This article critically assesses contemporary empirical educational research, directing attention toward overlooked facets of pedagogical practice. Here, Agnes Pfrang and Daniel Castner raise questions about predominant psychological approaches to empirical educational research, instead advocating for a holistic viewpoint that encompasses the subtleties of educational situations and experiences. They highlight the learning atmosphere and pedagogical relationships as crucial dimensions often neglected by researchers. By delving into the historical evolution of the relationship between educational research and empirical pedagogy, the article (...) underscores the ramifications of an increasing emphasis on evidence-based approaches. It contends that conventional control measures, focused on performance metrics and rankings, inadequately encapsulate the essence of pedagogy. Pfrang and Castner call for a paradigm shift, urging a more comprehensive and context-sensitive framework in both educational research and practice. This article serves as a rallying cry for a nuanced understanding that embraces the multifaceted nature of educational interactions, advocating for a move away from traditional metrics and toward more inclusive perspectives. (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)

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.

In the first book-length study of American philosophy at the turn of the century, Daniel J. Wilson traces the formation of philosophy as an academic discipline. Wilson shows how the rise of the natural and physical sciences at the end of the nineteenth century precipitated a "crisis of confidence" among philosophers as to the role of their discipline. Deftly tracing the ways in which philosophers sought to incorporate scientific values and methods into their outlook and to redefine philosophy itself, (...) Wilson moves between close analysis of philosophical texts and consideration of professional careers of illustrative philosophers, such as Charles Sanders Peirce, John Dewey, and Josiah Royce. The author situates the emergence of professional philosophy in the context of the professionalization of American higher education and articulates, in the case of philosophy, the structures and values of a professional discipline. One of the most important consequences of this transformation was a new emphasis on communal theories of truth. Peirce, Dewey, and Royce all developed sophisticated and important theories of community as they were engaged in reshaping and redefining the limits of philosophy. This book will be of great importance for those interested in the history of philosophy, the rise of professions, and American intellectual and educational history, and to all those seeking to understand the contemporary revival of pragmatic thought and theories of community. (shrink)

It has become customary to conceptualize the living cell as an intricate piece of machinery, different to a man-made machine only in terms of its superior complexity. This familiar understanding grounds the conviction that a cell's organization can be explained reductionistically, as well as the idea that its molecular pathways can be construed as deterministic circuits. The machine conception of the cell owes a great deal of its success to the methods traditionally used in molecular biology. However, the recent introduction (...) of novel experimental techniques capable of tracking individual molecules within cells in real time is leading to the rapid accumulation of data that are inconsistent with an engineering view of the cell. This paper examines four major domains of current research in which the challenges to the machine conception of the cell are particularly pronounced: cellular architecture, protein complexes, intracellular transport, and cellular behaviour. It argues that a new theoretical understanding of the cell is emerging from the study of these phenomena which emphasizes the dynamic, self-organizing nature of its constitution, the fluidity and plasticity of its components, and the stochasticity and non-linearity of its underlying processes. (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)

Stollenwerk, Daniel J In this essay on the social encyclical Caritas in Veritate, the author looks at Pope Benedict XVI's defense of reason in an age that has lost its faith in reason. Benedict insists we are faced with a choice between being closed within immanence - which leads to an irrational rejection of meaning and value - or open to reason that leads to the transcendent. Pope Benedict, the author concludes, is a contemporary apologist, claiming that Christianity is (...) not only the most reasonable of worldviews, but also necessary for the very survival of humanity. (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)

Can faith be valuable and, if so, under what conditions? We know of no theory-neutral way to address this question. So, we offer a theory of relational faith, and we supplement it with a complementary theory of relational faithfulness. We then turn to relationships of mutual faith and faithfulness with an eye toward exhibiting some of the ways in which, on our theory, faith and faithfulness can be valuable and disvaluable. We then extend the theory to other manifestations of faith (...) and faithfulness, propose a way to unify them under a theory of faith and faithfulness simpliciter, and explain how they can be neo-Aristotelian virtues and vices. We close with our solution to the value problem and avenues for further research. (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)

This article critically examines one of the most prevalent metaphors in modern biology, namely the machine conception of the organism (MCO). Although the fundamental differences between organisms and machines make the MCO an inadequate metaphor for conceptualizing living systems, many biologists and philosophers continue to draw upon the MCO or tacitly accept it as the standard model of the organism. This paper analyses the specific difficulties that arise when the MCO is invoked in the study of development and evolution. In (...) developmental biology the MCO underlies a logically incoherent model of ontogeny, the genetic program, which serves to legitimate three problematic theses about development: genetic animism, neo-preformationism, and developmental computability. In evolutionary biology the MCO is responsible for grounding unwarranted theoretical appeals to the concept of design as well as to the interpretation of natural selection as an engineer, which promote a distorted understanding of the process and products of evolutionary change. Overall, it is argued that, despite its heuristic value, the MCO today is impeding rather than enabling further progress in our comprehension of living systems. (shrink)

Fleming, Daniel J; Ryan, Thomas Three recent phrases of Pope Francis warrant attention and guide this article. First, there is his call for 'witnesses of God's love' in his tribute to modern martyrs. The second is 'the pedagogy of grace' and the work of the Spirit explained in 'Amoris Laetitia'. Third, from the same document, we find his discussion of accompaniment in the process of moral discernment within the church. With these as guideposts and drawing on recent studies in (...) moral philosophy and psychology, this article unfolds in five steps: setting the scene; witness in relation to moral understanding and intersubjectivity; intersubjectivity and conscience; a pedagogy of grace: Holy Spirit and nonbelievers; and a pedagogy of grace in relation to moral development. (shrink)

This paper compares between the evolution of financial reporting and corporate social responsibility reporting. Our comparison follows a framework of seven factors for exploring comparative accounting history put forth by Carnegie and Napier :689–718, 2002): Period, Places, People, Practices, Propagation, Products, and Profession. Using this framework allows for a comparison of similarities and differences as to how both types of reporting have evolved. Some of the defining moments in the evolution of financial reporting have yet to take place in the (...) development of CSR reporting; such as an event that legitimizes a CSR reporting standard or gives CSR reporting global recognition. The evolutionary process may not follow the same path as financial reporting did due to the varying stakeholders involved. However, there are enough similarities that still make the evolution of financial reporting a useful comparative tool to analyze the potential growth and development of CSR reporting. Financial reporting has evolved into a comparable and reliable market-based resource over the last 100 years. Relative to this timeline CSR reporting is still in its infancy. CSR reporting has come a long way since early reports were first issued, but there remain many deficiencies in comparability, consistency, reliability, and relevance. The results of this comparison provide some insight on the possible future development of CSR reporting. Our goal is that this paper contributes to an understanding of CSR reporting’s past and provides insights into CSR reporting’s present and future. (shrink)

How does trust relate to faith? We do not know of a theory-neutral way to answer our question. So, we begin with what we regard as a plausible theory of faith according to which, in slogan form, faith is resilient reliance. Next, we turn to contemporary theories of trust. They are not of one voice. Still, we can use them to indicate ways in which trust and faith might both differ from and resemble each other. This is what we do. (...) Along the way, we evaluate substantive issues related to these possible differences and similarities. (shrink)

During Leibniz's lifetime, interest in the interpretation of the Bible and biblical prophecy became central to the theological and political concerns of Protestant Europe. Leibniz's treatment of this phenomenon will be examined in the light of his views on the nature of revelation and its role in his defence of Christianity. It will be argued that Leibniz's defence of the miracle of revelation – unlike his arguments on behalf of the core Christian mysteries of the Trinity and Incarnation – is (...) demonstrable by purely natural and scientific means, especially the verification of history. (shrink)

The controversy over the old ideal of “value-free science” has cooled significantly over the past decade. Many philosophers of science now agree that even ethical and political values may play a substantial role in all aspects of scientific inquiry. Consequently, in the last few years, work in science and values has become more specific: Which values may influence science, and in which ways? Or, how do we distinguish illegitimate from illegitimate kinds of influence? In this paper, I argue that this (...) problem requires philosophers of science to take a new direction. I present two case studies in the influence of values on scientific inquiry: feminist values in archaeology and commercial values in pharmaceutical research. I offer a preliminary assessment of these cases, that the influence of values was legitimate in the feminist case, but not in the pharmaceutical case. I then turn to three major approaches to distinguish legitimate from illegitimate influences of values, including the distinction between epistemic and non-epistemic values and Heather Douglas’ distinction between direct and indirect roles for values. I argue that none of these three approaches gives an adequate analysis of the two cases. In the concluding section, I briefly sketch my own approach, which draws more heavily on ethics than the others, and is more promising as a solution to the current problem. This is the new direction in which I think science and values should move. (shrink)

The concept of mechanism in biology has three distinct meanings. It may refer to a philosophical thesis about the nature of life and biology (‘mechanicism’), to the internal workings of a machine-like structure (‘machine mechanism’), or to the causal explanation of a particular phenomenon (‘causal mechanism’). In this paper I trace the conceptual evolution of ‘mechanism’ in the history of biology, and I examine how the three meanings of this term have come to be featured in the philosophy of biology, (...) situating the new ‘mechanismic program’ in this context. I argue that the leading advocates of the mechanismic program (i.e., Craver, Darden, Bechtel, etc.) inadvertently conflate the different senses of ‘mechanism’. Specifically, they all inappropriately endow causal mechanisms with the ontic status of machine mechanisms, and this invariably results in problematic accounts of the role played by mechanism-talk in scientific practice. I suggest that for effective analyses of the concept of mechanism, causal mechanisms need to be distinguished from machine mechanisms, and the new mechanismic program in the philosophy of biology needs to be demarcated from the traditional concerns of mechanistic biology. (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)

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. Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and written reports revealing the ways lying weasels can use them.

One challenge to the rationality of religious commitment has it that faith is unreasonable because it involves believing on insufficient evidence. However, this challenge and influential attempts to reply depend on assumptions about what it is to have faith that are open to question. I distinguish between three conceptions of faith each of which can claim some plausible grounding in the Judaeo-Christian tradition. Questions about the rationality or justification of religious commitment and the extent of compatibility with doubt look different (...) on accounts of faith in which trust or hope, rather than belief, are the primary basis for the commitments. On such accounts, while the person of faith has a stake in the truth of the content, practical as well as epistemic considerations can legitimately figure in normative appraisals. Trust and hope can be appropriate in situations of recognized risk, need not involve self-deception, and are compatible with the idea that one's purely epistemic opinions should be responsive only to evidence.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.Authentic faith and acknowledged risk: dissolving the problem of faith and reasonVolume 49, Issue 1DANIEL J. MCKAUGHAN DOI: https://doi.org/10.1017/S0034412512000200Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. Authentic faith and acknowledged risk: dissolving the problem of faith and reasonVolume 49, Issue 1DANIEL J. MCKAUGHAN DOI: https://doi.org/10.1017/S0034412512000200Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. Authentic faith and acknowledged risk: dissolving the problem of faith and reasonVolume 49, Issue 1DANIEL J. MCKAUGHAN DOI: https://doi.org/10.1017/S0034412512000200Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

We address the ethics of scenarios in which one party entraps, intentionally tempts or intentionally tests the virtue of another. We classify, in a new manner, three distinct types of acts that are of concern, namely acts of entrapment, of intentional temptation and of virtue testing. Our classification is, for each kind of scenario, of itself neutral concerning the question whether the agent acts permissibly. We explain why acts of entrapment are more ethically objectionable than like acts of intentional temptation (...) and why these, in turn, are more ethically objectionable than like acts of virtue testing. Along the way, we scrutinize, and eventually reject, the view that acts of entrapment are ethically unacceptable because intentional temptation is involved in entrapment. (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)

Although it may seem like a truism to assert that biology is the science that studies organisms, during the second half of the twentieth century the organism category disappeared from biological theory. Over the past decade, however, biology has begun to witness the return of the organism as a fundamental explanatory concept. There are three major causes: (a) the realization that the Modern Synthesis does not provide a fully satisfactory understanding of evolution; (b) the growing awareness of the limits of (...) reductionism in molecular biology; and (c) the renewed interest in the nature of life as a genuine scientific problem. This essay examines these recent developments and considers the new epistemological roles being played by the organism in each of them. It also reflects on what the present resurgence of the organism means for the philosophy of biology. (shrink)

Popular discussions of faith often assume that having faith is a form of believing on insufficient evidence and that having faith is therefore in some way rationally defective. Here I offer a characterization of action-centered faith and show that action-centered faith can be both epistemically and practically rational even under a wide variety of subpar evidential circumstances.

Philosophy of biology is often said to have emerged in the last third of the twentieth century. Prior to this time, it has been alleged that the only authors who engaged philosophically with the life sciences were either logical empiricists who sought to impose the explanatory ideals of the physical sciences onto biology, or vitalists who invoked mystical agencies in an attempt to ward off the threat of physicochemical reduction. These schools paid little attention to actual biological science, and as (...) a result philosophy of biology languished in a state of futility for much of the twentieth century. The situation, we are told, only began to change in the late 1960s and early 1970s, when a new generation of researchers began to focus on problems internal to biology, leading to the consolidation of the discipline. In this paper we challenge this widely accepted narrative of the history of philosophy of biology. We do so by arguing that the most important tradition within early twentieth-century philosophy of biology was neither logical empiricism nor vitalism, but the organicist movement that flourished between the First and Second World Wars. We show that the organicist corpus is thematically and methodologically continuous with the contemporary literature in order to discredit the view that early work in the philosophy of biology was unproductive, and we emphasize the desirability of integrating the historical and contemporary conversations into a single, unified discourse. (shrink)

The authors argue that their target is orthogonal to the realism and instrumentalist debate. I argue that it is born directly from it. While the distinction is helpful in illuminating how some ontological commitments demand a theory of implementation, it's less clear whether different views cleanly map onto the epistemic and metaphysical uses defined in the paper.

Theorists attending to the epistemic condition on responsibility are divided over whether moral ignorance is ever exculpatory. While those who argue that reasonable expectation is required for blameworthiness often maintain that moral ignorance can excuse, theorists who embrace a quality of will approach to blameworthiness are not sanguine about the prospect of excuses among morally ignorant wrongdoers. Indeed, it is sometimes argued that moral ignorance always reflects insufficient care for what matters morally, and therefore that moral ignorance never excuses. Furthermore, (...) quality of will theorists treat their skepticism about excuses for the morally ignorant as a natural implication of their approach. It is therefore unsurprising that, while many have argued for the blamelessness of certain morally ignorant agents on grounds concerning reasonable expectation, the possibility that morally ignorant agents might be blameless even according to quality of will views has not been adequately addressed. I illustrate and explain how it is possible for morally ignorant agents to display sufficient care for the morally relevant features of their wrong behavior. Thus, even if quality of will views are correct, moral ignorance sometimes excuses. (shrink)

The machine conception of the organism (MCO) is one of the most pervasive notions in modern biology. However, it has not yet received much attention by philosophers of biology. The MCO has its origins in Cartesian natural philosophy, and it is based on the metaphorical redescription of the organism as a machine. In this paper I argue that although organisms and machines resemble each other in some basic respects, they are actually very different kinds of systems. I submit that the (...) most significant difference between organisms and machines is that the former are intrinsically purposive whereas the latter are extrinsically purposive. Using this distinction as a starting point, I discuss a wide range of dissimilarities between organisms and machines that collectively lay bare the inadequacy of the MCO as a general theory of living systems. To account for the MCO’s prevalence in biology, I distinguish between its theoretical, heuristic, and rhetorical functions. I explain why the MCO is valuable when it is employed heuristically but not theoretically, and finally I illustrate the serious problems that arise from the rhetorical appeal to the MCO. (shrink)

Friedrich Schleiermacher is often considered the Father of Modern Theology, known for his attempt to reconcile traditional Christian doctrines with philosophical criticisms and scientific discoveries. Despite the influence of his work on significant figures like Karl Barth, he has been largely ignored by contemporary theologians. Focussing on Schleiermacher's doctrine of sin, this book demonstrates how Schleiermacher has not only been misinterpreted, but also underestimated, and deserves a critical re-examination. The book approaches Schleiermacher on sin with respect to three themes: one, (...) its power to transcend an intractable metaethical dilemma at the heart of modern debates over sin; two, its intended compatibility with natural science; and three, to re-evaluating its place, and so Schleiermacher's place, in the history of theology. It solves and dissolves problems arising simultaneously from natural science, confessional theology, ethics, and metaphysics in a single, integrated account using Schleiermacher's understudied thought from his dogmatics The Christian Faith. In contrast to the account sometimes given of modern theology as marked by a break with "Greek metaphysics," Schleiermacher's account is shown to stand in stark contrast by retrieving, not excising, ancient thought in service of an account of sin adequate to natural science. This is a vital rediscovery of a foundational voice in theology. As such, it will greatly appeal to scholars of Modern Theology, theological ethics, and the history of Modern Christianity. (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 neurophysiological evidence from the Miyashita group's experiments on monkeys as well as cognitive experience common to us all suggests that local neuronal spike rate distributions might persist in the absence of their eliciting stimulus. In Hebb's cell-assembly theory, learning dynamics stabilize such self-maintaining reverberations. Quasi-quantitive modeling of the experimental data on internal representations in association-cortex modules identifies the reverberations (delay spike activity) as the internal code (representation). This leads to cognitive and neurophysiological predictions, many following directly from the language (...) used to describe the activity in the experimental delay period, others from the details of how the model captures the properties of the internal representations. (shrink)

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)

A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a relativistic field in which a quantized degree of freedom is associated to each point in spacetime. The purpose of this field is to mediate in the interaction between classical stochastic influences and conventional quantum fields. The equations of motion are Lorentz covariant, frame independent, and do not result in (...) divergent behavior. It is shown that the mathematical framework permits the specification of unambiguous local properties providing a connection between the model and evidence of real world phenomena. The collapse process is demonstrated for an idealized example. (shrink)