Synthetic Philosophy of Contemporary Mathematics

Author: Fernando Zalamea

Publisher: Urbanomic/Sequence Press

ISBN: 9780956775016

Category: Mathematics

Page: 385

View: 5054

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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: 1441146547

Category: Philosophy

Page: 352

View: 9988

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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.

Peirce's Logic of Continuity

A Conceptual and Mathematical Approach

Author: Fernando Zalamea

Publisher: N.A

ISBN: 9780983700494

Category: Mathematics

Page: 192

View: 6038

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Peirce's logic of continuity is explored from a double perspective: (i) Peirce's original understanding of the continuum, alternative to Cantor's analytical Real line, (ii) Peirce's original construction of a topological logic -- the existential graphs -- alternative to the algebraic presentation of propositional and first-order calculi. Peirce's general architectonics, oriented to back-and-forth hierarchical crossings between the global and the local, is reflected with great care both in the continuum and the existential graphs.

History and Philosophy of Modern Mathematics

Author: William Aspray,Philip Kitcher

Publisher: U of Minnesota Press

ISBN: 9780816615674

Category: Mathematics

Page: 386

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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.

Analyticity

Author: Cory Juhl,Eric Loomis

Publisher: Routledge

ISBN: 1135278407

Category: Philosophy

Page: 336

View: 7166

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Analyticity, or the 'analytic/synthetic' distinction is one of the most important and controversial problems in contemporary philosophy. It is also essential to understanding many developments in logic, philosophy of language, epistemology and metaphysics. In this outstanding introduction to analyticity Cory Juhl and Eric Loomis cover the following key topics: The origins of analyticity in the philosophy of Hume and Kant Carnap's arguments concerning analyticity in the early twentieth century Quine's famous objections to analyticity in his classic 'Two Dogmas of Empiricism' essay The relationship between analyticity and central issues in metaphysics, such as ontology The relationship between analyticity and epistemology Analyticity in the context of the current debates in philosophy, including mathematics and ontology Throughout the book the authors show how many philosophical controversies hinge on the problem of analyticity. Additional features include chapter summaries, annotated further reading and a glossary of technical terms making the book ideal to those coming to the problem for the first time.

The Poverty of Conceptual Truth

Kant's Analytic/synthetic Distinction and the Limits of Metaphysics

Author: R. Lanier Anderson

Publisher: Oxford University Press, USA

ISBN: 0198724578

Category: Philosophy

Page: 408

View: 2998

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R. Lanier Anderson presents a new account of Kant's distinction between analytic and synthetic judgments, and provides it with a clear basis within traditional logic. He reconstructs compelling claims about the syntheticity of elementary mathematics, and re-animates Kant's arguments against traditional metaphysics in the 'Critique of Pure Reason'

Isaac Newton on Mathematical Certainty and Method

Author: Niccolò Guicciardini

Publisher: MIT Press

ISBN: 0262013177

Category: Mathematics

Page: 422

View: 3707

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An analysis of Newton's mathematical work, from early discoveries to mature reflections, and a discussion of Newton's views on the role and nature of mathematics.

Transgression and the Inexistent

A Philosophical Vocabulary

Author: Mehdi Belhaj Kacem

Publisher: Bloomsbury Publishing

ISBN: 147252862X

Category: Political Science

Page: 256

View: 1344

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A contemporary philosopher of Tunisian origin, Mehdi Belhaj Kacem is here published in English for the first time. His new book, Transgression and the Inexistent: A Philosophical Vocabulary, is a comprehensive foray into Kacem's elaborate philosophical system in twenty-seven discreet chapters, each dedicated to a single concept. In each chapter, he explicates a critical re-thinking of ordinary lived experiences - such as desire, irony, play - or traditional philosophical ideas – such as catharsis, mimesis, techne – in light of 'the spirit of nihilism' that marks the contemporary human condition. Kacem gained notoriety in the domain of critical theory amid his controversial break with his mentor and leading contemporary philosopher, Alain Badiou. Transgression and the Inexistent lays out the essential concepts of his philosophical system: it is the most complete and synthetic book of his philosophical work, as well as being one of the most provocative in its claims. As a Francophone author engaging with contemporary world thought, he is able to develop novel philosophical perspectives that reach beyond the Middle East or the Continental, and the East/West binary. This is the book's first publication in any language, constituting a much-awaited first translation of Kacem into English.

Analysis and Synthesis in Mathematics

History and Philosophy

Author: Michael Otte,Marco Panza

Publisher: Springer Science & Business Media

ISBN: 9780792345701

Category: Mathematics

Page: 440

View: 2142

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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.

Principia Mathematica

Author: Alfred North Whitehead,Bertrand Russell

Publisher: N.A

ISBN: N.A

Category: Logic, Symbolic and mathematical

Page: N.A

View: 3616

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Kant and Contemporary Epistemology

Author: P. Parrini

Publisher: Springer Science & Business Media

ISBN: 940110834X

Category: Philosophy

Page: 379

View: 6629

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From the mid-1960s, after the important works by J. Hintikka, S. Körner, W. Sellars and P.F. Strawson, there has been a marked revival of Kantian epistemological thought. Against this background, featuring fruitful exchange between historical research and theoretical prospects, the main point of the book is the discussion of Kantian theory of scientific knowledge from the perspective of present-day analytical philosophy and philosophy of empirical and mathematical sciences. The main topics are the problem of a priori knowledge in logic, mathematics and physics, the distinction between analytic and synthetic judgments, the constitution of physical objectivity and the questions of realism and truth, the Kantian conception of time, causal laws and induction, the relations between Kantian epistemological thought, relativity theory, quantum theory and some recent developments of philosophy of science. The book is addressed to research workers, specialists and scholars in the fields of epistemology, philosophy of science and history of philosophy.

The Nature of Life

Classical and Contemporary Perspectives from Philosophy and Science

Author: Mark A. Bedau,Carol E. Cleland

Publisher: Cambridge University Press

ISBN: 1139488651

Category: Science

Page: N.A

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Bringing together the latest scientific advances and some of the most enduring subtle philosophical puzzles and problems, this book collects original historical and contemporary sources to explore the wide range of issues surrounding the nature of life. Selections ranging from Aristotle and Descartes to Sagan and Dawkins are organised around four broad themes covering classical discussions of life, the origins and extent of natural life, contemporary artificial life creations and the definition and meaning of 'life' in its most general form. Each section is preceded by an extensive introduction connecting the various ideas discussed in individual chapters and providing helpful background material for understanding them. With its interdisciplinary perspective, this fascinating collection is essential reading for scientists and philosophers interested in astrobiology, synthetic biology and the philosophy of life.

Kant’s Philosophy of Mathematics

Modern Essays

Author: C.J. Posy

Publisher: Springer Science & Business Media

ISBN: 9401580464

Category: Philosophy

Page: 380

View: 8384

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Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their authors. It also includes the most important recent work on Kant's philosophy of mathematics. The essays bring to bear a wealth of detailed Kantian scholarship, together with powerful new interpretative tools drawn from modern mathematics, logic and philosophy. The cumulative effect of this collection upon the reader will be a deeper understanding of the centrality of mathematics in all aspects of Kant's thought and a renewed respect for the power of Kant's thinking about mathematics. The essays contained in this volume will set the agenda for further work on Kant's philosophy of mathematics for some time to come.

Thinking about Mathematics

The Philosophy of Mathematics

Author: Stewart Shapiro

Publisher: OUP Oxford

ISBN: 9780192893062

Category: Philosophy

Page: 328

View: 1092

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Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

Squaring the Circle

The War Between Hobbes and Wallis

Author: Douglas M. Jesseph

Publisher: University of Chicago Press

ISBN: 9780226398990

Category: Mathematics

Page: 419

View: 1413

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In 1655, the philosopher Thomas Hobbes claimed he had solved the centuries-old problem of "squaring of the circle" (constructing a square equal in area to a given circle). With a scathing rebuttal to Hobbes's claims, the mathematician John Wallis began one of the longest and most intense intellectual disputes of all time. Squaring the Circle is a detailed account of this controversy, from the core mathematics to the broader philosophical, political, and religious issues at stake. Hobbes believed that by recasting geometry in a materialist mold, he could solve any geometric problem and thereby demonstrate the power of his materialist metaphysics. Wallis, a prominent Presbyterian divine as well as an eminent mathematician, refuted Hobbes's geometry as a means of discrediting his philosophy, which Wallis saw as a dangerous mix of atheism and pernicious political theory. Hobbes and Wallis's "battle of the books" illuminates the intimate relationship between science and crucial seventeenth-century debates over the limits of sovereign power and the existence of God.

Philosophy of Complex Systems

Author: N.A

Publisher: Elsevier

ISBN: 9780080931227

Category: Philosophy

Page: 952

View: 3985

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The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics. A few examples are in meteorology, ecological dynamics, and social and economic dynamics. These new ideas have profound implications for our understanding and practice in domains involving complexity, predictability and determinism, equilibrium, control, planning, individuality, responsibility and so on. Our intention is to draw together in this volume, we believe for the first time, a comprehensive picture of the manifold philosophically interesting impacts of recent developments in understanding nonlinear systems and the unique aspects of their complexity. The book will focus specifically on the philosophical concepts, principles, judgments and problems distinctly raised by work in the domain of complex nonlinear dynamical systems, especially in recent years. -Comprehensive coverage of all main theories in the philosophy of Complex Systems -Clearly written expositions of fundamental ideas and concepts -Definitive discussions by leading researchers in the field -Summaries of leading-edge research in related fields are also included

Cognition, Content, and the a Priori

A Study in the Philosophy of Mind and Knowledge

Author: Robert Hanna

Publisher: Oxford University Press, USA

ISBN: 019871629X

Category: A priori

Page: 464

View: 7251

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Robert Hanna works out a unified contemporary Kantian theory of rational human cognition and knowledge. Along the way, he provides accounts of intentionality and its contents, sense perception and perceptual knowledge, the analytic-synthetic distinction, the nature of logic, and a priori truth and knowledge in mathematics, logic, and philosophy. This book is specifically intended to reach out to two very different audiences: contemporary analytic philosophers ofmind and knowledge, and contemporary Kantian philosophers or Kant-scholars. At the same time, it rides the crest of a wave of exciting and revolutionary emerging new trends and new work in thephilosophy of mind and epistemology, with a special concentration on the philosophy of perception. What is revolutionary in this new wave are its strong emphases on action, on cognitive phenomenology, on disjunctivist direct realism, on embodiment, and on sense perception as a primitive and proto-rational capacity for cognizing the world. Hanna makes a fundamental contribution to this philosophical revolution by giving it a specifically contemporary Kantian twist, and by pushing these new linesof investigation radically further.

Philosophical Devices

Proofs, Probabilities, Possibilities, and Sets

Author: David Papineau

Publisher: OUP Oxford

ISBN: 0191656259

Category: Philosophy

Page: 224

View: 5079

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This book is designed to explain the technical ideas that are taken for granted in much contemporary philosophical writing. Notions like 'denumerability', 'modal scope distinction', 'Bayesian conditionalization', and 'logical completeness' are usually only elucidated deep within difficult specialist texts. By offering simple explanations that by-pass much irrelevant and boring detail, Philosophical Devices is able to cover a wealth of material that is normally only available to specialists. The book contains four sections, each of three chapters. The first section is about sets and numbers, starting with the membership relation and ending with the generalized continuum hypothesis. The second is about analyticity, a prioricity, and necessity. The third is about probability, outlining the difference between objective and subjective probability and exploring aspects of conditionalization and correlation. The fourth deals with metalogic, focusing on the contrast between syntax and semantics, and finishing with a sketch of Gödel's theorem. Philosophical Devices will be useful for university students who have got past the foothills of philosophy and are starting to read more widely, but it does not assume any prior expertise. All the issues discussed are intrinsically interesting, and often downright fascinating. It can be read with pleasure and profit by anybody who is curious about the technical infrastructure of contemporary philosophy.