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Field

Mathematik

Footnote

Erwiderung auf: Graham, L.R.: Do mathematical equations display social attributes? in: Mathematical intelligencer 22(2000) no.3, S.31-36

Source

Mathematical intelligencer. 23(2001) no.1, S.23-29

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Abstract

Ein weiterer Beitrag zur Frage, warum es keinen Nobelpreis für Mathematik gibt

Field

Mathematik

Source

Mathematical intelligencer. 23(2001) no.3, S.68-69

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Field

Mathematik

Footnote

Erwiderung auf: Graham, L.R.: Do mathematical equations display social attributes? in: Mathematical intelligencer 22(2000) no.3, S.31-36

Source

Mathematical intelligencer. 23(2001) no.1, S.18-22

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Field

Mathematik

Footnote

Erwiderung auf: Graham, L.R.: Do mathematical equations display social attributes? in: Mathematical intelligencer 22(2000) no.3, S.31-36

Source

Mathematical intelligencer. 23(2001) no.4, S.15-17

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Field

Mathematik

Footnote

Erwiderung auf: Graham, L.R.: Do mathematical equations display social attributes? in: Mathematical intelligencer 22(2000) no.3, S.31-36

Source

Mathematical intelligencer. 23(2001) no.4, S.15-17

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Content

Vgl.: https://www.semanticscholar.org/paper/Piaget-%E2%80%99-s-Constructivism-%2C-Papert-%E2%80%99-s-%3A-What-%E2%80%99-s-Ackermann/89cbcc1e740a4591443ff4765a6ae8df0fdf5554. Darunter weitere Hinweise auf verwandte Beiträge. Auch unter: Learning Group Publication 5(2001) no.3, S.438.

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BK

31.10 / Mathematische Logik / Mengenlehre
31.01 / Geschichte der Mathematik

Classification

SG 174 Mathematik / Biographien, Geschichte und Philosophie der Mathematik / Biographien / Einzelbiographien / gm - go
31.10 / Mathematische Logik / Mengenlehre
31.01 / Geschichte der Mathematik

RSWK

Gödel, Kurt / Mathematische Logik (GBV)

RVK

SG 174 Mathematik / Biographien, Geschichte und Philosophie der Mathematik / Biographien / Einzelbiographien / gm - go

Subject

Gödel, Kurt / Mathematische Logik (GBV)

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Abstract

Die Idee, die moderne Mathematik ein einem schmalen Band von 150 Seiten darzustellen, ist waghalsig und ermutigend zugleich. Wie Freeman Dyson in seinem Vorwort sagt: 'What Monastyrsky has produced is a road map to the territory of mathematics, with the Fields Medals as a convenient set of nodal points'. Das Buch wird vielen Spezialisten helfen, einen neuen Überblick über die Landschaft Mathematik zu gewinnen, in der sie täglich in der Tiefe nach neuen Schätzen graben

Date

23. 3.2002 19:48:47

Field

Mathematik

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Field

Mathematik

Footnote

Rez. in Mathematical intelligencer 23(2001) no.3, S.73-75 (J.W. Grossman)

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Date

11. 2.1997 20:11:23

Field

Mathematik

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BK

31.10 / Mathematische Logik / Mengenlehre

Classification

31.10 / Mathematische Logik / Mengenlehre

Date

27. 2.1999 16:23:24
26. 2.2008 15:58:22

RSWK

Mathematische Logik

Subject

Mathematische Logik

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Abstract

Ordnung hat in unserer Alltagssprache eine Fülle von Bedeutungen. Als mathematischer Begriff ist Ordnung mit einer begrenzten Bedeutung festgelegt, die als eine Abstraktion der Beziehungen 'ist enthalten in', 'ist ein Teil von' und 'ist kleiner als' verstanden werden kann. Der mathematische Ordnungsbegriff tritt in vielen Bereichen der Mathematik und ihrer Anwendungen auf. Seine aktuelle Verwendbarkeit, wie etwa im Bereich der theoretischen Informatik, machen die mathematische Ordnungstheorie zu einem attraktiven Teilgebiet der gegenwärtigen Mathematik

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Field

Mathematik
Mathematische Logik

Source

Mathematical intelligencer. 23(2001) no.2, S.59-64

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BK

31.10 Mathematische Logik Mengenlehre
31.11 Ordnungen allgemeine mathematische Systeme
31.02 Philosophie und Wissenschaftstheorie der Mathematik

Classification

31.10 Mathematische Logik Mengenlehre
31.11 Ordnungen allgemeine mathematische Systeme
31.02 Philosophie und Wissenschaftstheorie der Mathematik

Date

8. 9.2016 22:04:09

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Editor

Zentralblatt für Mathematik; Mathematical Reviews

Field

Mathematik

Footnote

Abgedruckt in den Sachregisterteilen des 'Zentralblatts für Mathematik' und 'Mathematical Reviews'. - Frühere Ausgaben: 1970; 1980; 1985

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Field

Mathematik

Source

Serials review. 23(1997) no.2, S.73-76

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Date

7. 2.2005 14:10:22

Field

Mathematik

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Abstract

Vortrag im Zentralblatt für Mathematik am 27.10.2011.

Field

Mathematik

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BK

31.02 / Philosophie und Wissenschaftstheorie der Mathematik
31.10 / Mathematische Logik / Mengenlehre

Classification

31.02 / Philosophie und Wissenschaftstheorie der Mathematik
31.10 / Mathematische Logik / Mengenlehre

Date

4.11.2007 12:23:27

Footnote

Die Murmel liefert das Hauptthema des Buchs. Die Seele, das Ich, ist eine Illusion. Es ist eine »seltsame Schleife« (a strange loop), die ihrerseits von einer Unzahl von Schleifen auf einem niedrigeren Niveau erzeugt wird. So kommt es, dass der Klumpen Materie innerhalb unseres Schädels nicht nur sich selbst beobachtet, sondern sich dessen auch bewusst ist. Seltsame, genauer: selbstbezügliche Schleifen faszinieren Hofstadter seit jeher. Er sieht sie überall. Sie sind das Herzstück von Gödels berühmtem Unbeweisbarkeitssatz. Sie lauern in den »Principia Mathematica« von Russell und Whitehead, stets bereit, die Fundamente der Mathematik zu untergraben. Ihre kürzeste Form sind logische Paradoxa wie »Dieser Satz ist falsch« oder die Karte, auf deren einer Seite steht »Der Satz auf der Rückseite ist wahr« und auf der anderen »Der Satz auf der Rückseite ist falsch«. In Kapitel 21 führt er ein verstörendes Gedankenexperiment ein, das auch Thema zahlreicher Sciencefiction-Geschichten ist: Ein Mann wird, wie in »Raumschiff Enterprise«, auf einen fremden Planeten und zurück gebeamt, indem eine Maschine ihn Molekül für Molekül abscannt und die Information an den Zielort übermittelt, wo sie zur Herstellung einer exakten Kopie dieses Menschen dient. Wenn dabei das Original zerstört wird, entsteht kein philosophisches Problem. Wenn es aber erhalten bleibt - oder mit derselben Information zwei Kopien hergestellt werden -, entsteht ein Paar identischer Zwillinge mit identischen Erinnerungen. Ist der so gebeamte Mensch derselbe wie das Original oder ein anderer?
Gewisse Themen können Hofstadters Zorn erregen, zum Beispiel die Diskussion über das so genannte inverted spectrum paradox. Wie kann ich sicher sein, dass ein anderer Mensch das, was ich als Rot erlebe, genauso erlebt wie ich und nicht etwa eine Empfindung hat, die ich als Blau bezeichnen würde? Oder das Konzept vom Zombie, einem Wesen, das sich in jeder Hinsicht so verhält wie ein gewöhnlicher Mensch, dem aber alle menschlichen Gefühle fehlen. Oder Bewusstsein und freier Wille. Hofstadter hält beides für Illusionen, für Trugbilder gleich der Murmel im Briefumschlagstapel, allerdings für unvermeidbare, machtvolle Trugbilder. Wir erleben, dass ein Ich in unserem Schädel steckt, aber das ist nur eine Illusion, die von Millionen kleiner Schleifen erzeugt wird, »einem Schwarm bunter Schmetterlinge in einem Obstgarten«. An dieser Stelle ist Hofstadter anderer Meinung als sein Freund, der Philosoph Daniel C. Dennett (mit dem zusammen er das Buch »The Mind's I«, deutsch »Einsicht ins lch«, herausgegeben hat). Aber wie Den-nett, der einem seiner Werke den dreisten Titel »Consciousness Explained« gab, glaubt er, er habe das Bewusstsein erklärt. Das stimmt leider nicht. Beide haben das Bewusstsein nur beschrieben. Einen Regenbogen zu beschreiben ist einfach, ihn zu erklären ist nicht so einfach. Bewusstsein zu beschreiben ist einfach, aber das Wunder zu erklären, durch das ein Haufen Moleküle es hervorbringt, ist nicht so einfach. Ich will meine Karten auf den Tisch legen. Ich gehöre zu der kleinen Gruppe der »Mysterianer«, zu denen auch die Philosophen John R. Searle (der Schurke in Hofstadters Buch), Thomas Nagel, Colin McGinn und Jerry Fodor sowie der Linguist Noam Chomsky, der Mathematiker Roger Penrose und einige andere zählen. Wir sind der Überzeugung, dass kein heute lebender Philosoph oder Naturwissenschaftler auch nur die nebelhafteste Ahnung davon hat, wie Bewusstsein und sein unzertrennlicher Begleiter, der freie Wille, aus einem materiellen Gehirn entstehen (was sie zweifellos tun). Wir sind überzeugt, dass kein Computer, wie wir ihn heute kennen - das heißt, der aus Schaltern und Verbindungsdrähten gebaut ist -, je ein Bewusstsein dessen erlangen wird, was er tut. Das stärkste Schachprogramm wird nicht wissen, dass es Schach spielt, ebenso wenig wie eine Waschmaschine weiß, dass sie Wäsche wäscht.
Einige wenige Mysterianer glauben, dass die Wissenschaft eines glorreichen Tages das Rätsel des Bewusstseins lüften wird. Penrose zum Beispiel ist davon überzeugt, dass das Mysterium einem tieferen Verständnis der Quantenmechanik weichen wird. Ich selbst gehöre zu einer radikaleren Fraktion. Wir halten es für den Gipfel der Selbstüberschätzung zu glauben, unser Gehirn sei der unübertreffliche Gipfel der Denkfähigkeit. Mit Sicherheit gibt es Wahrheiten, die unsere intellektuellen Fähigkeiten ebenso weit übersteigen wie unsere Weisheiten die intellektuellen Fähigkeiten einer Kuh. Warum hat das Universum eine mathematische Struktur? Warum gibt es sich, wie Stephen Hawking es ausdrückte, überhaupt die Mühe, zu existieren? Warum gibt es etwas und nicht nichts? Wie bringen die Schmetterlinge in unserem Hirn die seltsamen Schleifen des Bewusstseins zu Stande? Vielleicht kennen höherentwickelte Lebensformen in der Andromeda-Galaxie die Antworten. Ich kenne sie sicher nicht. Hofstadter und Dennett kennen sie nicht. Und Sie, verehrter Leser, auch nicht.

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Date

23. 3.2019 16:57:50

Field

Mathematik

Source

Journal of documentation. 36(1980) no.1, S.11-23