Mary Leng defends a philosophical account of the nature of mathematics which views it as a kind of fiction (albeit an extremely useful fiction). On this view, the claims of our ordinary mathematical theories are more closely analogous to utterances made in the context of storytelling than to utterances whose aim is to assert literal truths.
Author: Mary Leng
Publisher: Oxford University Press
Author: Robert Bartnik
Publisher: University Press of New England
Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
My Quest for the Ultimate Nature of Reality
Author: Max Tegmark
Mathematics is traditionally seen as the most neutral of disciplines, the furthest removed from the arguments and controversy of politics and social life. However, critical mathematics challenges these assumptions and actively attacks the idea that mathematics is pure, objective, and value?neutral. It argues that history, society, and politics have shaped mathematics—not only through its applications and uses but also through molding its concepts, methods, and even mathematical truth and proof, the very means of establishing truth. Critical mathematics education also attacks the neutrality of the teaching and learning of mathematics, showing how these are value?laden activities indissolubly linked to social and political life. Instead, it argues that the values of openness, dialogicality, criticality towards received opinion, empowerment of the learner, and social/political engagement and citizenship are necessary dimensions of the teaching and learning of mathematics, if it is to contribute towards democracy and social justice. This book draws together critical theoretic contributions on mathematics and mathematics education from leading researchers in the field. Recurring themes include: The natures of mathematics and critical mathematics education, issues of epistemology and ethics; Ideology, the hegemony of mathematics, ethnomathematics, and real?life education; Capitalism, globalization, politics, social class, habitus, citizenship and equity. The book demonstrates the links between these themes and the discipline of mathematics, and its critical teaching and learning. The outcome is a groundbreaking collection unified by a shared concern with critical perspectives of mathematics and education, and of the ways they impact on practice.
Theory, Praxis and Reality
Author: Paul Ernest,Bharath Sriraman,Nuala Ernest
This text examines issues related to the way modelling and simulation enable us to reconstruct aspects of the world we are investigating. It also investigates the processes by which we extract concrete knowledge from those reconstructions and how that knowledge is legitimated.
Models, Mathematics, and Simulations
Author: Margaret Morrison
Publisher: Oxford University Press, USA
What if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren’t even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry. In Love and Math, renowned mathematician Edward Frenkel reveals a side of math we’ve never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man’s journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century’s leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat’s last theorem, that had seemed intractable before. At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
The Heart of Hidden Reality
Author: Edward Frenkel
Publisher: Basic Books
Roberto Mangabeira Unger and Lee Smolin argue for a revolution in our cosmological ideas. Ideal for non-scientists, physicists and cosmologists.
Author: Roberto Mangabeira Unger,Lee Smolin
Publisher: Cambridge University Press
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the ``math inside'' understandable and enjoyable. An additional attractive feature is the leisurely treatment of some hot topics that have gained prominence in recent years, such as Fermat's Theorem, Kepler's packing problem, and the solution of the Poincare Conjecture. Or maybe you have heard about the Nash equilibrium (of ``A Beautiful Mind'' fame), or the strange future of quantum computers, and want to know what it is all about? Well, open the book and take an up-to-date trip into the fascinating world of the mathematics all around us.
Author: Martin Aigner,Ehrhard Behrends
Publisher: American Mathematical Soc.
This book challenges the views put forward by Pierre Cartier, one of the anchors of the famous Bourbaki group, and Cédric Villani, one of the most brilliant mathematicians of his generation, who received the Fields Medal in 2010. Jean Dhombres, mathematician and science historian, and Gerhard Heinzmann, philosopher of science and also a specialist in mathematics engage in a fruitful dialogue with the two mathematicians, prompting readers to reflect on mathematical activity and its social consequences in history as well as in the modern world. Cédric Villani’s popular success proves once again that a common awareness has developed, albeit in a very confused way, of the major role of mathematics in the construction and efficiency of natural sciences, which are at the origin of our technologies. Despite this, the idea that mathematics cannot be shared remains firmly entrenched, a perceived failing that has even been branded a lack of culture by vocal forces in the media as well as cultural and political establishment. The authors explore three major directions in their dialogue: the highly complex relationship between mathematics and reality, the subject of many debates and opposing viewpoints; the freedom that the construction of mathematics has given humankind by enabling them to develop the natural sciences as well as mathematical research; and the responsibility with which the scientific community and governments should address the role of mathematics in research and education policies.
Author: Pierre Cartier,Jean Dhombres,Gerhard Heinzmann,Cédric Villani
Examines the aims and tools of science for creating theories and explanations of phenomena, with an eye to answering the question of whether or not science actually leads to true comprehension of reality
Physical Theories and Reality
Author: Roger G. Newton
Publisher: Harvard University Press
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
Author: Morris Kline
Publisher: Courier Corporation
With wit and clarity, the authors progress from simple arithmetic to calculus and non-Euclidean geometry. Their subjects: geometry, plane and fancy; puzzles that made mathematical history; tantalizing paradoxes; more. Includes 169 figures.
Author: Edward Kasner,James Newman
Publisher: Courier Corporation
Physics: Imagination and Reality introduces the reader to major ideas and the conceptual structure of modern physics, by tracing its development from the introduction of fields into physics by Faraday and Maxwell in the last century. Because the approach is historical, the book provides a comprehensive overview of the subjects. It should appeal to anyone interested in a basic understanding of the contemporary physicists view of the physical world. It avoids all but the simplest mathematics and presents ideas and concepts in everyday language.Physics: Imagination and Reality attempts to provide educated citizens with an understanding of contemporary physics and, at the same time, shows that its ideas have a grandeur, a challenge to the imagination and an aesthetic appeal which merit its recognition as an integral part of our culture.
Imagination and Reality
Author: Philip Russell Wallace
Publisher: World Scientific
This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies.
A Transcendental-Idealist Perspective
Author: Jairo José da Silva
One of the major philosophical texts of the 20th century, Process and Reality is based on Alfred North Whitehead’s influential lectures that he delivered at the University of Edinburgh in the 1920s on process philosophy. Whitehead’s master work in philsophy, Process and Reality propounds a system of speculative philosophy, known as process philosophy, in which the various elements of reality into a consistent relation to each other. It is also an exploration of some of the preeminent thinkers of the seventeenth and eighteenth centuries, such as Descartes, Newton, Locke, and Kant. The ultimate edition of Whitehead’s magnum opus, Process and Reality is a standard reference for scholars of all backgrounds.
Author: Alfred North Whitehead
Publisher: Simon and Schuster
This book reveals the strain of a moment in American cultural history that led several remarkable writers -- including Emerson, Warner, and Melville -- to render the stark rupture of loss in innovative ways. Pushing Protestant culture's sense of loss into secular terrain, these three key writers rejected Calvinist and sentimental models of bereavement, creating instead the compensations of a mature American literature whose 'originality' stemmed from its capacity to mourn the loss of a common culture and, through such mourning, to assent to new social and cultural realities. Balaam locates this appeal to 'reality' in the analogies antebellum writers drew between their experience of bereavement, and the experiences of uncertainty and disillusionment, that followed the revolutions in science, the winding down of creedal systems and the economic instability typifying the pre-Civil War era.
Mourning, Compensation, and Reality in Antebellum American Literature
Author: Peter Balaam
Category: Literary Criticism
How does science work? Does it tell us what the world is "really" like? What makes it different from other ways of understanding the universe? In Theory and Reality, Peter Godfrey-Smith addresses these questions by taking the reader on a grand tour of one hundred years of debate about science. The result is a completely accessible introduction to the main themes of the philosophy of science. Intended for undergraduates and general readers with no prior background in philosophy, Theory and Reality covers logical positivism; the problems of induction and confirmation; Karl Popper's theory of science; Thomas Kuhn and "scientific revolutions"; the views of Imre Lakatos, Larry Laudan, and Paul Feyerabend; and challenges to the field from sociology of science, feminism, and science studies. The book then looks in more detail at some specific problems and theories, including scientific realism, the theory-ladeness of observation, scientific explanation, and Bayesianism. Finally, Godfrey-Smith defends a form of philosophical naturalism as the best way to solve the main problems in the field. Throughout the text he points out connections between philosophical debates and wider discussions about science in recent decades, such as the infamous "science wars." Examples and asides engage the beginning student; a glossary of terms explains key concepts; and suggestions for further reading are included at the end of each chapter. However, this is a textbook that doesn't feel like a textbook because it captures the historical drama of changes in how science has been conceived over the last one hundred years. Like no other text in this field, Theory and Reality combines a survey of recent history of the philosophy of science with current key debates in language that any beginning scholar or critical reader can follow.
An Introduction to the Philosophy of Science
Author: Peter Godfrey-Smith
Publisher: University of Chicago Press
Appearance and Reality: An Introduction to the Philosophy of Physics addresses quantum mechanics and relativity and their philosophical implications, focusing on whether these theories of modern physics can help us know nature as it really is, or only as it appears to us. The author clearly explains the foundational concepts and principles of both quantum mechanics and relativity and then uses them to argue that we can know more than mere appearances, and that we can know to some extent the way things really are. He argues that modern physics gives us reason to believe that we can know some things about the objective, real world, but he also acknowledges that we cannot know everything, which results in a position he calls "realistic realism." This book is not a survey of possible philosophical interpretations of modern physics, nor does it leap from a caricature of the physics to some wildly alarming metaphysics. Instead, it is careful with the physics and true to the evidence in arriving at its own realistic conclusions. It presents the physics without mathematics, and makes extensive use of diagrams and analogies to explain important ideas. Engaging and accessible, Appearance and Reality serves as an ideal introduction for anyone interested in the intersection of philosophy and physics, including students in philosophy of physics and philosophy of science courses.
An Introduction to the Philosophy of Physics
Author: Peter Kosso
Publisher: Oxford University Press, USA