Robustness properties of three equality of variances tests, the jackknife procedure, the k-sample Box-Andersen test, and Levene’s z test, were investigated and compared in a Monte Carlo study employing small samples from underlying gamma distributions and gamma mixtures. Overall, the jackknife test yielded rejection proportions usually closer to nominal levels under departures from normality, but the Box-Andersen test performed relatively well when departures from normality were not extreme. Four recommendations regarding testing variances were offered.

This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest (...) to logicians, computer scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

While experimental philosophy has fruitfully applied the tools and resources of psychology and cognitive science to debates within epistemology, metaphysics, and ethics, relatively little work has been done within philosophy of religion. And this isn’t due to a lack of need! Philosophers of religion frequently rely on empirical claims that can be either verified or disproven, but without exploring whether they are. And philosophers of religion frequently appeal to intuitions which may vary wildly according to education level, theological background, etc., (...) without concern for whether or not the psychological mechanisms that underwrite those intuitions are broadly shared or reliable. In this chapter, I explore some of the fruit and possibilities for the emerging field of experimental philosophy of religion. First, in Section 1, I will elucidate some of the historical grounding for experimental philosophy of religion. Then in Section 2, I briefly consider how the tools and resources of experimental philosophy might be fruitfully applied to a seminal topic within philosophy of religion, namely, the problem of evil. In Section 3, we’ll sketch some broader applications of experimental philosophy of religion. (shrink)

This volume contains the first publication in book form of an English translation of Thomas Aquinas's controversial disputed question De unione Verbi incarnati. This disputed question is a remarkable portal into the Angelic Doctor's theology of the hypostatic union, which is recognized as an area in which Aquinas forged some of his most original and penetrating articulations of the Christian faith. In the De unione Verbi incarnati Aquinas presents in five articles material that occupies more than eighteen questions in the (...) third part of the Summa theologiae. The attribution of an esse secundarium to Christ, in the fourth article of the De unione, has been the object of intense debate, for it seems to contradict the account of the Summa. In addition to Professor Nutt's English translation, the volume includes the critical Latin text published by Barbara Bartocci, Klaus Obenauer, and Walter Senner, as well as a substantial introduction. Professor Nutt's introduction carefully unfolds the historical background, technical concepts, sources, and speculative claims needed for understanding the breadth of the biblical and metaphysical contemplation represented in this work; it also includes a detailed exploration of the debate over the fourth article. (shrink)

Many psychiatric disorders involve problems with the recognition and preservation of personal boundaries. Philosophy can help to clarify what is at stake, both socially and phenomenologically, in drawing such boundaries. In particular, assignments of responsibility and determinations of loss are deeply implicated in the determination of personal boundaries. Understanding these implications can help make sense of the volatile emotions of borderline personality disorder, for example, and it can clarify what is missing from DSM descriptions more generally.

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

This book is intended to be used as a textbook by students of mathematics, and also within limitations as a reference work.

R.W. Church was an English churchman and writer. Church was also famous for being the dean of St. Paul's Cathedral in London.Bacon's most famous work is his biography on Francis Bacon, the great English philosopher.

Luck permeates our lives, and this raises a number of pressing questions: What is luck? When we attribute luck to people, circumstances, or events, what are we attributing? Do we have any obligations to mitigate the harms done to people who are less fortunate? And to what extent is deserving praise or blame a ected by good or bad luck? Although acquiring a true belief by an uneducated guess involves a kind of luck that precludes knowledge, does all luck undermine (...) knowledge? And how accurate are our luck attributions anyway? The academic literature has seen growing, interdisciplinary interest in luck, and this volume brings together and explains the most important areas of this research. It consists of 39 newly commissioned chapters, written by an internationally acclaimed team of philosophers and psychologists, for a readership of students and researchers. Its coverage is divided into six sections: (i) The History of Luck, (ii) The Nature of Luck, (iii) Moral Luck, (iv) Epistemic Luck, (v) The Psychology of Luck, and (vi) Future Research. The chapters in these sections cover a wide range of topics, from the problem of moral luck, to anti-luck epistemology, to the relationship between luck attributions and cognitive biases, to meta-questions regarding the nature of luck itself, to a range of other theoretical and empirical questions currently being investigated by ethicists, epistemologists, and psychologists. By bringing this research together, the Handbook serves as both a touchstone for understanding the relevant issues and a first port of call for future philosophical and psychological research on luck. (shrink)

Two intellectual vices seem to always tempt us: arrogance and diffidence. Regarding the former, the world is permeated by dogmatism and table-thumping close-mindedness. From politics, to religion, to simple matters of taste, zealots and ideologues all too often define our disagreements, often making debate and dialogue completely intractable. But to the other extreme, given a world with so much pluralism and heated disagreement, intellectual apathy and a prevailing agnosticism can be simply all too alluring. So the need for intellectual humility, (...) open-mindedness, and a careful, humble commitment to the truth are apparent. In this book, Dr Church and Dr Samuelson explicate a robust and vibrant account of the philosophy and science of this most valuable virtue, and they highlight how it can be best applied and personally developed. (shrink)

Jennifer Church presents a new account of perception, which shows how imagining alternative perspectives and possibilities plays a key role in creating and validating experiences of self-evident objectivity. She explores the nature of moral perception and aesthetic perception, and argues that perception can be both literal and substantive.

It was proposed that the data from Monte Carlo statistical investigations be subjected to analysis of variance methods rather than the conventional techniques of tabling, graphing, and inspecting the data. Two examples in which analysis of variance methods were applied to published Monte Carlo studies were presented. It was suggested that balanced factorial designs should be used whenever possible in Monte Carlo studies so that analysis of variance methods would be directly applicable. Finally, three advantages of analysis of variance methods (...) over conventional techniques were described and analysis of variance methods were contrasted with a possible alternative analytical method, multiple regression analysis. (shrink)