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)

Written by one of Ireland's leading medical law academics, this practical book comprehensively covers case law and regulations regarding the healthcare system, the law relating to human reproduction, and the key issues of consent and treatment. Designed to be used by lawyers and healthcare professionals, Medicine, Ethics and the Law in Ireland provides an invaluable reference tool for anybody who requires accurate information and guidance on this area of Irish law. This new edition includes: Medical research and clinical trials; Organ (...) donation and transportation; Patient safety and QA; and Biobanking. (shrink)

Thinking About Thinking: Mind and Meaning in the Era of Techno-Nihilism addresses our existential crisis by reminding us of the conditions for meaning that have been obscured by the modern technological mentality. Madden weaves together disparate insights from Wittgenstein, Hegel, Aristotle, Heidegger, Merleau-Ponty, Nietzsche, Sophocles, and others in an attempt to account for our mindedness in terms of its inextricable connection to a world capable of inspiring our care. The mind is not a discrete entity locked behind the skull (...) or withdrawn into a ghostly realm, but a participation in an inheritance (biological and cultural) held in common with other participants, and taking responsibility for that world is crucial for the meaning. The ever-increasing technological mediation of our lives undermines this worldliness. We are subsequently "losing our minds," and as our mindedness fades, so goes our sense of dignity and value. Madden makes this case deploying insights from phenomenology, analytic philosophy, Aristotelianism, neuroscience, and cognitive science, and along the way confronts the mind-body problem, freedom, artificial intelligence, transhumanism, and nihilism. More importantly, he invites the reader into an accessible dialogue concerning issues of grave importance to the meaning of our lives. (shrink)

From whence spring the sparks of creativity? It is to this very question that the field of depth psychology--especially that of C.G. Jung and his intellectual descendants--has much to contribute. Just as the Muses were the offspring of Mnemosyne, the goddess of memory, our memories are the ancestors of our creativity that finds its multifaceted expression in the written word, image, theater, dance, and music. The Unconscious Roots of Creativity seeks to push the investigation into that domain of memory that (...) is beyond our conscious reach. With articles from 16 contributors, the "red thread" running through each of the offerings in this volume is that, whatever its ultimate expression, the creative impulse has its roots deep in the psyche. Edited By Kathryn Madden, Leonard Cruz and Steven Buser with articles by Linda Carter, Anna Maria Costantino, Carol Thayer Cox, Leonard Cruz, Lisa Raye Garlock, James Hollis, Naomi Ruth Lowinsky, Ian Livingston, Kathryn Madden, Jordan S. Potash, Susan Rowland, Murray Stein, Ann Ulanov, Tjeu van den Berk, Robin van Loben Sels, and Heidi S. Volf. (shrink)

In 'Law as a Leap of Faith' Gardner's analogy of faith in law to faith in God may seem outlandish. But consider the implications of the positions Gardner's jurisprudential views assemble: law can give us reason to do what we would otherwise not have reason to do - in fact it can give us reason to do what would otherwise be immoral. This is the implication of a commitment to law's capacity to give exclusive reasons, on one hand, together with (...) the commitment, on the other, that any given law is valid because of its sources and not its moral merits. (shrink)

Written for students, Mind, Matter, and Nature presumes no prior philosophical training on the part of the reader. The book nevertheless holds the arguments discussed to rigorous standards and is conversant with recent literature, thus making it useful as well to more advanced students and professionals interested in a resource on Thomistic hylomorphism in the philosophy of mind.

In the “Appendix” to the Treatise, Hume claims that he has discovered a “very considerable” mistake in his earlier discussion of the self. Hume's expression of the problem is notoriously opaque, leading to a vast scholarly debate as to exactly what problem he identified in his earlier account of the self. I propose a new solution to this interpretive puzzle. I argue that a tension generated by Hume's conceptual skepticism about real “principles of union” and his account of fictions of (...) the imagination is the defect identified in the “Appendix.”. (shrink)

This paper reports on an investigation of issues surrounding the use of ethical codes/codes of conduct in Irish based companies. Using a comprehensive questionnaire survey, the paper examines the incidence, content and enforcement of codes of conduct among a sample of the top 1000 companies based in Ireland. The main findings indicate that the overall usage of codes of conduct amongst indigenous Irish companies has increased significantly from 1995 to 2000. However, in line with prior research, these codes focus primarily (...) on issues surrounding company and employee protection as opposed to society protection. Almost half of all codes are written by company personnel or provided by head office. Revisions of codes are common but formal ongoing methods of instructing new staff about codes are not prevalent. Less than one-third of companies with codes have formal channels for reporting violations but a high percentage have formal disciplinary procedures in place for breaches of codes. (shrink)

Hume’s claim that we project necessity onto objects we take to be causally related has been influential in contemporary discussions of modality, inspiring deflationary accounts of our modal commitments. Hume is commonly understood as holding that modal projection explains our judging that an effect must follow its cause. This misunderstands the role of projection in Hume’s discussions of causation and causal judgement. Projection is a diagnosis of a distinctively philosophical confusion: the commitment to mind-independent necessary connections. In arguing for this, (...) I provide an account of the psychological process that, in Hume’s view, underlies projection. This account resolves problems with Hume’s projectivism identified by his commentators. (shrink)

This essay contains an attempt to trace the evolution of the concept of wisdom as found in the thought of Aristotle and Aquinas in terms of how the philosophical concept of wisdom as an intellectual virtue is understood and used to express the theological concept of wisdom as a gift of the Holy Spirit. The main aim is to understand how Aquinas derived the concept of wisdom from Aristotle's metaphysics and developed it in his mysticism. This research is based on (...) a close study of Book Six of Aristotle's Nichomachean Ethics, the corresponding sections of Aquinas' Sententia libri Ethicorum and question forty-five of the second part of the second part of Aquinas' Summa Theologiae. The insights gained from the study are then used to decipher the theoretical meaning of Augustine's famous saying: "love and do what thou wilt" and to expound on the practical value of wisdom for religious leaders. (shrink)

This paper aims to clarify Locke’s distinction between simple and complex ideas. I argue that Locke accepts what I call the “compositional criterion of simplicity.” According to this criterion, an idea is simple just in case it does not have another idea as a proper part. This criterion is prima facie inconsistent with Locke’s view that there are simple ideas of extension. This objection was presented to Locke by his French translator, Pierre Coste, on behalf of Jean Barbeyrac. Locke responded (...) to Barbeyrac’s objection, but his response, along with a passage from Chapter XV of Book II of the Essay, “Of Duration and Expansion, considered together,” has been taken to show that he did not accept the compositional criterion. I examine these passages and argue that they are not in tension with but rather affirm that criterion. (shrink)

Storchak, Ehlis, and Fallgatter provide an extensive literature review on electrophysiological measurements, which indicate that general predictive deficits in self‐monitoring are associated with various positive symptoms in patients with schizophrenia.

In contemporary debates in religious epistemology, theistic philosophers provide differing responses to the evidentialist argument against religious beliefs. Plantinga’s strategy is to argue that evidence is not needed to justify religious beliefs while Swinburne’s strategy is to argue that religious beliefs can be justified by evidence. However, in Aquinas’ account of religious epistemology, he seems to employ both strategies. In his account of religious knowledge by faith, he argues that evidence is unnecessary for religious beliefs. But in his account of (...) religious knowledge by science, he argues that there is evidence for religious beliefs. In this paper, I argue that there is no real dichotomy between Plantinga’s and Swinburne’s responses to the evidentialist argument. From a Thomistic perspective, Reformed Epistemology and Natural Theology are different but compatible responses to Evidentialism. (shrink)

Four predictors were posited to affect business student attitudes about the social responsibilities of business, also known as corporate social responsibility (CSR). Applying Forsyth's (1980, "Journal of Personality and Social Psychology" 39, 175–184, 1992, "Journal of Business Ethics" 11, 461–470) personal moral philosophy model, we found that ethical idealism had a positive relationship with CSR attitudes, and ethical relativism a negative relationship. We also found materialism to be negatively related to CSR attitudes. Spirituality among business students did not significantly predict (...) CSR attitudes. Understanding the relationship between CSR attitudes and the significant predictors has important implications for researchers and teachers in particular. (shrink)

In this paper I address the phenomenon of syncretism with respect to Chinese religions. An analysis of the syncretism that takes place between the three major Chinese religious traditions is first done in its personal and social dimensions. The social structure of Chinese religion is then used as a framework to understand how Buddhism and Daoism were made compatible with Confucianism. All this will serve as a background for the case study of Macau, where Chinese religious syncretism is very much (...) alive. Three popular religious festivals are celebrated annually and simultaneously on the eighth day of the fourth lunar month, namely, zuilongjie (醉龍節) Feast of the Drunken Dragon, tangongdan (譚公誕) Tam Kung Festival and fodanjie (佛誕節) Feast of the Buddha. (shrink)

The Molyneux problem is one of the major questions addressed by early modern authors. Whereas Locke’s response to Molyneux’s question has been the subject of extensive scholarly discussion, Leibniz’s response has received comparatively little attention. This paper defends an interpretation of Leibniz’s nuanced response to the problem and criticizes a competing interpretation that has recently been proposed.

That Socrates took himself to possess a divine sign is well attested by ancient sources. Both Plato and Xenophon mention Socrates’ daimonion on numerous occasions. What is problematic for contemporary scholars is that Socrates unfailingly obeys the warnings of his sign. Scholars have worried that Socrates seems to ascribe greater epistemic authority to his sign than his own critical reasoning. Moreover, he never so much as questions the authority of his sign to guide his actions, much less its divine nature. (...) Socrates’ unquestioning obedience to his sign thus appears to be in conflict with another of Socrates’ defining characteristics: namely, his relentless rationality. However, Socrates does not seem to recognize such inconsistency. The problem of the daimonion, then, is this: is Socrates’ professed commitment to rationality consistent with his unquestioning deference to his daimonion’s warnings? And if so, how? In this paper, I first discuss several solutions to the problem of the daimonion. I aim to show that none of the accounts of Socrates’ sign that have appeared in the scholarly literature are adequate. I then propose a new account of the daimonion, which, I argue, secures the rationality of Socrates’ obedience to his divine sign. (shrink)

Confucian education is best captured by the programme described in the Great Learning. Education is presented first as the process of self-cultivation for the sake of developing virtuous character. Self-cultivation then allows for virtue to be cultivated in the familial, social and international dimensions. My central thesis is that Confucianism can serve as a universal framework of educating people for the common good in its promotion of personal cultivation for the sake of human progress. On this account the common good (...) specifically refers to the social order accomplished by the virtuous behaviour found in the members of society. In this paper I argue that the Confucian notion of “lesser learning” sheds light on the concept of general education and the notion of “greater learning” improves our understanding of liberal education. Under this analysis the necessity of general education is assured although its importance should not be overly exaggerated. Furthermore, the objectives of liberal education deserve greater emphasis due to their historical importance and enduring relevance to promoting the common good of universal humanity. (shrink)