An engaging and accessible introduction to mathematical proof incorporating ideas from real analysis A mathematical proof is an inferential argument for a mathematical statement. Since the time of the ancient Greek mathematicians, the proof has been a cornerstone of the science of mathematics. The goal of this book is to help students learn to follow and understand the function and structure of mathematical proof and to produce proofs of their own. An Introduction to Proof through Real Analysis is based on (...) course material developed and refined over thirty years by Professor Daniel J. Madden and was designed to function as a complete text for both first proofs and first analysis courses. Written in an engaging and accessible narrative style, this book systematically covers the basic techniques of proof writing, beginning with real numbers and progressing to logic, set theory, topology, and continuity. The book proceeds from natural numbers to rational numbers in a familiar way, and justifies the need for a rigorous definition of real numbers. The mathematical climax of the story it tells is the Intermediate Value Theorem, which justifies the notion that the real numbers are sufficient for solving all geometric problems. • Concentrates solely on designing proofs by placing instruction on proof writing on top of discussions of specific mathematical subjects • Departs from traditional guides to proofs by incorporating elements of both real analysis and algebraic representation • Written in an engaging narrative style to tell the story of proof and its meaning, function, and construction • Uses a particular mathematical idea as the focus of each type of proof presented • Developed from material that has been class-tested and fine-tuned over thirty years in university introductory courses An Introduction to Proof through Real Analysis is the ideal introductory text to proofs for second and third-year undergraduate mathematics students, especially those who have completed a calculus sequence, students learning real analysis for the first time, and those learning proofs for the first time. Daniel J. Madden, PhD, is an Associate Professor of Mathematics at The University of Arizona, Tucson, Arizona, USA. He has taught a junior level course introducing students to the idea of a rigorous proof based on real analysis almost every semester since 1990. Dr. Madden is the winner of the 2015 Southwest Section of the Mathematical Association of America Distinguished Teacher Award. Jason A. Aubrey, PhD, is Assistant Professor of Mathematics and Director, Mathematics Center of the University of Arizona. (shrink)

Epistemic consequentialists think that epistemic norms are about believing the truth and avoiding error. Recently, a number of authors have rejected epistemic consequentialism on the basis that it incorrectly sanctions tradeoffs of epistemic goodness. Here, I argue that epistemic consequentialists should borrow two lessons from ethical consequentialists to respond to these worries. Epistemic consequentialists should construe their view as an account of right belief, which they distinguish from other notions like rational and justified belief. Epistemic consequentialists should also make their (...) view ‘sophisticated,’ in the sense of Railton. Epistemic consequentialism, I conclude, is best construed as sharing much of its structure with prominent act-consequentialist views in ethics. Epistemic consequentialism has an advantage over its ethical counterpart though: the key claim of the view is practically universally accepted, which gives us an additional reason to think it’s true. (shrink)

A number of formal models, including a highly influential model from Hong and Page, purport to show that functionally diverse groups often beat groups of individually high-performing agents in solving problems. Thompson argues that in Hong and Page’s model, that the diverse groups are created by a random process explains their success, not the diversity. Here, I defend the diversity interpretation of the Hong and Page result. The failure of Thompson’s argument shows that to understand the value of functional diversity, (...) we should be clearer about how we conceive of and measure that diversity. (shrink)

People often fail to detect large changes to scenes, provided that the changes occur during a visual disruption. This phenomenon, known as ''change blindness,'' occurs both in the laboratory and in real-world situations in which changes occur unexpectedly. The pervasiveness of the inability to detect changes is consistent with the theoretical notion that we internally represent relatively little information from our visual world from one glance at a scene to the next. However, evidence for change blindness does not necessarily imply (...) the absence of such a representation-people could also miss changes if they fail to compare an existing representation of the pre-change scene to the post-change scene. In three experiments, we show that people often do have a representation of some aspects of the pre-change scene even when they fail to report the change. And, in fact, they appear to ''discover'' this memory and can explicitly report details of a changed object in response to probing questions. The results of these real-world change detection studies are discussed in the context of broader claims about change blindness. (shrink)

The ultimate goal of the pioneering project outlined in this book is to map our genome--the key to what makes us human--in detail. The Code of Codes is a collective exploration of the substance and possible consequences of th is project in relation to ethics, law, and society.

Sex differences in mortality rates stem from genetic, physiological, behavioral, and social causes that are best understood when integrated in an evolutionary life history framework. This paper investigates the Male-to-Female Mortality Ratio (M:F MR) from external and internal causes and across contexts to illustrate how sex differences shaped by sexual selection interact with the environment to yield a pattern with some consistency, but also with expected variations due to socioeconomic and other factors.

Standard approaches to defining and evaluating environmental risk tend to reflect technocratic rather than democratic values. One consequence is that institutional mechanisms for achieving citizen participation in risk decisions rarely are studied or evaluated. This article presents a survey of five institutional mechanisms for allowing the lay public to influence environmental risk decisions: public hearings, initiatives, public surveys, negotiated rule making, and citizens review panels. It also defines democratic process criteria for assessing these and other participatory mechanisms.

“Practice” has become a ubiquitous term in the history of science, and yet historians have not always reflected on its philosophical import and especially on its potential connections with ethics. In this essay, we draw on the work of the virtue ethicist Alasdair MacIntyre to develop a theory of “communal practices” and explore how such an approach can inform the history of science, including allegations about the corruption of science by wealth or power; consideration of scientific ethics or “moral economies”; (...) the role of values in science; the ethical distinctiveness of scientific vocations; and the relationship between history of science and the practice of science itself. (shrink)

Due to the state of globalized clinical research, questions have been raised as to what, if any, benefits those who contribute to research should receive. One model for compensating research participants is “benefit sharing,” and the basic premise is that, as a matter of justice, those who contribute to scientific research should share in its benefits. While incorporated into several international documents for over two decades, benefit sharing has only been sparsely implemented. This analysis begins by addressing the concept of (...) benefit sharing, its historical development, and how it has been applied in the context of virus sharing for influenza research. The second portion of this analysis presents recommendations for ensuring benefit sharing. These recommendations are threefold: 1) an emphasis on social pressure, 2) the revision of international documents as means to ensure benefit sharing, and 3) greater collaboration between sponsor IRB and host country IRB. Because clinical research is a globalized industry, a global model will be proposed in the second that focuses on collaboration between the sponsor and host country. This collaboration is vital in order to ensure that proper forms of benefit sharing are accomplished as a matter of justice. (shrink)

This meticulously researched study is based on a comprehensive reading of all the major Jewish sources from the Geonic period in the ninth century until the dawn of the Haskalah in the late eighteenth century. Its clearly written and carefully documented exposition of the philosophical arguments used by Jews to refute four central doctrines of Christianity (trinity, incarnation, transubstantiation, and virgin birth) makes a major contribution to a relatively neglected area of medieval Jewish intellectual history.

Some concepts relating to learned, structured functioning of local modules in neocortex are clarified in order to ensure that the integration from the small scale to the global attempted by Wright & Liley does not miss the target.

In this book Daly attempts to forge a new ethical approach to issues of social structures, an area of thought deficient in traditional Catholic ethics. Daly argues that the concept of the structures of virtue and vice provide the best ethical lens with which to scrutinize the effects of social structures on personal character and the well-being of the community. His argument relies on two premises: First, he considers the nexus between structures and individual moral agency - arguing that Catholic (...) ethics has failed to account for these realities adequately. The second premise concerns virtue theory, once again emphasizing the importance of accounting for the individual when approaching societal ethics. With the establishment of these premises, Daly furthers the book's ultimate goal: the development of ethical concepts capable of scrutinizing social structures regarding how they shape personal moral character, as well as how they causally impact the well-being of people and groups. Drawing on the works of Thomas Aquinas as well as social theories such as critical realism, Daly fills a lacuna in Catholic ethics that addresses the structure-agency problem that has plagued this field of study. (shrink)

Law and the legal system through which law is effected are very powerful, yet the power of the law has always been limited by the laws of nature, upon which the law has now direct grip. Human law now faces an unprecedented challenge, the emergence of a second limit on its grip, a new “species” of intelligent agents (AI machines) that can perform cognitive tasks that until recently only humans could. What happens, as a matter of law, when another species (...) interacts with us, can be integrated into human minds and bodies, makes “real-world” decisions—not through human proxies, but directly—and does all this “intelligently”, with what one could call autonomous agency or even a “mind” of its own? The article starts from the clear premise that control cannot be exercised directly on AI machines through human law. That control can only be effected through laws that apply to humans. This has several regulatory implications. The article’s first discusses what, in any attempt to regulate AI machines, the law can achieve. Having identified what the law can do, the article then canvases what the law should aim to achieve overall. The article encapsulate its analysis in a list of both doctrinal and normative principles that should underpin any regulation aimed at AI machines. Finally, the article compares three transnational options to implement the proposed regulatory approach. (shrink)

According to inferential role semantics, for any given expression to possess a particular meaning one must be disposed to make or, alternatively, acknowledge as correct certain inferential transitions involving it. As Williamson points out, pejoratives such as ‘Boche’ seem to provide a counter-example to IRS. Many speakers are neither disposed to use such expressions nor consider it proper to do so. But it does not follow, as IRS appears to entail, that such speakers do not understand pejoratives or that they (...) lack meaning. In this paper, I examine recent responses to this problem by Boghossian and Brandom and argue that their proposed construal of the kind of inferential rules governing a pejorative such as ‘Boche’ is to be ruled out on the grounds that it is non-conservative. I defend the appeal to conservatism in this instance against criticism and, in doing so, propose an alternative approach to pejoratives on behalf of IRS that resolves the problem Williamson poses. (shrink)

The author, a health insurance industry leader and a prominent voice in the national reform debate, shares his perspective on attempts to transform health care over nearly a decade. He advocates for a bipartisan solution to stabilize the health insurance market in the near term, and for private sector innovation in partnership with government to create sustainable long-term change. He encourages ASLME members to continue to lend their expertise to the process of transformation.

Research over the past half century has produced extensive evidence that observers cannot report or retain all of the details of their visual world from one moment to the next. During the past decade, a new set of studies has illustrated just how pervasive these limits are. For example, early evidence for the failure to detect changes to simple dot patterns (Phillips, 1974) and arrays of letters (Pashler, 1988) generalizes to more naturalistic displays such as photographs and motion pictures (e.g., (...) Levin & Simons, 1997; Rensink, O’Regan, & Clark, 1997; see Rensink, 2002 for a recent review). This failure to report changes (change blindness) can be induced in both simple and naturalistic displays, whenever the change co-occurs with a visual disruption such as an eye movement (Currie, McConkie, Carlson-Radvansky, & Irwin, 1995; Hollingworth, Schrock, & Henderson, 2001), image shift (Blackmore, Brelstaff, Nelson, & Troscianko, 1995), flashed blank screen (Rensink et al., 1997), blink (O’Regan, Deubel, Clark, & Rensink, 2000), transient (O’Regan, Rensink, & Clark, 1999; Rensink, O’Regan, & Clark, 2000), movie cut or pan (Levin & Simons, 1997; Simons, 1996), or an occlusion event (Levin, Simons, Angelone, & Chabris, 2002; Simons & Levin, 1998). Change blindness can also occur in the absence of a disruption, provided the change occurs gradually enough that it does not attract attention (Simons, Franconeri, & Reimer, 2000). -/- Failures of visual awareness have been induced in a number of ways. For example, observers often fail to report a visible but unexpected stimulus when attention is focused on some other object or event in the display (inattentional blindness). As for change blindness, inattentional blindness occurs for both simple (Mack & Rock, 1998; Most et al., 2001) and naturalistic stimuli (Simons & Chabris, 1999). Similarly, repeated instances of an item often go undetected when embedded in a rapid sequence (repetition blindness), a phenomenon that occurs for both words and pictures (Kanwisher, 1987; Kanwisher & Potter, 1990). Observers can also fail to detect a stimulus in a rapid stream of stimuli provided they had to perform an attention-demanding task shortly before the stimulus appeared (Shapiro, Arnell, & Raymond, 1997). The surprisingly large variety of conditions that induce failures of conscious perception reinforces the broad conclusion that we are often unaware of what would otherwise be fully-visible stimuli. -/- Along with an increased appreciation of the limitations of visual awareness has come a renewed interest in using these limitations to explore the nature of the representations and processes underlying our visual experience. Are these limitations due to failures of perception? Of attention? Of memory? What is preserved with and without awareness? -/- The papers in this special issue of the Journal of Vision provide examples of exciting new work on induced failures of visual awareness and the mechanisms that underlie them. For example, several papers examine whether observers are drawn to parts of a display by the stimulus features or whether top-down control or semantic comprehension influence search through a display. Others investigate the nature of and limits on the information that is preserved from one view to the next and how much information needs to be retained for effective perception and action. As guest editors, we hope that this special issue will illustrate how studying the relationship between visual awareness and visual representations can lead to important new insights into the nature of seeing. (shrink)

Medieval scholastics share a commitment to a substance-accident ontology and to an analysis of efficient causation in which agents act in virtue of their powers. Given these commitments, it seems ready-made which entities are the agents or powers: substances are agents and their accidents powers. William of Ockham, however, offers a rather different analysis concerning material substances and their essential powers, which this article explores. The article first examines Ockham’s account of propria and his reasons for claiming that a material (...) substance is essentially powerful sine accidentibus. However, the article subsequently argues that, given Ockham’s reductionism about material substance, only substantial forms – never substances – are truly agents and powers. Thus, a material substance is essentially powerful but only by courtesy – per accidens, as Ockham calls it – because it has a non-identical part, its substantial form, which does all the causal work by itself, per se. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Christian Naturalism: Christian Thinking for Living in This World Only by Karl E. PetersDaniel J. OttChristian Naturalism: Christian Thinking for Living in This World Only. Karl E. Peters. Boston: Wipf & Stock, 2022. xvi + 152 pp. $25.00 paperback; $22.00 eBook; $40.00 hardcover.The number of scholars who would call themselves Christian naturalists and the number of books that think through what it means to be both Christian and (...) naturalist are quite small. Karl E. Peters has been an outstanding figure in this small group for many years. He is a leader in the science and religion dialogue in the United States and has been thinking theologically for a long time about what it means to be a Christian in an age of science. For these reasons, I was eager to read Peters’s Christian Naturalism as it promised to be a concise and systematic summary of his thinking about Christian Naturalist theology. What I found was a book that may have its uses but is not always successful in both its approach and its argumentation.Peters states in the Introduction that the book is “intentionally written for a general audience” (xi), and he maintains an accessible style and vocabulary throughout. Often, the book has an autobiographical quality as Peters weaves in reflection on his own educational journey in both science and theology. Chapters 1 and 3 helpfully lay out a brief comparison of ancient cosmologies and a contemporary scientific cosmology. Chapter 3 is a good example of some of the interesting heuristics that Peters uses throughout as he tells the story of the beginnings of the universe and the emergence of life on Earth in a first-person narrative. The rest of the book proceeds in brief and accessible treatments of categories one would typically find in theology primers: God, Jesus, evil and sin, salvation, ethics, and after death. The remainder of this review will take up two of these categories: 1) evil, sin, and ethics and 2) after death. The former will serve as an example of the book’s relative weaknesses and the latter as an example of the book’s promise and usefulness.“Human Evil,” chapter 4, begins promisingly. Peters builds on an earlier introduction to the idea that we can associate “God” with the creative processes at work in the universe or with creativity itself. Here, Peters argues that being faithful to creativity becomes the norm for Christian faith and morality. “So, being moral means sustaining the well-being of already created dynamic systems and at the same time being open to creativity (God) and the emergence of new systems” (42). Perhaps these arguments would be better positioned at the [End Page 97] beginning of a chapter on morality and ethics rather than the chapter on evil and sin, though, especially since the corollary definition of sin doesn’t come for another twenty-four pages. There, Peters explains that “sin (the Christian term for human evil) is the attempt to limit the work of creativity (God) and to limit what is included in the family of life that arises from the work of creativity (God)” (66). These two definitions taken together offer one of the most theologically pregnant ideas in the book. Unfortunately, they are not pursued and applied in a systematic way throughout the remainder of this chapter and into chapters 7 and 8 on ethics and Christian practice. What we get, instead, is a collection of reflections on various ethical topics including: racism, xenophobia, sexism, and climate change.Perhaps if these sections were retitled “Karl’s Reflections on Wrestling with White, Male Privilege,” the reader would have the right expectation and their usefulness would reemerge. But as they stand they often lose the thread of their connections to his theological definitions and sometimes slip into problematic assumptions. The latter is exhibited when Peters employs the first-person again, this time in reference to certain social histories, as when “you and I” migrated from north Africa to the Caucasus Mountains (47), or when “you and I arrived in America from England in 1630” (58). The assumed “you” seems to be white, male people of anglo origin and therefore cuts... (shrink)

Addresses perceived irresolvable paradoxes regarding reality as presented by a number of philosophers.

In public health, the issue of pharmaceutical pricing is a perennial problem. Recent high-profile examples, such as the September 2015 debacle involving Martin Shkreli and Turing Pharmaceuticals, are indicative of larger, systemic difficulties that plague the pharmaceutical industry in regards to drug pricing and the impact it yields on their reputation in the eyes of the public. For public health ethics, the issue of pharmaceutical pricing is rather crucial. Simply, individuals within a population require pharmaceuticals for disease prevention and management. (...) In order to be effective, these pharmaceuticals must be accessibly priced. This analysis will explore the notion of corporate social responsibility in regards to pharmaceutical pricing with an aim of restoring a positive reputation upon the pharmaceutical industry in the public eye. The analysis will utilize the 2005 United Nations Educational, Scientific, and Cultural Organization’s Universal Declaration on Bioethics and Human Rights to establish implications regarding the societal responsibilities of pharmaceutical companies in a global context. To accomplish this, Article 14 of the UDBHR—social responsibility and health—will be articulated in order to advocate a viewpoint of socially responsible capitalism in which pharmaceutical companies continue as profit-making ventures, yet establish moral concern for the welfare of all their stakeholders, including the healthcare consumer. (shrink)

Building on a number of recent studies that have turned to Hobbes in light of covid-19, I explore the context of Hobbes’ own encounters with plague while at Oxford, along with efforts to mitigate plague by the regime of James I. I then explore what role his encounters with plague may have played as he wrote his philosophical masterpiece, Leviathan.

ABSTRACTRecent rejections of epistemic consequentialism, like those from Firth, Jenkins, Berker, and Greaves, have argued that consequentialism is committed to objectionable trade-offs and suggest...