Explains how our innate pattern-making abilities allow us to perform mathematical reasoning.

Classical logic, beginning with the work of Aristotle, has developed into a powerful and rigorous mathematical theory with many applications in mathematics and ...

"[Goodbye, Descartes] is certain to attract attention and controversy..a fascinating journey to the edges of logical thinking and beyond." -Publishers Weekly Critical Acclaim for Keith Devlin's Previous Book Mathematics: The Science of Patterns "A book such as this belongs in the personal library of everyone interested in learning about some of the most subtle and profound works of the human spirit." -American Scientist "Devlin's very attractive book is a well-written attempt to explain mathematics to educated nonmathematicians. the (...) basic ideas are presented in a clear, concise, and easily understood manner. Highly recommended." -Choice "[Devlin] has found an interesting way of exhibiting how mathematics is unified. the author's presentation is a tour de force." -Mathematical Reviews A Selection of the Newbridge Library of Science and Reader's Subscription. (shrink)

"[Goodbye, Descartes] is certain to attract attention and controversy..a fascinating journey to the edges of logical thinking and beyond." -Publishers Weekly Critical Acclaim for Keith Devlin's Previous Book Mathematics: The Science of Patterns "A book such as this belongs in the personal library of everyone interested in learning about some of the most subtle and profound works of the human spirit." -American Scientist "Devlin's very attractive book is a well-written attempt to explain mathematics to educated nonmathematicians. the (...) basic ideas are presented in a clear, concise, and easily understood manner. Highly recommended." -Choice "[Devlin] has found an interesting way of exhibiting how mathematics is unified. the author's presentation is a tour de force." -Mathematical Reviews A Selection of the Newbridge Library of Science and Reader's Subscription. (shrink)

Recent years have seen a growing acknowledgement within the mathematical community that mathematics is cognitively/socially constructed. Yet to anyone doing mathematics, it seems totally objective. The sensation in pursuing mathematical research is of discovering prior (eternal) truths about an external (abstract) world. Although the community can and does decide which topics to pursue and which axioms to adopt, neither an individual mathematician nor the entire community can choose whether a particular mathematical statement is true or false, based on the given (...) axioms. Moreover, all the evidence suggests that all practitioners work with the same ontology. (My number 7 is exactly the same as yours.) How can we reconcile the notion that people construct mathematics, with this apparent choice-free, predetermined objectivity? I believe the answer is to be found by examining what mathematical thinking is (as a mental activity) and the way the human brain acquired the capacity for mathematical thinking. (shrink)

In [2], Prikry showed that if κ is a weakly inaccessible cardinal which carries a Rowbottom filter, then there is a Boolean extension of V (the universe), having the same cardinals as V, in which cf(κ) = ω. In this note, we obtain necessary and sufficient conditions which a filter D on κ must possess in order that this may be done.

Various equivalents and weakenings of the combinatorial principle $\diamond$ are considered. The paper contains both absolute results and consistency results. Also included is a new characterisation of the notion of a stationary subset of ω 1.

I argue that the role played by infons in the kind of mathematical theory of information being developed by several workers affiliated to CSLI is analogous to that of the various number systems in mathematics. In particular, I present a mathematical construction of infons in terms of representations and informational equivalences between them. The main theme of the paper arose from an electronic mail exchange with Pat Hayes of Xeroxparc. The exposition derives from a talk I gave at theTheories of (...) Partial Information conference held at the University of Texas at Austin, January 1990. (shrink)

Various equivalents and weakenings of the combinatorial principle $\diamond$ are considered. The paper contains both absolute results and consistency results. Also included is a new characterisation of the notion of a stationary subset of $\omega_1$.

For most of the 1980s, Jon Barwise focused much of his research in the area of natural language semantics. This article surveys his research publications in that area.Most, but not all, of those publications were in the area of situation semantics, a new approach to natural language semantics Barwise developed jointly with his colleague John Perry in the first half of the 1980s. That work was both blessed, and cursed, by becoming closely identified in academic circles with the award of (...) a $23 million gift to Stanford from the System Development Foundation for the establishment in 1983 of its Center for the Study of Language and Information. The development of situation semantics, and in due course its underlying mathematical foundation Situation Theory, carried out for the most part within the framework of CSLI's STASS research group, was actually a relatively small part of the overall research program at CSLI. But because Barwise and Perry were leading figures at CSLI, were centrally involved in securing the SDF gift, and were respectively the first and second directors of CSLI, a general impression sprung up that the two of them had been awarded millions of dollars to develop situation semantics.A major consequence of this false impression was that from the theory's early days, a great deal of interest was shown in the project. With so many accomplished scholars pouring over the work while the ink was still wet on the manuscript pages, Barwise and Perry were able to take advantage of a broad range of helpful criticism. This meant that they were able to develop the new theory much more rapidly than would otherwise have been the case. (shrink)

We consider various strengthenings of the combinatorial principle ⋄ + which are provable from V = L, and give applications in set theory.

For most of the 1980s, Jon Barwise focused much of his research in the area of natural language semantics. This article surveys his research publications in that area.Most, but not all, of those publications were in the area of situation semantics, a new approach to natural language semantics Barwise developed jointly with his colleague John Perry in the first half of the 1980s. That work was both blessed, and cursed, by becoming closely identified in academic circles with the award of (...) a $23 million gift to Stanford from the System Development Foundation for the establishment in 1983 of its Center for the Study of Language and Information. The development of situation semantics, and in due course its underlying mathematical foundation Situation Theory, carried out for the most part within the framework of CSLI's STASS research group, was actually a relatively small part of the overall research program at CSLI. But because Barwise and Perry were leading figures at CSLI, were centrally involved in securing the SDF gift, and were respectively the first and second directors of CSLI, a general impression sprung up that the two of them had been awarded millions of dollars to develop situation semantics.A major consequence of this false impression was that from the theory's early days, a great deal of interest was shown in the project. With so many accomplished scholars pouring over the work while the ink was still wet on the manuscript pages, Barwise and Perry were able to take advantage of a broad range of helpful criticism. This meant that they were able to develop the new theory much more rapidly than would otherwise have been the case. (shrink)

In this important new text, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the accepted definition of knowledge as justified true belief, Lehrer explores the truth, belief and justification conditions on the way to a thorough examination of foundation theories of knowledge, externalism and naturalized epistemologies, internalism and modern coherence theories as well as recent reliabilist and causal theories. Lehrer gives all views careful examination and concludes that external factors must be matched (...) by appropriate internal ones to yield knowledge. Readers of Professor Lehrer's earlier book _Knowledge_ will want to know that this text adopts the framework of that classic text. But _Theory of Knowledge_ is a completely rewritten and updated version of that book that has been simplified throughout for student use. (shrink)

In this important new text, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the accepted definition of knowledge as justified true belief, Lehrer explores the truth, belief and justification conditions on the way to a thorough examination of foundation theories of knowledge, externalism and naturalized epistemologies, internalism and modern coherence theories as well as recent reliabilist and causal theories. Lehrer gives all views careful examination and concludes that external factors must be matched (...) by appropriate internal ones to yield knowledge. Readers of Professor Lehrer's earlier book _Knowledge_ will want to know that this text adopts the framework of that classic text. But _Theory of Knowledge_ is a completely rewritten and updated version of that book that has been simplified throughout for student use. (shrink)

In this important new text, Keith Lehrer introduces students to the major traditional and contemporary accounts of knowing. Beginning with the accepted definition of knowledge as justified true belief, Lehrer explores the truth, belief and justification conditions on the way to a thorough examination of foundation theories of knowledge, externalism and naturalized epistemologies, internalism and modern coherence theories as well as recent reliabilist and causal theories. Lehrer gives all views careful examination and concludes that external factors must be matched (...) by appropriate internal ones to yield knowledge. Readers of Professor Lehrer's earlier book _Knowledge_ will want to know that this text adopts the framework of that classic text. But _Theory of Knowledge_ is a completely rewritten and updated version of that book that has been simplified throughout for student use. (shrink)

To understand better why evidence of student cheating is often ignored, a national sample of psychology instructors was sampled for their opinions. The 127 respondents overwhelmingly agreed that dealing with instances of academic dishonesty was among the most onerous aspects of their profession. Respondents cited insufficient evidence that cheating has occurred as the most frequent reason for overlooking student behavior or writing that might be dishonest. A factor analysis revealed 4 other clusters of reasons as to why cheating may be (...) ignored. Emotional reasons included stress and lack of courage. Difficult reasons included the extensive time and effort required to deal with cheating students. Fear reasons included concern about retaliation or a legal challenge. Denial reasons included beliefs that cheating students would fail anyway and that the worst offenders do not get caught. The reasons why instances of academic dishonesty should be proactively confronted are presented. (shrink)

Author note: Keith E. Yandell is Professor of Philosophy and South Asian Studies at the University of Wisconsin-Madison.

In an incisive critique of Professor Hick's Evil and the God of Love , Professor Puccetti claims to ‘carry the campaign as well as the battle’—i.e. to show that, with respect to evil, theists ‘are either “explaining it away” or saying it cannot be explained at all. And in both cases they are in effect admitting they have no rational defence to offer. Which means that despite appearances they really are abandoning the battlefield.’.

A philosopher, rabbi, religious historian, and Gnostic, Jacob Taubes was for many years a correspondent and interlocutor of Carl Schmitt, a German jurist, philosopher, political theorist, law professor -- and self-professed Nazi. Despite their unlikely association, Taubes and Schmitt shared an abiding interest in the fundamental problems of political theology, believing the great challenges of modern political theory were ancient in pedigree and, in many cases, anticipated the works of Judeo-Christian eschatologists. In this collection of Taubes's writings on Schmitt, (...) the two intellectuals work through ideas of the apocalypse and other central concepts of political theology. Taubes acknowledges Schmitt's reservations about the weakness of liberal democracy yet distances himself from his prescription to rectify it, arguing the apocalyptic worldview requires less of a rigid hierarchical social ordering than a community committed to the importance of decision making. In these writings, a sharper and more nuanced portrait of Schmitt's thought emerges, as well as a more complicated understanding of Taubes, who has shaped the work of Giorgio Agamben, Peter Sloterdijk, and other major twentieth-century theorists. (shrink)

This monograph represents the first comprehensive study dedicated to the interdisciplinary French philosopher Michel Serres. As the title of this project unequivocally suggests, Serres s prolific body of work paints a rending portrait of what it means for a sentient being to live in the modern world. This book reflects Serres s profound conviction that philosopher c est anticiper / to philosophize (about something) is to anticipate ( Philosophie Magazine ). According to Serres, a philosopher is someone who possesses an (...) extremely broad base of knowledge coupled with the uncanny ability to envision what "might" transpire based upon his or her astute observations concerning phenomena that are already starting to unfold in a given society. Serres s explanation of what engaging in philosophical inquiry entails encourages us to imagine all of the present and future ramifications of certain trajectories that are clearly visible all around us. From 1968 to the present, Serres has been generating forceful, prophetic visions in his works that mingle philosophy, religion, theology, contemporary science, and literature. Comprehensive and insightful introduction both illuminates pressing contemporary issues and presages potential futures-to-come. This is a remarkable achievement and a genuine gift to readers both new and old to Serres s work. -Steven D. Brown, Professor of Psychology, University of Leicester An essential book for becoming aware of the threat of a return of obscurantism despite the development of new technologies and of the necessity of a new century of "Lumieres." -Issa Asgarally, Associate Professor, Mauritius Institute of Education, founder, Foundation for Interculturality and Peace Moser s engaging prose makes this study a great read, and he demonstrates a formidable grasp on the connections within Serres work, as well as the links between Serres and other major twentieth century thinkers. -Tom Trzyna, Professor Emeritus of English, Seattle Pacific University Both timely and thorough. His provocative critique of societal malaise, from our relationship to the planet, to ourselves, to each other, and to technology, as well as the solutions envisioned through an erudite and thoughtful analysis of Serres entire philosophical corpus is a remarkable contribution to Philosophy and French Studies. -Isaac Joslin, University of Denver Keith Moser s pioneering vision of the post-Marxist era, as reflected in the syncretism of philosophy, religion, theology, science and literature in Michel Serres body of work during the last half a century, transforms human consciousness beyond its illusory genophobia that has damaged the very semiotics of life. Moser s monograph taps into a tremendous flow of energy that evokes a passionate desire in a dead humanity to re-live and re-think. -Professor Ananta Sukla, Editor, Journal of Comparative Literature and Aesthetics Keith Moser is Associate Professor of French at Mississippi State University. He is the author of "A Practical Guide to French Harki Literature, J.M.G. Le Clezio: A Concerned Citizen of the Global Village, Le Clezio dans la foret des paradoxes" (co-editor), and "Privileged Moments in the Novels and Short Stories of Le Clezio: His Contemporary Development of a Traditional French Literary Device." Moser has also contributed approximately forty essays to peer-reviewed publications such as "The French Review, The International Journal of Francophone Studies, Romance Notes, Dalhousie French Studies, Les Cahiers Le Clezio, Modern Language Review, French Cultural Studies, Forum for Modern Language Studies" (Oxford), "Interdisciplinary Studies in Literature and Environment" (Oxford), and "Pennsylvania Literary Journal."". (shrink)

What is it that statesmen have generally wanted from science? They have not wanted admonitions or collaboration, much less interference, in the business of government, which is the exercise of power over persons, nor in the political maneuverings to secure and retain control over governments. From science, all the statesmen and politicians want are instrumentalities, powers but not power: weapons, techniques, information communications, and so on. As for scientists, what have they wanted of governments? They have expressly not wished to (...) be politicized. They have wanted support, in the obvious form of funds, but also in the shape of institutionalization and in provision of authority for the legitimation of their community in its existence and in its activities, or in other words for its professional status. (shrink)

In these fifteen essays, one Of Germany's most distinguished philosophers of history invokes an extraordinary array of witnesses and texts to explore the concept of historical time. The witnesses include politicians, philosophers, theologians, and poets, and the texts range from Renaissance paintings to the dreams of German citizens in the 1930s. Using these remarkable materials, Koselleck investigates the relationship of history to language, and of language to the deeper movements of human understanding.Reinhart Koselleck is Professor of the Theory of (...) History at the University of Bielefeld. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Ideas 64.4 (2003) 599-618 [Access article in PDF] The "Herbert Butterfield Problem" and its Resolution Keith C. Sewell Dordt College Herbert Butterfield (1900-1979) 1 published The Whig Interpretation of History in 1931, a year after he became a Lecturer in the University of Cambridge. 2 He became Professor of Modern History in the university in 1944, the same year in which he (...) published The Englishman and His History. 3 This discussion addresses what J.G.A. Pocock referred to as das Herbert Butter-fieldproblem—that is, the problem of ascertaining the precise relationship between the arguments presented in these volumes. 4The Whig Interpretation of History of 1931 (hereafter, The Whig Interpretation) was a sustained critique of the motivation, methods and fallacious conclusions of the "Whig" practice of staging historiographical narratives anachronistically so as to produce a ratification of the present, or justification of a position currently espoused by the author. 5 The term "Whig," as Butterfield used it in 1931, referred to the nineteenth-century school of historiography that praised "progress," "protestantism," and "liberty" and that generally attributed the triumph of such principles to the beliefs and activities of generations of Whig politicians. 6 [End Page 599]The Whig Interpretation argued that the judgments concerning both progressive and reactionary individuals and movements in Whig historiography were anachronistic, in that they were based on general propositions held by the Whig historian in the present. To correct this error Butterfield argued that historiography should not be based upon any general propositions. Basing historiographical narratives on general propositions purporting to be of universal and unchanging validity was seen as inevitably placing them on an anachronistic basis. In The Whig Interpretation Butterfield required the historian to represent past "life itself " but to avoid doing so on the basis of a view or "interpretation" of past human experience and action. Historiographical narration should be free of any interpretative standpoint and equally open to any possible subsequent interpretation. For Butterfield "the historian carries us away from the world of general ideas. It is not for him to give a philosophical explanation of what happens in time and space"; "any history that he writes ought to be as capable of varied philosophical interpretation as life itself seems to be... the historian's explanation... is not a piece of general reasoning," and "if at any point we need further elucidation all that he can do is to take us into greater detail." 7 It seems appropriate to refer to this as Butterfield's "neutrality postulate." Butterfield subsequently used the term "technical history" to denote this methodological concept. 8As might be expected, such a neutrality postulate was replete with problems, however valid Butterfield's strictures towards Whig historiographical anachronism. How is the historian to abridge for the purposes of narration and explanation without interpreting? Butterfield argued that we are right to demand of the historian that "he shall not change the meaning and purport of the historical story in the mere act of abridging it." No theory should intrude. As the detailed complexity is abridged, there should be no loss of "the purport and tenor of the whole." 9 Abridgment was to be accomplished without interpretative perspective, even though sympathy and imagination are indispensable. 10 Such was Butterfield's prescribed antidote. Yet the exercise he recommended requires more than a specific statement of the concrete, the individual, and the particular. It also requires a general idea of the "meaning" of "the whole" that the historian is called upon not to distort. Indeed, Butterfield drew attention to the basis of his historical thinking when he asserted that while historical research does not provide proof of the existence of a providential order, it nevertheless provides evidence of how profound and mysterious are its workings. 11In The Whig Interpretation no attempt was made to reconcile the advocacy of a non-interpretative neutrality dealing exclusively with the individual, the [End Page 600] concrete and the particular, and Butterfield's actual belief in a providential order to which the historical process is subject. After 1931... (shrink)

Conservatives in the United States have grown increasingly critical of universities and their faculty, convinced that professors are ideologues from the political left. Universities, for their part, have increasingly adopted a mantra of diversity and inclusivity, but have shown little interest in diversifying the political and ideological profile of their faculties. This essay argues that the lack of political diversity among American university faculty hampers the ability of universities to fulfill their core mission of advancing and disseminating knowledge. The argument (...) is advanced through a series of four questions: Is it true that university faculty are not ideologically diverse? Why might it be true? Does it matter? How might it be fixed. (shrink)

Festschrift for Michiel van Lambalgen on the occasion of his retirement as professor of logic and cognitive science at the University of Amsterdam.

All volumes of Professor Guthrie's great history of Greek philosophy have won their due acclaim. The most striking merits of Guthrie's work are his mastery of a tremendous range of ancient literature and modern scholarship, his fairness and balance of judgement and the lucidity and precision of his English prose. He has achieved clarity and comprehensiveness.

This book brings together the latest research in education in relation to science and religion. Leading international scholars and practitioners provide vital insights into the underlying debates and present a range of practical approaches for teaching. Key themes include the origin of the universe, the theory of evolution, the nature of the human person, the nature of science and Artificial Intelligence. These are explored in a range of international contexts. The book provides a valuable resource for teachers, students and researchers (...) in the fields of education, science, religious education and the growing specialist field of science and religion. Science and Religion in Education is a compelling read for current and future generations of academic researchers and teachers who wish to explore the fascinating intersect between science education and religious studies. The research findings and insights presented by these international scholars offer new dimensions on contemporary practice. - Vaille Dawson, Professor of Science Education, University of Western Australia Science and Religion in Education offers a fascinating and diverse collection of chapters surveying the current state of thinking about how science and religion can be understood in education. The book offers a wealth of thought-provoking material for anyone interested in the natures of science and religion, their relationship, or their representation within the curriculum. - Professor Keith Taber, University of Cambridge Science education and religious education are uncomfortable bedfellows. This book, written in part as a response to the – perhaps too clear – accounts of Ian Barbour, provides suitably nuanced pictures of how science and religion are dealt with in schools. Whatever the views of specialists, young people ‘receive’ an education in both science and religion: hearing their voices is refreshing in such a serious academic account. - Julian Stern, Professor of Education and Religion, York St John University Humans have long endeavored to make sense of the world often using science and religion. Yet, these two great traditions are frequently seen as incompatible. This useful volume features thoughtful contributions from experts whose work straddles the divide and provides educators with arguments, engaging strategies and historical perspectives to help build a bridge and allow a fruitful discussion in schools. - William F. McComas, Distinguished Professor of Science Education, University of Arkansas Equal parts critical examination of existing models for the relationship between science and religion, scholarly exposition of newer models, and insights toward practical application in classrooms, this book is an invaluable resource for science and religion educators. If you have been thinking it is time we looked beyond Barbour’s taxonomy, you will want to read this book. If you have not, I implore you to read this book. - Jason Wiles, Associate Professor of Biology and Science Education, Syracuse University. (shrink)

Professor Ruse has been a philosopher of biology for twenty years, so he tells us in both the introduction and conclusion to this new 'handbook to the philosophy of biology'. In that time he has come to occupy a commanding position at the centre of the discipline, not least through his new journal Biology and Philosophy; this book serves primarily to reinforce that position. Eight of the ten chapters are concerned with evolutionary biology, broadly conceived to include aspects of (...) molecular biology and sociobiology (but not ecology). (shrink)

All volumes of Professor Guthrie's great history of Greek philosophy have won their due acclaim. The most striking merits of Guthrie's work are his mastery of a tremendous range of ancient literature and modern scholarship, his fairness and balance of judgement and the lucidity and precision of his English prose. He has achieved clarity and comprehensiveness.

All volumes of Professor Guthrie's great history of Greek philosophy have won their due acclaim. The most striking merits of Guthrie's work are his mastery of a tremendous range of ancient literature and modern scholarship, his fairness and balance of judgement and the lucidity and precision of his English prose. He has achieved clarity and comprehensiveness.

Andrei A. Buckareff is Assistant Professor at Marist College, USA --.