The Conceptual Roots Of Mathematics
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The Conceptual Roots Of Mathematics
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Author : J.R. Lucas
language : en
Publisher:
Release Date : 2005
The Conceptual Roots Of Mathematics written by J.R. Lucas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
Conceptual Roots Of Mathematics
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Author : J.R. Lucas
language : en
Publisher: Routledge
Release Date : 2002-09-11
Conceptual Roots Of Mathematics written by J.R. Lucas and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-11 with Philosophy categories.
The Conceptual Roots of Mathematics is a comprehensive study of the foundation of mathematics. J.R. Lucas, one of the most distinguished Oxford scholars, covers a vast amount of ground in the philosophy of mathematics, showing us that it is actually at the heart of the study of epistemology and metaphysics.
Postmodern Philosophy And The Scientific Turn
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Author : Dorothea E. Olkowski
language : en
Publisher: Indiana University Press
Release Date : 2012-04-23
Postmodern Philosophy And The Scientific Turn written by Dorothea E. Olkowski and has been published by Indiana University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-23 with Philosophy categories.
A groundbreaking, interdisciplinary approach to the study of consciousness: “Beautifully written, engaging throughout, and captivating” (Claire Colebrook, The Pennsylvania State University). What can come of a scientific engagement with postmodern philosophy? Some scientists have claimed that the social sciences and humanities have nothing to contribute, except perhaps peripherally, to their research. Dorothea E. Olkowski shows that mathematics itself—the historic link between science and philosophy—plays a fundamental role in the development of the worldviews that drive both fields. Focusing on language, its usage and expression of worldview, she develops a phenomenological account of human thought and action to explicate the role of philosophy in the sciences. Olkowski proposes a model of phenomenology, both scientific and philosophical, that helps make sense of reality and composes an ethics for dealing with unpredictability in our world.
The Chinese Roots Of Linear Algebra
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Author : Roger Hart
language : en
Publisher: JHU Press
Release Date : 2011-01-01
The Chinese Roots Of Linear Algebra written by Roger Hart and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-01 with Mathematics categories.
A monumental accomplishment in the history of non-Western mathematics, The Chinese Roots of Linear Algebra explains the fundamentally visual way Chinese mathematicians understood and solved mathematical problems. It argues convincingly that what the West "discovered" in the sixteenth and seventeenth centuries had already been known to the Chinese for 1,000 years. Accomplished historian and Chinese-language scholar Roger Hart examines Nine Chapters of Mathematical Arts—the classic ancient Chinese mathematics text—and the arcane art of fangcheng, one of the most significant branches of mathematics in Imperial China. Practiced between the first and seventeenth centuries by anonymous and most likely illiterate adepts, fangcheng involves manipulating counting rods on a counting board. It is essentially equivalent to the solution of systems of N equations in N unknowns in modern algebra, and its practice, Hart reveals, was visual and algorithmic. Fangcheng practitioners viewed problems in two dimensions as an array of numbers across counting boards. By "cross multiplying" these, they derived solutions of systems of linear equations that are not found in ancient Greek or early European mathematics. Doing so within a column equates to Gaussian elimination, while the same operation among individual entries produces determinantal-style solutions. Mathematicians and historians of mathematics and science will find in The Chinese Roots of Linear Algebra new ways to conceptualize the intellectual development of linear algebra.
The Origin Of The Logic Of Symbolic Mathematics
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Author : Burt C. Hopkins
language : en
Publisher: Indiana University Press
Release Date : 2011-09-07
The Origin Of The Logic Of Symbolic Mathematics written by Burt C. Hopkins and has been published by Indiana University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-07 with Philosophy categories.
Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.
Dictionary Of Twentieth Century British Philosophers
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Author : Stuart Brown
language : en
Publisher: Bloomsbury Publishing
Release Date : 2005-06-01
Dictionary Of Twentieth Century British Philosophers written by Stuart Brown and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-06-01 with Philosophy categories.
This is a two-volume work with entries on individuals who made some contribution to philosophy in the period 1900 to 1960 or soon after. The entries deal with the whole philosophical work of an individual or, in the case of philosophers still living, their whole work to date. Typically the individuals included have been born by 1935 and by now have made their main contributions. Contributions to the subject typically take the form of books or journal articles, but influential teachers and people otherwise important in the world of philosophy may also be included. The dictionary includes amateurs as well as professional philosophers and, where appropriate, thinkers whose main discipline was outside philosophy. There are special problems about the term "British" in the twentieth century, partly because of human migration, partly because of decolonialization and the changing denotation of the term. The intention has been to include not only those who were British subjects at least for a significant part of their lives (even if they mostly lived outside what is now the U.K.) but also people who spent a significant part of their lives in Britain itself, irrespective of their nationality or country of origin. In the first category are included, for instance, a number of people who were born and educated in Britain but who subsequently taught in universities abroad. In the second category are included those who were born elsewhere but who came to Britain and contributed to its philosophical culture.
Introducing Philosophy Of Mathematics
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Author : Michele Friend
language : en
Publisher: Routledge
Release Date : 2014-12-05
Introducing Philosophy Of Mathematics written by Michele Friend and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Philosophy categories.
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.
Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science
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Author : Stanisław Krajewski
language : en
Publisher: IOS Press
Release Date : 2007
Topics In Logic Philosophy And Foundations Of Mathematics And Computer Science written by Stanisław Krajewski and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
This volume honors Professor Andrzej Grzegorczyk, the nestor of Polish logicians, on his 85th anniversary. The editors would like to express the respect and sympathy they have for him. His textbook The Outline of Mathematical Logic has been published in many editions and translated into several languages. It was this textbook that introduced many of us into the world of mathematical logic. Professor Grzegorczyk has made fundamental contributions to logic and to philosophy. His results, mainly on hierarchy of primitive recursive functions, known as the Grzegorczyk hierarchy, are of fundamental importance to theoretical computer science. In particular, they were precursory for the computational complexity theory. The editors would like to stress that this special publication celebrates a scientist who is still actively pursuing genuinely innovative directions of research. Quite recently, Andrzej Grzegorczyk gave a new proof of undecidability of the first order functional calculus. His proof does not use the arithmetization of Kurt Gödel. In recognition of his merits, the University of Clermont-Ferrand conferred to Professor Andrzej Grzegorczyk the Doctorat Honoris Causa. The work and life of Professor Andrzej Grzegorczyk is presented in the article by Professors Stanislaw Krajewski and Jan Wolenski. The papers in this collection have been submitted on invitational basis.
Primary Mathematics Teaching For Understanding
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Author : Patrick Barmby
language : en
Publisher: McGraw-Hill Education (UK)
Release Date : 2009-09-16
Primary Mathematics Teaching For Understanding written by Patrick Barmby and has been published by McGraw-Hill Education (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-16 with Education categories.
"One feature of this book that sets it apart from others is the care that is taken to clarify the authors’ interpretation of the phrase 'teaching for understanding'. Each component of this interpretation – connections, representations, reasoning, communication and misconceptions – is then successfully incorporated as a theme in the subsequent chapters that develop important mathematical topics." Ian Thompson, Visiting Professor at Edge Hill University and Northumbria University, UK This important book aims to support and develop teachers' understanding of the key primary mathematics topics. It takes an innovative approach by defining exactly what is meant by 'understanding' and uses this model to examine and explain various mathematical topics. The authors emphasize the importance of the different representations that can be used for mathematical concepts and inform the reasoning process. By focusing on understanding, the book also draws attention to common misconceptions that teachers may encounter in the classroom. Key features: Specific focus on 'understanding' to offer new insights in to how to teach the topics Case studies to demonstrate how to communicate mathematical topics in the classroom End of chapter questions to stimulate discussion The authors integrate research and theory throughout, to highlight core issues. This theoretical background is also linked directly to classroom practice and informs suggestions for how topics can be communicated in the classroom. This offers valuable guidance to trainee teachers on how to teach the topics and presents experienced teachers with the opportunity to develop their subject and pedagogical knowledge.
The Neighbor
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Author : Slavoj Žižek
language : en
Publisher: University of Chicago Press
Release Date : 2013-07-12
The Neighbor written by Slavoj Žižek 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 2013-07-12 with Religion categories.
In Civilization and Its Discontents, Freud made abundantly clear what he thought about the biblical injunction, first articulated in Leviticus 19:18 and then elaborated in Christian teachings, to love one's neighbor as oneself. “Let us adopt a naive attitude towards it,” he proposed, “as though we were hearing it for the first time; we shall be unable then to suppress a feeling of surprise and bewilderment.” After the horrors of World War II, the Holocaust, and Stalinism, Leviticus 19:18 seems even less conceivable—but all the more urgent now—than Freud imagined. In The Neighbor, three of the most significant intellectuals working in psychoanalysis and critical theory collaborate to show how this problem of neighbor-love opens questions that are fundamental to ethical inquiry and that suggest a new theological configuration of political theory. Their three extended essays explore today's central historical problem: the persistence of the theological in the political. In “Toward a Political Theology of the Neighbor,” Kenneth Reinhard supplements Carl Schmitt’s political theology of the enemy and friend with a political theology of the neighbor based in psychoanalysis. In “Miracles Happen,” Eric L. Santner extends the book's exploration of neighbor-love through a bracing reassessment of Benjamin and Rosenzweig. And in an impassioned plea for ethical violence, Slavoj Žižek’s “Neighbors and Other Monsters” reconsiders the idea of excess to rehabilitate a positive sense of the inhuman and challenge the influence of Levinas on contemporary ethical thought. A rich and suggestive account of the interplay between love and hate, self and other, personal and political, The Neighbor has proven to be a touchstone across the humanities and a crucial text for understanding the persistence of political theology in secular modernity. This new edition contains a new preface by the authors.