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.
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Bibliographic data
Copyright year
2015
ISBN-Print
978-3-465-03906-8
ISBN-Online
978-3-465-13906-5
Publisher
Klostermann, Frankfurt am Main
Series
Studies in Theoretical Philosophy
Volume
2
Language
English
Pages
270
Product type
Book Titles
Table of contents
ChapterPages
Titelei/Inhaltsverzeichnis No access Pages I - X
Preface No access Pages XI - XII
Introduction No access Pages XIII - XVI
1.1 Logical Theories No access
1.2 Classical and Intuitionistic Logic No access
1.3 Arguing Against a Logical Theory No access
1.4 Relevance No access
1.5 Empty Singular Terms No access
2.1 Mathematical Languages No access
2.2 Logical Vocabulary No access
2.3 Mathematical Vocabulary No access
2.4 The Simplicity of Understanding No access
3.1 A Mathematical Conflict No access
3.2 Justifications of UP and CP No access
3.3 Weak Counterexamples No access
3.4 A Logical Basis of Mathematics? No access
4.1 A Sketch of the Manifestation Argument No access
4.2 Truth Conditional Semantics No access
4.3 Understanding and Knowledge No access
4.4 Understanding and Use No access
4.5 The Simplicity of Manifestability No access
5.1 Proof-Theoretic Preliminaries No access
5.2 Accounts of Meaning and Logical Frameworks No access
5.3 Tennant´s Proof-Theoretic Argument No access
5.4 Harmony No access
5.5 Dummett´s Proof-Theoretc Argument No access
5.6 Against Dummett´s Proof-Theoretic Argument No access
