In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...) by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the existence of infinitesimals from their successful use. By a detailed analysis of Leibniz’s arguments in his De quadratura of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom. (shrink)

Our question “How many chickens does it take to make an egg?” was inspired by the successful replacement of egg-based mayonnaise with plant-based mayonnaise in general dining at the University of California, Santa Barbara, in order to increase animal welfare. Our indicator of improved animal welfare due to decreased egg consumption was the reduction in number of chickens in the stressful and unhealthy conditions of the US egg industry. To measure this we calculated the ratio of chickens to eggs and (...) found it takes 6.3 chickens to make 1000 eggs. This equals 158 eggs per chicken, less than half the amount of eggs per laying hen because of mortality from hatching to entering the laying flock, including the disposal of male chicks. In addition, greenhouse gas emissions, irrigation water, reactive nitrogen, and land use would be reduced 43–98% from that of eggs. While the impact of plant-based mayonnaise was relatively small, we also estimated the substitution of eggs with tofu, which had a much greater impact: substituting 50% of eggs with tofu in first-year student breakfasts on all UC campuses would reduce the number of chickens in the egg industry by 9245. If this substitution was made by the US population, the welfare and environmental benefits would be 29 thousand times greater. Reducing egg consumption would greatly improve chicken welfare even if welfare certified eggs are replaced, since the requirements of the most commonly used chicken welfare certification programs do relatively little to reduce chicken suffering. (shrink)

Emptiness is a strange phenomenon that haunts us in many ways. Most of us have felt empty at one time or another, though we don’t often talk about it. We have a sense that something is missing in life. This absence extends beyond human experience to the physical world. As contemporary science has revealed to us on both a macroscopic and subatomic level, curiously, the vast majority of the universe is composed mostly of nothing but empty space. Emptiness is “abundant” (...) and beckons for our attention. Drawing on the Judeo-Christian wisdom of the Bible, in conversation with Eastern and Celtic thought, David Arthur Auten offers us an eye-opening and profoundly practical examination of the much neglected gift of absence. Nothing, ironically, turns out to be endlessly fascinating and significant. (shrink)

The problem of God today In some famously — some might say infamously — provocative letters from prison in June and July Dietrich Bonhoeffer reflects on the ...

This book is a lively and readable introduction to the basic problems in the philosophy of religion. As well as dealing with traditional questions about the relationship between faith, belief, theology and reason, the attributes and existence of God, the possibility of immortality, the character of morality and its place in religious belief, and the significance of claims about experience, Dr Pailin discusses fundamental and searching questions about the relationship between faith and culture, the nature of interpretation, the theological significance (...) of references to the past, and the complexity of religious language. The result is an illuminating introduction whose probing honesty will challenge as well as stimulate its readers' reflections on the fundamentals of religious faith and whose references to other works will indicate to readers where they may follow up its ideas. Book jacket. (shrink)

Can a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets, or less level-by-level agreement, such as requiring it only on measure one sets, then yes, it can.

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal κ for which 2κ = κ+, another for which 2κ = κ++ and another in which the least strongly compact cardinal is supercompact. If there is a (...) strongly compact cardinal, then there is an inner model with a strongly compact cardinal, for which the measurable cardinals are bounded below it and another inner model W with a strongly compact cardinal κ, such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${H^{V}_{\kappa^+} \subseteq {\rm HOD}^W}$$\end{document}. Similar facts hold for supercompact, measurable and strongly Ramsey cardinals. If a cardinal is supercompact up to a weakly iterable cardinal, then there is an inner model of the Proper Forcing Axiom and another inner model with a supercompact cardinal in which GCH + V = HOD holds. Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between strong compactness and supercompactness. If a cardinal is strongly compact up to a weakly iterable cardinal, then there is an inner model in which the least measurable cardinal is strongly compact. If there is a weakly iterable limit δ of <δ-supercompact cardinals, then there is an inner model with a proper class of Laver-indestructible supercompact cardinals. We describe three general proof methods, which can be used to prove many similar results. (shrink)

Husserl has enjoyed a revival of interest in recent years and the Cartesian Meditations is perhaps his most widely read text. The book is an introduction to Husserl's phenomenology and is based on Descartes' Meditations on First Philosophy . Husserl attempts to show how Descartes discovered the "transcendental" perspective which is essential to any genuine philosophy. Until now there has never been a secondary text on this important and influential work on philosophy. This book, in conjunction with the text itself, (...) will serve as a proper introduction to Husserlian phenomenology. A.D. Smith introduces and assesses the key concepts that arise in the book in clear and engaging ways. His style is highly accessible and suitable for anyone coming to the Cartesian Meditations for the first time. (shrink)

We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardinals can be strong cardinals, have trivial Mitchell rank or even contain a club disjoint from the set of measurable cardinals. These results improve and (...) unify Theorems 1 and 2 of [5], due to the first author. (shrink)

Do our lives have meaning? Should we create more people? Is death bad? Should we commit suicide? Would it be better to be immortal? Should we be optimistic or pessimistic? Since Life, Death, and Meaning: Key Philosophical Readings on the Big Questions first appeared, David Benatar's distinctive anthology designed to introduce students to the key existential questions of philosophy has won a devoted following among users in a variety of upper-level and even introductory courses.

Arthur Danto is the Johnsonian Professor Emeritus of Philosophy at Columbia University and the most influential philosopher of art in the last half century. As an art critic for The Nation for 25 years and frequent contributor to other widely read outlets such as the New York Review of Books, Danto also has become one of the most respected public intellectuals of his generation. He is the author of some two dozen important books, along with hundreds of articles and (...) reviews which have been the center of both controversy and discussion. In this volume Danto offers his intellectual autobiography and responds to essays by 27 of the keenest critics of his thought from the worlds of philosophy and the arts. The book includes 16 pages of color art reproductions. Danto is the author dozens of books on art, philosophy, the philosophy of art, and art criticism. He is a rare philosopher who is also a public intellectual. (shrink)

This book discusses the effects that power generation has had on the land, the water, the air, and the biosphere.

The research project described in this report represents one of the most extensive studies of character education ever undertaken, including over 10,000 students and 255 teachers in schools across England, Scotland, Northern Ireland and Wales. Research techniques consisted of a mixture of surveys, moral dilemmas and semi-structured interviews. This report explores: - The current situation in character education, both in the UK and internationally - How developed British students are with respect to moral character and the extent to which they (...) are able to understand and apply moral virtues, especially those aged 14 and 15 - How teachers in the UK understand their role in terms of students’ moral and character development - What helps or hinders the development of children’s characters according to teachers in UK schools. (shrink)

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hypothesize that people use scale words—thousand, million, billion—to carve the large number line into categories, stretching linear responses across items within each category. If so, discontinuities in position and response time (...) are expected near the boundaries between categories. In contrast to previous work that suggested only that a minority of college undergraduates employed categorical boundaries, we find that discontinuities near category boundaries occur in most or all participants, but that accurate and inaccurate participants respond in opposite ways to category boundaries. Accurate participants highlight contrasts within a category, whereas inaccurate participants adjust their responses toward category centers. (shrink)

Army Officers face increased moral pressure in modern warfare, where character judgement and ethical judgement are vital. This article reports the results of a study of 242 junior British Army officers using the Army Intermediate Concept Measure, comprising a series of professionally oriented moral dilemmas developed for the UK context. Results are suggestive of appropriate application of Army values to the dilemmas and of ethical reasoning aligning with Army excellence. The sample does slightly less well, however, for justification than for (...) action reasoning, and there are differences following initial training for infantry and artillery officers versus other branches of service. Dilemmas involving anti-torture methods and not covering up soldiers' failings generated best results compared to those requiring balance between compassion and mission, and negotiating personal relationships with military needs. Gender differences favouring women were less than those observed for other professional groups using similar measures. This research further develops a much-needed measure of ethical reasoning among junior Army officers, with potential for use among other ranks. This approach is advocated for other professional groups. (shrink)

Written by major scholars and practitioners of Goethean science today, this book considers the philosophical foundations of Goethe's approach and applies the ...

Institutions receiving federal funding for research from the U.S.Public Health Service need to have policies and procedures to both prevent research misconduct and to adjudicate it when it occurs. The person who is designated to handle research misconduct is typically referred to as the research integrity officer (RIO). In this interview study we report on 79 RIOs who describe how they would handle allegations of research misconduct. Their responses were compared to two expert RIOs. The responses to the allegations in (...) the scenarios demonstrated that RIOs are not uniformly well prepared to handle activities associated with reported allegations of research misconduct. We recommend greater preparation through directed training, use of check lists of possible behaviors necessary to consider when situations arise, being involved in a network of RIOs so one can discuss options, and the possible need to certify RIOs. (shrink)

Language comprehension requires a simulation that uses neural systems involved in perception, action, and emotion. A review of recent literature as well as new experiments support five predictions derived from this framework. 1. Being in an emotional state congruent with sentence content facilitates sentence comprehension. 2. Because women are more reactive to sad events and men are more reactive to angry events, women understand sentences about sad events with greater facility than men, and men understand sentences about angry events with (...) greater facility than women. 3. Because it takes time to shift from one emotion to another, reading a sad sentence slows the reading of a happy sentence more for women than men, whereas reading an angry sentence slows the reading of a happy sentence more for men than for women. 4. Because sad states motivate affiliative actions and angry states motivate aggressive action, gender and emotional content of sentences interact with the response mode. 5. Because emotion simulation requires particular action systems, adapting those action systems will affect comprehension of sentences with emotional content congruent with the adapted action system. These results have implications for the study of language, emotion, and gender differences. (shrink)

This report describes research focusing on virtues and character in teaching, by which we mean the kind of personal qualities professional teachers need to facilitate learning and overall flourishing in young people that goes beyond preparing them for a life of tests. The ‘good’ teacher is someone who, alongside excellent subject knowledge and technical expertise, cares about students, upholds principles of honesty and integrity both towards knowledge and student–teacher relationships, and who does good work . In the Framework for Character (...) Education , we considered the character of teachers to be a crucial ingredient in the development of flourishing children. This new report describes research that examined how teachers thought about, and drew upon, character strengths and virtues in their daily professional lives. (shrink)

In the realm of corporate leadership and organisational theory, the work of the German philosopher, Martin Heidegger, has received little if any attention from scholars and practitioners alike. We argue in this paper that Heidegger’s work has an important message to convey with regard to the ability and perhaps the obligation of leaders to enable the ‘releasement’ and ‘opening up’ of the members of an organisational community to their ‘authentic possibilities’ within the realm of the work environment. We apply the (...) Heideggerian concepts of calculative and reflective thinking, as well as his philosophy of ‘being’ to the role of authentic leaders and their leadership possibilities. And we distinguish this approach to leadership from that which we identify as ‘inauthentic’ in which both leaders and members of organisations are alienated from their possibilities. (shrink)

In the realm of corporate leadership and organisational theory, the work of the German philosopher, Martin Heidegger, has received little if any attention from scholars and practitioners alike. We argue in this paper that Heidegger’s work has an important message to convey with regard to the ability and perhaps the obligation of leaders to enable the ‘releasement’ and ‘opening up’ of the members of an organisational community to their ‘authentic possibilities’ within the realm of the work environment. We apply the (...) Heideggerian concepts of calculative and reflective thinking, as well as his philosophy of ‘being’ to the role of authentic leaders and their leadership possibilities. And we distinguish this approach to leadership from that which we identify as ‘inauthentic’ in which both leaders and members of organisations are alienated from their possibilities. (shrink)

Can parents who choose not to vaccinate their children be held legally liable for any harm that results? The state of laboratory and epidemiological understanding of a disease such as measles makes it likely that a persuasive causal link can be established between a decision to not vaccinate, a failure to take appropriate precautions to isolate a non-vaccinated child who may have been exposed to measles from highly vulnerable persons, and a death. This paper argues that, even if a parent (...) chooses to not vaccinate a child under a state law permitting exemptions, that decision does not create complete protection against liability for the adverse consequences of that choice. (shrink)

Consider this hypothetical scenario involving a choice not to vaccinate a child. Ms. S has a niece who is autistic. The girl's parents are suspicious that there is some relationship between her autism and her Measles Mumps and Rubella vaccination. They have shared their concerns with Ms. S. She then declines to have her own daughter, Jinny S., vaccinated with the MMR vaccine. To bypass the state's mandatory vaccination requirement, Ms. S claims a state-legislated philosophical exemption, whereby she simply attests (...) to the fact that she is opposed to vaccinating her daughter due to a conscientiously held belief. At the age of four, Jinny goes on a trip by airplane to Germany with her mother. After returning to the United States, she attends daycare despite having some mild cold symptoms. Subsequently, she develops a classic measles rash, at which point her mother brings her to a pediatrician and keeps her home from daycare. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.