The most important questions in life are questions about what we should do and what we should believe. The first kind of question has received considerable attention by normative ethicists, who search for a complete systematic account of right action. This book is about the second kind of question. Right Belief and True Belief starts by defining a new field of inquiry named 'normative epistemology' that mirrors normative ethics in searching for a systematic account of right belief. The book then (...) lays out and defends a deeply truth-centric account of right belief called `truth-loving epistemic consequentialism.' Truth-loving epistemic consequentialists say that what we should believe (and what credences we should have) can be understood in terms of what conduces to us having the most accurate beliefs (credences). The view straight-forwardly vindicates the popular intuition that epistemic norms are about getting true beliefs and avoiding false beliefs, and it coheres well with how scientists, engineers, and statisticians think about what we should believe. Many epistemologists have rejected similar views in response to several persuasive objections, most famously including trade-off and counting-blades-of-grass objections. Right Belief and True Belief shows how a simple truth-based consequentialist account of epistemic norms can avoid these objections and argues that truth-loving epistemic consequentialism can undergird a general truth-centric approach to many questions in epistemology. (shrink)

Public discussions of political and social issues are often characterized by deep and persistent polarization. In social psychology, it’s standard to treat belief polarization as the product of epistemic irrationality. In contrast, we argue that the persistent disagreement that grounds political and social polarization can be produced by epistemically rational agents, when those agents have limited cognitive resources. Using an agent-based model of group deliberation, we show that groups of deliberating agents using coherence-based strategies for managing their limited resources tend (...) to polarize into different subgroups. We argue that using that strategy is epistemically rational for limited agents. So even though group polarization looks like it must be the product of human irrationality, polarization can be the result of fully rational deliberation with natural human limitations. (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)

The standard view says that epistemic normativity is normativity of belief. If you’re an evidentialist, for example, you’ll think that all epistemic reasons are reasons to believe what your evidence supports. Here we present a line of argument that pushes back against this standard view. If the argument is right, there are epistemic reasons for things other than belief. The argument starts with evidentialist commitments and proceeds by a series of cases, each containing a reason. As the cases progress, the (...) reasons change from counting in favor of things like having a belief to things like performing ordinary actions. We argue that each of those reasons is epistemic. If the argument succeeds, we should think there are epistemic reasons to consider hypotheses, conduct thought and physical experiments, extend one’s evidence, and perform mundane tasks like eating a sandwich, just as there are epistemic reasons to believe what one’s evidence supports. (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)

The is-ought gap is Hume’s claim that we can’t get an ‘ought’ from just ‘is’s. Prior (“The Autonomy of Ethics,” 1960) showed that its most straightforward formulation, a staple of introductory philosophy classes, fails. Many authors attempt to resurrect the claim by restricting its domain syntactically or by reformulating it in terms of models of deontic logic. Those attempts prove to be complex, incomplete, or incorrect. I provide a simple reformulation of the is-ought gap that closely fits Hume’s description of (...) it. My formulation of the gap avoids the proposed counterexamples from Prior and offers a natural explanation of why they seem compelling. Moreover, I show that my formulation of the gap is guaranteed by standard theories of the semantics of normative terms, and that provides a more general reason to accept it. (shrink)

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...

The Hong and Page ‘diversity trumps ability’ result has been used to argue for the more general claim that a diverse set of agents is epistemically superior to a comparable group of experts. Here we extend Hong and Page’s model to landscapes of different degrees of randomness and demonstrate the sensitivity of the ‘diversity trumps ability’ result. This analysis offers a more nuanced picture of how diversity, ability, and expertise may relate. Although models of this sort can indeed be suggestive (...) for diversity policies, we advise against interpreting such results overly broadly. (shrink)

We motivate a picture of social epistemology that sees forgetting as subject to epistemic evaluation. Using computer simulations of a simple agent-based model, we show that how agents forget can have as large an impact on group epistemic outcomes as how they share information. But, how we forget, unlike how we form beliefs, isn’t typically taken to be the sort of thing that can be epistemically rational or justified. We consider what we take to be the most promising argument for (...) this claim and find it lacking. We conclude that understanding how agents forget should be as central to social epistemology as understanding how agents form beliefs and share information with others. (shrink)

We motivate a picture of social epistemology that sees forgetting as subject to epistemic evaluation. Using computer simulations of a simple agent-based model, we show that how agents forget can have as large an impact on group epistemic outcomes as how they share information. But, how we forget, unlike how we form beliefs, isn’t typically taken to be the sort of thing that can be epistemically rational or justified. We consider what we take to be the most promising argument for (...) this claim and find it lacking. We conclude that understanding how agents forget should be as central to social epistemology as understanding how agents form beliefs and share information with others. (shrink)

A scientific community can be modeled as a collection of epistemic agents attempting to answer questions, in part by communicating about their hypotheses and results. We can treat the pathways of scientific communication as a network. When we do, it becomes clear that the interaction between the structure of the network and the nature of the question under investigation affects epistemic desiderata, including accuracy and speed to community consensus. Here we build on previous work, both our own and others’, in (...) order to get a firmer grasp on precisely which features of scientific communities interact with which features of scientific questions in order to influence epistemic outcomes. (shrink)

In the original publication of the article, the Acknowledgement section was inadvertently not included. The Acknowledgement is given in this Correction.

There is a puzzle about Hume's is-ought gap involving an epistemic `ought'. From the premise `Snow is white,' we can infer `Sophia's belief that snow is white is correct.' `Snow is white' is paradigmatically non-normative, and that Sophia's belief is correct, a claim about what belief she ought to have, seems to be normative. The argument seems valid, so the is-ought gap is supposed to block this kind of inference. The puzzle is over whether we should give up on the (...) is-ought game or find another way to resolve the conflict. In the first chapter, I provide a formulation of the is-ought gap in a general semantic framework that avoids some other known problems. I turn in chapter 2 to discussing the puzzle about correct belief. I cast doubt on a solution proposed by Allan Gibbard by showing that it can admit of no epistemology of the normative. In chapter 3, I defend a solution to the puzzle while more directly tackling the question of the nature of oughts for belief. I offer a new explanation of why we ought to believe the truth. At the heart of the account is the idea that it's a conceptual truth beliefs ought to be true, which I provide a new argument for. I then claim that being an agent requires being subject to this norm of belief. This results in a non-moral, distinctly doxastic, account of why we ought to believe the truth. My conclusion is that asking why we ought to believe the truth is like asking why a bachelor must be unmarried: the answer is contained in the ideas that make up the question. In the final chapter, I respond to Gibbard's claim that an analogous story cannot work for `ought' claims for degreed belief. I pose a worry for Gibbard's proposed alternative explanation, and I undermine Gibbard's motivation for pursuing such an account in the first place. By taking belief to have an aim in a normative sense, I sketch how we can make sense of epistemic rationality in terms of that aim. (shrink)

It is widely accepted that the way information transfers across networks depends importantly on the structure of the network. Here, we show that the mechanism of information transfer is crucial: in many respects the effect of the specific transfer mechanism swamps network effects. Results are demonstrated in terms of three different types of transfer mechanism: germs, genes, and memes. With an emphasis on the specific case of transfer between sub-networks, we explore both the dynamics of each of these across networks (...) and a measure of their comparative fitness. Germ and meme transfer exhibit very different dynamics across linked networks. For germs, measured in terms of time to total infection, network type rather than degree of linkage between sub-networks is the primary factor. For memes or belief transfer, measured in terms of time to consensus, it is the opposite: degree of linkage trumps network type in importance. The dynamics of genetic information transfer is unlike either germs or memes. Transfer of genetic information is robust across network differences to which both germs and memes prove sensitive. We also consider function: how well germ, gene, and meme transfer mechanisms can meet their respective objectives of infecting the population, mixing and transferring genetic information, and spreading a message. A shared formal measure of fitness is introduced for purposes of comparison, again with an emphasis on linked sub-networks. Meme transfer proves superior to transfer by genetic reproduction on that measure, with both memes and genes superior to infection dynamics across all networks types. What kinds of network structure optimize fitness also differ among the three. Both germs and genes show fairly stable fitness with added links between sub-networks, but genes show greater sensitivity to the structure of sub-networks at issue. Belief transfer, in contrast to the other two, shows a clear decline in fitness with increasingly connected networks. When it comes to understanding how information moves on networks, our results indicate that questions of information dynamics on networks cannot be answered in terms of networks alone. A primary role is played by the specific mechanism of information transfer at issue. We must first ask about how a particular type of information moves. (shrink)

Understanding the dynamics of information is crucial to many areas of research, both inside and outside of philosophy. Using computer simulations of three kinds of information, germs, genes, and memes, we show that the mechanism of information transfer often swamps network structure in terms of its effects on both the dynamics and the fitness of the information. This insight has both obvious and subtle implications for a number of questions in philosophy, including questions about the nature of information, whether there (...) is genetic information, and how to arrange scientific communities. (shrink)

Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or 'votes' and 'talk.' The Condorcet Jury Theorem is appealed to as a justification in terms of votes, and the Hong-Page "Diversity Trumps Ability" result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore how these (...) results hold up if we vary the model so as to reflect the more familiar democratic structure of a representative hierarchy. We first recount extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem, but we question the ability of the result to shine light on real representative systems. We then show that, when we move from votes to talk, as modeled in Hong-Page, representation holds its own and even has a slight edge. (shrink)

Beyond belief change and meme adoption, both genetics and infection have been spoken of in terms of information transfer. What we examine here, concentrating on the specific case of transfer between sub-networks, are the differences in network dynamics in these cases: the different network dynamics of germs, genes, and memes. Germs and memes, it turns out, exhibit a very different dynamics across networks. For infection, measured in terms of time to total infection, it is network type rather than degree of (...) linkage between sub-networks that is of primary importance. For belief transfer, measured in terms of time to consensus, it is degree of linkage rather than network type that is crucial. Genes model each of these other dynamics in part, but match neither in full. For genetics, like belief transfer and unlike infection, network type makes little difference. Like infection and unlike belief, on the other hand, the dynamics of genetic information transfer within single and between linked networks are much the same. In ways both surprising and intriguing, transfer of genetic information seems to be robust across network differences crucial for the other two. (shrink)

In a series of formal studies and less formal applications, Hong and Page offer a ‘diversity trumps ability’ result on the basis of a computational experiment accompanied by a mathematical theorem as explanatory background (Hong & Page 2004, 2009; Page 2007, 2011). “[W]e find that a random collection of agents drawn from a large set of limited-ability agents typically outperforms a collection of the very best agents from that same set” (2004, p. 16386). The result has been extremely influential as (...) an epistemic justification for diversity policy initiatives. Here we show that the ‘diversity trumps ability’ result is tied to the particular random landscape used in Hong and Page’s simulation. We argue against interpreting results on that random landscape in terms of ‘ability’ or ‘expertise.’ These concepts are better modeled on smother and more realistic landscapes, but keeping other parameters the same those are landscapes on which it is groups of the best performing that do better. Smoother landscapes seem to vindicate both the concept and the value of expertise. Change in other parameters, however, also vindicates diversity. With an increase in the pool of available heuristics, diverse groups again do better. Group dynamics makes a difference as well; simultaneous ‘tournament’ deliberation in a group in place of the ‘relay’ deliberation in Hong and Page’s original model further emphasizes an advantage for diversity. ‘Tournament’ 2 dynamics particularly shows the advantage of mixed groups that include both experts and non-experts. As a whole, our modeling results suggest that relative to problem characteristics and conceptual resources, the wisdom of crowds and the wisdom of the few each have a place. We regard ours as a step toward attempting to calibrate their relative virtues in different modelled contexts of intellectual exploration. (shrink)

Polarization is a topic of intense interest among social scientists, but there is significant disagreement regarding the character of the phenomenon and little understanding of underlying mechanics. A first problem, we argue, is that polarization appears in the literature as not one concept but many. In the first part of the article, we distinguish nine phenomena that may be considered polarization, with suggestions of appropriate measures for each. In the second part of the article, we apply this analysis to evaluate (...) the types of polarization generated by the three major families of computational models proposing specific mechanisms of opinion polarization. (shrink)

Polarization is a topic of intense interest among social scientists, but there is significant disagreement regarding the character of the phenomenon and little understanding of underlying mechanics. A first problem, we argue, is that polarization appears in the literature as not one concept but many. In the first part of the article, we distinguish nine phenomena that may be considered polarization, with suggestions of appropriate measures for each. In the second part of the article, we apply this analysis to evaluate (...) the types of polarization generated by the three major families of computational models proposing specific mechanisms of opinion polarization. (shrink)

Agent-based models have played a prominent role in recent debates about the merits of democracy. In particular, the formal model of Lu Hong and Scott Page and the associated “diversity trumps ability” result has typically been seen to support the epistemic virtues of democracy over epistocracy (i.e., governance by experts). In this paper we first identify the modeling choices embodied in the original formal model and then critique the application of the Hong-Page results to philosophical debates on the relative merits (...) of democracy. In particular we argue that the “best-performing agents” in Hong-Page model should not be interpreted as experts. We next explore a closely related model in which best-performing agents are more plausibly seen as experts and show that the diversity trumps ability result fails to hold. However, with changes in other parameters (such as the deliberation dynamic) the diversity trumps ability result is restored. The sensitivity of this result to parameter choices illustrates the complexity of the link between formal modeling and more general philosophical claims; we use this debate as a platform for a more general discussion of when and how agent-based models can contribute to philosophical discussions. (shrink)

ABSTRACT This article distinguishes nine senses of polarization and provides formal measures for each one to refine the methodology used to describe polarization in distributions of attitudes. Each distinct concept is explained through a definition, formal measures, examples, and references. We then apply these measures to GSS data regarding political views, opinions on abortion, and religiosity—topics described as revealing social polarization. Previous breakdowns of polarization include domain-specific assumptions and focus on a subset of the distribution’s features. This has conflated multiple, (...) independent features of attitude distributions. The current work aims to extract the distinct senses of polarization and demonstrate that by becoming clearer on these distinctions we can better focus our efforts on substantive issues in social phenomena. (shrink)

This article aims to describe the last 10 years of the collaborative scientific endeavors on polarization in particular and collective problem-solving in general by our multidisciplinary research team. We describe the team’s disciplinary composition—social psychology, political science, social philosophy/epistemology, and complex systems science— highlighting the shared and unique skill sets of our group members and how each discipline contributes to studying polarization and collective problem-solving. With an eye to the literature on team dynamics, we describe team logistics and processes that (...) we believe make our multidisciplinary team persistent and productive. We emphasize challenges and difficulties caused by disciplinary differences in terms of terminology, units/levels of analysis, methodology, and theoretical assumptions. We then explain how work disambiguating the concepts of polarization and developing an integrative theoretical and methodological framework with complex systems perspectives has helped us overcome these challenges. We summarize the major findings that our research has produced over the past decade, and describe our current research and future directions. Last, we discuss lessons we have learned, including difficulties in a “three models” project and how we addressed them, with suggestions for effective multidisciplinary team research. (shrink)

Epistemic justifications for democracy have been offered in terms of two different aspects of decision-making: voting and deliberation, or ‘votes’ and ‘talk.’ The Condorcet Jury Theorem is appealed to as a justification in terms votes, and the Hong-Page “Diversity Trumps Ability” result is appealed to as a justification in terms of deliberation. Both of these, however, are most plausibly construed as models of direct democracy, with full and direct participation across the population. In this paper, we explore how these results (...) hold up if we vary the model so as to reflect the more familiar democratic structure of a representative hierarchy. We first recount extant analytic work that shows that representation inevitably weakens the voting results of the Condorcet Jury Theorem, but we question the ability of that result to shine light on real representative systems. We then show that, when we move from votes to talk, as modeled in Hong-Page, representation holds its own and even has a slight edge. (shrink)

In order to understand the transmission of a disease across a population we will have to understand not only the dynamics of contact infection but the transfer of health-care beliefs and resulting health-care behaviors across that population. This paper is a first step in that direction, focusing on the contrasting role of linkage or isolation between sub-networks in (a) contact infection and (b) belief transfer. Using both analytical tools and agent-based simulations we show that it is the structure of a (...) network that is primary for predicting contact infection—whether the networks or sub-networks at issue are distributed ring networks or total networks (hubs, wheels, small world, random, or scale-free for example). Measured in terms of time to total infection, degree of linkage between sub-networks plays a minor role. The case of belief is importantly different. Using a simplified model of belief reinforcement, and measuring belief transfer in terms of time to community consensus, we show that degree of linkage between sub-networks plays a major role in social communication of beliefs. Here, in contrast to the case of contract infection, network type turns out to be of relatively minor importance. What you believe travels differently. In a final section we show that the pattern of belief transfer exhibits a classic power law regardless of the type of network involved. (shrink)

Public health care interventions—regarding vaccination, obesity, and HIV, for example—standardly take the form of information dissemination across a community. But information networks can vary importantly between different ethnic communities, as can levels of trust in information from different sources. We use data from the Greater Pittsburgh Random Household Health Survey to construct models of information networks for White and Black communities--models which reflect the degree of information contact between individuals, with degrees of trust in information from various sources correlated with (...) positions in that social network. With simple assumptions regarding belief change and social reinforcement, we use those modeled networks to build dynamic agent-based models of how information can be expected to flow and how beliefs can be expected to change across each community. With contrasting information from governmental and religious sources, the results show importantly different dynamic patterns of belief polarization within the two communities. (shrink)

In this paper we make a simple theoretical point using a practical issue as an example. The simple theoretical point is that robustness is not 'all or nothing': in asking whether a system is robust one has to ask 'robust with respect to what property?' and 'robust over what set of changes in the system?' The practical issue used to illustrate the point is an examination of degrees of linkage between sub-networks and a pointed contrast in robustness and fragility between (...) the dynamics of (1) contact infection and (2) information transfer or belief change. Time to infection across linked sub-networks, it turns out, is fairly robust with regard to the degree of linkage between them. Time to infection is fragile and sensitive, however, with regard to the type of sub-network involved: total, ring, small world, random, or scale-free. Aspects of robustness and fragility are reversed where it is belief updating with reinforcement rather than infection that is at issue. In information dynamics, the pattern of time to consensus is robust across changes in network type but remarkably fragile with respect to degree of linkage between sub-networks. These results have important implications for public health interventions in realistic social networks, particularly with an eye to ethnic and socio-economic sub-communities, and in social networks with sub-communities changing in structure or linkage. (shrink)

A first take, matured in later work, in modeling belief polarization.

In the eighteenth century the category of the aesthetic sought to bridge the gap between the prevalent dualities of Cartesian thought: art and science, history and science, prejudice and truth. This special issue of _boundary 2_ addresses current debates about the status of art in the context of global modernity. The range of arguments represented here cover a broad historical scope—from Cartesianism to present-day global modernity—of cultural discourse on the aesthetic to bring a focus to contemporary discussions of the corollary (...) concepts of beauty, virtue, taste, and truth. These essays present a rich and provocative account of the place of the aesthetic in late-twentieth-century culture. Included in this volume are considerations of the relation between theories of art and the avant-garde; art’s relation to cognition; the aesthetic as history; the aesthetic as a unique access to modernity; and its impact on problems of identity formation, ideology, and resistances to the institutional powers inherent in dominant social formations. _Contributors. _Charles Altieri, Peter Burger, David Carroll, Anthony J. Cascardi, Howard Caygill, Allen Dunn, Eric Gans, Agnes Heller, Ronald A. T. Judy, Marie-Rose Logan, Daniel T. O’Hara, Donald E. Pease, Alan Singer. (shrink)

This collection of essays explores the metaphysical thesis that the living world is not made up of substantial particles or things, as has often been assumed, but is rather constituted by processes. The biological domain is organised as an interdependent hierarchy of processes, which are stabilised and actively maintained at different timescales. Even entities that intuitively appear to be paradigms of things, such as organisms, are actually better understood as processes. Unlike previous attempts to articulate processual views of biology, which (...) have tended to use Alfred North Whitehead’s panpsychist metaphysics as a foundation, this book takes a naturalistic approach to metaphysics. It submits that the main motivations for replacing an ontology of substances with one of processes are to be found in the empirical findings of science. Biology provides compelling reasons for thinking that the living realm is fundamentally dynamic, and that the existence of things is always conditional on the existence of processes. The phenomenon of life cries out for theories that prioritise processes over things, and it suggests that the central explanandum of biology is not change but rather stability, or more precisely, stability attained through constant change. This edited volume brings together philosophers of science and metaphysicians interested in exploring the consequences of a processual philosophy of biology. The contributors draw on an extremely wide range of biological case studies, and employ a process perspective to cast new light on a number of traditional philosophical problems, such as identity, persistence, and individuality. (shrink)

While the contemporary philosophical literature is replete with discussion of the control or freedom required for moral responsibility, only more recently has substantial attention been devoted to the knowledge or awareness required, otherwise called the epistemic condition. This area of inquiry is rapidly expanding, as are the various positions within it. This chapter introduces two major positions: the reasonable expectation view and the quality of will view. The chapter then explores two dimensions of the epistemic condition that serve as fault (...) lines along which these two views diverge. The first dimension concerns different kinds of ignorance. The second concerns what agents can be directly blameworthy for. The chapter closes by sketching a novel approach that incorporates advantages of opposing positions on this topic. (shrink)

This chapter draws on insights from non-equilibrium thermodynamics to demonstrate the ontological inadequacy of the machine conception of the organism. The thermodynamic character of living systems underlies the importance of metabolism and calls for the adoption of a processual view, exemplified by the Heraclitean metaphor of the stream of life. This alternative conception is explored in its various historical formulations and the extent to which it captures the nature of living systems is examined. Following this, the chapter considers the metaphysical (...) implications of reconceptualizing the organism from complex machine to flowing stream. What do we learn when we reject the mechanical and embrace the processual? Three key lessons for biological ontology are identified. The first is that activity is a necessary condition for existence. The second is that persistence is grounded in the continuous self-maintenance of form. And the third is that order does not entail design. (shrink)

Introduction: sustainable critique and the lost vocation of international relations -- "For we born after:" the challenge of sustainable critique -- Sustainable critique and critical IR theory: against emancipation -- The realist dilemma: politics and the limits of theory -- Communitarian IR theory -- Individualist IR theory: disharmonious cooperation -- Conclusion: toward sustainably critical international theory.

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)

Lovejoy (1873-1962) was America's foremost historian of ideas, a major participant in the philosophical debates of the twentieth century, and a prominent advocate of academic freedom. The product of an emotionally unsettled childhood and an evangelical father, Lovejoy reacted against his father by postulating the certainty of self-sufficient reason. He believed that only the principles of reason could order the world and so make our universe intelligible. Originally published in 1980. A UNC Press Enduring Edition -- UNC Press Enduring Editions (...) use the latest in digital technology to make available again books from our distinguished backlist that were previously out of print. These editions are published unaltered from the original, and are presented in affordable paperback formats, bringing readers both historical and cultural value. (shrink)

Ethics for School Leaders: The Human Condition and Organizational Dynamics focuses on the ethically complex situations school leaders face and how they balance a complex array of organizational demands, interpersonal dynamics, and ethical concerns to achieve the greater good for their students and for everyone else in the school environment.

The History and Philosophy of Science: A Reader brings together seminal texts from antiquity to the end of the nineteenth century and makes them accessible in one volume for the first time. With readings from Aristotle, Aquinas, Copernicus, Galileo, Descartes, Newton, Lavoisier, Linnaeus, Darwin, Faraday, and Maxwell, it analyses and discusses major classical, medieval and modern texts and figures from the natural sciences. Grouped by topic to clarify the development of methods and disciplines and the unification of theories, each section (...) includes an introduction, suggestions for further reading and end-of-section discussion questions, allowing students to develop the skills needed to: § read, interpret, and critically engage with central problems and ideas from the history and philosophy of science § understand and evaluate scientific material found in a wide variety of professional and popular settings § appreciate the social and cultural context in which scientific ideas emerge § identify the roles that mathematics plays in scientific inquiry Featuring primary sources in all the core scientific fields - astronomy, physics, chemistry, and the life sciences - The History and Philosophy of Science: A Reader is ideal for students looking to better understand the origins of natural science and the questions asked throughout its history. By taking a thematic approach to introduce influential assumptions, methods and answers, this reader illustrates the implications of an impressive range of values and ideas across the history and philosophy of Western science. (shrink)

This chapter begins with a brief review of the theory of parent-offspring conflict and considers the role of this conflict in the cognitive development of human infants. It then discusses the evolution of theory of mind — which is taken to have its origins in human evolution — and considers how this human cognitive specialization might have interacted with existing parent-offspring dynamics. How the epigenetic systems of infants might have responded is shown by elaborating upon existing cognitive and behavioural systems, (...) or by canalizing later developing ones earlier into development, in order to recruit higher degrees of parental investment. The merits of this framework is assessed in the context of the development of behaviours considered by some researchers to be indicative of a certain degree of social understanding, namely, gaze-following, pointing, social smiling, and neonatal imitation. The chapter concludes by showing how this proposal makes several longstanding theoretical and methodological difficulties for the field of cognitive development even more vexing. (shrink)

Winner of the National Business Book Award From the New York Times bestselling author of The Organized Mind and This Is Your Brain on Music, a primer to the critical thinking that is more necessary now than ever We are bombarded with more information each day than our brains can process—especially in election season. It's raining bad data, half-truths, and even outright lies. New York Times bestselling author Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and (...) written reports, revealing the ways lying weasels can use them. It's becoming harder to separate the wheat from the digital chaff. How do we distinguish misinformation, pseudo-facts, and distortions from reliable information? Levitin groups his field guide into two categories—statistical information and faulty arguments—ultimately showing how science is the bedrock of critical thinking. Infoliteracy means understanding that there are hierarchies of source quality and bias that variously distort our information feeds via every media channel, including social media. We may expect newspapers, bloggers, the government, and Wikipedia to be factually and logically correct, but they so often aren't. We need to think critically about the words and numbers we encounter if we want to be successful at work, at play, and in making the most of our lives. This means checking the plausibility and reasoning—not passively accepting information, repeating it, and making decisions based on it. Readers learn to avoid the extremes of passive gullibility and cynical rejection. Levitin's charming, entertaining, accessible guide can help anyone wake up to a whole lot of things that aren't so. And catch some weasels in their tracks! (shrink)

This chapter argues that scientific and philosophical progress in our understanding of the living world requires that we abandon a metaphysics of things in favour of one centred on processes. We identify three main empirical motivations for adopting a process ontology in biology: metabolic turnover, life cycles, and ecological interdependence. We show how taking a processual stance in the philosophy of biology enables us to ground existing critiques of essentialism, reductionism, and mechanicism, all of which have traditionally been associated with (...) substance ontology. We illustrate the consequences of embracing an ontology of processes in biology by considering some of its implications for physiology, genetics, evolution, and medicine. And we attempt to locate the subsequent chapters of the book in relation to the position we defend. (shrink)