Download or read book Synthetic Philosophy of Contemporary Mathematics written by Fernando Zalamea and published by MIT Press. This book was released on 2012-09-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
Download or read book Synthetic Philosophy of Contemporary Mathematics written by Fernando Zalamea and published by National Geographic Books. This book was released on 2012-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest. A panoramic survey of the vast spectrum of modern and contemporary mathematics and the new philosophical possibilities they suggest, this book gives the inquisitive non-specialist an insight into the conceptual transformations and intellectual orientations of modern and contemporary mathematics. The predominant analytic approach, with its focus on the formal, the elementary and the foundational, has effectively divorced philosophy from the real practice of mathematics and the profound conceptual shifts in the discipline over the last century. The first part discusses the specificity of modern (1830–1950) and contemporary (1950 to the present) mathematics, and reviews the failure of mainstream philosophy of mathematics to address this specificity. Building on the work of the few exceptional thinkers to have engaged with the “real mathematics” of their era (including Lautman, Deleuze, Badiou, de Lorenzo and Châtelet), Zalamea challenges philosophy's self-imposed ignorance of the “making of mathematics.” In the second part, thirteen detailed case studies examine the greatest creators in the field, mapping the central advances accomplished in mathematics over the last half-century, exploring in vivid detail the characteristic creative gestures of modern master Grothendieck and contemporary creators including Lawvere, Shelah, Connes, and Freyd. Drawing on these concrete examples, and oriented by a unique philosophical constellation (Peirce, Lautman, Merleau-Ponty), in the third part Zalamea sets out the program for a sophisticated new epistemology, one that will avail itself of the powerful conceptual instruments forged by the mathematical mind, but which have until now remained largely neglected by philosophers.
Download or read book Mathematics Ideas and the Physical Real written by Albert Lautman and published by A&C Black. This book was released on 2011-06-02 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.
Download or read book Philosophy of Mathematics written by Stewart Shapiro and published by Oxford University Press. This book was released on 1997-08-07 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Do numbers, sets, and so forth, exist? What do mathematical statements mean? Are they literally true or false, or do they lack truth values altogether? Addressing questions that have attracted lively debate in recent years, Stewart Shapiro contends that standard realist and antirealist accounts of mathematics are both problematic. As Benacerraf first noted, we are confronted with the following powerful dilemma. The desired continuity between mathematical and, say, scientific language suggests realism, but realism in this context suggests seemingly intractable epistemic problems. As a way out of this dilemma, Shapiro articulates a structuralist approach. On this view, the subject matter of arithmetic, for example, is not a fixed domain of numbers independent of each other, but rather is the natural number structure, the pattern common to any system of objects that has an initial object and successor relation satisfying the induction principle. Using this framework, realism in mathematics can be preserved without troublesome epistemic consequences. Shapiro concludes by showing how a structuralist approach can be applied to wider philosophical questions such as the nature of an "object" and the Quinean nature of ontological commitment. Clear, compelling, and tautly argued, Shapiro's work, noteworthy both in its attempt to develop a full-length structuralist approach to mathematics and to trace its emergence in the history of mathematics, will be of deep interest to both philosophers and mathematicians.
Download or read book Analysis and Synthesis in Mathematics written by Michael Otte and published by Springer Science & Business Media. This book was released on 1997 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses the main interpretations of the classical distinction between analysis and synthesis with respect to mathematics. In the first part, this is discussed from a historical point of view, by considering different examples from the history of mathematics. In the second part, the question is considered from a philosophical point of view, and some new interpretations are proposed. Finally, in the third part, one of the editors discusses some common aspects of the different interpretations.
Download or read book The Continuous the Discrete and the Infinitesimal in Philosophy and Mathematics written by John L. Bell and published by Springer Nature. This book was released on 2019-09-09 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks; the elements of early Chinese, Indian and Islamic thought; and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Part one of the book concludes with a chapter on divergent conceptions of the continuum, with the work of nineteenth and early twentieth century philosophers and mathematicians, including Veronese, Poincaré, Brouwer, and Weyl. Part two of this book covers contemporary mathematics, discussing topology and manifolds, categories, and functors, Grothendieck topologies, sheaves, and elementary topoi. Among the theories presented in detail are non-standard analysis, constructive and intuitionist analysis, and smooth infinitesimal analysis/synthetic differential geometry. No other book so thoroughly covers the history and development of the concepts of the continuous and the infinitesimal.
Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book History and Philosophy of Modern Mathematics written by William Aspray and published by U of Minnesota Press. This book was released on 1988 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In History and Philosophy of Modern Mathematics, William Aspray and Philip Kitcher bring together distinguished scholars from mathematics, history, and philosophy to assess the current state of the field. Their essays, which grow out of a 1985 conference at the University of Minnesota, develop the basic premise that mathematical thought needs to be studied from an interdisciplinary perspective. The opening essays study issues arising within logic and the foundations of mathematics, a traditional area of interest to historians and philosophers. The second section examines issues in the history of mathematics within the framework of established historical periods and questions. Next come case studies that illustrate the power of an interdisciplinary approach to the study of mathematics. The collection closes with a look at mathematics from a sociohistorical perspective, including the way institutions affect what constitutes mathematical knowledge.
Download or read book Collapse Volume 1 written by Robin Mackay and published by MIT Press. This book was released on 2019-01-15 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: An investigation of the nature and philosophical uses of number. The first volume of Collapse investigates the nature and philosophical uses of number. The volume includes an interview with Alain Badiou on the relation between philosophy, mathematics, and science, an in-depth interview with mathematician Matthew Watkins on the strange connections between physics and the distribution of prime numbers, and contributions that demonstrate the many ways in which number intersects with philosophical thought—from the mathematics of intensity to terrorism, from occultism to information theory, and graphical works of multiplicity.
Download or read book Homotopy Type Theory Univalent Foundations of Mathematics written by and published by Univalent Foundations. This book was released on with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book America An Integral Weave written by Fernando Zalamea and published by MIT Press. This book was released on 2021-10-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: A dynamic critical and philosophical study of modern North American and Latin American cultures via art, architecture, philosophy and mathematics. With an unprecedented ease of movement between literature, music, art, architecture, mathematics, and philosophy, this richly illustrated study enters into the "electromagnetic field" between Latin America and North America with two complementary essays examining some of the principal features of their intellectual and creative landscapes throughout the nineteenth and twentieth centuries. "Under the Sign of Jonah" explores how nineteenth-century North American culture adopted and transformed the legacy of romanticism, with sensitive readings of the work of Herman Melville, Albert Pinkham Ryder, and Charles Sanders Peirce among others, before turning to the continued presence of romantic problematics in Edgar Varèse’s music, Frank Gehry’s architecture, and the conceptual mathematics of William Lawvere. "The Borders and the Pendulum" addresses Latin America as a margin in continual dialogue with 'major' culture, detailing the movement from a universalist panoscopy which imagined an integrated American culture to a mid-century microscopy focused on the regional, to late twentieth-century responses to postmodernism in the form of a telescopy that operates both a differentiation into the local and a transversal integration into universal modernity. Continually shuttling across disciplinary borders, Zalamea approaches his subjects with a philosophical depth and conceptual agility that is a mark of the true polymath; his thought-diagrams of a dynamic continent are an indispensable guide to the transits and syntheses not only between the Americas, but between the romantic, the modern, and the contemporary, supplying the attentive reader with all the equipment they need to venture off the beaten paths of (post)modernity.
Download or read book Philosophy of Mathematics written by Øystein Linnebo and published by Princeton University Press. This book was released on 2020-03-24 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
Download or read book The Mathematical Imagination written by Matthew Handelman and published by Fordham Univ Press. This book was released on 2019-03-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an archeology of the undeveloped potential of mathematics for critical theory. As Max Horkheimer and Theodor W. Adorno first conceived of the critical project in the 1930s, critical theory steadfastly opposed the mathematization of thought. Mathematics flattened thought into a dangerous positivism that led reason to the barbarism of World War II. The Mathematical Imagination challenges this narrative, showing how for other German-Jewish thinkers, such as Gershom Scholem, Franz Rosenzweig, and Siegfried Kracauer, mathematics offered metaphors to negotiate the crises of modernity during the Weimar Republic. Influential theories of poetry, messianism, and cultural critique, Handelman shows, borrowed from the philosophy of mathematics, infinitesimal calculus, and geometry in order to refashion cultural and aesthetic discourse. Drawn to the austerity and muteness of mathematics, these friends and forerunners of the Frankfurt School found in mathematical approaches to negativity strategies to capture the marginalized experiences and perspectives of Jews in Germany. Their vocabulary, in which theory could be both mathematical and critical, is missing from the intellectual history of critical theory, whether in the work of second generation critical theorists such as Jürgen Habermas or in contemporary critiques of technology. The Mathematical Imagination shows how Scholem, Rosenzweig, and Kracauer’s engagement with mathematics uncovers a more capacious vision of the critical project, one with tools that can help us intervene in our digital and increasingly mathematical present.
Download or read book Carnap Tarski and Quine at Harvard written by Greg Frost-Arnold and published by Open Court. This book was released on 2013-08-27 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reconstruction of the lines of argument used by Carnap, Tarski, and Quine, highlighting their historical significance and contemporary relevance based on Carnap's own notes from his conversations of the time.During the academic year 1940-1941, several giants of analytic philosophy congregated at Harvard, holding regular private meetings, with Carnap, Tarski, and Quine. 'Carnap, Tarski, and Quine at Harvard' allows the reader to act as a fly on the wall for their conversations. Carnap took detailed notes during his year at Harvard. This book includes both a German transcription of these shorthand notes and an English translation in the appendix section. Carnap's notes cover a wide range of topics, but surprisingly, the most prominent question is: If the number of physical items in the universe is finite, what form should scientific discourse take? This question is closely connected to anabiding philosophical problem: What is the relationship between the logico-mathematical realm and the material realm? Carnap, Tarski, and Quine's attempts to answer this question involve issues central to philosophy today.This book focuses on three such issues: nominalism, the unity of science, and analyticity. In short, the book reconstructs the lines of argument represented in these Harvard discussions, discusses their historical significance (especially Quine's break from Carnap),and relates them when possible to contemporary treatments of these issues.
Download or read book Indiscrete Thoughts written by Gian-Carlo Rota and published by Springer Science & Business Media. This book was released on 2009-11-03 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Indiscrete Thoughts gives a glimpse into a world that has seldom been described - that of science and technology as seen through the eyes of a mathematician. The era covered by this book, 1950 to 1990, was surely one of the golden ages of science and of the American university. Cherished myths are debunked along the way as Gian-Carlo Rota takes pleasure in portraying, warts and all, some of the great scientific personalities of the period. Rota is not afraid of controversy. Some readers may even consider these essays indiscreet. This beautifully written book is destined to become an instant classic and the subject of debate for decades to come.
Download or read book Analyticity written by Cory Juhl and published by Routledge. This book was released on 2009-09-11 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analyticity, or the 'analytic/synthetic' distinction is one of the most important and controversial problems in contemporary philosophy. In this outstanding introduction to analyticity Cory Juhl and Eric Loomis provide a clear and thorough survey of the problem.
Download or read book Visual Thinking in Mathematics written by Marcus Giaquinto and published by Oxford University Press. This book was released on 2007-07-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing from philosophical work on the nature of concepts and from empirical studies of visual perception, mental imagery, and numerical cognition, Giaquinto explores a major source of our grasp of mathematics, using examples from basic geometry, arithmetic, algebra, and real analysis.
