Brouwer meets Husserl: On the Phenomenology of Choice Sequences (Synthese Library Book 335)

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. Content: Cover -- Contents -- Preface -- Acknowledgements -- CH 1 An Informal Introduction -- CH 2 Introduction -- 2.1 The Aim -- 2.2 The Thesis -- 2.3 Motivation -- 2.4 Method, and an Assumption -- 2.5 The Literature -- CH 3 The Argument -- 3.1 Presentation -- 3.2 Comments -- CH 4 The Original Positions -- 4.1 The Incompatibility of Husserl's and Brouwer's Positions -- 4.2 Two Sources of Mutual Pressure -- 4.2.1 Similarity of Methods -- 4.2.2 Initial Plausibility of Both Positions -- 4.3 Resolving the Conflict: The Options, and a Proposal -- 4.3.1 Deny That Some Mathematical Objects are Intratemporal, Dynamic and Unbounded -- 4.3.2 Deny That Mathematical Objects are Omnitemporal -- 4.3.3 Deny That Mathematical Objects are Within the Temporal Realm -- 4.3.4 Deny That Mathematics is About Objects -- 4.3.5 A Proposal: The Heterogeneous Universe -- CH 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 -- 5.3 Husserl's Implied Strong Revisionism -- 5.4 The Incompleteness of Husserl's Argument -- 5.4.1 From Atemporality to Omnitemporality -- 5.4.2 Possible Influence of Husserl's Informants -- 5.5 The Irreflexivity of Brouwer's Philosophy -- CH 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 -- 6.3.1 The Temporality of Choice Sequences -- 6.3.2 The Formal Character of Choice Sequences -- 6.3.3 The Subject-dependency of Choice Sequences -- CH 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 -- CH 8 Concluding Remarks -- Appendix: Intuitionistic Remarks on Husserl's Analysis of Finite Number in the Philosophy of Arithmetic -- Notes -- References -- Name and Citation Index -- Subject Index -- Last Page. 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.--book Jacket. Preface -- Acknowledgments -- An Informal Introduction -- 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. By Mark Van Atten. Includes Bibliographical References (p. 169-180) And Indexes.