Proofs and Refutations

The Logic of Mathematical Discovery

Author: Imre Lakatos

Publisher: Cambridge University Press

ISBN: 1316425339

Category: Science

Page: N.A

View: 9254

Imre Lakatos's Proofs and Refutations is an enduring classic, which has never lost its relevance. Taking the form of a dialogue between a teacher and some students, the book considers various solutions to mathematical problems and, in the process, raises important questions about the nature of mathematical discovery and methodology. Lakatos shows that mathematics grows through a process of improvement by attempts at proofs and critiques of these attempts, and his work continues to inspire mathematicians and philosophers aspiring to develop a philosophy of mathematics that accounts for both the static and the dynamic complexity of mathematical practice. With a specially commissioned Preface written by Paolo Mancosu, this book has been revived for a new generation of readers.
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Beweise und Widerlegungen

Die Logik mathematischer Entdeckungen

Author: Imre Lakatos

Publisher: Springer-Verlag

ISBN: 3663001962

Category: Mathematics

Page: 163

View: 6261

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Was ist ein Naturgesetz?

Author: David M. Armstrong

Publisher: N.A

ISBN: 9783936532326

Category:

Page: 233

View: 2347

Das Buch ist eine systematisch gegliederte Untersuchung zu einem zentralen und kontrovers diskutierten Gegenstand sowohl der modernen Metaphysik, als auch der Wissenschaftsphilosophie, nämlich dem Wesen der Naturgesetze. D.M. Armstrong arbeitet klar und detailgenau einen weitgehend neuen Standpunkt heraus, demzufolge Naturgesetze Beziehungen zwischen Eigenschaften bzw. Universalien sind. Diese Theorie geht Hand in Hand mit einer realistischen Darstellung der Universalien, und folgt damit dem naturwissenschaftlichen Realismus, den der Autor bereits in früheren Publikationen entwickelt hat. Er beginnt mit einer detaillierten Kritik der orthodoxen und skeptischen Sichtweise, die ausgehend von David Hume behauptet, Naturgesetze seien lediglich eine Regelmässigkeit der Übereinstimmung zwischen Eigenschaftsinstanzen. Ausgehend von dieser Kritik entwickelt Armstrong ein abschließendes Urteil gegenüber dieser Position. Er fährt fort mit der systematischen Darlegung seiner eigenen Theorie, die er gegen die naheliegendsten Einwände verteidigt und rundet diese und seine Theorie der Universalien mit einer Integration funktionaler und statistischer (wahrscheinlichkeitsbefangener) Gesetze ab. Die Behandlung des Themas ist erfrischend präzise und lebendig. Armstrong fachte mit diesem Buch bei seinem Erscheinen im angesächsischen Kulturkreis eine anhaltende philosophische Debatte neu an.
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Foundational Theories of Classical and Constructive Mathematics

Author: Giovanni Sommaruga

Publisher: Springer Science & Business Media

ISBN: 9789400704312

Category: Mathematics

Page: 316

View: 2696

The book "Foundational Theories of Classical and Constructive Mathematics" is a book on the classical topic of foundations of mathematics. Its originality resides mainly in its treating at the same time foundations of classical and foundations of constructive mathematics. This confrontation of two kinds of foundations contributes to answering questions such as: Are foundations/foundational theories of classical mathematics of a different nature compared to those of constructive mathematics? Do they play the same role for the resp. mathematics? Are there connections between the two kinds of foundational theories? etc. The confrontation and comparison is often implicit and sometimes explicit. Its great advantage is to extend the traditional discussion of the foundations of mathematics and to render it at the same time more subtle and more differentiated. Another important aspect of the book is that some of its contributions are of a more philosophical, others of a more technical nature. This double face is emphasized, since foundations of mathematics is an eminent topic in the philosophy of mathematics: hence both sides of this discipline ought to be and are being paid due to.
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New Directions in the Philosophy of Mathematics

An Anthology

Author: Thomas Tymoczko

Publisher: Princeton University Press

ISBN: 9780691034980

Category: Mathematics

Page: 436

View: 3604

The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.
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Mathematics, Science and Epistemology: Volume 2, Philosophical Papers

Author: Imre Lakatos

Publisher: Cambridge University Press

ISBN: 9780521280303

Category: Mathematics

Page: 296

View: 9846

Volume I brings together his very influential but scattered papers on the philosophy of the physical sciences, and includes one important unpublished essay on the effect of Newton's scientific achievement. Volume 2 presents his work on the philosophy of mathematics together with some critical essays on contemporary philosophers of science.
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Connecting Humans to Equations

A Reinterpretation of the Philosophy of Mathematics

Author: Ole Ravn,Ole Skovsmose

Publisher: Springer

ISBN: 3030013375

Category: Education

Page: 188

View: 6789

Connecting Humans to Equations: A Reinterpretation of the Philosophy of Mathematics presents some of the most important positions in the philosophy of mathematics, while adding new dimensions to this philosophy. Mathematics is an integral part of human and social life, meaning that a philosophy of mathematics must include several dimensions. This book describes these dimensions by the following four questions that structure the content of the book: Where is mathematics? How certain is mathematics? How social is mathematics? How good is mathematics? These four questions refer to the ontological, epistemological, social, and ethical dimension of a philosophy of mathematics. While the ontological and epistemological dimensions have been explored in all classic studies in the philosophy of mathematics, the exploration of the book is unique in its social and ethical dimensions. It argues that the foundation of mathematics is deeply connected to human and social actions and that mathematics includes not just descriptive but also performative features. This human-centered and accessible interpretation of mathematics is relevant for students in mathematics, mathematics education, and any technical discipline and for anybody working with mathematics.
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Vermutungen und Widerlegungen

das Wachstum der wissenschaftlichen Erkenntnis

Author: Karl R. Popper

Publisher: N.A

ISBN: 9783161473111

Category:

Page: 627

View: 8284

Die Bände I und II der Vermutungen und Widerlegungen liegen nun in einer preiswerten einbändigen Studienausgabe vor. Die beiden Teilbände in den bisherigen Ausgaben sind weiterhin lieferbar."In Vorträgen, also in lockerer Form, führt Popper seine wichtigsten Gedanken vor: daß die Wissenschaft durch kühne Hypothesen vorangetrieben wird; daß sich Theorien nicht bestätigen, sondern nur falsifizieren lassen; daß die Menschen die Chance haben, aus Fehlern zu lernen, und diese Chance nutzen sollten. Popper glaubt ..., daß ein Wachstum der Erkenntnis möglich ist."K.A. in Frankfurter Allgemeine Zeitung vom 25.11.1994, S. 39"Nach mehr als dreißig Jahren Abstand erscheinen so viele Passagen noch immer treffend und aktuell. Seine Kritik am neopositivistisch gefaßten Induktionsprinzip oder der Wissenschaft des Wiener Kreises insgesamt ... wird hier noch einmal aufgegriffen und ausführlicher entwickelt. ... Zahlreiche hier zusammengetragene Vorträge und Aufsätze beschäftigen sich scheinbar mit nur philosophiehistorisch interessanten Fragen. Doch immer versucht Popper die dahinterstehenden sachlichen Probleme zu fassen, die zu dieser jeweiligen philosophischen Theorie geführt haben."Philosophischer Literaturanzeiger 1998, S. 84
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New Directions in Economic Methodology

Author: Roger E. Backhouse

Publisher: Routledge

ISBN: 1134864396

Category: Business & Economics

Page: 416

View: 4456

In recent years there has been a flowering of work on economic methodology. However there is no longer any consensus about which direction this should take or, indeed, even what the role and content of economic methodology should be. This book reflects this diversity. Its contributors are responsible for the major developments in this field and together they give an account of all the major positions which currently prevail in economic methodology. These include attempts to rehabilitate the 'falsification' of Kuhn, Lakatos and Popper, sociology of knowledge approaches, different forms of realism, contributions from the 'rhetoric' project and other perspectives which view the economy as a text.
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Encyclopedia of Educational Theory and Philosophy

Author: D. C. Phillips

Publisher: SAGE Publications

ISBN: 1483364755

Category: Education

Page: 952

View: 8963

Education is a field sometimes beset by theories-of-the-day and with easy panaceas that overpromise the degree to which they can alleviate pressing educational problems. The two-volume Encyclopedia of Educational Theory and Philosophy introduces readers to theories that have stood the test of time and those that have provided the historical foundation for the best of contemporary educational theory and practice. Drawing together a team of international scholars, this invaluable reference examines the global landscape of all the key theories and the theorists behind them and presents them in the context needed to understand their strengths and weaknesses. In addition to interpretations of long-established theories, this work offers essays on cutting-edge research and concise, to-the-point definitions of key concepts, ideas, schools, and figures. Features: Over 300 signed entries by trusted experts in the field are organized into two volumes and overseen by a distinguished General Editor and an international Editorial Board. Entries are followed by cross references and further reading suggestions. A Chronology of Theory within the field of education highlights developments over the centuries; a Reader’s Guide groups entries thematically, and a master Bibliography facilitates further study. The Reader’s Guide, detailed index, and cross references combine for strong search-and-browse capabilities in the electronic version. Available in a choice of print or electronic formats, Encyclopedia of Educational Theory and Philosophy is an ideal reference for anyone interested in the roots of contemporary educational theory.
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The Cambridge Companion to Classical Islamic Theology

Author: Tim Winter

Publisher: Cambridge University Press

ISBN: 1107494419

Category: Religion

Page: 350

View: 8668

This series of critical reflections on the evolution and major themes of pre-modern Muslim theology begins with the revelation of the Koran, and extends to the beginnings of modernity in the eighteenth century. The significance of Islamic theology reflects the immense importance of Islam in the history of monotheism, to which it has brought a unique approach and style, and a range of solutions which are of abiding interest. Devoting especial attention to questions of rationality, scriptural fidelity, and the construction of 'orthodoxy', this volume introduces key Muslim theories of revelation, creation, ethics, scriptural interpretation, law, mysticism, and eschatology. Throughout the treatment is firmly set in the historical, social and political context in which Islam's distinctive understanding of God evolved. Despite its importance, Islamic theology has been neglected in recent scholarship, and this book provides a unique, scholarly but accessible introduction.
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Change and Progress in Modern Science

Papers related to and arising from the Fourth International Conference on History and Philosophy of Science, Blacksburg, Virginia, November 1982

Author: Joseph C. Pitt

Publisher: Springer Science & Business Media

ISBN: 9400965257

Category: Science

Page: 400

View: 7859

The papers presented here derive from the 4th International Confe:--ence on History and Philosophy of Science held in Blacksburg, Virginia, U.S.A., November 2-6, 1982. The Conference was sponsored by the I nternational Union of History and Philosophy of Science and Virginia Polytechnic Institute and State University (Virginia Tech). Particular thanks go to L. Jonathan Cohen, Secretary of the Union, as well as to Dean Henry Bauer of the College of Arts & Sciences, Wilfred Jewkes and the Center for Programs in the Humanities, Arthur Donovan and the Center for the Study of Science in Society and the Department of Philoso phy and Religion at Virginia Tech. Not only did they come through with the necessat"y funds, but they were all always ready with a helping hand when things got confusing. Two additional groups of individuals require a special note of thanks. First, considerable appreciation is due the mem bers of the Joint Commission of the I nternational Union of History and Philosophy of Science: Maurice Crosland, Risto Hilpinen and Vladimir Kirsanov. They were more than gen erous in thei r advice and co-operation. The Local Organizing Committee (Kenneth Alpern, Roger Ariew, Arthur Donovan, Larry Laudan, Ann La Berge, Duncan Porter, Eleonore Stump and Dennis Welch) not only demon strated efficiency and insured a pleasant stay for' all participants, but also went out of their way on numerous occasions to make everyone feel at home.
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Philosophical Papers

Author: Imre Lakatos

Publisher: N.A

ISBN: N.A

Category: Science

Page: N.A

View: 7956

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Mathematik und Plausibles Schließen

Band 2: Typen und Strukturen plausibler Folgerung

Author: G. Polya

Publisher: Birkhäuser

ISBN: 9783764307158

Category: Science

Page: 326

View: 8114

10 in denen meine Beobachtungen meine Schlusse zu stutzen scheinen. Aber ich achte das Urteil des Lesers und will ihn nicht zwingen oder auf irgendeine unsaubere Weise dazu bringen, meine Schlusse anzu nehmen. Naturlich erheben die hier gebotenen Ansichten keinen Anspruch auf Endgultigkeit. Ich konnte in der Tat eine Reihe von Stellen ange ben, wo ich klar empfinde, dass eine grossere oder kleinere Verbesse rung am Platz ware. Ich glaube jedoch, dass die Hauptrichtung richtig ist, und ich hoffe, dass die Ausfuhrungen und vor allem die Beispiele in diesem Werk dazu beitragen mogen, die -Doppelnatun und die -komplementaren Aspekte) plausiblen, insbesondere induktiven Schliessens, zu erhellen, das zuweilen als -objektiv) und zuweilen als -subjektiv) erscheint. Stanford University Georg P6lya Mai 1953 VORWORT ZUR ZWEITEN AUFLAGE Die vorliegende zweite Auflage wurde erweitert durch einen An hang. Dieser enthalt einen Aufsatz -Heuristische Schlussweisen in der Zahlentheorie), entnommen dem American Mathematical Monthly mit der Genehmigung des herausgebenden Vereins, und zusatzliche Bemerkungen und Aufgaben zu verschiedenen Kapiteln. Herzlichen Dank Fraulein Dr. A. Roth fur die gewissenhafte Uber setzung und Frau H. Bretscher fur freundliche Hilfe."
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Der Staat

Author: Platon

Publisher: BoD – Books on Demand

ISBN: 3843030944

Category: Philosophy

Page: 356

View: 6634

Platon: Der Staat Entstanden etwa in der Mitte der siebziger Jahre des 4. Jahrhunderts v. Chr. Erstdruck (in lateinischer Übersetzung durch Marsilio Ficino) in: Opera, Florenz o. J. (ca. 1482/84). Erstdruck des griechischen Originals in: Hapanta ta tu Platônos, herausgegeben von M. Musuros, Venedig 1513. Erste deutsche Übersetzung (in Auszügen) durch G. Lauterbeck unter dem Titel »Summa der Platonischen Lere, von den Gesetzen und Regierung des gemeinen Nutzes« in: G. Lauterbeck, Regentenbuch, Leipzig 1572. Erste vollständige deutsche Übersetzung durch Johann Friedrich Kleuker unter dem Titel »Die Republik oder ein Gespräch über das Gerechte« in: Werke, 2. Band, Lemgo 1780. Der Text folgt der Übersetzung durch Wilhelm Siegmund Teuffel (Buch I-V) und Wilhelm Wiegand (Buch VI-X) von 1855/56. Vollständige Neuausgabe mit einer Biographie des Autors. Herausgegeben von Karl-Maria Guth. Berlin 2013. Textgrundlage ist die Ausgabe: Platon: Sämtliche Werke. Berlin: Lambert Schneider, [1940]. Die Paginierung obiger Ausgabe wird in dieser Neuausgabe als Marginalie zeilengenau mitgeführt. Umschlaggestaltung von Thomas Schultz-Overhage unter Verwendung des Bildes: Raffael, Die Schule von Athen (Detail). Gesetzt aus Minion Pro, 11 pt.
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Praktische Ethik

Author: Peter Singer

Publisher: N.A

ISBN: 9783150189191

Category: Ethics

Page: 564

View: 7533

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