Brouwer meets Husserl: On the Phenomenology of Choice Sequences

Description

Can a line be analysed mathematically such a way that it does not fall apart into a set of discrete points? Are there objects of pure mathematics that can change through time? L. E. J. Brouwer argued that the two questions are related and that the answer to both is "yes", introducing the concept of choice sequences. This book subjects Brouwer's choice sequences to a phenomenological critique in the style of Husserl. 1402050860......Page 1 Contents......Page 8 Preface......Page 10 Acknowledgements......Page 11 1. An Informal Introduction......Page 14 2.3 Motivation......Page 18 2.5 The Literature......Page 20 3.2 Comments......Page 22 4.1 The Incompatibility of Husserl's and Brouwer's Positions......Page 24 4.2 Two Sources of Mutual Pressure......Page 30 4.2.1 Similarity of Methods......Page 31 4.2.2 Initial Plausibility of Both Positions......Page 40 4.3.1 Deny That Some Mathematical Objects are Intratemporal, Dynamic and Unbounded......Page 50 4.3.2 Deny That Mathematical Objects are Omnitemporal......Page 52 4.3.4 Deny That Mathematics is About Objects......Page 53 4.3.5 A Proposal: The Heterogeneous Universe......Page 64 5.1 The Phenomenological Standard for a Correct Argument in Ontology......Page 66 5.2 Husserl's Weak Revisionism......Page 68 5.3 Husserl's Implied Strong Revisionism......Page 72 5.4.1 From Atemporality to Omnitemporality......Page 80 5.4.2 Possible Influence of Husserl's Informants......Page 85 5.5 The Irreflexivity of Brouwer's Philosophy......Page 87 6.1 A Motivation for Choice Sequences......Page 97 6.2 Choice Sequences as Objects......Page 101 6.3 Choice Sequences as Mathematical Objects......Page 107 6.3.1 The Temporality of Choice Sequences......Page 108 6.3.2 The Formal Character of Choice Sequences......Page 109 6.3.3 The Subject-dependency of Choice Sequences......Page 110 7.1 The Weak Continuity Principle......Page 114 7.2 An Argument That Does Not Work......Page 116 7.3 A Phenomenological Argument......Page 117 8. Concluding Remarks......Page 122 Appendix: Intuitionistic Remarks on Husserl's Analysis of Finite Number in the Philosophy of Arithmetic......Page 123 Notes......Page 137 References......Page 178 B......Page 190 H......Page 191 L......Page 192 S......Page 193 Y......Page 194 C......Page 195 D......Page 196 O......Page 197 T......Page 198 W......Page 199