Much scientific thinking and thinking about science involves assumptions that there is a deep and pervasive order to the world that it is the business of science to disclose. A paradigmatic statement of such a view can be found in a widely discussed paper by a prominent economist, Milton Friedman (a paper which will be discussed in more detail shortly): A fundamental hypothesis of science is that appearances are deceptive and that there is a way of looking at or interpreting (...) or organizing the evidence that will reveal superficially disconnected and diverse phenomena to be manifestations of a more fundamental and relatively simple structure. (1953/1984, p.231) On the other hand, the person sometimes described as the father of modern science, Francis Bacon, wrote: The human understanding is of its own nature prone to suppose the existence of more order and regularity in the world than it finds. And though there be many things in nature which are singular and unmatched, yet it devises for them conjugates and relatives which do not exist. (1620/1960, p. 50). (shrink)

FROM VARIOUS THINKERS and in different languages we have been receiving an identical message: the philosophy of the subject initiated by Descartes' cogito has reached a definitive impasse. Critical reactions range from attempts to dispose of the subject altogether to efforts to restore pre-Cartesian theories. The authors here presented adopt positions different from either of those extremes. Fully aware of the modern predicament they advocate neither a return to a pre-Cartesian past nor do they dismiss outright the post-Cartesian subjective starting (...) point. Theoretical attitudes once adopted cannot simply be discarded: philosophy has to work its way through them. Still, the proposed answers vary substantially. In Philosophy and the Mirror of Nature, Richard Rorty advocates abandoning traditional truth claims in favor of a rational "conversation" carried on between incommensurable positions. Francis Jacques's Différence et subjectivité reverses the traditional priority of subject to relation. In Généalogie de la psychanalyse Michel Henry attempts to reclaim a theory of "pure" subjectivity from the wild growth of its objectivist deviations. Alasdair MacIntyre exposes the disastrous moral consequences that have resulted from the primacy of an autonomous, isolated subject and proposes a program for a socially and historically more integrated ethical reconstruction. No idea has of late more consistently come under fire than that of the subject as sole source of meaning and value. Heidegger attributed it to Descartes, and three of the studies show the direct impact of his reading. Yet similar tendencies had been at work in analytic philosophy. Rorty presents pragmatic anti-subjective interpretations of language going back to Wittgenstein; Francis Jacques supports his attack by Russell's theory of relations. (shrink)

Résumé éditeur : "Nous avons perdu les deux repères qui permettaient autrefois de nous définir entre les dieux et les bêtes. Nous ne savons plus qui nous sommes, nous autres humains. De nouvelles utopies en naissent. D'un côté, le post-humanisme prétend nier notre animalité et faire de nous des dieux promis à l'immortalité par les vertus de la technique. D'un autre côté, l'animalisme veut faire de nous des animaux comme les autres et inviter les autres animaux à faire partie de (...) notre communauté morale. Alors forgeons une nouvelle utopie à notre mesure. Ne cherchons plus à nier les frontières naturelles - celles qui nous séparent des dieux ou des animaux - et défendons un humanisme conséquent, c'est-à-dire un cosmopolitisme sans frontières.". (shrink)

We address three fundamental questions: What does it mean for an entity to be living? What is the role of inter-organismic collaboration in evolution? What is a biological individual? Our central argument is that life arises when lineage-forming entities collaborate in metabolism. By conceiving of metabolism as a collaborative process performed by functional wholes, which are associations of a variety of lineage-forming entities, we avoid the standard tension between reproduction and metabolism in discussions of life – a tension particularly evident (...) in discussions of whether viruses are alive. Our perspective assumes no sharp distinction between life and non-life, and does not equate life exclusively with cellular or organismal status. We reach this conclusion through an analysis of the capabilities of a spectrum of biological entities, in which we include the pivotal case of viruses as well as prions, plasmids, organelles, intracellular and extracellular symbionts, unicellular and multicellular life-forms. The usual criterion for classifying many of the entities of our continuum as non-living is autonomy. This emphasis on autonomy is problematic, however, because even paradigmatic biological individuals, such as large animals, are dependent on symbiotic associations with many other organisms. These composite individuals constitute the metabolic wholes on which selection acts. Finally, our account treats cooperation and competition not as polar opposites but as points on a continuum of collaboration. We suggest that competitive relations are a transitional state, with multi-lineage metabolic wholes eventually outcompeting selfish competitors, and that this process sometimes leads to the emergence of new types or levels of wholes. Our view of life as a continuum of variably structured collaborative systems leaves open the possibility that a variety of forms of organized matter – from chemical systems to ecosystems – might be usefully understood as living entities. (shrink)

This paper attacks the perennial philosophical and scientific quest for a simple and unified vision of the world. Without denying the attraction of this vision, I argue that such a goal often seriously distorts our understanding of complex phenomena. The argument is illustrated with reference to simplistic attempts to provide extremely general views of biology, and especially of human nature, through the theory of evolution. Although that theory is a fundamental ingredient of our scientific world view, it provides only one (...) of a number of perspectives that are required for an understanding of biology in general, and human behaviour in paticular. The argument is connected to the replacement of views of science in terms of universal laws with views that emphasise ranges of models more locally suited to specific phenomena. (shrink)

In an earlier paper (Dupré 1984), I criticized a thesis sometimes defended by theorists of probabilistic causality, namely, that a probabilistic cause must raise the probability of its effect in every possible set of causally relevant background conditions (the "contextual unanimity thesis"). I also suggested that a more promising analysis of probabilistic causality might be sought in terms of statistical relevance in a fair sample. Ellery Eells (1987) has defended the contextual unanimity thesis against my objections, and also raised (...) objections of his own to my positive claims. In this paper I defend and amplify both my objections to the contextual unanimity thesis and my constructive suggestion. (shrink)

El siguiente trabajo tiene como objetivo principal describir y analizar la percepción de Manuel Baldomero Ugarte sobre Estados Unidos. Ugarte fue literato y político, pero también fue un pensador interesado por los asuntos internacionales de América Latina. Evidencia de ello son sus propuestas integracionistas y antiimperialistas, en las cuales la presencia de Estados Unidos era evidente. Debido a lo anterior, se estima conveniente explicar qué pensó Ugarte sobre la nación norteamericana, y desde esa perspectiva, contribuir a la discusión sobre tan (...) trascendental intelectual latinoamericano. The purpose of this work is to describe and analyze the perception of Manuel Baldomero Ugarte about the United States. Ugarte was a writer and a politician, but it was also a thinker interested in the Latin America’s international affairs. Testimony of this are his integrationist and anti-imperialist proposals, in which the U.S. presence was evident. Thus, it is considered advisable to explain what he thought about the American nation, and from this perspective, to contribute to the discussion around this important Latin American intellectual. (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)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 42.2 (2004) 220-221 [Access article in PDF] Clyde Lee Miller. Reading Cusanus: Metaphor and Dialectic in a Conjectural Universe. Washington, D.C.: Catholic University of America Press, 2003. Pp. viii + 276. Cloth, $64.95. In an age where the idea of postmodernity gains more and more ground, the period of postmodern thinking has turned into a major challenge to the human mind. Whereas the (...) project of modernity revokes itself through the contradictions it has generated, the need to find new perspectives makes us wonder what happened in the 15th century when the Renaissance paved the way to modernity and still contained seeds of alternative developments which for one reason or another did not get a chance to germinate. This is an invitation to concentrate on the work of Nicholas of Cusa (1401-1464) as one of the major Renaissance thinkers.Miller's book is an attempt to promote the understanding of Cusanus by a close reading of six of the major works of this author. In reading these works he focuses on Cusan thought both as this thought presents itself in these works, and as it appears against the background of traditional philosophy, especially when seen in the light of the Neoplatonic tradition.The works in question are the books On Learned Ignorance (De docta ignorantia) and On Conjectures (De coniecturis), aptly presented under the title: "Envisiong the Whole," and "Conjecturing Oneness and Otherness" respectively. The remaining four works concern the The Layman: About Mind (Idiota de mente) in which Cusanus develops his understanding of the mind and of intellectual authenticity; The Vision of God (De visione Dei), a treatise on mystical theology and an invitation to enter the divine mystery through a combination of prayer and reflection; On the Not Other (De non aliud), a highly speculative work on divine immanence and transcendence; and The Hunt for Wisdom (De venatione sapientiae) in which Cusanus gives an account of his philosophy by connecting it with the metaphor of a hunt in ten different fields. [End Page 220]Miller begins his book with an Introduction in which he outlines his approach to Cusanus, taking the cue from Plato's image of the divided line with its emphasis on the dialectical distinction between noesis (intellect) and dianoia (reason), and from the dialogue On the Hidden God (De Deo abscondito), a brief discussion between a Heathen and a Christian in which Cusanus connects the theme of learned ignorance with the act of adoration. The distinction between reason and intellect is important because the work of Cusanus is a continuous effort to cope with the meaning of distinctions and their impact on our ways of thinking. The reference to the dialogue is significant because this text clearly indicates that the quest for God is the central issue in the thought of Cusanus, and that the notion of ignorance is actually connected with the theoretical and practical meaning of God.In his discussion of the six works Miller follows the text of Cusanus which he presents in the form of argumentative summaries and complementary reflections. His presentation is lucid and to the point. In his reflections on the text and context of Cusan thought he gives valuable insights into the historical position of Cusanus and the manner in which Nicholas appropriated and transformed traditional ways of thinking. At the same time Miller keeps track of the reception of Cusanus by contemporary scholarship and the various interpretations it has to offer.The book ends with a "reprise" of the previous chapters which provides "an overall perspective on Nicholas' thought and its main themes and proposals" (241). The central elements of this perspective are "the metaphysics of the Infinite and the finite" (242) and the doctrine of perspectival relations as it has been developed in De coniecturis. What connects them with one another finds expression in the distinction (and transition) between explanatory and exploratory metaphors (252); that is, between metaphors such as "image-exemplar" and "unfolding-enfolding," which provide explanatory structures for the interpretation of reality, and metaphors such... (shrink)

Analytic metaphysics has recently discovered biology as a means of grounding metaphysical theories. This has resulted in long-standing metaphysical puzzles, such as the problems of personal identity and material constitution, being increasingly addressed by appeal to a biological understanding of identity. This development within metaphysics is in significant tension with the growing tendency amongst philosophers of biology to regard biological identity as a deep puzzle in its own right, especially following recent advances in our understanding of symbiosis, the evolution of (...) multi-cellular organisms and the inherently dynamical character of living systems. Moreover, and building on these biological insights, the broadly substance ontological framework of metaphysical theories of biological identity appears problematic to a growing number of philosophers of biology who invoke process ontology instead. This volume addresses this tension, exploring to what extent it can be dissolved. For this purpose, the volume presents the first selection of essays exclusively focused on biological identity and written by experts in metaphysics, the philosophy of biology and biology. The resulting cross-disciplinary dialogue paves the way for a convincing account of biological identity that is both metaphysically constructive and scientifically informed, and will be of interest to metaphysicians, philosophers of biology and theoretical biologists. (shrink)

This book is a collection of essays by a leading philosopher of biology and spans his career over almost the last twenty years. Most of the topics that have been of concern to philosophers of biology in this period are touched on to some extent, and the collection of these essays in a convenient volume will certainly be welcomed by everyone working in this field. The essays are arranged chronologically, and divided into three sections. Although the chapters in the first (...) section have substantial interconnections, being involved with fundamental conceptual issues in evolutionary theory, on the whole there is not much attempt to tie the book into anything more than a sequence of independent essays. The later sections, moreover, cover a quite diverse range of topics. The whole is neither more nor less than the sum of the parts. For. (shrink)

Standard microbial evolutionary ontology is organized according to a nested hierarchy of entities at various levels of biological organization. It typically detects and defines these entities in relation to the most stable aspects of evolutionary processes, by identifying lineages evolving by a process of vertical inheritance from an ancestral entity. However, recent advances in microbiology indicate that such an ontology has important limitations. The various dynamics detected within microbiological systems reveal that a focus on the most stable entities (or features (...) of entities) over time inevitably underestimates the extent and nature of microbial diversity. These dynamics are not the outcome of the process of vertical descent alone. Other processes, often involving causal interactions between entities from distinct levels of biological organisation, or operating at different time scales, are responsible not only for the destabilisation of pre-existing entities, but also for the emergence and stabilisation of novel entities in the microbial world. In this article we consider microbial entities as more or less stabilised functional wholes, and sketch a network-based ontology that can represent a diverse set of processes including, for example, as well as phylogenetic relations, interactions that stabilise or destabilise the interacting entities, spatial relations, ecological connections, and genetic exchanges. We use this pluralistic framework for evaluating (i) the existing ontological assumptions in evolution (e.g. whether currently recognized entities are adequate for understanding the causes of change and stabilisation in the microbial world), and (ii) for identifying hidden ontological kinds, essentially invisible from within a more limited perspective. We propose to recognize additional classes of entities that provide new insights into the structure of the microbial world, namely “processually equivalent” entities, “processually versatile” entities, and “stabilized” entities. (shrink)

Although molecular biology has meant different things at different times, the term is often associated with a tendency to view cellular causation as conforming to simple linear schemas in which macro-scale effects are specified by micro-scale structures. The early achievements of molecular biologists were important for the formation of such an outlook, one to which the discovery of recombinant DNA techniques, and a number of other findings, gave new life even after the complexity of genotype–phenotype
relations had become apparent. Against this (...) background we outline how a range of scientific developments and conceptual considerations can be regarded as enabling and perhaps necessitating contemporary systems approaches. We suggest that philosophical ideas have a valuable part to play in making sense of complex scientific and disciplinary issues. (shrink)

In the context of scientists' reflections on genomics, we examine some fundamental issues in the emerging postgenomic discipline of systems biology. Systems biology is best understood as consisting of two streams. One, which we shall call ‘pragmatic systems biology’, emphasises large‐scale molecular interactions; the other, which we shall refer to as ‘systems‐theoretic biology’, emphasises system principles. Both are committed to mathematical modelling, and both lack a clear account of what biological systems are. We discuss the underlying issues in identifying systems (...) and how causality operates at different levels of organisation. We suggest that resolving such basic problems is a key task for successful systems biology, and that philosophers could contribute to its realisation. We conclude with an argument for more sociologically informed collaboration between scientists and philosophers. BioEssays 27:1270–1276, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

Viruses have been virtually absent from philosophy of biology. In this editorial introduction, we explain why we think viruses are philosophically important. We focus on six issues, and we show how they relate to classic questions of philosophy of biology and even general philosophy.

Regardless of leaders’ efforts to do the right thing and meet performance expectations, they make mistakes, with possible ramifications for followers’ and leaders’ well-being. Some leaders will apologize following transgressions, which may have positive implications for their followers’ and their own well-being, contingent upon the nature and severity of the transgressions. We examine these relationships in two separate studies. In Study 1, leader apologies had a positive relationship with followers’ psychological well-being and emotional health, and these relationships were moderated by (...) the severity of the transgression. In Study 2, leader apologies had a positive relationship with their own psychological well-being, positive emotional health and authentic pride. In addition, the nature of transgressions moderated the relationship between leader apologies and leaders’ positive emotions and authentic pride, while the severity of transgressions moderated the relationship between leader apologies and their positive emotions, psychological health, and authentic pride. Implications and future research directions are discussed. (shrink)

Concerning beauty, order, harmony, design.--Concerning moral good and evil.

THE LIFE Of FRANCIS BACON, LORD HIGH CHANCELLOR OF ENGLAND. THE ancient Egyptians had a law, which ordained that the actions and characters of their dead ...

An Essay on the Nature and Conduct of the Passions and Affections, with Illustrations on the Moral Sense (1728), jointly with Francis Hutcheson’s earlier work Inquiry into the Original of Our Ideas of Beauty and Virtue (1725), presents one of the most original and wide-ranging moral philosophies of the eighteenth century. These two works, each comprising two semi-autonomous treatises, were widely translated and vastly influential throughout the eighteenth century in England, continental Europe, and America. -/- The two works had (...) their greatest impact in Scotland and influenced many well-known Scottish philosophers, particularly those writing after the last Jacobite upheaval, in 1745. This can be seen in the concern of the post-1745 generation with analyzing human nature as the foundation of moral theory, with the “moral sense” and moral epistemology more generally, with the impartial spectator and the calm passions, and with the independence of benevolence from self-interest. In addition to the influence of his writings, Hutcheson was also a famed teacher whose Glasgow students, notably Adam Smith, held sway over generations of Scottish moral philosophers. -/- Despite their impact on Scottish letters, the four treatises were in fact written in Dublin, and the philosophers to whom Hutcheson responded and with whom he debated were in the main not Scottish but English, Irish, French, Roman, and Greek. Consequently, part of Hutcheson’s legacy was a cosmopolitan outlook among enlightened Scots, who learned to turn their eyes far from home. (shrink)

Managers often ask why their firm should have an ethics program, especially if no one has complained about unethical behavior. The pursuit of business ethics can cost money, they say. It can lose sales to less scrupulous competitors and can drain management time and energy. But as Harvard business professor Francis Aguilar points out, ethics scandals (such as over Beech-Nut's erzatz "apple juice" or Sears's padded car repair bills) can severely damage a firm, with punishing legal penalties, bad publicity, (...) and irreparably injured customer relations. Equally important if less obvious, unethical behavior can undermine a firm's organizational spirit. On the other hand, Aguilar argues, in a well run firm, ethical programs can actually enhance corporate performance, strengthening the company at every level and supercharging employee risk taking and innovation. In Managing Corporate Ethics, Aguilar shows managers how to create ethical programs within their organizations that not only discourage large-scale wrongdoing, but can contribute substantially to the achievement of corporate excellence. Aguilar's program is down-to-earth and comprehensive, and based on his extensive research on highly successful, ethical companies, both large and small. He recommends action on three fronts: first, get senior management to provide effective ethical leadership; second, set up an ethics program that promotes concern for the interests of people affected by the firm's operations and that provides safeguards against corrupting business pressures; and third, staff the company with ethical people and surround the organization with ethical advisors (including legal, financial, accounting, tax, and marketing consultants). To illuminate this three-step program, Aguilar incorporates the lessons learned in his in-depth study of ten prominent firms with proven successful ethics programs--among them Hewlett-Packard, Johnson & Johnson, Nucor Steel, Cray Research, ServiceMaster, and Texas Instruments. He examines Lincoln Electric's attention to compensation and job security to ensure quality products and to reduce the pressure or temptation to act unethically. He shows how General Mills, while pushing product line managers to compete aggressively, uses corporate staff units to guard against illegal or unacceptable claims (testing cake recipes, for example, to see if a product's quality fails under the less-than-perfect conditions of a normal kitchen). And he details how Armstrong World Industries uses pep talks, inspirational stories, role models, and ready access to management to promote ethical standards among employees. Throughout, Aguilar demonstrates convincingly that an ethical program pays dividends: that employees, suppliers, customers, and the community at large know when they are being treated in a positive and constructive manner, and are likely to respond in kind. Packed with real life examples of successful (and failed) ethical programs, Managing Corporate Ethics is a valuable roadmap to an often overlooked source of business success. (shrink)

This is the third of four volumes presenting all of Francis Ellingwood Abbot's major published articles. Any scholar or library interested in American philosophy, religious thought, and social and intellectual history should find this edition of his essays a useful addition to the collection. Francis E. Abbot was a noted American philosopher and champion of Free Religion. He was a member of C.S. Peirce's Metaphysical Club, the first American philosopher to support Charles Darwin, the founding editor of The (...) Index, a founder of the Free Religious Association, and the founding President of the National Liberal League of America. In addition to over six hundred articles, he was the author of Scientific Theism (1885), The Way Out of Agnosticism, Or The Philosophy of Free Religion (1890), and The Syllogistic Philosophy, or Prolegomena to Science (1906). (shrink)

This paper considers the applicability of standard accounts of causation to living systems. In particular it examines critically the increasing tendency to equate causal explanation with the identification of a mechanism. A range of differences between living systems and paradigm mechanisms are identified and discussed. While in principle it might be possible to accommodate an account of mechanism to these features, the attempt to do so risks reducing the idea of a mechanism to vacuity. It is proposed that the solution (...) to this problem requires the development of a philosophical account of process adequate to apply to living systems. (shrink)

This paper considers the applicability of standard accounts of causation to living systems. In particular it examines critically the increasing tendency to equate causal explanation with the identification of a mechanism. A range of differences between living systems and paradigm mechanisms are identified and discussed. While in principle it might be possible to accommodate an account of mechanism to these features, the attempt to do so risks reducing the idea of a mechanism to vacuity. It is proposed that the solution (...) to this problem requires the development of a philosophical account of process adequate to apply to living systems. (shrink)

It is a welcome development when academic philosophy starts to concern itself with practical issues, in such a way as to influence people's lives. Recently this has happened with one moral issue in particular—but infortunately it is the wrong issue, and people's actions have been influenced in the wrong way. The issue is that of the moral status and treatment of animals. A number of philosophers have argued for what they call ‘animal liberation’, comparing it directly with egalitarian causes such (...) as women's liberation and racial equality and suggesting that, if racism and sexism are rationally indefensible, so is ‘speciesism’. If one ought to give equal consideration to the interests of all human beings, then, so they daim, one must on the same grounds and in the same way recognize that ‘all animals are equal’, be they human or non-human. We believe that this assimilation of ‘animal liberation’ to human liberation movements is mistaken. (shrink)

Analytic metaphysics has recently discovered biology as a means of grounding metaphysical theories. This has resulted in long-standing metaphysical puzzles, such as the problems of personal identity and material constitution, being increasingly addressed by appeal to a biological understanding of identity. This development within metaphysics is in significant tension with the growing tendency amongst philosophers of biology to regard biological identity as a deep puzzle in its own right, especially following recent advances in our understanding of symbiosis, the evolution of (...) multi-cellular organisms and the inherently dynamical character of living systems. Moreover, and building on these biological insights, the broadly substance ontological framework of metaphysical theories of biological identity appears problematic to a growing number of philosophers of biology who invoke process ontology instead. This volume addresses this tension, exploring to what extent it can be dissolved. For this purpose, the volume presents the first selection of essays exclusively focused on biological identity and written by experts in metaphysics, the philosophy of biology and biology. The resulting cross-disciplinary dialogue paves the way for a convincing account of biological identity that is both metaphysically constructive and scientifically informed, and will be of interest to metaphysicians, philosophers of biology and theoretical biologists. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

Introduction -- Note on the texts -- An inquiry into the original of our ideas of beauty and virtue -- Treatise I -- An inquiry concerning beauty, order, & c. -- Treatise II -- An inquiry concerning the original of our ideas of virtue or moral good.

THE P R E F A C E, Giving fome ACCOUNT of the LIFE, WRITINGS, and CHARACTER of the AUTHOR. T"\R. FRANCIS HUTCHESON was born on the 8th of ...

This article identifies four approaches to arguing for democracy, showing that none has an adequate way of supporting both full adult inclusion and the exclusion of children. I focus in Section 2 on the arguments of David Estlund and Thomas Christiano, showing that their arguments against guardianship call into question the exclusion of children from the franchise. In Section 3, I explain why the exclusion of children constitutes an injustice, and in the final section, I consider two approaches to remedying (...) that injustice. Key Words: justice • democracy • children. (shrink)

The issue of energy and its potential localizability in general relativity has challenged physicists for more than a century. Many non-invariant measures were proposed over the years but an invariant measure was never found. We discovered the invariant localized energy measure by expanding the domain of investigation from space to spacetime. We note from relativity that the finiteness of the velocity of propagation of interactions necessarily induces indefiniteness in measurements. This is because the elements of actual physical systems being measured (...) as well as their detectors are characterized by entire four-velocity fields, which necessarily leads to information from a measured system being processed by the detector in a spread of time. General relativity adds additional indefiniteness because of the variation in proper time between elements. The uncertainty is encapsulated in a generalized uncertainty principle, in parallel with that of Heisenberg, which incorporates the localized contribution of gravity to energy. This naturally leads to a generalized uncertainty principle for momentum as well. These generalized forms and the gravitational contribution to localized energy would be expected to be of particular importance in the regimes of ultra-strong gravitational fields. We contrast our invariant spacetime energy measure with the standard 3-space energy measure which is familiar from special relativity, appreciating why general relativity demands a measure in spacetime as opposed to 3-space. We illustrate the misconceptions by certain authors of our approach. (shrink)

An inclusive vision of mathematics-- its beauty, its humanity, and its power to build virtues that help us all flourish. For mathematician Francis Su, a society without mathematical affection is like a city without museums. To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas. In this profound book, written for a diverse audience but especially for those disenchanted by their past experiences, an award-winning mathematician and educator weaves personal reflections, puzzles, and stories (...) to show how mathematics meets basic human desires and cultivates virtues essential for human flourishing. Readers will explore mathematical concepts-- and see how mathematical thinking can even fulfill such longings as for love, play, freedom, justice, and community. Some lessons come from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's, and Christopher Jackson, who discovered mathematics as an inmate in a federal prison. Christopher Jackson's letters to the author appear throughout the book and show how this intellectual pursuit can-- and must-- be open to all. (shrink)