Synthese Library

On the Phenomenology of Choice Sequences

By: Mark van Atten

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Hardcover | 9 November 2006

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Hardcover
224 Pages

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24.13 x 16.51 x 1.27

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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?

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.

Industry Reviews

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"It is almost as if one could hear the two rebels arguing their case in a European cafe 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, USA

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Preface	p. ix
Acknowledgements	p. xi
An Informal Introduction	p. 1
Introduction	p. 5
The Aim	p. 5
The Thesis	p. 5
Motivation	p. 5
Method, and an Assumption	p. 7
The Literature	p. 7
The Argument	p. 9
Presentation	p. 9
Comments	p. 9
The Original Positions	p. 11
The Incompatibility of Husserl's and Brouwer's Positions	p. 11
Two Sources of Mutual Pressure	p. 17
Similarity of Methods	p. 18
Initial Plausibility of Both Positions	p. 27
Resolving the Conflict: The Options, and a Proposal	p. 37
Deny That Some Mathematical Objects are Intratemporal, Dynamic and Unbounded	p. 37
Deny That Mathematical Objects are Omnitemporal	p. 39
Deny That Mathematical Objects are Within the Temporal Realm	p. 40
Deny That Mathematics is About Objects	p. 40
A Proposal: The Heterogeneous Universe	p. 51
The Phenomenological Incorrectness of the Original Arguments	p. 53
The Phenomenological Standard for a Correct Argument in Ontology	p. 53
Husserl's Weak Revisionism	p. 55
Husserl's Implied Strong Revisionism	p. 59
The Incompleteness of Husserl's Argument	p. 67
From Atemporality to Omnitemporality	p. 67
Possible Influence of Husserl's Informants	p. 72
The Irreflexivity of Brouwer's Philosophy	p. 74
The Constitution of Choice Sequences	p. 85
A Motivation for Choice Sequences	p. 85
Choice Sequences as Objects	p. 89
Choice Sequences as Mathematical Objects	p. 95
The Temporality of Choice Sequences	p. 96
The Formal Character of Choice Sequences	p. 97
The Subject-dependency of Choice Sequences	p. 98
Application: An Argument for Weak Continuity	p. 103
The Weak Continuity Principle	p. 103
An Argument That Does Not Work	p. 105
A Phenomenological Argument	p. 106
Concluding Remarks	p. 111
Intuitionistic Remarks on Husserl's Analysis of Finite Number in the Philosophy of Arithmetic	p. 113
Notes	p. 127
References	p. 169
Name and Citation Index	p. 181
Subject Index	p. 187
Table of Contents provided by Ingram. All Rights Reserved.

Synthese Library

On the Phenomenology of Choice Sequences

At a Glance

Hardcover

Industry Reviews

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Defective items

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