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Philosophy Of Mathematics

Author: James Robert Brown
Publisher: Routledge
ISBN: 1135902399
Size: 13.33 MB
Format: PDF, ePub
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In his long-awaited new edition of Philosophy of Mathematics, James Robert Brown tackles important new as well as enduring questions in the mathematical sciences. Can pictures go beyond being merely suggestive and actually prove anything? Are mathematical results certain? Are experiments of any real value? This clear and engaging book takes a unique approach, encompassing non-standard topics such as the role of visual reasoning, the importance of notation, and the place of computers in mathematics, as well as traditional topics such as formalism, Platonism, and constructivism. The combination of topics and clarity of presentation make it suitable for beginners and experts alike. The revised and updated second edition of Philosophy of Mathematics contains more examples, suggestions for further reading, and expanded material on several topics including a novel approach to the continuum hypothesis.

Argumentieren Mit Multiplen Und Dynamischen Repr Sentationen

Author: Andreas Bauer
Publisher: BoD – Books on Demand
ISBN: 3958260225
Size: 10.55 MB
Format: PDF, ePub
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Kaum eine mathematische Tätigkeit bestimmt das Wesen der Mathematik so sehr wie das Argumentieren. Dies gilt gleichermaßen für den Mathematikunterricht in der Sekundarstufe. Wer argumentiert, benötigt jedoch Informationen, um Aussagen formulieren zu können. Diese werden in der Mathematik durch Repräsentationen mathematischer Objekte bereitgestellt. Durch den Einzug des Rechners in den Mathematikunterricht wurden hierzu neue Möglichkeiten geschaffen: Multiple und dynamische Repräsentationen, die über Darstellungsgrenzen hinweg verschiedene Blickwinkel auf das gleiche Objekt verknüpfen, können heute mühelos erzeugt und interaktiv variiert werden. Mit Hilfe bestehender Theorien zu Repräsentationen und dem Argumentieren beantwortet die Arbeit die Frage, welchen Einfluss diese neuartigen Repräsentationen auf die Argumentationen von Schülerinnen und Schülern besitzen und leistet so einen Beitrag zur Diskussion über den Einsatz von digitalen Technologien im Mathematikunterricht.

Philosophy Of Mathematics Oxford Bibliographies Online Research Guide

Author: Oxford University Press
Publisher: Oxford University Press, USA
ISBN: 9780199808939
Size: 73.69 MB
Format: PDF, Mobi
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This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.

An Historical Introduction To The Philosophy Of Mathematics A Reader

Author: Russell Marcus
Publisher: Bloomsbury Publishing
ISBN: 1472529480
Size: 45.37 MB
Format: PDF, Kindle
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A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

Eine Kurze Geschichte Der Menschheit

Author: Yuval Noah Harari
Publisher: DVA
ISBN: 364110498X
Size: 77.94 MB
Format: PDF, ePub
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Krone der Schöpfung? Vor 100 000 Jahren war der Homo sapiens noch ein unbedeutendes Tier, das unauffällig in einem abgelegenen Winkel des afrikanischen Kontinents lebte. Unsere Vorfahren teilten sich den Planeten mit mindestens fünf weiteren menschlichen Spezies, und die Rolle, die sie im Ökosystem spielten, war nicht größer als die von Gorillas, Libellen oder Quallen. Vor 70 000 Jahren dann vollzog sich ein mysteriöser und rascher Wandel mit dem Homo sapiens, und es war vor allem die Beschaffenheit seines Gehirns, die ihn zum Herren des Planeten und zum Schrecken des Ökosystems werden ließ. Bis heute hat sich diese Vorherrschaft stetig zugespitzt: Der Mensch hat die Fähigkeit zu schöpferischem und zu zerstörerischem Handeln wie kein anderes Lebewesen. Anschaulich, unterhaltsam und stellenweise hochkomisch zeichnet Yuval Harari die Geschichte des Menschen nach und zeigt alle großen, aber auch alle ambivalenten Momente unserer Menschwerdung.

Philosophy Of Science

Author: Alexander Rosenberg
Publisher: Psychology Press
ISBN: 041515281X
Size: 49.45 MB
Format: PDF, Docs
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This user-friendly text covers key issues in the philosophy of science in an accessible and philosophically serious way. It will prove valuable to students studying philosophy of science as well as science students. Prize-winning author Alex Rosenberg explores the philosophical problems that science raises by its very nature and method. He skilfully demonstrates that scientific explanation, laws, causation, theory, models, evidence, reductionism, probability, teleology, realism and instrumentalism actually pose the same questions that Plato, Aristotle, Descartes, Hume, Kant and their successors have grappled with for centuries.