The Precipice: Existential Risk and the Future of Humanity.Toby Ord -2020 - London: Bloomsbury.detailsHumanity 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)
Beyond Action: Applying Consequentialism to Decision Making and Motivation.Toby Ord -2009 - Dissertation, University of OxforddetailsIt 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)
The many forms of hypercomputation.Toby Ord -178 -Journal of Applied Mathematics and Computation 178:142-153.detailsThis 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.
Hypercomputation: Computing more than the Turing machine.Toby Ord -2002 - Dissertation, University of MelbournedetailsIn 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.
Moral Uncertainty.William MacAskill,Krister Bykvist &Toby Ord -2020 - Oxford University Press.detailsHow 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.
A New Counterexample to Prioritarianism.Toby Ord -2015 -Utilitas 27 (3):298-302.detailsPrioritarianism 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.
The diagonal method and hypercomputation.Toby Ord &Tien D. Kieu -2005 -British Journal for the Philosophy of Science 56 (1):147-156.detailsThe 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)
The scourge: Moral implications of natural embryo loss.Toby Ord -2008 -American Journal of Bioethics 8 (7):12 – 19.detailsIt 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)
How to be a consequentialist about everything.Toby Ord -2008detailsOver the last few decades, there has been an increasing interest in global consequentialism. Where act-consequentialism assesses acts in terms of their consequences, global consequentialism goes much further, assessing acts, rules, motives — and everything else — in terms of the relevant consequences. Compared to act-consequentialism it offers a number of advantages: it is more expressive, it is a simpler theory, and it captures some of the benefits of ruleconsequentialism without the corresponding drawbacks. In this paper, I explore the four (...) different approaches to global consequentialism made by Parfit, Pettit and Smith, Kagan, and Feldman. I break these up into their constituent components, demonstrating the space of possible global consequentialist theories, and I present two new theories within this space. (shrink)
Response to Open Peer Commentaries on “The Scourge: Moral Implications of Natural Embryo Loss”.Toby Ord -2008 -American Journal of Bioethics 8 (7):W1 - W3.detailsMany of the commentaries have made similar points regarding the nature of full moral status, so I shall begin by addressing these together. They argue that my representation of the Claim is stronger than many proponents of full moral status would accept (Ord 2008). Robert Card (2008) says that I assume that it is equally bad to lose human life at all stages. Russell DiSilvestro (2008) says that I assume a flawed principle that he calls (M). Marianne Burda (2008) says (...) that I assume that life must be saved or prolonged at all costs. Christopher Dodsworth and colleagues (2008) say that I assume embryos have as much to lose as adults. I assume none of these things. The argument I put forward works just as well for more subdued claims about the moral status of the embryo. All that is required is to find the badness of embryo death to be at least roughly comparable to the badness of adult death, so that when a proponent of full moral status hears that 30 times more of our moral equals die of spontaneous abortion than die of cancer, their views would require urgent action if such action is possible. The comparison between the badness of adult death and of fetal or embryonic death is made routinely in the literature in support of restrictions upon abortion, in vitro fertilization (IVF) and stem cell research, and it appears to be a mainstream view worthy of serious attention.1 If a large proportion of those who claim that the embryo has full moral status are none-the-less quite sure that each embryo death is much less bad than an adult death, then they owe it to their readers to be more clear about this. Let us now consider the other points of each commentary in turn. (shrink)
Moral Uncertainty About Population Axiology.Hilary Greaves &Toby Ord -2017 -Journal of Ethics and Social Philosophy 12 (2):135-167.detailsGiven the deep disagreement surrounding population axiology, one should remain uncertain about which theory is best. However, this uncertainty need not leave one neutral about which acts are better or worse. We show that, as the number of lives at stake grows, the Expected Moral Value approach to axiological uncertainty systematically pushes one toward choosing the option preferred by the Total View and critical-level views, even if one’s credence in those theories is low.
Consequentialism and Decision Procedures.Toby Ord -2005 - Dissertation, University of OxforddetailsConsequentialism is often charged with being self-defeating, for if a person attempts to apply it, she may quite predictably produce worse outcomes than if she applied some other moral theory. Many consequentialists have replied that this criticism rests on a false assumption, confusing consequentialism’s criterion of the rightness of an act with its position on decision procedures. Consequentialism, on this view, does not dictate that we should be always calculating which of the available acts leads to the most good, but (...) instead advises us to decide what to do in whichever manner it is that will lead to the best outcome. Whilst it is typically afforded only a small note in any text on consequentialism, this reply has deep implications for the practical application of consequentialism, perhaps entailing that a consequentialist should eschew calculation altogether. (shrink)
Exploitation and peacekeeping: introducing more sophisticated interactions to the iterated prisoner's dilemma.Toby Ord &Alan Blair -2002 -World Congress on Computational Intelligence:1-6.details– We present a new paradigm extending the Iterated Prisoner's Dilemma to multiple players. Our model is unique in granting players information about past interactions between all pairs of players – allowing for much more sophisticated social behaviour. We provide an overview of preliminary results and discuss the implications in terms of the evolutionary dynamics of strategies.
Using biased coins as oracles.Toby Ord &Tien D. Kieu -2009 -International Journal of Unconventional Computing 5:253-265.detailsWhile it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more than a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set X may be coded as a probability pX such that if a Turing machine is given a coin which lands heads with probability pX it can compute any function recursive in X with arbitrarily high probability. We also show how (...) the assumption of a non-recursive bias can be weakened by using a.. (shrink)
Play in School – Toward an Ecosystemic Understanding and Perspective.Helle Marie Skovbjerg &Anne-Lene Sand -2022 -Frontiers in Psychology 12.detailsBased on a design-based research project and long-term observations of children’s play in school, this article develops the concept of play order, which points to interaction, coherence and holistic orientation as central values for the approach to play in school. Through concrete empirical analysis, the article shows how play in school is established and maintained, and how school as context interacts with play, which is often in ways that undermine the space and opportunities play is given. Based on existing research, (...) the article is critical of the tendency to accord a secondary role to play in school or to instrumentalize play as a didactic tool for learning. The article links to existing play theory, but at the same time develops the concept of play order, through an ecosystemic understanding, which makes it possible to look holistically at how play in school can be integrated and provided for. Considering that more and more pedagogues are working in schools and directly involved in teaching, and afterschool clubs are increasingly handling schooling tasks, the authors of the article argue that play is worthy of recognition in both practice and theory. (shrink)
Contacts et influences entre Pierre Poiret et les groupes piétistes allemands.Klaus vom Orde -2021 -Revue de Théologie Et de Philosophie 153 (1):67-84.detailsL’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)
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Moral Trade.Toby Ord -2015 -Ethics 126 (1):118-138.detailsIf 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)
Glaube und Skepsis: Beiträge zur Religionsphilosophie Heinz Robert Schlettes.Cornelius Hell,Paul Petzel &Knut Wenzel (eds.) -2011 - Ostfildern: Matthias Grünewald Verlag.detailsHeinz Robert Schlettes skeptische Religionsphilosophie - bereits in ihrer Entstehungszeit quer zum Mainstream - hat in besonders intensiver Weise fundamentale Infragestellungen der Religion durch die Moderne einbezogen. Im Stichwort Empörung hat sie den humanen Gehalt der Religions-kritik aufgenommen - und sowohl religions-philosophisch identifiziert als auch für eine heute noch rechtfertigbare religiöse Haltung reklamiert. Schlettes Ansatz heute in die veränderten Konstellationen einer globalisierten Säkularisierungsdynamik und neuen Religionspräsenz wie eine Sonde einzuführen, verspricht erhellend aufklärerische Wirkung. Dies unternehmen die hier versammelten Beiträge im (...) Spektrum aus Philosophie, Theologie und literarischem Essay. (shrink)
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Ω in number theory.Toby Ord -2007 - In Christian Calude,Randomness & Complexity, from Leibniz to Chaitin. World Scientific Pub Co. pp. 161-173.detailsWe present a new method for expressing Chaitin’s random real, Ω, through Diophantine equations. Where Chaitin’s method causes a particular quantity to express the bits of Ω by fluctuating between finite and infinite values, in our method this quantity is always finite and the bits of Ω are expressed in its fluctuations between odd and even values, allowing for some interesting developments. We then use exponential Diophantine equations to simplify this result and finally show how both methods can also be (...) used to create polynomials which express the bits of Ω in the number of positive values they assume. (shrink)
Probing the improbable: Methodological challenges for risks with low probabilities and high stakes.Toby Ord,Rafaela Hillerbrand &Anders Sandberg -2010 -Journal of Risk Research 13:191-205.detailsSome 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)
Modernity and the Holocaust, or, Listening to Eurydice.Julia Hell -2010 -Theory, Culture and Society 27 (6):125-154.detailsIn this article, I offer a literary-critical reading of Modernity and the Holocaust, arguing that Bauman’s non-Hobbesian ethics is linked to a form of Orphic authorship. I contextualize this reading with a study of three literary authors: W.G. Sebald, Peter Weiss and Janina Bauman, and their respective versions of this post-Holocaust authorship. At stake is the drama of the forbidden gaze, the moment when Orpheus turns to look at Eurydice, killing her a second time. Using Levinas’ ethics and his scenario (...) of recognition, Bauman re-writes this fateful gaze as a loving gaze, implicitly proposing a counter-model to the Schmittian gaze — always ready to recognize the enemy, always ready to kill. (shrink)
The reversal test: Eliminating status quo bias in applied ethics.Nick Bostrom &Toby Ord -2006 -Ethics 116 (4):656-679.detailsSuppose 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)
The social thought of Georg Simmel.Horst JürgenHelle -2015 - Los Angeles: Sage Publications.detailsThis new volume of the SAGE Social Thinkers series, The Social Thought of Georg Simmel provides a concise introduction to the work, life, and influences of Georg Simmel. Horst J.Helle closely examines the writings and ideas of Simmel that introduced a new way of looking at culture and society and helped establish sociology’s place among the academic fields. The book focuses on the key intellectual concerns of Simmel, including the process of individualization, religion, private and family life, cities, (...) and modernization. It is ideal for use as a self-contained volume or in conjunction with other sociological theory books. (shrink)
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Einfluss des G-DRG-Systems auf die rekonstruktive Behandlung des Mundhöhlenkarzinoms: Ethische Implikationen und innermedizinische Rationalität.Berthold Hell,Dominik Groß,Sebastian Schleidgen &Saskia Wilhelmy -2024 -Ethik in der Medizin 37 (1):31-47.detailsBackground The German Diagnosis-Related Groups (G-DRG) system has led to a revenue-orientated hospital financing system. This article examines the ethical implications and consequences of this system using the example of reconstructive measures (defect care) in patients with oral cavity carcinoma. At the same time, the interplay between the G‑DRG system and guideline development must also be scrutinized. This is preceded by introductory information on oral cavity carcinoma and the existing treatment options: conventional reconstruction techniques versus cost-intensive high-end surgery. Methods The (...) case scenario “treatment of medium-sized defects after tumor resection” forms the methodological basis and argumentative reference point of the study. Results and discussion The G‑DRG system and the economic incentives lead to far-reaching ethical implications concerning the demand-orientated treatment of patients and lead to multidimensional interactions. The existing tendency towards high-end surgery harbors the risk of overuse and misuse and, therefore, runs counter to the principles of beneficence and nonmaleficence. The one-sided indication in favor of high-end surgery also suggests that patient information is given in a directive manner (violation of respect for patient autonomy). Moreover, costly high-end procedures counteract the principle of economic efficiency and, thus, touch on issues of distributive justice. Finally, the clinical favoring of high-end procedures also affects logic within medicine, namely the publication landscape (publication bias), the design of the relevant guidelines, and surgical expertise. Conclusions There is a need to raise the awareness of all those working in the field of surgery (surgeons, guideline experts, reviewers). (shrink)
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Datafied knowledge production: Introduction to the special theme.Rasmus Helles,Mikkel Flyverbom &Nanna Bonde Thylstrup -2019 -Big Data and Society 6 (2).detailsFraming datafication as new form of knowledge production has become a trope in both academic and commercial contexts. This special theme examines and ultimately rejects the familiar grand claims of datafication, to instead pay attention to emergent conversations that seek to take a more nuanced stock of the status and nature of datafied knowledge production. The articles in this special theme thus engage with datafied knowledge production through elaborate explorations of how datafied knowledge depends on the contexts of its production (...) and the forms of knowledge production that precede it in those contexts. Our basic argument is that while the resources, material features and analytical operations involved in datafied knowledge production may be different, many fundamental concerns about epistemology, ontology and methods remain relevant to understand what shapes it. We still need to understand and explicate the assumptions, operations and consequences of emergent forms of knowledge production. If datafied knowledge production is neither a clean revolutionary break with past forms of knowledge production nor a balloon of pure hype, the articles in this special theme ask: what does the phenomenon of datafied knowledge production look like? Which digital and datafied infrastructures support its future development? And what potentialities and limits do such forms of analysis and knowledge production contain? (shrink)
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Collective action in watershed management -- experiences from the Andean hillsides.Helle Munk Ravnborg &María del Pilar Guerrero -1999 -Agriculture and Human Values 16 (3):257-266.detailsWatersheds constitute a special case of multiple-use common pool resources (CPRs). In a textual sense, watersheds tend to be mosaics of privately owned and managed patches of land. At the same time, however, watersheds are also ecosystems in which multiple resources and people interact through an infinity of bio-physical processes. Through such interaction, new watershed-level qualities emerge that, together with other factors, condition watershed users' continued resource use and access. In this perspective, watersheds become common-pool resources. Hence, watershed users do (...) not only manage their individual plots, crops, forests, etc., knowingly or not, they manage landscape patterns and bio-physical processes that transcend their private property. In this context, drawing on experiences gained through participatory action research in a micro-watershed in the Andean hillsides of southern Colombia, this paper describes a process aimed at fostering collective watershed management. The paper illustrates the importance of platforms as a mechanism for negotiating and coordinating collective action by multiple users and discusses the issues of representation on such platforms as well as the importance of third party facilitation. (shrink)
Adorno and art: aesthetic theory contra critical theory.James Hellings -2014 - Houndmills, Basingstoke, Hampshire: Palgrave-Macmillan.detailsAnti-introduction: Paint it Black -- PART I: MESSAGES IN A BOTTLE: AESTHETIC THEORY CONTRA CRITICAL THEORY -- 1. Introduction -- 2. Critical Messages in a Bottle and Restoration -- 3. Excursus I: The Prevalence of a View: Being Uncompromisingly Critical at the Grand Hotel Abyss -- 4. Excursus II: The Prevalence of a View: 'Don't participate:' The Politics of Social Praxis -- 5. Aesthetic Messages in a Bottle and Progress -- 6. Messages in a Bottle as the Work of Art (...) -- PART II: ART ITSELF THINKS: THE POLITICS OF AESTHETIC (MIS-)EDUCATION -- 7. Introduction -- 8. The Politics of Artistic Practice: 'What artist isn't socially engaged?' -- 9. The Politics of Spectatorship: Shocking Spectators -- 10. The Politics of Aesthetic (Mis-)Education -- 11. Contemporary Art Itself Thinking: Making the Invisible Visible? -- Anti-conclusion: The Russian Ending. (shrink)
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Why Maximize Expected Choice‐Worthiness?1.William MacAskill &Toby Ord -2018 -Noûs 54 (2):327-353.detailsThis 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)
Felix Kaufmann’s Theory and Method in the Social Sciences.Robert S. Cohen &Ingeborg K. Helling (eds.) -2014 - Cham: Springer.detailsThis volume contains the English translation of Felix Kaufmann's (1895-1945) main work Methodenlehre der Sozialwissenschaften (1936). In this book, Kaufmann develops a general theory of knowledge of the social sciences in his role as a cross-border commuter between Husserl's phenomenology, Kelsen's pure theory of law and the logical positivism of the Vienna Circle. This multilayered inquiry connects the value-oriented reflections of a general philosophy of science with the specificity of the methods and theories of the social sciences, as opposed to (...) abstract natural science and psychology. The core focus of the study is the attempt to elucidate how and under what conditions scientific knowledge about social facts, empirically justified and theoretically embedded, can be obtained. The empirical basis of knowledge within the social sciences forms a phenomenological concept of experience. According to Kaufmann, this concept of experience exhibits a complex structure. Within the meaning-interpretation of human action as the core of knowledge in the social sciences, this structure reaches out across the isolated act of verification toward the synthesis of external and internal experiences. The book opens with a detailed and useful introduction by Ingeborg K. Helling, which introduces the historical and theoretical background of Kaufmann's study and specifically illuminates his relation to Alfred Schütz and John Dewey. Finally, it contains interviews with and letters to members of his family, colleagues and students. (shrink)
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99 Variations on a Proof.Philip Ording -2018 - Princeton: Princeton University Press.detailsAn 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)