From Dedekind to Gödel

Essays on the Development of the Foundations of Mathematics
1996
ISBN: 978-0-7923-3484-2
Verlag: Springer Netherlands

Buch, Englisch, Band 251, 460 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1890 g

Reihe: Synthese Library

Discussions of the foundations of mathematics and their history are frequently restricted to logical issues in a narrow sense, or else to traditional problems of analytic philosophy. From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics illustrates the much greater variety of the actual developments in the foundations during the period covered. The viewpoints that serve this purpose included the foundational ideas of working mathematicians, such as Kronecker, Dedekind, Borel and the early Hilbert, and the development of notions like model and modelling, arbitrary function, completeness, and non-Archimedean structures. The philosophers discussed include not only the household names in logic, but also Husserl, Wittgenstein and Ramsey. Needless to say, such logically-oriented thinkers as Frege, Russell and Gödel are not entirely neglected, either.

Audience: Everybody interested in the philosophy and/or history of mathematics will find this book interesting, giving frequently novel insights.

Zielgruppe

Research

Autoren/Hrsg.

Hintikka, Jaakko

Fachgebiete

• Geisteswissenschaften Philosophie Geschichte der Westlichen Philosophie Westliche Philosophie: 20./21. Jahrhundert
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie

Inhaltsverzeichnis

Tracking Contradictions in Geometry: The Idea of a Model from Kant to Hilbert.- Standard vs. Nonstandard Distinction: A Watershed in the Foundations of Mathematics.- Kronecker on the Foundations of Mathematics.- The Mysteries of Richard Dedekind.- Frege’s Letters.- Frege’s Principle.- Husserl and Hilbert on Completeness.- Hahn’s Über die nichtarchimedischen Grössensysteme and the Development of the Modern Theory of Magnitudes and Numbers to Measure Them.- The Origins of Russell’s Paradox: Russell, Couturat, and the Antinomy of Infinite Number.- The Emergence of Descriptive Set Theory.- Chance Against Constructibility.- Thoralf Skolem, Hermann Weyl and ‘Das Gefühl der Welt als begrenztes Ganzes’.- On Tarski’s Background.- Wittgenstein and Ramsey on Identity.- On Saying What You Really Want to Say: Wittgenstein, Gödel, and the Trisection of the Angle.- Gödel and Husserl.- Index of Names.- Index of Subjects and Titles.

Über Autor(innen)

Jaakko Hintikka is the author or co-author of thirty volumes and of some 300 scholarly articles in mathematical and philosophical logic, epistemology, language theory, philosophy of science, history of ideas and history of philosophy, including Aristotle, Descartes, Leibniz, Kant, Peirce, The Bloomsbury Group, Husserl and Wittgenstein. He has also been active in international scholarly organizations, most recently as the First Vice-President of FISP, Vice-President of IIP and Co-Chair of the American Organizing Committee of the Twentieth World Congress of Philosophy. He has been Editor-in-Chief of the International Journal Synthese and the Managing Editor of Synthese Library since 1965.