Intuitionism vs. Classicism

A Mathematical Attack on Classical Logic
1., 2015
ISBN: 978-3-465-03906-8
Verlag: Klostermann Vittorio GmbH

Buch, Englisch, Band 2, 270 Seiten, KART, Format (B × H): 157 mm x 238 mm, Gewicht: 436 g

Reihe: Studies in Theoretical Philosophy

In the early twentieth century, the Dutch mathematician L.E.J. Brouwer launched a powerful attack on the prevailing mathematical methods and theories. He developed a new kind of constructive mathematics, called intuitionism, which seems to allow for a rigorous refutation of widely accepted mathematical assumptions including fundamental principles of classical logic. Following an intense mathematical debate esp. in the 1920s, Brouwer's revolutionary criticism became a central philosophical concern in the 1970s, when Michael Dummett tried to substantiate it with meaning-theoretic considerations. Since that time, the debate between intuitionists and classicists has remained a central philosophical dispute with far-reaching implications for mathematics, logic, epistemology, and semantics.

In this book, Nick Haverkamp presents a detailed analysis of the intuitionistic criticism of classical logic and mathematics. The common assumption that intuitionism and classicism are equally legitimate enterprises corresponding to different understandings of logical or mathematical expressions is investigated and rejected, and the major intuitionistic arguments against classical logic are scrutinised and repudiated. Haverkamp argues that the disagreement between intuitionism and classicism is a fundamental logical and mathematical dispute which cannot be resolved by means of meta-mathematical, epistemological, or semantic considerations.

Zielgruppe

Philosophen, Mathematiker

Autoren/Hrsg.

Haverkamp, Nick

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie

Über Autor(innen)

Haverkamp, Nick
Nick Haverkamp ist wissenschaftlicher Mitarbeiter am Philosophischen Seminar der Universität Mainz.