The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics
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The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics
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Author : John L. Bell
language : en
Publisher: Springer Nature
Release Date : 2019-09-09
The Continuous The Discrete And The Infinitesimal In Philosophy And Mathematics written by John L. Bell and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-09 with Mathematics categories.
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.
The Continuous And The Infinitesimal In Mathematics And Philosophy
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Author : John Lane Bell
language : en
Publisher: Polimetrica s.a.s.
Release Date : 2005
The Continuous And The Infinitesimal In Mathematics And Philosophy written by John Lane Bell and has been published by Polimetrica s.a.s. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Axiomatic Thinking Ii
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Author : Fernando Ferreira
language : en
Publisher: Springer Nature
Release Date : 2022-09-17
Axiomatic Thinking Ii written by Fernando Ferreira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-17 with Mathematics categories.
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Introduction To Mathematical Philosophy
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Author : Bertrand Russell
language : en
Publisher: Cosimo, Inc.
Release Date : 2007-04-01
Introduction To Mathematical Philosophy written by Bertrand Russell and has been published by Cosimo, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-01 with Philosophy categories.
Not to be confused with the philosophy of mathematics, mathematical philosophy is the structured set of rules that govern all existence. Or, in a word: logic. While this branch of philosophy threatens to be an intimidating and abstract subject, it is one that is surprisingly simple and necessarily sensible, particularly at the pen of writer Bertrand Russell, who infuses this work, first published in 1919, with a palpable and genuine desire to assist the reader in understanding the principles he illustrates. Anyone interested in logic and its development and application here will find a comprehensive and accessible account of mathematical philosophy, from the idea of what numbers actually are, through the principles of order, limits, and deduction, and on to infinity. British philosopher and mathematician BERTRAND ARTHUR WILLIAM RUSSELL (1872-1970) won the Nobel Prize for Literature in 1950. Among his many works are Why I Am Not a Christian (1927), Power: A New Social Analysis (1938), and My Philosophical Development (1959).
Trilogy Of Numbers And Arithmetic Book 1 History Of Numbers And Arithmetic An Information Perspective
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Author : Mark Burgin
language : en
Publisher: World Scientific
Release Date : 2022-04-22
Trilogy Of Numbers And Arithmetic Book 1 History Of Numbers And Arithmetic An Information Perspective written by Mark Burgin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-22 with Mathematics categories.
The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.
The History Of Continua
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Author : Stewart Shapiro
language : en
Publisher: Oxford University Press (UK)
Release Date : 2021
The History Of Continua written by Stewart Shapiro and has been published by Oxford University Press (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
Mathematical and philosophical thought about continuity has changed considerably over the ages, from Aristotle's insistence that a continuum is a unified whole, to the dominant account today, that a continuum is composed of infinitely many points. This book explores the key ideas and debates concerning continuity over more than 2500 years.
The Being Of Negation In Post Kantian Philosophy
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Author : Gregory S. Moss
language : en
Publisher: Springer Nature
Release Date : 2022-11-13
The Being Of Negation In Post Kantian Philosophy written by Gregory S. Moss and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-13 with Philosophy categories.
By drawing on the insights of diverse scholars from around the globe, this volume systematically investigates the meaning and reality of the concept of negation in Post-Kantian Philosophy—German Idealism, Early German Romanticism, and Neo-Kantianism. The reader benefits from the historical, critical, and systematic investigations contained which trace not only the significance of negation in these traditions, but also the role it has played in shaping the philosophical landscape of Post-Kantian philosophy. By drawing attention to historically neglected thinkers and traditions, and positioning the dialogue within a global and comparative context, this volume demonstrates the enduring relevance of Post-Kantian philosophy for philosophers thinking in today’s global context. This text should appeal to graduate students and professors of German Idealism, Post-Kantian philosophy, comparative philosophy, German studies, and intellectual history.
Politics Of The Many
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Author : Benjamin Halligan
language : en
Publisher: Bloomsbury Publishing
Release Date : 2021-09-09
Politics Of The Many written by Benjamin Halligan and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Philosophy categories.
Politics of the Many draws inspiration from Percy Bysshe Shelley's celebrated call to arms: 'Ye are many – they are few!' This idea of the Many, as a general form of emancipatory subjectivity that cannot be erased for the sake of the One, is the philosophical and political assumption shared by contributors to this book. They raise questions of collective agency, and its crisis in contemporary capitalism, via new engagements with Marxist philosophy, psychoanalysis, theories of social reproduction and value-form, and post-colonial critiques, and drawing on activist thought and strategies. This book interrogates both established and emergent formations of the Many (the people, classes, publics, crowds, masses, multitudes), tracing their genealogies, their recent failures and victories, and their potentials to change the world. The book proposes and explores an intense and provoking series of new or reinvented concepts, figures, and theoretical constellations, including dividuality, the centaur, unintentional vanguard, insomnia at work, always-on capitalism, multitude (from its 'voiding' to a '(non)emergence'), crowds, necropolitics, and the link between political subjectivity and value-form. The contributors to Politics of the Many are both acclaimed and emergent thinkers including Carina Brand, Rebecca Carson, Luhuna Carvalho, Lorenzo Chiesa, Jodi Dean, Dario Gentili, Benjamin Halligan, Marc James Léger, Paul Mazzocchi, Alexei Penzin, Stefano Pippa, Gerald Raunig, and Stevphen Shukaitis.
Logic And Its Applications
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Author : Mohua Banerjee
language : en
Publisher: Springer Nature
Release Date : 2023-02-22
Logic And Its Applications written by Mohua Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-22 with Mathematics categories.
Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023. Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.
Conceptual Harmonies
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Author : Paul Redding
language : en
Publisher: University of Chicago Press
Release Date : 2023-06-12
Conceptual Harmonies written by Paul Redding and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-12 with Philosophy categories.
A new reading of Hegel’s Science of Logic through the history of European mathematics. Conceptual Harmonies develops an original account of G. W. F. Hegel’s perplexing Science of Logic from a simple insight: philosophical and mathematical thought have shaped each other since classical times. Situating Science of Logic within the rise of modern mathematics, Redding stresses Hegel’s attention to Pythagorean ratios, Platonic reason, and Aristotle’s geometrically inspired logic. He then explores how later traditions shaped Hegel’s world, through both Leibniz and new forms of algebraic geometry. This enlightening reading recovers an overlooked stream in Hegel’s philosophy that remains, Redding argues, important for contemporary conceptions of logic.