Phenomenology and Mathematics / Edition 1

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Overview

The present collection gathers together the contributions of the world leading scholars working in the intersection of phenomenology and mathematics. During Edmund Husserl's lifetime (1859-1938) modern logic and mathematics developed rapidly toward their current outlook and Husserl's writings can be fruitfully compared and contrasted with both 19th century figures such as Boole, Schröder and Weierstrass as well as the 20th century characters like Heyting, Zermelo, and Gödel. Besides the more historical studies, both 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. The present 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 form various angles, the volume charts answers to the question “What kind of philosophy of mathematics is phenomenology”

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Editorial Reviews

From the Publisher
From the reviews:

“The volume Phenomenology and Mathematics contains nine articles based on the presentations given at the 2007 conference of the same name in Tampere, Finland. … the quality of the individual articles is very high as they present mostly mature positions. Hence, it is certainly a good volume and an important contribution to the trend of growing interest in Husserl’s (early) work on the philosophy of logic and mathematics and their relation to phenomenology.”­­­ (Carlo Ierna, History and Philosophy of Logic, Vol. 32, November, 2011)

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Product Details

  • ISBN-13: 9789048137282
  • Publisher: Springer Netherlands
  • Publication date: 4/14/2010
  • Series: Phaenomenologica Series , #195
  • Edition description: 2010
  • Edition number: 1
  • Pages: 216
  • Product dimensions: 6.40 (w) x 9.30 (h) x 0.80 (d)

Meet the Author

Mirja Hartimo (Ph.D, Docent) graduated from Boston University in 2005 with a dissertation entitled "Edmund Husserl’s Phenomenology and the Development of Mathematics in the Late Nineteenth Century" (Boston University, 2005). Currently she works as a post doctoral researcher funded by the Academy of Finland, at the University of Helsinki, Finland. She has published articles especially on Husserl and mathematics in journals such as Synthese, Journal of History and Philosophy of Logic, and Southern Journal of Philosophy.

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Table of Contents

I Mathematical Realism and Transcendental Phenomenological Idealism Richard Tieszen 1

§I Standard Simple Formulations of Realism and Idealism (Anti-Realism) About Mathematics 3

§II Mathematical Realism 4

§III Transcendental Phenomenological Idealism 8

§IV Mind-Independence and Mind-Dependence in Formulations of Mathematical Realism 14

§V Compatibility or Incompatibility? 17

§VI Brief Interlude: Where to Place Gödel, Brouwer, and Other Mathematical Realists and Idealists in our Schematization? 20

§VII A Conclusion and an Introduction 21

§References 22

II Platonism, Phenomenology, and Interderivability Guillermo E. Rosado Haddock 23

§I Introduction 23

§II Phenomenology, Constructivism and Platonism 26

§III Interderivability 30

§IV Situations of Affairs: Historical Preliminaries 33

§V Situations of Affairs: Systematic Treatment 38

§VI Conclusion 41

§References 44

III Husserl On Axiomatization and Arithmetic Claire Ortiz Hill 47

§I Introduction 47

§II Husserl's Initial Opposition to the Axiomatization of Arithmetic 49

§III Husserl's Volte-Face 50

§IV Analysis of the Concept of Number 52

§V Calculating with Concepts and Propositions 56

§VI Three Levels of Logic 57

§VII Manifolds and Imaginary Numbers 59

§VIII Mathematics and Phenomenology 61

§IX What Numbers Could Not Be For Husserl 63

§X Conclusion 66

§References 69

IV Intuition in Mathematics: On the Function of Eidetic Variation in Mathematical Proofs Dieter Lohmar 73

§I Some Basic Features of Husserl's Theory of Knowledge 75

§II The Method of Seeing Essences in Mathematical Proofs 78

§References 90

V How Can A Phenomenologist Have A Philosophy of Mathematics? Jaakko Hinrikka 91

§References 104

VI The Development of Mathematics and the Birth of Phenomenology Mirja Hartimo 107

§I Weierstrass and Mathematics as Rigorous Science 109

§II Husserl in Weierstrass's Footsteps 110

§III Philosophy of Arithmetic as an Analysis of the Concept of Number 112

§IV Logical Investigations and the Axiomatic Approach 114

§V Categorial Intuition 116

§VI Aristotle or Plato (and Which Plato)? 117

§VII Platonism of the Eternal, Self-Identical, Unchanging Objectivities 118

§VIII Platonism as an Aspiration for Reflected Foundations 119

§IX Conclusion 120

§References 120

VII Beyond Leibniz: Husserl's Vindication of Symbolic Knowledge Jairo José da Silva 123

§I Introduction 123

§II Symbolic Knowledge 125

§III Meaningful Symbols in PA 127

§IV Meaningless Symbols in PA 129

§V Logical Systems 130

§VI Imaginary Elements: Earlier Treatment 132

§VII Imaginary Elements: Later Treatment 135

§VIII Formal Ontology 136

§IX Critical Considerations 141

§X The Problem of Symbolic Knowledge in the Development of Husserl's Philosophy 144

§References 145

VIII Mathematical Truth Regained Robert Hanna 147

§I Introduction 148

§II Benacerraf's Dilemma and Some Negative or Skeptical Solutions 151

§III Benacerrafs Dilemma and Kantian Structuralism 155

§IV he HW Theory 170

§V Conclusion: Benacerraf's Dilemma Again and “Recovered Paradise” 178

§References 180

IX On Referring to Gestalts Olav K. Wiegand 183

§I Introduction 183

§II R-Structured Wholes 185

§III On Relations 197

§IV Mereological Semantics: Logig As Philosophy? 206

§References 209

Index 213

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