In this book, best-selling author and mathematician Haim Shapira presents an introduction to mathematical theories which deal with the most beautiful concept ever invented by humankind: infinity. Written in clear, simple language and aimed at a lay audience, this book also offers some strategies that will allow readers to try their ability at solving truly fascinating mathematical problems. Infinity is a deeply counter-intuitive concept that has inspired many great thinkers. In this book we will meet many sages, both (...) familiar and unfamiliar: Zeno and Pythagoras, Georg Cantor and Bertrand Russell, Sofia Kovalevskaya and Emmy Noether, al-Khwarizmi and Euclid, Sophie Germain and Srinivasa Ramanujan. The world of infinity is inhabited by many paradoxes, and so is this book: Zeno paradoxes, Hilbert's "Infinity Hotel", Achilles and the gods paradox, the paradox of heaven and hell, the Ross-Littlewood paradox involving tennis balls, the Galileo paradox and many more. Aimed at the curious but non-technical reader, this book refrains from using any fearsome mathematical symbols. It uses only the most basic operations of mathematics: adding, subtracting, multiplication, division, powers and roots - that is all. But that doesn't mean that a bit of deep thinking won't be necessary and rewarding. Writing with humour and lightness of touch, Haim Shapira banishes the chalky pallor of the schoolroom and offers instead a truly thrilling intellectual journey. Fasten your seatbelt - we are going to Infinity, and beyond! (shrink)

The semantic paradoxes, whose paradigm is the Liar, played a crucial role at a crucial juncture in the development of modern logic. In his 1908 seminal paper, Russell outlined a system, soon to become that of the Principia Mathematicae, whose main goal was the solution of the logical paradoxes, both semantic and settheoretic. Russell did not distinguish between the two and his theory of types was designed to solve both kinds in the same uniform way. Set theoreticians, however, were content (...) to treat only the set-theoretic paradoxes, putting aside the semantic ones as a non-mathematical concern. This separation was explicitly proposed, eighteen years after Russell’s paper, by Ramsey, though he, like Russell, advocated a system that addresses both kinds. Since then, the semantic paradoxes have been viewed within the perspective of the theory of truth, where they have occupied a respectable niche, but one of rather specialized interest. (shrink)

Many philosophers in the field of meta-ethics believe that rational degrees of confidence in moral judgments should have a probabilistic structure, in the same way as do rational degrees of belief. The current paper examines this position, termed “moral Bayesianism,” from an empirical point of view. To this end, we assessed the extent to which degrees of moral judgments obey the third axiom of the probability calculus, ifP(A∩B)=0thenP(A∪B)=P(A)+P(B), known as finite additivity, as compared to degrees of beliefs on the one (...) hand and degrees of desires on the other. Results generally converged to show that degrees of moral judgment are more similar to degrees of belief than to degrees of desire in this respect. This supports the adoption of a Bayesian approach to the study of moral judgments. To further support moral Bayesianism, we also demonstrated its predictive power. Finally, we discuss the relevancy of our results to the meta-ethical debate between moral cognitivists and moral non-cognitivists. (shrink)

This engaging work of comparative philosophy puts the Chinese and American philosophical traditions into a mutually informative and transformative philosophical dialogue on the way to developing a new form of Confucian pragmatism.

"מהדורה מוערת ומבוארת של ספר מגלה טמירין על פי דפוס ראשון, כתבי יד מפוזרים, והשוואה לנוסח הספר ביידיש. לספר נלווה כרך מיוחד של נספחים שנוגעים להתהוות הספר ולתכניו, וכלולים בו דיונים עקרוניים שקשורים לכמה סוגיות שעולות בו: מדרש השמות המוצפנים, מקורותיו החסידיים של המחבר, הנוסחים השונים בכתב-יד, והנוסח המיוחד של הספר ביידיש" -- מעטפת אחורית.

Many aspects relating to the conduct of mediation are left to mediator choice, but mediators often lack adequate guidance on how their discretion ought to be exercised. In this book, Omer Shapira identifies the ethical norms that govern mediators' conduct. Adopting a professional ethics perspective on the basis of role-morality and applying it to a core definition of mediators' role, Shapira argues that all mediators are placed in ethical relationships with mediation parties, the mediation profession, the public, and (...) their employers or principals that produce ethical obligations. (shrink)

The legal system affects behavior not just directly, by imposing sanctions, but also indirectly, by producing information on how people behave. For example, internal company documents exposed during litigation will help third parties assess whether they trust a company and want to keep doing business with it. The law therefore affects behavior by shaping reputations. Drawing on economics, communications, and a nascent multidisciplinary literature on reputation, Roy Shapira highlights how reputation works, and how information from the courtroom affects the (...) court of public opinion, with a particular emphasis on the role of the media. By fleshing out interactions between law and reputation, Shapira corrects common misperceptions about the ability of market forces to discipline corporate behavior and adds to timely, ongoing debates such as the desirability of heightened pleading standards or mandatory arbitration clauses. Law and Reputation should interest any scholar who invokes notions of market discipline in their work. (shrink)

In his classic book “the Foundations of Statistics” Savage developed a formal system of rational decision making. The system is based on (i) a set of possible states of the world, (ii) a set of consequences, (iii) a set of acts, which are functions from states to consequences, and (iv) a preference relation over the acts, which represents the preferences of an idealized rational agent. The goal and the culmination of the enterprise is a representation theorem: Any preference relation that (...) satisfies certain arguably acceptable postulates determines a (finitely additive) probability distribution over the states and a utility assignment to the consequences, such that the preferences among acts are determined by their expected utilities. Additional problematic assumptions are however required in Savage's proofs. First, there is a Boolean algebra of events (sets of states) which determines the richness of the set of acts. The probabilities are assigned to members of this algebra. Savage's proof requires that this be a σ-algebra (i.e., closed under infinite countable unions and intersections), which makes for an extremely rich preference relation. On Savage's view we should not require subjective probabilities to be σ-additive. He therefore finds the insistence on a σ-algebra peculiar and is unhappy with it. But he sees no way of avoiding it. Second, the assignment of utilities requires the constant act assumption: for every consequence there is a constant act, which produces that consequence in every state. This assumption is known to be highly counterintuitive. The present work contains two mathematical results. The first, and the more difficult one, shows that the σ-algebra assumption can be dropped. The second states that, as long as utilities are assigned to finite gambles only, the constant act assumption can be replaced by the more plausible and much weaker assumption that there are at least two non-equivalent constant acts. The second result also employs a novel way of deriving utilities in Savage-style systems -- without appealing to von Neumann-Morgenstern lotteries. The paper discusses the notion of “idealized agent" that underlies Savage's approach, and argues that the simplified system, which is adequate for all the actual purposes for which the system is designed, involves a more realistic notion of an idealized agent. (shrink)

Chinese Philosophy provides a clear, accessible conception of the Chinese philosophical sensibility and its evolution throughout history.

We present experimental evidence that supports the thesis :602–625, 2015, Br J Philos Sci 70:77–102, 2019; Bradley in Decisions theory with a human face, Cambridge University Press, Cambridge, 2017; Goldschmidt and Nissan-Rozen in Synthese 198:7553–7575, 2021) that people might positively or negatively desire risky prospects conditional on only some of the prospects’ outcomes obtaining. We argue that this evidence has important normative implications for the central debate in normative decision theory between two general approaches on how to rationalize several common (...) patterns of preference, which are ruled out as irrational by orthodox decision theory, namely the re-individuation approach and the non-expected utility approach. (shrink)

The War Inside is a groundbreaking history of the contribution of British psychoanalysis to the making of social democracy, childhood, and the family during World War II and the postwar reconstruction. Psychoanalysts informed understandings not only of individuals, but also of broader political questions. By asserting a link between a real 'war outside' and an emotional 'war inside', psychoanalysts contributed to an increased state responsibility for citizens' mental health. They made understanding children and the mother-child relationship key to the successful (...) creation of a democratic citizenry. Using rich archival sources, the book revises the common view of psychoanalysis as an elite discipline by taking it out of the clinic and into the war nursery, the juvenile court, the state welfare committee, and the children's hospital. It traces the work of the second generation of psychoanalysts after Freud in response to total war and explores its broad postwar effects on British society. (shrink)

Karl Popper is one of this century's most influential philosophers, but his life in fin-de siècle and interwar Vienna, and his exile in New Zealand during World War II, have so far remained shrouded in mystery. This intellectual 2001 biography recovers the legacy of the young Popper; the progressive, cosmopolitan, Viennese socialist who combated fascism, revolutionized the philosophy of science, and envisioned the Open Society. Malachi Hacohen delves into his archives and draws a compelling portrait of the philosopher, the assimilated (...) Jewish intelligentsia, and the vanished culture of Red Vienna, which was decimated by Nazism. Hacohen's adventurous biography restores Popper's works to their original Central European contexts and, at the same time, shows that they have urgent messages for contemporary politics and philosophy. (shrink)

The Covid-19 pandemic that entered our lives suddenly in 2020 compelled higher education systems throughout the world to transfer to online learning, including online evaluation. A severe problem of online evaluation is that it enables various technological possibilities that facilitate students' unethical behaviors. The research aimed to investigate these behaviors, as well as the reasons for their appearance, as practiced in exams held for the first time during the Covid-19 pandemic, and to elicit students' and lecturers' perceptions of students' academic (...) dishonesty during this period. The sample included 81 students and 50 lecturers from several Israeli colleges and universities. The findings expand extant knowledge on academic dishonesty, identifying significant differences between the perceptions of students and lecturers concerning attitudes towards online exams and the reasons for dishonest behaviors. The findings among the students also indicate that younger students and Arab students tended to cheat more in online exams. Moreover, the findings indicated a lack of mutual trust between students and lecturers with regard to academic dishonesty, a deep distrust that will probably continue even after the Covid-19 crisis. This last finding should be a cause of concern for higher education policy-makers, affecting future policies for improving lecturer-student relations, especially during crises. Recommendations are proposed for addressing academic dishonesty in exams in general and during the pandemic in particular. (shrink)

本书系作者专心致志撰写22年而成的150余万字的《新伦理学》(商务印书馆2008年修订版)之精粹。它几乎将每个理论问题都化为一个鲜活的人生案例,通过解析各个案例而系统展现伦理学博大精深之原理,因而名之 为《伦理学与人生》。.

From Descartes to Spinoza, Western philosophers have attempted to propose an axiomatic systemization of ethics. However, without consensus on the contents and objects of ethics, the system remains incomplete. This four-volume set presents a model that highlights a Chinese philosopher's insights on ethics after a 22 year study. Three essential components of ethics are examined: metaethics, normative ethics, and virtue ethics. This volume is the second part of the discussion on normative ethics. The author analyzes humanity, liberty, justice, happiness, and (...) systems of moral rules. He puts forward 26 value standards that construct a system of measuring state instruction; reveals the relationship between humanity, liberty and justice; puts forward three objective laws of happiness; and discusses the goodness of important moral rules, such as honesty, self-respect and courage. This set is an essential read for students and scholars of ethics and philosophy in general. (shrink)

This book takes a unique organizational approach towards understanding the concept of ethics in educational systems. It provides a global perspective and connects theory and praxis through team-based simulations, case studies and scenarios, thus presenting an integrative approach towards tackling teachers' withdrawal behaviors.