Synthetic Philosophy Of Contemporary Mathematics

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Synthetic Philosophy of Contemporary Mathematics

Author : Fernando Zalamea
Publisher : MIT Press
ISBN 13 : 1913029328
Total Pages : 394 pages
Book Rating : 4.9/5 (13 download)

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Book Synopsis Synthetic Philosophy of Contemporary Mathematics by : Fernando Zalamea

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.

Mathematics, Ideas and the Physical Real

Author : Albert Lautman
Publisher : A&C Black
ISBN 13 : 1441146547
Total Pages : 354 pages
Book Rating : 4.4/5 (411 download)

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Book Synopsis Mathematics, Ideas and the Physical Real by : Albert Lautman

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.

The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics

Author : John L. Bell
Publisher : Springer Nature
ISBN 13 : 3030187071
Total Pages : 313 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics by : John L. Bell

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.

Analysis and Synthesis in Mathematics

Author : Michael Otte
Publisher : Springer Science & Business Media
ISBN 13 : 9780792345701
Total Pages : 476 pages
Book Rating : 4.3/5 (457 download)

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Book Synopsis Analysis and Synthesis in Mathematics by : Michael Otte

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.

Diagrammatic Immanence

Author : Rocco Gangle
Publisher : Edinburgh University Press
ISBN 13 : 1474404200
Total Pages : 264 pages
Book Rating : 4.4/5 (744 download)

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Book Synopsis Diagrammatic Immanence by : Rocco Gangle

Download or read book Diagrammatic Immanence written by Rocco Gangle and published by Edinburgh University Press. This book was released on 2016-08-18 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A renewal of immanent metaphysics through diagrammatic methods and the tools of category theorySpinoza, Peirce and Deleuze are, in different ways, philosophers of immanence. Rocco Gangle addresses the methodological questions raised by a commitment to immanence in terms of how diagrams may be used both as tools and as objects of philosophical investigation. He integrates insights from Spinozist metaphysics, Peircean semiotics and Deleuzes philosophy of difference in conjunction with the formal operations of category theory. Category theory reveals deep structural connections among logic, topology and a variety of different areas of mathematics, and it provides constructive and rigorous concepts for investigating how diagrams work. Gangle introduces the methods of category theory from a philosophical and diagrammatic perspective, allowing philosophers with little or no mathematical training to come to grips with this important field. This coordination of immanent metaphysics, diagrammatic method and category theoretical mathematics opens a new horizon for contemporary thought.

Introduction to Mathematical Philosophy

Author : Bertrand Russell
Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introduction to Mathematical Philosophy by : Bertrand Russell

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:

Collapse, Volume 1

Author : Robin Mackay
Publisher : MIT Press
ISBN 13 : 0993045820
Total Pages : 294 pages
Book Rating : 4.9/5 (93 download)

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Book Synopsis Collapse, Volume 1 by : Robin Mackay

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.

America—An Integral Weave

Author : Fernando Zalamea
Publisher : MIT Press
ISBN 13 : 1733628185
Total Pages : 248 pages
Book Rating : 4.7/5 (336 download)

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Book Synopsis America—An Integral Weave by : Fernando Zalamea

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.

Philosophy of Mathematics

Author : Øystein Linnebo
Publisher : Princeton University Press
ISBN 13 : 069120229X
Total Pages : 214 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Philosophy of Mathematics by : Øystein Linnebo

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.

Plato's Ghost

Author : Jeremy Gray
Publisher : Princeton University Press
ISBN 13 : 1400829046
Total Pages : 528 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Plato's Ghost by : Jeremy Gray

Download or read book Plato's Ghost written by Jeremy Gray and published by Princeton University Press. This book was released on 2008-09-02 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions. Plato's Ghost evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincaré, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of naïve set theory and the revived axiomatic method—debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism. Plato's Ghost is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.

The Mathematical Imagination

Author : Matthew Handelman
Publisher : Fordham Univ Press
ISBN 13 : 0823283852
Total Pages : 256 pages
Book Rating : 4.8/5 (232 download)

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Book Synopsis The Mathematical Imagination by : Matthew Handelman

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.

Homotopy Type Theory: Univalent Foundations of Mathematics

Author :
Publisher : Univalent Foundations
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4./5 ( download)

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Book Synopsis Homotopy Type Theory: Univalent Foundations of Mathematics by :

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:

Visual Thinking in Mathematics

Author : Marcus Giaquinto
Publisher : Oxford University Press
ISBN 13 : 0199285942
Total Pages : 298 pages
Book Rating : 4.1/5 (992 download)

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Book Synopsis Visual Thinking in Mathematics by : Marcus Giaquinto

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.

Category Theory in Physics, Mathematics, and Philosophy

Author : Marek Kuś
Publisher : Springer Nature
ISBN 13 : 3030308960
Total Pages : 134 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Category Theory in Physics, Mathematics, and Philosophy by : Marek Kuś

Download or read book Category Theory in Physics, Mathematics, and Philosophy written by Marek Kuś and published by Springer Nature. This book was released on 2019-11-11 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.

Carnap, Tarski, and Quine at Harvard

Author : Greg Frost-Arnold
Publisher : Open Court
ISBN 13 : 0812698304
Total Pages : 273 pages
Book Rating : 4.8/5 (126 download)

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Book Synopsis Carnap, Tarski, and Quine at Harvard by : Greg Frost-Arnold

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.

Conceptual Change and the Philosophy of Science

Author : David J. Stump
Publisher : Routledge
ISBN 13 : 1317495381
Total Pages : 194 pages
Book Rating : 4.3/5 (174 download)

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Book Synopsis Conceptual Change and the Philosophy of Science by : David J. Stump

Download or read book Conceptual Change and the Philosophy of Science written by David J. Stump and published by Routledge. This book was released on 2015-05-15 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, David Stump traces alternative conceptions of the a priori in the philosophy of science and defends a unique position in the current debates over conceptual change and the constitutive elements in science. Stump emphasizes the unique epistemological status of the constitutive elements of scientific theories, constitutive elements being the necessary preconditions that must be assumed in order to conduct a particular scientific inquiry. These constitutive elements, such as logic, mathematics, and even some fundamental laws of nature, were once taken to be a priori knowledge but can change, thus leading to a dynamic or relative a priori. Stump critically examines developments in thinking about constitutive elements in science as a priori knowledge, from Kant’s fixed and absolute a priori to Quine’s holistic empiricism. By examining the relationship between conceptual change and the epistemological status of constitutive elements in science, Stump puts forward an argument that scientific revolutions can be explained and relativism can be avoided without resorting to universals or absolutes.

The Significance of the New Logic

Author : Willard Van Orman Quine
Publisher : Cambridge University Press
ISBN 13 : 1316836320
Total Pages : 218 pages
Book Rating : 4.3/5 (168 download)

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Book Synopsis The Significance of the New Logic by : Willard Van Orman Quine

Download or read book The Significance of the New Logic written by Willard Van Orman Quine and published by Cambridge University Press. This book was released on 2018-05-10 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: W. V. Quine was one of the most influential figures of twentieth-century American analytic philosophy. Although he wrote predominantly in English, in Brazil in 1942 he gave a series of lectures on logic and its philosophy in Portuguese, subsequently published as the book O Sentido da Nova Lógica. The book has never before been fully translated into English, and this volume is the first to make its content accessible to Anglophone philosophers. Quine would go on to develop revolutionary ideas about semantic holism and ontology, and this book provides a snapshot of his views on logic and language at a pivotal stage of his intellectual development. The volume also includes an essay on logic which Quine also published in Portuguese, together with an extensive historical-philosophical essay by Frederique Janssen-Lauret. The valuable and previously neglected works first translated in this volume will be essential for scholars of twentieth-century philosophy.