Set Theory and Its Philosophy

Author: Michael D. Potter
Publisher: University of Hawaii Press
ISBN: 0199270414
Release Date: 2004
Genre: Mathematics

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Set Theory and its Philosophy

Author: Michael Potter
Publisher: Clarendon Press
ISBN: 9780191556432
Release Date: 2004-01-15
Genre: Philosophy

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Enzyklop die Philosophie und Wissenschaftstheorie

Author: Jürgen Mittelstraß
Publisher: Springer-Verlag
ISBN: 9783476001405
Release Date: 2016-08-16
Genre: Philosophy

Das gesamte Wissen der Philosophie und Wissenschaftstheorie. Die Sach- und Personenartikel des Nachschlagewerks erfassen nicht nur den klassischen Bestand des philosophischen Wissens, sondern werden auch den neueren Entwicklungen in der Philosophie gerecht. Insbesondere in den Bereichen Logik, Erkenntnis- und Wissenschaftstheorie sowie Sprachphilosophie. Jetzt erscheint der fünfte Band der Neuauflage mit über 70 neuen Artikeln u. a. zu diesen Begriffen: antike Logik, Lüge, Macht, Medizin, Nano und Neurowissenschaften. Mit neuen Personenartikeln, darunter Luhmann, Lyotard, Maturana.

Wittgenstein und die Philosophie der Mathematik

Author: Joachim Bromand
Publisher: mentis Verlag GmbH
ISBN: 9783957438218
Release Date: 2018-09-04
Genre: Philosophy

Ludwig Wittgenstein selbst hielt seine Überlegungen zur Mathematik für seinen bedeutendsten Beitrag zur Philosophie. So beabsichtigte er zunächst, dem Thema einen zentralen Teil seiner Philosophischen Untersuchungen zu widmen. Tatsächlich wird kaum irgendwo sonst in Wittgensteins Werk so deutlich, wie radikal die Konsequenzen seines Denkens eigentlich sind. Vermutlich deshalb haben Wittgensteins Bemerkungen zur Mathematik unter all seinen Schriften auch den größten Widerstand provoziert: Seine Bemerkungen zu den Gödel'schen Unvollständigkeitssätzen bezeichnete Gödel selbst als Nonsens, und Alan Turing warf Wittgenstein vor, dass aufgrund seiner scheinbar toleranten Haltung gegenüber Widersprüchen Brücken einstürzen könnten, die Mithilfe mathematischer Berechnungen in Wittgensteins Sinne errichtet würden. Die Beiträge des Bandes erklären zentrale Überlegungen Wittgensteins zur Mathematik, räumen weit verbreitete Missverständnisse aus und analysieren kritisch Wittgensteins Bedeutung für die traditionelle Philosophie der Mathematik. Ebenfalls wird die Frage verfolgt, inwieweit Wittgensteins Bemerkungen zur Philosophie der Mathematik über seine Philosophischen Untersuchungen hinausführen.

Badiou s Being and Event

Author: Christopher Norris
Publisher: Bloomsbury Publishing
ISBN: 9781441130020
Release Date: 2009-05-24
Genre: Philosophy

Alain Badiou's Being and Event is the most original and significant work of French philosophy to have appeared in recent decades. It is the magnum opus of a thinker who is widely considered to have re-shaped the character and set new terms for the future development of philosophy in France and elsewhere. This book has been written very much with a view to clarifying Badiou's complex and demanding work for non-specialist readers. It offers guidance on philosophical and intellectual context, key themes, reading the text, reception and influence; and further reading.

Derrida Badiou and the Formal Imperative

Author: Christopher Norris
Publisher: A&C Black
ISBN: 9781441193971
Release Date: 2012-08-02
Genre: Philosophy

In this path-breaking study Christopher Norris proposes a transformed understanding of the much-exaggerated differences between analytic and continental philosophy. While keeping the analytic tradition squarely in view his book focuses on the work of Jacques Derrida and Alain Badiou, two of the most original and significant figures in the recent history of ideas. Norris argues that these thinkers have decisively reconfigured the terrain of contemporary philosophy and, between them, pointed a way beyond some of those seemingly intractable issues that have polarised debate on both sides of the notional rift between the analytic and continental traditions. In particular his book sets out to show - against the received analytic wisdom - that continental philosophy has its own analytic resources and is capable of bringing some much-needed fresh insight to bear on problems in philosophy of language, logic and mathematics. Norris provides not only a unique comparative account of Derrida's and Badiou's work but also a remarkably wide-ranging assessment of their joint contribution to philosophy's current - if widely resisted - potential for self-transformation.

Great Events from History

Author: Robert F. Gorman
Publisher: Salem PressInc
ISBN: PSU:000066904717
Release Date: 2007
Genre: History

Presents essays arranged in chronological order on key world events that occurred in such areas as politics, science, medicine, communications, literature, music, philosophy, and international affairs during the first forty years of the twentieth century.

Alain Badiou

Author: Jason Barker
Publisher: Pluto Press
ISBN: 0745318002
Release Date: 2002
Genre: Philosophy

Alain Badiou is rapidly emerging as one of the most radical and influential philosophers of our time. Badiou opposes the contemporary reduction of philosophy to nothing but a matter of language and premature announcements of the end of philosophy and thus sets himself against both analytic and continental modes of philosophy.Setting the traditional platonic concerns of philosophy, truth and being, against the modern sophists of postmodernism, Badiou has articulated a powerful systematic philosophy with profound ethical and political consequences.