Hartimo Phenomenology and Mathematics

1. Auflage 2010
ISBN: 978-90-481-3729-9
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 216 Seiten

Reihe: Humanities, Social Sciences and Law

During Edmund Husserl’s lifetime, modern logic and mathematics rapidly developed toward their current outlook and Husserl’s writings can be fruitfully compared and contrasted with both 19 century figures (Boole, Schröder, Weierstrass) as well as the 20 century characters (Heyting, Zermelo, Gödel). Besides the more historical studies, the internal ones on Husserl alone and the external ones attempting to clarify his role in the more general context of the developing mathematics and logic, Husserl’s phenomenology offers also a systematically rich but little researched area of investigation. This volume aims to establish the starting point for the development, evaluation and appraisal of the phenomenology of mathematics. It gathers the contributions of the main scholars of this emerging field into one publication for the first time. Combining both historical and systematic studies from various angles, the volume charts answers to the question "What kind of philosophy of mathematics is phenomenology?"

Autoren/Hrsg.

Hartimo, Mirja

Inhaltsverzeichnis

1;Contents;6
2;Acknowledgements;10
3;Contributors;12
4;List of Abbreviations;16
5;Introduction;20
6;I Mathematical Realism and Transcendental Phenomenological Idealism;29
6.1;I. Standard Simple Formulations of Realism and Idealism (Anti-Realism) About Mathematics;31
6.2;II. Mathematical Realism;32
6.3;III. Transcendental Phenomenological Idealism;36
6.4;IV. Mind-Independence and Mind-Dependence in Formulations of Mathematical Realism;42
6.5;V. Compatibility or Incompatibility?;45
6.6;VI. Brief Interlude: Where to Place Gdel, Brouwer, and Other Mathematical Realists and Idealists in our Schematization?;48
6.7;VII. A Conclusion and an Introduction;48
6.8;References;50
7;II Platonism, Phenomenology, and Interderivability;51
7.1;I. Introduction;51
7.2;II. Phenomenology, Constructivism and Platonism;54
7.3;III. Interderivability;58
7.4;IV. Situations of Affairs: Historical Preliminaries;61
7.5;V. Situations of Affairs: Systematic Treatment;66
7.6;VI. Conclusion;69
7.7;VII. Appendix;69
7.8;References;72
8;III husserl on axiomatization andarithmetic;75
8.1;I. Introduction;75
8.2;II. Husserls Initial Opposition to the Axiomatization of Arithmetic;77
8.3;III. Husserls VOLTE-FACE Volte-Face ;78
8.4;IV. Analysis of the Concept of Number;80
8.5;V. Calculating with Concepts and Propositions;84
8.6;VI. Three Levels of Logic;85
8.7;VII. Manifolds and Imaginary Numbers;87
8.8;VIII. Mathematics and Phenomenology;89
8.9;IX. What Numbers Could Not Be For Husserl;91
8.10;X. Conclusion;94
8.11;References;97
9;IV Intuition in Mathematics: on the Function of Eidetic Variation in Mathematical Proofs;100
9.1;I. Some Basic Features of Husserls Theory of Knowledge;102
9.2;II. The Method of Seeing Essences in Mathematical Proofs;105
9.2.1;1. The Eidetic Method (Wesensschau) Used for Real Objects;105
9.2.2;2. Eidetics in Material Mathematical Disciplines;109
9.2.3;3. Eidetics in Formal-Axiomatic Contexts;114
9.3;References;117
10;V How Can a Phenomenologist Have a Philosophy of Mathematics?;118
10.1;References;131
11;VI The Development of Mathematics and the Birth of Phenomenology;133
11.1;I. Weierstrass and Mathematics as Rigorous Science;135
11.2;II. Husserl in Weierstrasss Footsteps;136
11.3;III. Philosophy of Arithmetic as an Analysis of the Concept of Number;138
11.4;IV. Logical Investigations and the Axiomatic Approach;140
11.5;V. Categorial Intuition;45
11.6;VI. Aristotle or Plato (and Which Plato)?;143
11.7;VII. Platonism of the Eternal, Self-Identical, Unchanging Objectivities;144
11.8;VIII. Platonism as an Aspiration for Reflected Foundations;145
11.9;IX. Conclusion;146
11.10;References;146
12;VII Beyond Leibniz: Husserl's Vindication of Symbolic Knowledge;148
12.1;I. Introduction;148
12.2;II. Symbolic Knowledge;150
12.3;III. Meaningful Symbols in PA ;152
12.4;IV. Meaningless Symbols in PA ;42
12.5;V. Logical Systems;45
12.6;VI. Imaginary Elements: Earlier Treatment;48
12.7;VII. Imaginary Elements: Later Treatment;48
12.8;VIII. Formal Ontology;89
12.9;IX. Critical Considerations;91
12.10;X. The Problem of Symbolic Knowledge in the Development of Husserls Philosophy;93
12.11;References;170
13;VIII Mathematical Truth Regained;171
13.1;I. Introduction;31
13.2;II. Benacerrafs Dilemma and Some Negative or Skeptical Solutions;32
13.2.1;1. Pre-emptive Negative or Skeptical Solutions;105
13.2.2;2. Concessive Negative or Skeptical Solutions;109
13.3;III. Benacerrafs Dilemma and Kantian Structuralism;45
13.4;IV. The HW Theory;48
13.5;V. Conclusion: Benacerrafs Dilemma Again and Recovered Paradise;48
13.6;References;204
14;IX On Referring to Gestalts;206
14.1;I. Introduction;31
14.2;II. R-Structured Wholes;32
14.2.1;1. Preliminaries;105
14.2.2;2. The Part-of Relation;109
14.2.3;3. One Sort of Structured Wholes: R-Structured Wholes;114
14.2.4;4. Questions of Identify;217
14.3;III. On Relations;220
14.4;IV. Mereological Semantics: Logig As Philosophy?;229
14.5;References;232
15;INDEX;235