'The infinite! No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.' David Hilbert (1862-1943). This interdisciplinary study of infinity explores the concept through the prism of mathematics and then offers more expansive investigations in areas beyond mathematical boundaries to reflect the broader, deeper implications of infinity for human intellectual thought. More than a dozen (...) world-renowned researchers in the fields of mathematics, physics, cosmology, philosophy, and theology offer a rich intellectual exchange among various current viewpoints, rather than a static picture of accepted views on infinity. The book starts with a historical examination of the transformation of infinity from a philosophical and theological study to one dominated by mathematics. It then offers technical discussions on the understanding of mathematical infinity. Following this, the book considers the perspectives of physics and cosmology: Can infinity be found in the real universe? Finally, the book returns to questions of philosophical and theological aspects of infinity"--Provided by publisher. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The English Polydaedali:How Gabriel Harvey Read Late Tudor LondonNicholas PopperHarvey and GauricoIn 1590 Gabriel Harvey read his copy of Luca Gaurico's 1552 Tractatus Astrologicus, a collection of genitures and commentaries for cities and individuals.1 Harvey had spent the previous twenty-five years at Oxford and Cambridge, mastering Greek and Latin, earning renown as a rhetorician, and promoting English letters. He was a well-known partisan of the French (...) Calvinist Peter Ramus, whose works on curriculum reform had sparked vicious [End Page 351] controversies in the English universities. But Harvey read Gaurico far removed from the schools where he had acquired fame and notoriety as an orator and poet. He had recently relocated to London, where he daily faced a dense, active city unlike his native Saffron Walden and the university towns. Nevertheless he read as he always had, carefully recording his reactions in the margins of the printed text, filling blank spaces with his own commentaries on the subjects presented by Gaurico. The notes disclose an experience of reading that intervened in contemporary debates regarding technology, astrology and utility.2 They also place Harvey among a group of scholars in London in the 1590s, such as Francis Bacon and Hugh Plat, who were examining the benefits local artisans might offer the commonwealth and reconsidering the intellectual status of craft knowledge.Harvey read and annotated Gaurico on several occasions, but the particular strain of notes that I will follow, united by a common ink and hand, engages the learning and erudition of Gaurico's subjects.3 Concentrated almost [End Page 352] exclusively in Book Four, which discussed learned men, these annotations evaluate the poets, philosophers, philologists, and others whom Gaurico had canonized as especially learned.There are only spare annotations prior to Book Four. On the title page of Book Two, devoted to churchmen, Harvey observes the quality of the individuals Gaurico presented and details his own method of evaluation:The most excellent Exemplars of this century [are] in Gaurico, and Cardano: Giovio, and Guiccardini. There are as many of the wisest men as of the greatest actors. Still others live, whether inferior, equal, or superior. And it is of interest to every skillful artificer, to know those most outstanding in their class, and the most celebrated professors of all. Certainly it is very profitable to observe exquisitely the most perfect artificers either of the world or of neighboring nations, or at least of your own people, and to consider with most cunning reason what it is, where it comes from, and what is most excellent. But seriously, and solidly, and always to the point, seeing that singular things are efficacious and are useful to polytechnoscopy. It is judicious to avoid all trivial detail, and to consider only the most pregnant theorists and practitioners of operating.4The notion of a sophisticated form of active knowledge labeled "polytechnoscopy" is the most striking element of this passage. This term seems to have been Harvey's own invention, with no direct precedents; nor was it adopted or used by others after him.Harvey repeatedly referred to polytechnoscopy in his notes. A carefully designed triptych annotation on the title page of Book Four clarifies it as a category uniting practice and knowledge. To the left Harvey wrote, "it is my task to observe the most excellent examples of this age which are useful for polytechnoscopy." On the right, "a polytechnic, polymechanic, polydaedalic, and almost panepistemic book; and likewise sufficiently polychristian. For philologists should be skimmed through; while polytechnics should be examined closely; as I did not only in the Lives of Giovio, but also in those of [End Page 353] Laertius, Eunapius, Philostratus, and others."5 The related Greek descriptors "polymechanic" and "polydaedalic" shed further light on polytechnoscopy. This constellation of terms refers to a method of garnering information by deploying technical knowledge. While not a systematic discipline, its practices—active applicability, craft expertise, observation of experience—constitute a significant realm of learning.In the central panel of the triptych, Harvey notes:[I] compared [this] to Giovio's Elegies of Learned Men. Give me the best man outdoors, and his image at home. For even true life is... (shrink)

According to relationism, for Alice to believe that some rabbits can speak is for Alice to stand in a relation to a further entity, some rabbits can speak. But what could this further entity possibly be? Higher-order metaphysics seems to offer a simple, natural answer. On this view (roughly put), expressions in different syntactic categories (for instance: names, predicates, sentences) in general denote entities in correspondingly different ontological categories. Alice's belief can thus be understood to relate her to a sui (...) generis entity denoted by "some rabbits can speak", belonging to a different ontological category than Alice herself. This straightforward account of the attitudes has historically been deemed so attractive that it was seen as providing an important motivation for higher-order metaphysics itself (Prior [1971]). But I argue that it is not as straightforward as it might seem, and in fact that propositional attitudes present a foundational challenge for higher-order metaphysics. (shrink)

I hold no view as to what actions are basic, but I shall attempt to show in what follows that actions like raising an arm never are. My contention is that these actions involve actions of physical exertion on the part of the agent, the involvement being of a sort generally taken to be excluded by an actions being basic.

Some of the most significant policy responses to cases of fraudulent and questionable conduct by scientists have been to strengthen professionalism among scientists, whether by codes of conduct, integrity boards, or mandatory research integrity training programs. Yet there has been little systematic discussion about what professionalism in scientific research should mean. In this paper I draw on the sociology of the professions and on data comparing codes of conduct in science to those in the professions, in order to examine what (...) precisely the model of professionalism implies for scientific research. I argue that professionalism, more than any other single organizational logic, is appropriate for scientific research, and that codes of conduct for scientists should strengthen statements concerning scientific autonomy and competence, as well as the scientific service ideal. (shrink)

Over the last half century, a multijurisdictional, multiscale system of governance has emerged to address concerns associated with toxic chemicals that have the capacity to bioaccumulate in organisms and biomagnify in food chains, leading to fish consumption advisories. Components of this system of governance include international conventions (such as the Stockholm Convention on Persistent Organic Pollutants and the Minamata Convention on Mercury), laws enacted by nation states and their subjurisdictions, and efforts to adaptively manage regional ecosystems (such as the U.S.–Canadian (...) Great Lakes). Given that many of these compounds – including mercury, industrial chemicals such as polychlorinated biphenyls, and pesticides such as toxaphene – circulate throughout the globe through cycles of deposition and reemission, regional efforts to eliminate the need for fish consumption advisories cannot be successful without efforts to reduce emissions everywhere in the world. This paper argues that the scientific community, by monitoring the concentrations of these compounds in the atmosphere and by modeling their fate and transport, play an important role in connecting the various jurisdictional scales of governance. In addition, the monitoring networks that this community of scientists has established can be visualized as a technology of governance essential in an era in which societies have the capacity to produce and release such chemicals on an industrial scale. (shrink)

A salient if under researched feature of the new age of global inequalities is the rise to prominence of entrepreneurial philanthropy, the pursuit of transformational social goals through philanthropic investment in projects animated by entrepreneurial principles. Super-wealthy entrepreneurs in this way extend their suzerainty from the domain of the economic to the domains of the social and political. We explore the ethics and ethical implications of entrepreneurial philanthropy through systematic comparison with what we call customary philanthropy, which preferences support for (...) established institutions and social practices. We analyse the ethical statements made at interview by 24 elite UK philanthropists, 12 customary and 12 entrepreneurial, to reveal the co-existence of two ethically charged narratives of elite philanthropic motivations, each instrumental in maintaining the established socio-economic order. We conclude that entrepreneurial philanthropy, as an ostensibly efficacious instrument of social justice, is ethically flawed by its unremitting impulse toward ideological purity. (shrink)

Social media has invaded our private, professional, and public lives. While corporations continue to portray social media as a celebration of self-expression and freedom, public opinion, by contrast, seems to have decidedly turned against social media. Yet we continue to use it just the same. What is social media, and how should we live with it? Is it the promise of a happier and more interconnected humanity, or a vehicle for toxic self-promotion? In this essay I examine the very structure (...) of social media communications in order to sketch how we should engage with social media. Social media communications are, I argue, a public communication of private content. This allows connections to be made with others in ways that would not otherwise be possible; however, it also submits the private to a status competition, which in turn is linked to mental health challenges. A ‘virtuous’ engagement with social media means being aware of these dynamics, and choosing to subordinate social media to other, more important goods. (shrink)

Unmatched in scholarship and scope, The International Encyclopedia of Ethics is the definitive single-source reference work on Ethics, available both in print and online. Comprises over 700 entries, ranging from 1000 to 10,000 words in length, written by an international cast of subject experts Is arranged across 9 fully cross-referenced volumes including a comprehensive index Provides clear definitions and explanations of all areas of ethics including the topics, movements, arguments, and key figures in Normative Ethics, Metaethics, and Practical Ethics Covers (...) the major philosophical and religious traditions Offers an unprecedented level of authority, accuracy and balance with all entries being blind peer-reviewed. (shrink)

I argue that the reference for “God” is determined by the definite description “the being that is worthy of our worship.” I describe two desiderata for rival theories of the reference of “God” to meet: accessibility and scope. I explain the deficiencies of a view where God is dubbed “God” and the name passed down by causal chains and a view where “God” picks out the unique satisfier of a traditional definite description. After articulating the “Worship-Worthiness” view, I show how (...) it best satisfies the desiderata. I then respond to some putative counterexamples to the view. (shrink)

“Meta-argument allegations” consist of protestations that an interlocutor’s speech is wrongfully offensive or will trigger undesirable social consequences. Such protestations are meta-argument in the sense that they do not interrogate the soundness of an opponent’s argumentation, but instead focus on external features of that argument. They are allegations because they imply moral wrongdoing. There is a legitimate place for meta-argument allegations, and the moral and epistemic goods that can come from them will be front of mind for those levelling such (...) allegations. But I argue there is a dark side to such allegations, and their epistemic and moral costs must be seriously weighed. Meta-argument allegations have a concerning capacity to derail discussions about important topics, stymieing argumentational interactions and the goods they provide. Such allegations can license efforts to silence, punish and deter—even as they provoke the original speaker to retaliate in kind. Used liberally, such allegations can escalate conflicts, block open-mindedness, and discourage constructive dialogues. In response, I defend “argumentational tolerance”—a principled wariness in employing meta-argument allegations—as a virtue of ethical argument. (shrink)

This article examines the emergence of the Nyāya distinction between vāda and jalpa as didactic-scientific and agonistic-sophistical forms of debate, respectively. Looking at the relevant sutras in Gautama’s Nyāya-sūtra (NS 1.2.1-3) in light of the earlier discussion of the types of debate in Caraka Saṃhitā 8, the article argues that certain ambiguities and obscurities in the former text can be explained on the hypothesis that the early Nyāya presupposed an agonistic understanding of vāda similar to what we find in Caraka.

This essay was first presented in somewhat different form at the National Humanities Center, Research Triangle Park, North Carolina, in January 1987, when the author was in residence there on a fellowship sponsored by the Mellon Foundation.

The Nuffield Council on Bioethics examines ethical issues raised by new developments in biology and medicine. Established by the Nuffield Foundation in 1991, the Council is an independent body, funded jointly by the Foundation, the Medical Research Council and the Wellcome Trust. Independence and quality are the underlining principles of the Council, and the way the Council works has been designed to ensure that its reports are thorough, authoritative and provide a novel, policy-oriented approach to difficult ethical dilemmas. Recent reports (...) have considered the issues raised by public health and critical care decisions in fetal and neonatal medicine. The Council is currently considering the ethical dilemmas surrounding dementia. (shrink)

Embryonic development combines paradoxical properties: it has great precision, it is usually conducted at breakneck speed and it is flexible on relatively short evolutionary time scales, particularly at early stages. While these features appear mutually exclusive, we consider how they may be reconciled by the properties of key early regulatory networks. We illustrate these ideas with the network that controls development of endoderm progenitors. We argue that this network enables precision because of its intrinsic stability, self propagation and dependence on (...) signalling. The network enables high developmental speed because it is rapidly established by maternal inputs at multiple points. In turn these properties confer flexibility on an evolutionary time scale because they can be initiated in many ways, while buffering essential progenitor cell populations against changes in their embryonic environment on both evolutionary and developmental time scales. Although stable, these networks must be capable of rapid dissolution as cell differentiation progresses. While we focus on the core early endodermal network of vertebrates, we argue that these properties are likely to be general in early embryonic stem cell populations, such as mammalian ES cells. BioEssays 30:757–765, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

The results of this paper concern the effective cardinal structure of the subsets of [ω1]<ω1, the set of all countable subsets of ω1. The main results include dichotomy theorems and theorems which show that the effective cardinal structure is complicated.

First published in 1994. Routledge is an imprint of Taylor & Francis, an informa company.

Are religious experiences evidence about God's nature? How should we judge between two religious experiences with conflicting contents, when both have passed the tests we would normally use to sort reliable from misleading experiences? Divine Disclosures argues that the best arguments for skepticism about religious experience stem from a lack of a good answer to the second question, and sets out to devise and defend a method for evaluating religious experiences in a way that avoids charges of vicious circularity and (...) lack of precision. On the way, it presents contributions to the use of decision and probability theory in meta-ethics and philosophy of religion, and applies contemporary philosophy of language to method in theology to argue that all parties to debates about God's nature must agree on a root understanding of God as a perfect being. (shrink)

Presents reflections on museum philosophy for the 21st century from an international group of contributors.

This chapter considers the most notorious and controversial aspect of the Marxist theory of law: the persistent hostility which Marxists have shown towards law. Two closely related claims have been made by Marxists. In the first place it has been predicted that there will be no law in a Communist society. The second argument against the necessity for law goes further: not only will law disappear under Communism, but it is also contended that legal systems represent the deepest evils of (...) modern social formations, and, that the absence of law will be a key feature of a truly free society. Before explaining and defending those bold claims, the chapter considers a preliminary attack mounted by Marxists against the contrary view that law is necessary for human civilization. This orthodoxy of modern political theory is dubbed by Marxists with the title ‘fetishism of law’. This signifies that it is a mistaken assumption which leads to a distorted understanding of the world. After considering how this erroneous view has become so widespread and why it is false, the chapter turns to the arguments which demonstrate the thesis that law is unnecessary, and that it will disappear in a Communist society. (shrink)

It is a little understood fact that the system of formal logic presented in Wittgenstein’s Tractatusprovides the basis for an alternative general semantics for a predicate calculus that is consistent and coherent, essentially independent of the metaphysics of logical atomism, and philosophically illuminating in its own right. The purpose of this paper is threefold: to describe the general characteristics of a Tractarian-style semantics, to defend the Tractatus system against the charge of expressive incompleteness as levelled by Robert Fogelin, and to (...) give a semantics for a formal language that is the Tractarian equivalent of a first-order predicate calculus. Of note in regard to the latter is the fact that a Tractatusstyle truth-definition makes no appeal to the technical trick of defining truth in terms of the satisfaction of predicates by infinite sequences of objects, yet is materially equivalent to the usual Tarski-style truth-definitions. (shrink)