Ad Infinitum... The Ghost in Turing's Machine


Book Description

This ambitious work puts forward a new account of mathematics-as-language that challenges the coherence of the accepted idea of infinity and suggests a startlingly new conception of counting. The author questions the familiar, classical, interpretation of whole numbers held by mathematicians and scientists, and replaces it with an original and radical alternative--what the author calls non-Euclidean arithmetic. The author's entry point is an attack on the notion of the mathematical infinite in both its potential and actual forms, an attack organized around his claim that any interpretation of "endless" or "unlimited" iteration is ineradicably theological. Going further than critique of the overt metaphysics enshrined in the prevailing Platonist description of mathematics, he uncovers a covert theism, an appeal to a disembodied ghost, deep inside the mathematical community's understanding of counting.




What Painting Is


Book Description

In this classic text, James Elkins communicates the experience of painting beyond the traditional vocabulary of art history. Alchemy provides a strange language to explore what it is a painter really does in the studio—the smells, the mess, the struggle to control the uncontrollable, the special knowledge only painters hold of how colors will mix, and how they will look. Written from the perspective of a painter-turned-art historian, this anniversary edition includes a new introduction and preface by Elkins in which he further reflects on the experience of painting and its role in the study of art today.




Quantum Anthropologies


Book Description

In Quantum Anthropologies, the renowned feminist theorist Vicki Kirby contends that some of the most provocative aspects of deconstruction have yet to be explored. Deconstruction’s implications have been curtailed by the assumption that issues of textuality and representation are specific to the domain of culture. Revisiting Derrida’s claim that there is “no outside of text,” Kirby argues that theories of cultural construction developed since the linguistic turn have inadvertently reproduced the very binaries they intended to question, such as those between nature and culture, matter and ideation, and fact and value. Through new readings of Derrida, Husserl, Saussure, Butler, Irigaray, and Merleau-Ponty, Kirby exposes the limitations of theories that regard culture as a second-order system that cannot access—much less be—nature, body, and materiality. She suggests ways of reconceiving language and culture to enable a more materially implicated outcome, one that keeps alive the more counterintuitive and challenging aspects of poststructural criticism. By demonstrating how fields, including cybernetics, biology, forensics, mathematics, and physics, can be conceptualized in deconstructive terms, Kirby fundamentally rethinks deconstruction and its relevance to nature, embodiment, materialism, and science.




Ethics and Mathematics Education


Book Description

This edited volume is an inquiry into the ethics of mathematics education, and to a lesser extent, the ethics of mathematics. The imposition of mathematics for all raises questions of ethics. What are the ethics of teaching school mathematics? What are the costs as well as the benefits? What are the ethical issues raised by the official aims of mathematics teaching, the planned curriculum, the pedagogies employed in school and college mathematics and the assessment systems? These questions are addressed in the book as well as what systems of ethics we might use. The volume ventures into a burgeoning new field. It offers a unique set of investigations, both theoretical and in terms of practices. It announces the ethics of mathematics education as a new subfield of research and includes valuable contributions from many of the best-known researchers in mathematics education; additionally, it is a valuable resource for students, teachers and researchers in the field. This is an enduring and classic source book in the field. From the wisdom of leading scholars to the little heard voices of students, this collection offers the reader many striking new insights into the ethics of mathematics and education.




Social Constructivism as a Philosophy of Mathematics


Book Description

Extends the ideas of social constructivism to the philosophy of mathematics, developing a powerful critique of traditional absolutist conceptions of mathematics, and proposing a reconceptualization of the philosophy of mathematics.




Connectionism and the Philosophy of Psychology


Book Description

In this volume, the authors present their view of cognition. They propose that unlike the classical paradigm that takes the mind to be a computer, the mind is best understood as a dynamical system realized in a neural network.




Logic and Computational Complexity


Book Description

This book contains revised versions of papers invited for presentation at the International Workshop on Logic and Computational Complexity, LCC '94, held in Indianapolis, IN in October 1994. The synergy between logic and computational complexity has gained importance and vigor in recent years, cutting across many areas. The 25 revised full papers in this book contributed by internationally outstanding researchers document the state-of-the-art in this interdisciplinary field of growing interest; they are presented in sections on foundational issues, applicative and proof-theoretic complexity, complexity of proofs, computational complexity of functionals, complexity and model theory, and finite model theory.




Reassembling the Social


Book Description

French sociologist Bruno Latour has previously written about the relationship between people, science and technology. In this book he sets out his own ideas about 'actor network theory' and its relevance to management and organisation theory.




New Directions in the Philosophy of Mathematics


Book Description

The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.




Culturally Responsive Mathematics Education


Book Description

At a time of rapid demographic change and amidst the many educational challenges facing the US, this critical new collection presents mathematics education from a culturally responsive perspective. It tackles the most crucial issues of teaching mathematics to an ethnically diverse school population, including the political dimension of mathematics education within the context of governmental efforts to improve achievement in school mathematics. Culturally Responsive Mathematics Education moves beyond a point of view that is internal to mathematics education as a discipline, and instead offers a broad perspective of mathematics as a significant, liberating intellectual force in our society. The editors of this volume bring together contributions from many of the leading teachers, teacher educators, researchers, scholars, and activists who have been working to reorient mathematics education in ways that reflect mathematics education as accomplished, first and foremost, through human interactions.