Intuition And The Axiomatic Method
DOWNLOAD
Download Intuition And The Axiomatic Method PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Intuition And The Axiomatic Method book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Intuition And The Axiomatic Method
DOWNLOAD
Author : Emily Carson
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-24
Intuition And The Axiomatic Method written by Emily Carson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-24 with Mathematics categories.
Following developments in modern geometry, logic and physics, many scientists and philosophers in the modern era considered Kant’s theory of intuition to be obsolete. But this only represents one side of the story concerning Kant, intuition and twentieth century science. Several prominent mathematicians and physicists were convinced that the formal tools of modern logic, set theory and the axiomatic method are not sufficient for providing mathematics and physics with satisfactory foundations. All of Hilbert, Gödel, Poincaré, Weyl and Bohr thought that intuition was an indispensable element in describing the foundations of science. They had very different reasons for thinking this, and they had very different accounts of what they called intuition. But they had in common that their views of mathematics and physics were significantly influenced by their readings of Kant. In the present volume, various views of intuition and the axiomatic method are explored, beginning with Kant’s own approach. By way of these investigations, we hope to understand better the rationale behind Kant’s theory of intuition, as well as to grasp many facets of the relations between theories of intuition and the axiomatic method, dealing with both their strengths and limitations; in short, the volume covers logical and non-logical, historical and systematic issues in both mathematics and physics.
Axiomatic Method And Category Theory
DOWNLOAD
Author : Andrei Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-14
Axiomatic Method And Category Theory written by Andrei Rodin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-14 with Philosophy categories.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Bourbaki
DOWNLOAD
Author : Maurice Mashaal
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Bourbaki written by Maurice Mashaal and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Biography & Autobiography categories.
The name Bourbaki is known to every mathematician. This book presents accounts of the origins of Bourbaki, their meetings, their seminars, and the members themselves. It also discusses the lasting influence that Bourbaki has had on mathematics, through both the Elements and the Seminaires.
Intuition In Science And Mathematics
DOWNLOAD
Author : Efraim Fischbein
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-19
Intuition In Science And Mathematics written by Efraim Fischbein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-19 with Education categories.
In writing the present book I have had in mind the following objectives: - To propose a theoretical, comprehensive view of the domain of intuition. - To identify and organize the experimental findings related to intuition scattered in a wide variety of research contexts. - To reveal the educational implications of the idea, developed for science and mathematics education. Most of the existing monographs in the field of intuition are mainly concerned with theoretical debates - definitions, philosophical attitudes, historical considerations. (See, especially the works of Wild (1938), of Bunge (1 962) and of Noddings and Shore (1 984).) A notable exception is the book by Westcott (1968), which combines theoretical analyses with the author’s own experimental studies. But, so far, no attempt has been made to identify systematically those findings, spread throughout the research literature, which could contribute to the deciphering of the mechanisms of intuition. Very often the relevant studies do not refer explicitly to intuition. Even when this term is used it occurs, usually, as a self-evident, common sense term.
A History Of Analysis
DOWNLOAD
Author : Hans Niels Jahnke
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
A History Of Analysis written by Hans Niels Jahnke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Analysis as an independent subject was created as part of the scientific revolution in the seventeenth century. Kepler, Galileo, Descartes, Fermat, Huygens, Newton, and Leibniz, to name but a few, contributed to its genesis. Since the end of the seventeenth century, the historical progress of mathematical analysis has displayed unique vitality and momentum. No other mathematical field has so profoundly influenced the development of modern scientific thinking. Describing this multidimensional historical development requires an in-depth discussion which includes a reconstruction of general trends and an examination of the specific problems. This volume is designed as a collective work of authors who are proven experts in the history of mathematics. It clarifies the conceptual change that analysis underwent during its development while elucidating the influence of specific applications and describing the relevance of biographical and philosophical backgrounds. The first ten chapters of the book outline chronological development and the last three chapters survey the history of differential equations, the calculus of variations, and functional analysis. Special features are a separate chapter on the development of the theory of complex functions in the nineteenth century and two chapters on the influence of physics on analysis. One is about the origins of analytical mechanics, and one treats the development of boundary-value problems of mathematical physics (especially potential theory) in the nineteenth century. The book presents an accurate and very readable account of the history of analysis. Each chapter provides a comprehensive bibliography. Mathematical examples have been carefully chosen so that readers with a modest background in mathematics can follow them. It is suitable for mathematical historians and a general mathematical audience.
Discourse On A New Method
DOWNLOAD
Author : Mary Domski
language : en
Publisher: Open Court
Release Date : 2010-09-10
Discourse On A New Method written by Mary Domski and has been published by Open Court this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-10 with Philosophy categories.
Addressing a wide range of topics, from Newton to Post-Kuhnian philosophy of science, these essays critically examine themes that have been central to the influential work of philosopher Michael Friedman. Special focus is given to Friedman's revealing study of both history of science and philosophy in his work on Kant, Newton, Einstein, and other major figures. This interaction of history and philosophy is the subject of the editors' "manifesto" and serves to both explain and promote the essential ties between two disciplines usually regarded as unrelated.
Discipline Filosofiche 2015 1
DOWNLOAD
Author : Mario Alai
language : en
Publisher: Quodlibet
Release Date : 2015-01-15
Discipline Filosofiche 2015 1 written by Mario Alai and has been published by Quodlibet this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-15 with Philosophy categories.
Contents: Mario Alai, Andrea Sereni and Giorgio Volpe, Guest Editors’ Preface • Ernest Sosa, Philosophical Intuitions and Metaphysical Analysis • Jonathan M. Weinberg, The Methodological Necessity of Experimental Philosophy • Steven Bland, Conceptual Analysis, Analytic Philosophy, and the Psychologistic Turn • Bryce Huebner, The Construction of Philosophical Intuitions • Alfredo Tomasetta, Physicalist Naturalism in the Philosophy of Mind (far less Warranted than Usually Thought) • Markus Pantsar, Assessing the “Empirical Philosophy of Mathematics” • Huginn Freyr Thorsteinsson, Experimental Philosophy and the Importance of Intuitions in the Philosophy of Language • Francesca Ervas, Elisabetta Gola, Antonio Ledda and Giuseppe Sergioli, Lexical Ambiguity in Elementary Inferences: an Experimental Study • Richard Davies, How to Point a Philosophical Armchair
Kant S Transcendental Semantics
DOWNLOAD
Author : Zeljko Loparic
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-12-16
Kant S Transcendental Semantics written by Zeljko Loparic and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-16 with Philosophy categories.
Kant’s Transcendental Semantics is a translation of the most influential monograph on Kant published in Brazil, one that launched the “Semantic School” in a country with a thriving tradition of Kant scholarship. Zeljko Loparic differs from most interpreters of the Critique of Pure Reason in claiming that Kant’s main aim is neither metaphysical nor epistemological nor methodological but semantic in asking for the conditions for meaning and reference of terms in order to justify the possibility of meaningful discourse of different types. Loparic asks how our claims can have any meaning at all, how they relate to actual and possible objects, how our terms can ground scientific problem-solving, and what the truth-conditions are for various kinds of statements that differ according to the grounds of their meaning and the targets of their reference. Loparic argues for distinct uses for concepts of perception, concepts of experience, mathematical concepts, pure concepts of the understanding (the categories), and the heuristic ideas of reason. Because Kant’s main worry in the Critique of Pure Reason is with the possibility of synthetic a priori judgments, Loparic labels Kant’s defense of those judgments a transcendental semantics.
Perspectives On Psychologism
DOWNLOAD
Author : Mark Amadeus Notturno
language : en
Publisher: BRILL
Release Date : 2023-03-13
Perspectives On Psychologism written by Mark Amadeus Notturno and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-13 with Architecture categories.
Handbook Of The History And Philosophy Of Mathematical Practice
DOWNLOAD
Author : Bharath Sriraman
language : en
Publisher: Springer Nature
Release Date : 2024-04-26
Handbook Of The History And Philosophy Of Mathematical Practice written by Bharath Sriraman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
The purpose of this unique handbook is to examine the transformation of the philosophy of mathematics from its origins in the history of mathematical practice to the present. It aims to synthesize what is known and what has unfolded so far, as well as to explore directions in which the study of the philosophy of mathematics, as evident in increasingly diverse mathematical practices, is headed. Each section offers insights into the origins, debates, methodologies, and newer perspectives that characterize the discipline today. Contributions are written by scholars from mathematics, history, and philosophy – as well as other disciplines that have contributed to the richness of perspectives abundant in the study of philosophy today – who describe various mathematical practices throughout different time periods and contrast them with the development of philosophy. Editorial Advisory Board Andrew Aberdein, Florida Institute ofTechnology, USA Jody Azzouni, Tufts University, USA Otávio Bueno, University of Miami, USA William Byers, Concordia University, Canada Carlo Cellucci, Sapienza University of Rome, Italy Chandler Davis, University of Toronto, Canada (1926-2022) Paul Ernest, University of Exeter, UK Michele Friend, George Washington University, USA Reuben Hersh, University of New Mexico, USA (1927-2020) Kyeong-Hwa Lee, Seoul National University, South Korea Yuri Manin, Max Planck Institute for Mathematics, Germany (1937-2023) Athanase Papadopoulos, University of Strasbourg, France Ulf Persson, Chalmers University of Technology, Sweden John Stillwell, University of San Francisco, USA David Tall, University of Warwick, UK (1941-2024) This book with its exciting depth and breadth, illuminates us about the history, practice, and the very language of our subject; about the role of abstraction, ofproof and manners of proof; about the interplay of fundamental intuitions; about algebraic thought in contrast to geometric thought. The richness of mathematics and the philosophy encompassing it is splendidly exhibited over the wide range of time these volumes cover---from deep platonic and neoplatonic influences to the most current experimental approaches. Enriched, as well, with vivid biographies and brilliant personal essays written by (and about) people who play an important role in our tradition, this extraordinary collection of essays is fittingly dedicated to the memory of Chandler Davis, Reuben Hersh, and Yuri Manin. ---Barry Mazur, Gerhard Gade University Professor, Harvard University This encyclopedic Handbook will be a treat for all those interested in the history and philosophy of mathematics. Whether one is interested in individuals (from Pythagoras through Newton and Leibniz to Grothendieck), fields (geometry, algebra, number theory, logic, probability, analysis), viewpoints (from Platonism to Intuitionism), or methods (proof, experiment, computer assistance), the reader will find a multitude of chapters that inform and fascinate. ---John Stillwell, Emeritus Professor of Mathematics, University of San Francisco; Recipient of the 2005 Chauvenet Prize Dedicating a volume to the memory of three mathematicians – Chandler Davis, Reuben Hersh, and Yuri Manin –, who went out of their way to show to a broader audience that mathematics is more than what they might think, is an excellent initiative. Gathering authors coming from many different backgrounds but who are very strict about the essays they write was successfully achieved by the editor-in-chief. The result: a great source of potential inspiration! ---Jean-Pierre Bourguignon; Nicolaas Kuiper Honorary Professor at the Institut des Hautes Études Scientifiques