroy ourselves, without the wisdom to ensure we won’t. Since then, these dangers have only multiplied, from climate change to engineered pandemics and unaligned artificial intelligence. If we do not (...) act fast to reach a place of safety, it may soon be too late. -/- The Precipice explores the science behind the risks we face. It puts them in the context of the greater story of humanity: showing how ending these risks is among the most pressing moral issues of our time. And it points the way forward, to the actions and strategies we can take today to safeguard humanity’s future. (shrink)

Instead of conceiving ethical commands as divine revelations or as the discoveries of brilliant thinkers, we should see our ethical practices as evolving over tens of thousands of years, as members of our species have worked out how to live together and prosper. Here, Kitcher elaborates his radical vision of this millennia-long ethical project.

How should we make decisions when we're uncertain about what we ought, morally, to do? Decision-making in the face of fundamental moral uncertainty is underexplored terrain: MacAskill, Bykvist, and Ord argue that there are distinctive norms by which it is governed, and which depend on the nature of one's moral beliefs.

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...

Introductory Chapter to the _Cambridge Handbook of Situated Cognition_ (CUP, 2009).

An esteemed philosopher discusses his theory of universal freedom, describing how even those who are members of free societies may find their liberties curtailed and includes tests of freedom including the eyeball test and the tough-luck test.

It is often claimed that from the moment of conception embryos have the same moral status as adult humans. This claim plays a central role in many arguments against abortion, in vitro fertilization, and stem cell research. In what follows, I show that this claim leads directly to an unexpected and unwelcome conclusion: that natural embryo loss is one of the greatest problems of our time and that we must do almost everything in our power to prevent it. I examine (...) the responses available to those who hold that embryos have full moral status and conclude that they cannot avoid the force of this argument without giving up this key claim. (shrink)

A person presented with adequate but not conclusive evidence for a proposition is in a position voluntarily to acquire a belief in that proposition, or to suspend judgment about it. The availability of doxastic options in such cases grounds a moderate form of doxastic voluntarism not based on practical motives, and therefore distinct from pragmatism. In such cases, belief-acquisition or suspension of judgment meets standard conditions on willing: it can express stable character traits of the agent, it can be responsive (...) to reasons, and it is compatible with a subjective awareness of the available options. (shrink)

In “Scientific Knowledge,” Philip Kitcher challenges arguments that deny the truth of the theoretical claims of science, and he attempts to discover reasons for endorsing the truth of such claims. He suggests that the discovery of such reasons might succeed if we ask why anyone thinks that the theoretical claims we accept are true and then look for answers that reconstruct actual belief‐generating processes. To this end, Kitcher presents the “homely argument” for scientific truth, which claims that when a (...) field of science is continually applied to yield precise predictions, then it is at least approximately true. He defends this approach and offers a supplementary account that gives more attention to detail. This account includes a historical aspect that must answer to skeptical challenges and a social aspect. (shrink)

Suppose that we develop a medically safe and affordable means of enhancing human intelligence. For concreteness, we shall assume that the technology is genetic engineering (either somatic or germ line), although the argument we will present does not depend on the technological implementation. For simplicity, we shall speak of enhancing “intelligence” or “cognitive capacity,” but we do not presuppose that intelligence is best conceived of as a unitary attribute. Our considerations could be applied to specific cognitive abilities such as verbal (...) fluency, memory, abstract reasoning, social intelligence, spatial cognition, numerical ability, or musical talent. It will emerge that the form of argument that we use can be applied much more generally to help assess other kinds of enhancement technologies as well as other kinds of reform. However, to give a detailed illustration of how the argument form works, we will focus on the prospect of cognitive enhancement. (shrink)

It is common to allocate scarce health care resources by maximizing QALYs per dollar. This approach has been attacked by disability-rights advocates, policy-makers, and ethicists on the grounds that it unjustly discriminates against the disabled. The main complaint is that the QALY-maximizing approach implies a seemingly unsatisfactory conclusion: other things being equal, we should direct life-saving treatment to the healthy rather than the disabled. This argument pays insufficient attention to the downsides of the potential alternatives. We show that this sort (...) of discrimination is one of four unpalatable consequences that any approach to priority setting in health care must face. We argue that, given the alternatives, it is far from clear that we should revise the QALY-maximizing approach in response to this objection. (shrink)

This paper argues in favor of a particular account of decision‐making under normative uncertainty: that, when it is possible to do so, one should maximize expected choice‐worthiness. Though this position has been often suggested in the literature and is often taken to be the ‘default’ view, it has so far received little in the way of positive argument in its favor. After dealing with some preliminaries and giving the basic motivation for taking normative uncertainty into account in our decision‐making, we (...) consider and provide new arguments against two rival accounts that have been offered—the accounts that we call ‘My Favorite Theory’ and ‘My Favorite Option’. We then give a novel argument for comparativism—the view that, under normative uncertainty, one should take into account both probabilities of different theories and magnitudes of choice‐worthiness. Finally, we further argue in favor of maximizing expected choice‐worthiness and consider and respond to five objections. (shrink)

Research on personality psychology is making important contributions to psychological science and applied psychology. This second edition of The Cambridge Handbook of Personality Psychology offers a one-stop resource for scientific personality psychology. It summarizes cutting-edge personality research in all its forms, including genetics, psychometrics, social-cognitive psychology, and real-world expressions, with informative and lively chapters that also highlight some areas of controversy. The team of renowned international authors, led by two esteemed editors, ensures a wide range of theoretical perspectives. Each research (...) area is discussed in terms of scientific foundations, main theories and findings, and future directions for research. The handbook also features advances in technology, such as molecular genetics and functional neuroimaging, as well as contemporary statistical approaches. An invaluable aid to understanding the central role played by personality in psychology, it will appeal to students, researchers, and practitioners in psychology, behavioral neuroscience, and the social sciences. (shrink)

In this chapter, we consider ethical and philosophical aspects of trust in the practice of medicine. We focus on trust within the patient-physician relationship, trust and professionalism, and trust in Western (allopathic) institutions of medicine and medical research. Philosophical approaches to trust contain important insights into medicine as an ethical and social practice. In what follows we explain several philosophical approaches and discuss their strengths and weaknesses in this context. We also highlight some relevant empirical work in the section on (...) trust in the institutions of medicine. It is hoped that the approaches discussed here can be extended to nursing and other topics in the philosophy of medicine. (shrink)

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

Examines what is necessary for a group to constitute an agent that can display akrasia, and what steps such a group might take to establish self‐control. The topic has some interest in itself, and the discussion suggests some lessons about how we should think of akrasia in the individual as well as in the collective case. Under the image that the lessons support, akrasia is a sort of constitutional disorder: a failure to achieve a unity projected in the avowal of (...) agency. This image fits well with the constitutional model of the soul in Plato's Republic. (shrink)

Some recent accounts of testimonial warrant base it on trust, and claim that doing so helps explain asymmetries between the intended recipient of testimony and other non-intended hearers, e.g. differences in their entitlement to challenge the speaker or to rebuke the speaker for lying. In this explanation ‘dependence-responsiveness’ is invoked as an essential feature of trust: the trustor believes the trustee to be motivationally responsive to the fact that the trustor is relying on the trustee. I argue that dependence-responsiveness is (...) not essential to trust and that the asymmetries, where genuine, can be better explained without reference to trust. (shrink)

There has recently been a revival of interest in panpsychism as a theory of consciousness. The hope of the contemporary proponents of panpsychism is that the view enables us to integrate consciousness into our overall theory of reality in a way that avoids the deep difficulties that plague the more conventional options of physicalism on the one hand and dualism on the other. However, panpsychism comes in two forms — strong and weak emergentist — and there are arguments that seem (...) to show that weak emergentist panpsychism faces problems analogous to those of physicalism whilst strong emergentist panpsychism faces problems analogous to those of dualism. In this paper, I will develop a new hybrid of the strong and weak emergentist forms of panpsychism, a view according to which subjects of experience are strongly emergent but their phenomenal properties are weakly emergent. I will argue that this hybrid view manages to avoid the challenges facing both physicalism and dualism, and the analogues of those challenges that seem to undermine standard forms of panpsychism. (shrink)

This chapter outlines three programs that aim to use biological insights in support of philosophical positions in ethics: Aristotelian approaches found, for example, in Thomas Hurka and Philippa Foot; Humean approaches found in Simon Blackburn and Allan Gibbard; and biologically grounded approaches found in of Elliott Sober and Brian Skyrms. The first two approaches begin with a philosophical view, and seek support for it in biology. The third approach begins with biology, and uses it to illuminate the status of morality. (...) This chapter pursues a version of the third program. A major accomplishment of evolutionary biology has been the explanation of biological altruism, which opens the door to a similar explanation of psychological altruism, or “fellow-feeling.” The chapter conjectures that humans have evolved a capacity for normative governance by socially shared rules. A process of cultural evolution led to the social rules with which we are familiar. This genealogical story poses a challenge, for the idea of moral truth plays no role in it. The story therefore lends support to non-cognitivism or anti-realist expressivism. The chapter concludes by exploring the implications of the genealogical story for moral knowledge, moral objectivity, and the idea of moral authority. (shrink)

Prioritarianism is the moral view that a fixed improvement in someone's well-being matters more the worse off they are. Its supporters argue that it best captures our intuitions about unequal distributions of well-being. I show that prioritarianism sometimes recommends acts that will make things more unequal while simultaneously lowering the total well-being and making things worse for everyone ex ante. Intuitively, there is little to recommend such acts and I take this to be a serious counterexample for prioritarianism.

Trust should be able to explain cooperation, and its failure should help explain the emergence of cooperation-enabling institutions. This proposed methodological constraint on theorizing about trust, when satisfied, can then be used to differentiate theories of trust with some being able to explain cooperation more generally and effectively than others. Unrestricted views of trust, which take trust to be no more than the disposition to rely on others, fare well compared to restrictive views, which require the trusting person to have (...) some further attitude in addition to this disposition. The same methodological constraint also favours some restrictive views over others. (shrink)

This chapter defends a divine command theory consisting of two central claims. First, a kind of action is morally obligatory just in case God has commanded that actions of that kind be performed. Second, God’s commanding that a kind of action be performed is what makes it obligatory. God’s commands bring it about that the wrong actions are wrong, and the required actions are required. Moreover, God’s goodness ensures that His commands are not arbitrary. God is the standard of Goodness. (...) Something is good just in case it resembles God in a relevant way. Since God resembles Himself, He is good, and His commands are suited to ground moral obligations. Deontic or duty-related properties depend on God’s commands, but axiological or evaluative properties, such as goodness, do not. (shrink)

In this report I provide an introduction to the burgeoning field of hypercomputation – the study of machines that can compute more than Turing machines. I take an extensive survey of many of the key concepts in the field, tying together the disparate ideas and presenting them in a structure which allows comparisons of the many approaches and results. To this I add several new results and draw out some interesting consequences of hypercomputation for several different disciplines.

L’influence de Pierre Poiret sur le milieu piétiste en Allemagne est très hétérogène. Il a lui-même découvert les idées d’Antoinette Bourignon à Francfort et s’est chargé de diffuser ses enseignements à travers les groupes piétistes, notamment les « piétistes radicaux ». Les idées millénaristes de J. W. et J. E. Petersen sont assez comparables à celles de Poiret. La Kirchen- und Ketzerhistorie de G. Arnold a mieux fait connaître l’importance de Poiret à propos du franchissement des frontières entre les confessions (...) religieuses. Les piétistes du Wurtemberg comme J. A. Bengel et Chr. F. Oetinger ont été influencés par le projet théologique de Poiret tel qu’il est esquissé dans l’Œconomie divine. Dans l’orphelinat de Halle, les écrits de Poiret sont publiés par A. H. Francke et A. W. Böhme. En même temps, Poiret est fortement critiqué par Ph. J. Spener, J. W. Jäger et J. Lange. Il fait enfin connaître la piété mystique par les biographies de plusieurs auteurs mystiques de la fin du Moyen Âge. Via G. Tersteegen, ces biographies sont mieux connues en Allemagne. Les dirigeants du mouvement de réveil (catholique) de l’Allgäu (début du XIXe siècle) ainsi que Hedwig von Redern, écrivain de la Gemeinschaftsbewegung (fin du XIXe siècle) ont repris ces biographies mystiques dans leur enseignement de la vie pieuse. (shrink)

If people have different resources, tastes, or needs, they may be able to exchange goods or services such that they each feel they have been made better off. This is trade. If people have different moral views, then there is another type of trade that is possible: they can exchange goods or services such that both parties feel that the world is a better place or that their moral obligations are better satisfied. We can call this moral trade. I introduce (...) the idea of moral trade and explore several important theoretical and practical implications. (shrink)

This is a book about the aesthetics of wonder, about wonder as it figures in our relation to the visual world and to rare or new experiences.

This paper surveys a wide range of proposed hypermachines, examining the resources that they require and the capabilities that they possess. 2005 Elsevier Inc. All rights reserved.

This article draws on the antebellum political thought of Black abolitionists Frederick Douglass and Martin Delany in critically assessing the efficacy of reasonableness in advancing the aims of emancipatory politics in political discourse. I argue, through a reading of Douglass and Delany, that comporting oneself reasonably in the face of oppressive ideology can be counterproductive, if one’s aim is to undermine such ideology and the institutions it supports. Douglass and Delany, I argue, also provide us with a framework for evaluating (...) alternative discursive strategies we might wish to employ in light of the limited value of reasonableness for emancipatory politics. (shrink)

Some risks have extremely high stakes. For example, a worldwide pandemic or asteroid impact could potentially kill more than a billion people. Comfortingly, scientific calculations often put very low probabilities on the occurrence of such catastrophes. In this paper, we argue that there are important new methodological problems which arise when assessing global catastrophic risks and we focus on a problem regarding probability estimation. When an expert provides a calculation of the probability of an outcome, they are really providing the (...) probability of the outcome occurring, given that their argument is watertight. However, their argument may fail for a number of reasons such as a flaw in the underlying theory, a flaw in the modeling of the problem, or a mistake in the calculations. If the probability estimate given by an argument is dwarfed by the chance that the argument itself is flawed, then the estimate is suspect. We develop this idea formally, explaining how it differs from the related distinctions of model and parameter uncertainty. Using the risk estimates from the Large Hadron Collider as a test case, we show how serious the problem can be when it comes to catastrophic risks and how best to address it. (shrink)

The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes either contradiction or arbitrariness in other theoretical models of computation which claim to be able to solve the halting problem for Turing machines. We show that such arguments are flawed—a contradiction only occurs if a type of machine can compute its own diagonal function. We then demonstrate why such a situation (...) does not occur for the methods of hypercomputation under attack, and why it is unlikely to occur for any other serious methods. Introduction Issues with specific hypermachines Conclusions for hypercomputation. (shrink)

It is often said that there are three great traditions of normative ethics: consequentialism, deontology and virtue ethics. Each is based around a compelling intuition about the nature of ethics: that what is ultimately important is that we produce the best possible outcome, that ethics is a system of rules which govern our behaviour, and that ethics is about living a life that instantiates the virtues, such as honesty, compassion and loyalty. This essay is about how best to interpret consequentialism. (...) I show that if we take consequentialism beyond the assessment of acts, using a consequentialist criterion to assess decision making, motivation, and character, then the resulting theory can also capture many of the intuitions about systems of moral rules and excellences of character that lead people to deontology and virtue ethics. I begin by considering the argument that consequentialism is self-defeating because its adoption would produce bad outcomes. I take up the response offered by the classical utilitarians: when properly construed, consequentialism does not require us to make our decisions by a form of naïve calculation, or to be motivated purely by universal benevolence. Instead it requires us to use the decision procedure that will produce the best outcome and to have the motives that lead to the best outcome. I take this idea as my starting point, and spend the thesis developing it and considering its implications. I demonstrate that neither act-consequentialism nor rule-consequentialism has the resources to adequately assess decision making and motivation. I therefore turn to the idea of global consequentialism, which assesses everything in terms of its consequences. I then spend the greater part of the essay exploring how best to set up such a theory and how best to apply it to decision making and motivation. I overcome some important objections to the approach, and conclude by showing how the resulting approach to consequentialism helps to bridge the divide between the three traditions. (shrink)

Both accessible and definitive, Deleuze and Guattari provides a critical examination of the writing of two notoriously difficult thinkers. This important introduction is divided into three sections--knowledge, power, and desire--and provides a systematic account of the intellectual context as well as an exhaustive analysis of the key themes informing Deleuze and Guattari's work. Providing a framework for reading the important and influential study Capitalism and Schizophrenia, this volume is attentive to the needs of the student by providing a lexicon of (...) the difficult ideas used in Deleuze and Guattari's discussion of philosophy, art, and politics. Deleuze and Guattari is an important addition to the critical literature on some of the most challenging work in recent social theory. It will be the standard introduction to Deleuze and Guattari for students of philosophy and social theory. (shrink)

The _Platform Sutra_ records the teachings of Hui-neng, the Sixth Patriarch, who is revered as one of the two great figures in the founding of Ch'an (Zen) Buddhism. This translation is the definitive English version of the eighth-century Ch'an classic. Phillip B. Yampolsky has based his translation on the Tun-huang manuscript, the earliest extant version of the work. A critical edition of the Chinese text is given at the end of the volume. Dr. Yampolsky also furnishes a lengthy and detailed (...) historical introduction which contains much information hitherto unavailable even to scholars, and provides the context essential to an understanding of Hui-neng's work. He gives an account of the history and legends of Ch'an Buddhism, with particular attention to the traditions associated with Hui-neng, quoting or summarizing the most important narratives. He then discusses the various texts of the _Platform Sutra_, and analyzes its contents. (shrink)

In “Epistemology in Philosophy of Religion,” Philip Quinn focuses on the central problem of religious epistemology for monotheistic religions: the epistemic status of belief in the existence of God. He explores what epistemic conditions arguments for God's existence would have to satisfy to be successful and whether any arguments satisfy those conditions. Turning to the claims of reformed epistemology about belief in God, Quinn assesses Alvin Plantinga's claim that belief in God is for many theists properly basic, that is, (...) has positive epistemic status even when it is not based on arguments or any other kind of propositional evidence. Quinn distinguishes two versions of this claim. According to the first, emphasized in Plantinga's earlier work, theistic belief is properly basic with respect to justification or rationality, while according to the second version, prominent in Plantinga's more recent work, theistic belief is properly basic with respect to warrant. (shrink)

How Galileo created the problem of consciousness -- Is there a ghost in the machine? -- Can physical science explain consciousness? -- How to solve the problem of consciousness -- Consciousness and the meaning of life.

Strong claims have been made for emergence as a new paradigm for understanding science, consciousness, and religion. Tracing the past history and current definitions of the concept, Clayton assesses the case for emergent phenomena in the natural world and their significance for philosophy and theology. Complex emergent phenomena require irreducible levels of explanation in physics, chemistry and biology. This pattern of emergence suggests a new approach to the problem of consciousness, which is neither reducible to brain states nor proof of (...) a mental substance or soul. Although emergence does not entail classical theism, it is compatible with a variety of religious positions. Clayton concludes with a defence of emergentist panentheism and a Christian constructive theology consistent with the new sciences of emergence. (shrink)

_Time_ offers a comprehensive history of the philosophy of time in western philosophy from the Greeks through to the twentieth century. In the first half of the book, Philip Turetzky explores theories in ancient and modern philosophy chronologically: from Aristotle to Nietzsche. In the latter half, Turetzky describes the philosophy of time in three twentieth-century philosophical traditions: * analytic philosophy including philosophers such as McTaggart and Mellor * phenomenology Husserl and Heidegger * a distaff tradition which Turetzky identifies as (...) including Bergson and Deleuze. (shrink)

Experiments in particle physics have hitherto failed to produce any significant evidence for the many explicit models of physics beyond the Standard Model (BSM) that had been proposed over the past decades. As a result, physicists have increasingly turned to model-independent strategies as tools in searching for a wide range of possible BSM effects. In this paper, we describe the Standard Model Effective Field Theory (SM-EFT) and analyse it in the context of the philosophical discussions about models, theories, and (bottom-up) (...) effective field theories. We find that while the SM-EFT is a quantum field theory, assisting experimentalists in searching for deviations from the SM, in its general form it lacks some of the characteristic features of models. Those features only come into play if put in by hand or prompted by empirical evidence for deviations. Employing different philosophical approaches to models, we argue that the case study suggests not to take a view on models that is overly permissive because it blurs the lines between the different stages of the SM-EFT research strategies and glosses over particle physicists' motivations for undertaking this bottom-up approach in the first place. Looking at EFTs from the perspective of modelling does not require taking a stance on some specific brand of realism or taking sides in the debate between reduction and emergence into which EFTs have recently been embedded. (shrink)

There are a number of assumptions made in our accepted psychology of moral decision-making that consequentialism seems to violate:: value connectionism, pluralism and dispositionalism. But consequentialism violates them only on a utilitarian or similar theory of value, not on the rival sort of theory that is sketched here.