This unique book presents a comprehensive and rigorous treatment of the theory of computability which is introductory yet self-contained. It takes a novel approach by looking at the subject using computation models rather than a limitation orientation, and is the first book of its kind to include software. Accompanying software simulations of almost all computational models are available for use in conjunction with the text, and numerous examples are provided on disk in a user-friendly format. Its applications to computer science (...) itself include interesting links to programming language theory, compiler design theory, and algorithm design. The software, numerous examples, and solutions make this book ideal for self-study by computer scientists and mathematicians alike. (shrink)

On Zermelo's view, any mathematical theory presupposes a non-empty domain, the elements of which enjoy equal status; furthermore, mathematical axioms must be chosen from among those propositions that reflect the equal status of domain elements. As for which propositions manage to do this, Zermelo's answer is, those that are ?symmetric?, meaning ?invariant under domain permutations?. We argue that symmetry constitutes Zermelo's conceptual analysis of ?general proposition?. Further, although others are commonly associated with the extension of Klein's Erlanger Programme to logic, (...) Zermelo's name has a place in that story. (shrink)

This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies (...) in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text. (shrink)

This essay summarizes key insights across the essays in the Hastings Center Report's special report “Time to Rebuild: Essays on Trust in Health Care and Science.” These insights concern trust and trustworthiness as distinct concepts, competence as a necessary but not sufficient input to trust, trust as a reciprocal good, trust as an interpersonal as well as structural phenomena, the ethical impermissibility of seeking to win trust without being trustworthy, building and borrowing trust as distinct strategies, and challenges to trustworthiness (...) posed by the contingent nature of science. Together, these insights stand to advance an area of research that we believe has been historically stymied by conceptual confusion and a long‐standing insistence on treating trust as a purely instrumental good. (shrink)

If I miss not the tenor of points and counterpoints, a recent discussion in this journal has been a novelly natural transaction in behalf of a great question at which many philosophers have labored—What is the place of Mind? R. S. Lillie, an eminent physiologist has been working toward a philosophical justification of certain biological key-facts, and H. Heath Bawden, a pioneer naturalist in philosophy and psychology, has been urging a physiological counter-statement. Both are logical men of science and aim (...) to rest on facts. Why do they define and value the “psychical” differently? (shrink)

In papers published between 1930 and 1935. Zermelo outlines a foundational program, with infinitary logic at its heart, that is intended to (1) secure axiomatic set theory as a foundation for arithmetic and analysis and (2) show that all mathematical propositions are decidable. Zermelo's theory of systems of infinitely long propositions may be termed "Cantorian" in that a logical distinction between open and closed domains plays a signal role. Well-foundedness and strong inaccessibility are used to systematically integrate highly transfinite concepts (...) of demonstrability and existence. Zermelo incompleteness is then the analogue of the Problem of Proper Classes, and the resolution of these two anomalies is similarly analogous. (shrink)

This study investigated (1) whether potential future purchasing agents were predisposed to accept gratuities or whether the practice of gratuity acceptance is a manifestation of the job itself, (2) whether the existence of a code of ethics forbidding gratuity acceptance curtails the occurrence, and (3) whether disparities in ethics policies between the sales and purchasing functions affect gratuity acceptance. Hypotheses based upon the concepts of organizational concern and institutionalized ethics are developed and empirically tested. Results suggest that future purchasing agents (...) are predisposed to accept gratuities and that formal written ethics policies decrease the acceptance of gratuities. Disparities in ethics policies between the sales and purchasing functions concerning gratuities failed to affect gratuity acceptance significantly. (shrink)

Although the terminology of Big Data has so far gained little traction in economics, the availability of unprecedentedly rich datasets and the need for new approaches – both epistemological and computational – to deal with them is an emerging issue for the discipline. Using interviews conducted with a cross-section of economists, this paper examines perspectives on Big Data across the discipline, the new types of data being used by researchers on economic issues, and the range of responses to this opportunity (...) amongst economists. First, we outline the areas in which it is being used, including the prediction and ‘nowcasting’ of economic trends; mapping and predicting influence in the context of marketing; and acting as a cheaper or more accurate substitute for existing types of data such as censuses or labour market data. We then analyse the broader current and potential contributions of Big Data to economics, such as the ways in which econometric methodology is being used to shed light on questions beyond economics, how Big Data is improving or changing economic models, and the kinds of collaborations arising around Big Data between economists and other disciplines. (shrink)

Symmetric propositions over domain $\mathfrak{D}$ and signature $\Sigma = \langle R^{n_1}_1, \ldots, R^{n_p}_p \rangle$ are characterized following Zermelo, and a correlation of such propositions with logical type- $\langle \vec{n} \rangle$ quantifiers over $\mathfrak{D}$ is described. Boolean algebras of symmetric propositions over $\mathfrak{D}$ and Σ are shown to be isomorphic to algebras of logical type- $\langle \vec{n} \rangle$ quantifiers over $\mathfrak{D}$. This last result may provide empirical support for Tarski’s claim that logical terms over fixed domain are all and only those (...) invariant under domain permutations. (shrink)

An idea attributable to Russell serves to extend Zermelo’s theory of systems of infinitely long propositions to infinitary relations. Specifically, relations over a given domain \ of individuals will now be identified with propositions over an auxiliary domain \ subsuming \. Three applications of the resulting theory of infinitary relations are presented. First, it is used to reconstruct Zermelo’s original theory of urelements and sets in a manner that achieves most, if not all, of his early aims. Second, the new (...) account of infinitary relations makes possible a concise characterization of parametric definability with respect to a purely relational structure. Finally, based on his foundational philosophy of the primacy of the infinite, Zermelo rejected Gödel’s First Incompleteness Theorem; it is shown that the new theory of infinitary relations can be brought to bear, positively, in that connection as well. (shrink)

What we call first‐order logic over fixed domain was initiated, in a certain guise, by Peirce around 1885 and championed, albeit in idiosyncratic form, by Zermelo in papers from the 1930s. We characterise such logics model‐ and proof‐theoretically and argue that they constitute exploration of a clearly circumscribed conception of domain‐dependent generality. Whereas a logic, or family of such, can be of interest for any of a variety of reasons, we suggest that one of those reasons might be that said (...) logic fosters some clarification regarding just what qualifies as a logical concept, a logical operation, or a logical law. (shrink)

Bringing between two covers the most influential and accessible articles on Plato's Republic, this collection illuminates what is widely held to be the most important work of Western philosophy and political theory. It will be valuable not only to philosophers, but to political theorists, historians, classicists, literary scholars, and interested general readers.

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

Responding to volatile criticisms frequently leveled at Leo Strauss and those he influenced, the prominent contributors to this volume demonstrate the profound influence that Strauss and his students have exerted on American liberal democracy and contemporary political thought. By stressing the enduring vitality of classic books and by articulating the theoretical and practical flaws of relativism and historicism, the contributors argue that Strauss and the Straussians have identified fundamental crises of modernity and liberal democracy.

This book is a collection of secondary essays on America's most important philosophic thinkers—statesmen, judges, writers, educators, and activists—from the colonial period to the present. Each essay is a comprehensive introduction to the thought of a noted American on the fundamental meaning of the American regime.

Intellectual humility, which entails openness to other views and a willingness to listen and engage with them, is crucial for facilitating civil dialogue and progress in debate between opposing sides. In the present research, we tested whether intellectual humility can be reliably detected in discourse and experimentally increased by a prior self-affirmation task. Three-hundred and three participants took part in 116 audio and video-recorded group discussions. Blind to condition, linguists coded participants’ discourse to create an intellectual humility score. As expected, (...) the self-affirmation task increased the coded intellectual humility, as well as participants’ self-rated prosocial affect (e.g., empathy). Unexpectedly, the effect on prosocial affect did not mediate the link between experimental condition and intellectual humility in debate. Self-reported intellectual humility and other personality variables were uncorrelated with expert-coded intellectual humility. Implications of these findings for understanding the social psychological mechanisms underpinning intellectual humility are considered. (shrink)

Depending on how one construes the Greek at Apology at 30b2-4, Socrates says either that money and everything else good for men comes from virtue or that money and everything else becomes good for men because of virtue. I defend the first option (which is agreed to be the more natural construal) against arguments (from Burnet, Taylor and Burnyeat) that it commits Socrates to something he could not have held.

_Theurgy and the Soul_ is a study of Iamblichus of Syria, whose teachings set the final form of pagan spirituality prior to the Christianization of the Roman Empire. Gregory Shaw focuses on the theory and practice of theurgy, the most controversial and significant aspect of Iamblichus's Platonism. Theurgy literally means "divine action." Unlike previous Platonists who stressed the elevated status of the human soul, Iamblichus taught that the soul descended completely into the body and thereby required the performance of (...) theurgic rites—revealed by the gods—to unite the soul with the One. Iamblichus was once considered one of the great philosophers whose views on the soul and the importance of ritual profoundly influenced subsequent Platonists such as Proclus and Damascius. The Emperor Julian followed Iamblichus's teachings to guide the restoration of traditional pagan cults in his campaign against Christianity. Although Julian was unsuccessful, Iamblichus's ideas persisted well into the Middle Ages and beyond. His vision of a hierarchical cosmos united by divine ritual became the dominant world view for the entire medieval world and played an important role in the Renaissance Platonism of Marsilio Ficino. Even Ralph Waldo Emerson wrote that he expected a reading of Iamblichus to cause a "revival in the churches." But modern scholars have dismissed him, seeing theurgy as ritual magic or "manipulation of the gods." Shaw, however, shows that theurgy was a subtle and intellectually sophisticated attempt to apply Platonic and Pythagorean teachings to the full expression of human existence in the material world. (shrink)

"First Published in 1999, Routledge is an imprint of Taylor & Francis, an informa company.".

Many discussions of J. S. Mill's concept of liberty focus too narrowly on On Liberty and fail to acknowledge that his treatment of related issues elsewhere may modify its leading doctrines. Mill and Paternalism demonstrates how a contextual reading suggests that in Principles of Political Economy, and also his writings on Ireland, India and on domestic issues like land reform, Mill proposed a substantially more interventionist account of the state than On Liberty seems to imply. This helps to explain Mill's (...) sympathies for socialism after 1848, as well as his Malthusianism and feminism, which, in conjunction with Harriet Taylor's views, are central to his later discussions of the family and marriage. Feminism, indeed, is shown to provide the answer to the problem which most agitated Mill, overpopulation. Thus Gregory Claeys sheds new lights on many of Mill's overarching preoccupations, including the theory of liberty at the heart of On Liberty. (shrink)

First published in 1995. Routledge is an imprint of Taylor & Francis, an informa company.

In the last two decades, a number of political theorists have published a great deal of theory that argues for the centrality of the idea of recognition. In the most prominent of these papers, Charles Taylor makes the claim that “recognition is a human need.”1 The immediate spur for this flurry of interest has been a discussion of multiculturalism and its attendant issues, which are expressed in terms of “group recognition.”2 This work focuses on the importance of group identity (...) or social characteristics, as well as on their relation to individualism and liberalism. These issues are important, and there is…. (shrink)

Charles Taylor has recently provided an in-depth exploration of secularity, with a central characteristic being the understanding that religious commitment is optional. This essay extends this analysis, considering the possibility that American society may be entering a second stage of secularity, one in which the possibility of religious commitment ceases to be an option at all for many. The possible implications of such a development are considered for the theology-and-science dialogue.

Ralph Cudworth, Doctor of Divinity, Master of Christ’s College at Cambridge, and philosophical chieftain of the Cambridge Platonists, published The True Intellectual System of the Universe in 1678 to disprove “the fatal necessity of all actions and events.” This disproof would destroy the various atheisms founded upon such “fatal necessity”; it would also correct those Christians who mistakenly honoured God by subjecting men to a divinely administered fate. Cudworth, with a constant eye on Hobbes, whom he did not name, (...) struck at atheism by establishing a “true intellectual system” and by arguing away its principle of fate. His design swelled as he worked to meet the various versions of “fatal necessity” with the various atheisms founded upon them, to establish the true doctrine, and to accommodate his own copious learning, and it swelled too much for the published work to be more than a first instalment of his whole design. (shrink)

The claim that photographs are fictionally incompetent (i.e. that they can only depict those particulars they are appropriately causally related to) is argued by Noël Carroll, Gregory Currie, and Nigel Warburton to be falsified by cinematic works of fiction. In response I firstly argue that it does not follow from cinema's having a capacity for the representation of ficta that photography has a capacity for the representation of ficta. Secondly, and inspired by the work of Roger Scruton, I develop (...) an account of how it is that cinema represents ficta on which this is fundamentally a matter of dramatic/theatrical representation. I argue that in cinematic fiction photography delivers a pre-existent representation of ficta rather than creating or generating fictional content. With this being so, the claim that photography is fictionally incompetent is compatible with cinematic fiction. 1. (shrink)

John Stuart Mill (1806-73) is widely regarded as the leading liberal philosopher, economist, and political theorist of nineteenth century Britain. In his lifetime he was best known for his System of Logic (1843) and the Principles of Political Economy (1848). Today Mill is chiefly identified with On Liberty (1859), perhaps the definitive text of modern liberal statement of its subject, and probably the single most important work of modern political thought. Mill was also the first major male feminist thinker of (...) the period (author of The Subjection of Women, 1869), and the first, as an MP, to introduce a bill for female enfranchisement before Parliament. This Very Short Introduction offers a brief survey of the life and key ideas of this most influential Victorian British writer. Moving chronologically, Gregory Claeys outlines the philosophical background out of which Mill developed, chiefly through the ideas of Jeremy Bentham and James Mill. He demonstrates how Mill's personal life, especially his 'mental crisis' of 1827, and his relationship with Harriet Taylor, were integral to his intellectual development. Throughout Claeys considers Mill's key works set within the context of his lesser writings and correspondence, and discusses the more controversial aspects of his thought concerning religion, secularism, and birth control. (shrink)

"First Published in 1999, Routledge is an imprint of Taylor & Francis, an informa company.".

"First Published in 1999, Routledge is an imprint of Taylor & Francis, an informa company.".

Human geography, as a subject, has become widely recognized since its connections with the social sciences have widened and deepended the study of people, places and social structures. Horizons in Human Geography provides a clear and accessible sketch map of some of the latest and most promising developments in the subject. The book starts by assessing the role and limitations of techniques, models and theories and proceeds to provide a broad-ranging overview of the major social, cultural, urban, regional, political, economic (...) and environmental issues confronting geographers today. Contents: Introduction; Part I: Beyond The Quantitative Revolution; Part II: People and Places, Societies and Spaces; Part III: Explorations in the City; IV: Landscapes of Production; Part V: Regional Geographies and Global Perspectives; Part VI: Politicising The Environment. Contributors: Derek Gregory, Rex Walford, Michael J. Clark, Alan Wilson, R. J. Johnston, John Eyles, Denis Cosgrove, Linda McDowell, Roger Lee, Keith Bassett, John Short, Richard Dennis, Ian Douglas, Doreen Massey, Richard Meegan, John Harriss, Barbara Hariss, Nigel Thrift, Michael Taylor, Peter Taylor, Graham E. Smith, Stuart Cobridge, Judith Rees, Timothy O'Riordan and Bill Mead. (shrink)

Christiane Bailey and Chloë Taylor (Editorial Introduction) Sue Donaldson (Stirring the Pot - A short play in six scenes) Ralph Acampora (La diversification de la recherche en éthique animale et en études animales) Eva Giraud (Veganism as Affirmative Biopolitics: Moving Towards a Posthumanist Ethics?) Leonard Lawlor (The Flipside of Violence, or Beyond the Thought of Good Enough) Kelly Struthers Montford (The “Present Referent”: Nonhuman Animal Sacrifice and the Constitution of Dominant Albertan Identity) James Stanescu (Beyond Biopolitics: Animal Studies, (...) Factory Farms, and the Advent of Deading Life) Ian Werkheiser (Domination and Consumption: An Examination of Veganism, Anarchism, and Ecofeminism) Cynthia Willett (Water and Wing Give Wonder: Trans-Species Cosmopolitanism) Corey Lee Wrenn (Nonhuman Animal Rights, Alternative Food Systems, and the Non-Profit Industrial Complex) Emily R. Douglas (Eat or Be Eaten: A Feminist Phenomenology of Women as Food) Gary Steiner’s Animals and the Limits of Postmodernism (New York: Columbia University Press, 2013) Chloë Taylor (“Postmodern” Critical Animal Theory: A Defense) Patrick Llored (La déconstruction derridienne peut-elle fonder une communauté politique et morale entre vivants humains et non humains?) Jan Dutkiewicz (“Postmodernism,” Politics, and Pigs) Gary Steiner (Response to Commentators). (shrink)

First Published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.