ISBN:
9781402050879
Language:
English
Pages:
Online-Ressource (XIII, 206 p, online resource)
Series Statement:
Synthese Library 335
Series Statement:
SpringerLink
Series Statement:
Bücher
Parallel Title:
Druckausg. Atten, Mark van, 1973 - Brouwer meets Husserl
Keywords:
Mathematics
;
Metaphysics
;
Ontology
;
Phenomenology
;
Mathematical logic
;
Metaphysics
;
Ontology
;
Phenomenology
;
Philosophy (General)
;
Logic, Symbolic and mathematical
;
Phänomenologie
;
Wahlfolge
;
Brouwer, Luitzen E. J. 1881-1966
;
Wahlfolge
;
Phänomenologie
;
Intuitionistische Mathematik
;
Husserl, Edmund 1859-1938
;
Brouwer, Luitzen E. J. 1881-1966
;
Husserl, Edmund 1859-1938
Abstract:
An Informal Introduction -- The Argument -- The Original Positions -- The Phenomenological Incorrectness of the Original Arguments -- The Constitution of Choice Sequences -- Application: An Argument for Weak Continuity -- Concluding Remarks.
Abstract:
Can the straight line be analysed mathematically such that it does not fall apart into a set of discrete points, as is usually done but through which its fundamental continuity is lost? And are there objects of pure mathematics that can change through time? The mathematician and philosopher L.E.J. Brouwer argued that the two questions are closely related and that the answer to both is "yes''. To this end he introduced a new kind of object into mathematics, the choice sequence. But other mathematicians and philosophers have been voicing objections to choice sequences from the start. This book aims to provide a sound philosophical basis for Brouwer's choice sequences by subjecting them to a phenomenological critique in the style of the later Husserl. "It is almost as if one could hear the two rebels arguing their case in a European café or on a terrace, and coming to a common understanding, with both men taking their hat off to the other, in admiration and gratitude. Dr. van Atten has convincingly applied Husserl's method to Brouwer's program, and has equally convincingly applied Brouwer's intuition to Husserl's program. Both programs have come out the better." Piet Hut, professor of Interdisciplinary Studies, Institute for Advanced Study, Princeton, U.S.A.
Description / Table of Contents:
CONTENTS; Preface; Acknowledgements; 1 An Informal Introduction; 2 Introduction; 2.1 The Aim; 2.2 The Thesis; 2.3 Motivation; 2.4 Method, and an Assumption; 2.5 The Literature; 3 The Argument; 3.1 Presentation; 3.2 Comments; 4 The Original Positions; 4.1 The Incompatibility of Husserl's and Brouwer's Positions; 4.2 Two Sources of Mutual Pressure; 4.3 Resolving the Conflict: The Options, and a Proposal; 5 The Phenomenological Incorrectness of the Original Arguments; 5.1 The Phenomenological Standard for a Correct Argument in Ontology; 5.2 Husserl's Weak Revisionism
Description / Table of Contents:
5.3 Husserl's Implied Strong Revisionism5.4 The Incompleteness of Husserl's Argument; 5.5 The Irreflexivity of Brouwer's Philosophy; 6 The Constitution of Choice Sequences; 6.1 A Motivation for Choice Sequences; 6.2 Choice Sequences as Objects; 6.3 Choice Sequences as Mathematical Objects; 7 Application: An Argument for Weak Continuity; 7.1 The Weak Continuity Principle; 7.2 An Argument That Does Not Work; 7.3 A Phenomenological Argument; 8 Concluding Remarks; Appendix: Intuitionistic Remarks on Husserl's Analysis of Finite Number in the Philosophy of Arithmetic; Notes; References
Description / Table of Contents:
Name and Citation IndexSubject Index
Note:
Includes bibliographical references and index
DOI:
10.1007/978-1-4020-5087-9
URL:
Volltext
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