Phenomenology and Mathematics (eBook)

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.

Contents 6
Acknowledgements 10
Contributors 12
List of Abbreviations 16
Introduction 20
I Mathematical Realism and Transcendental Phenomenological Idealism 29
I. Standard Simple Formulations of Realism and Idealism (Anti-Realism) About Mathematics 31
II. Mathematical Realism 32
III. Transcendental Phenomenological Idealism 36
IV. Mind-Independence and Mind-Dependence in Formulations of Mathematical Realism 42
V. Compatibility or Incompatibility? 45
VI. Brief Interlude: Where to Place Gdel, Brouwer, and Other Mathematical Realists and Idealists in our Schematization? 48
VII. A Conclusion and an Introduction 48
References 50
II Platonism, Phenomenology, and Interderivability 51
I. Introduction 51
II. Phenomenology, Constructivism and Platonism 54
III. Interderivability 58
IV. Situations of Affairs: Historical Preliminaries 61
V. Situations of Affairs: Systematic Treatment 66
VI. Conclusion 69
VII. Appendix 69
References 72
III husserl on axiomatization andarithmetic 75
I. Introduction 75
II. Husserls Initial Opposition to the Axiomatization of Arithmetic 77
III. Husserls VOLTE-FACE Volte-Face 78
IV. Analysis of the Concept of Number 80
V. Calculating with Concepts and Propositions 84
VI. Three Levels of Logic 85
VII. Manifolds and Imaginary Numbers 87
VIII. Mathematics and Phenomenology 89
IX. What Numbers Could Not Be For Husserl 91
X. Conclusion 94
References 97
IV Intuition in Mathematics: on the Function of Eidetic Variation in Mathematical Proofs 100
I. Some Basic Features of Husserls Theory of Knowledge 102
II. The Method of Seeing Essences in Mathematical Proofs 105
1. The Eidetic Method (Wesensschau) Used for Real Objects 105
2. Eidetics in Material Mathematical Disciplines 109
3. Eidetics in Formal-Axiomatic Contexts 114
References 117
V How Can a Phenomenologist Have a Philosophy of Mathematics? 118
References 131
VI The Development of Mathematics and the Birth of Phenomenology 133
I. Weierstrass and Mathematics as Rigorous Science 135
II. Husserl in Weierstrasss Footsteps 136
III. Philosophy of Arithmetic as an Analysis of the Concept of Number 138
IV. Logical Investigations and the Axiomatic Approach 140
V. Categorial Intuition 45
VI. Aristotle or Plato (and Which Plato)? 143
VII. Platonism of the Eternal, Self-Identical, Unchanging Objectivities 144
VIII. Platonism as an Aspiration for Reflected Foundations 145
IX. Conclusion 146
References 146
VII Beyond Leibniz: Husserl's Vindication of Symbolic Knowledge 148
I. Introduction 148
II. Symbolic Knowledge 150
III. Meaningful Symbols in PA 152
IV. Meaningless Symbols in PA 42
V. Logical Systems 45
VI. Imaginary Elements: Earlier Treatment 48
VII. Imaginary Elements: Later Treatment 48
VIII. Formal Ontology 89
IX. Critical Considerations 91
X. The Problem of Symbolic Knowledge in the Development of Husserls Philosophy 93
References 170
VIII Mathematical Truth Regained 171
I. Introduction 31
II. Benacerrafs Dilemma and Some Negative or Skeptical Solutions 32
1. Pre-emptive Negative or Skeptical Solutions 105
2. Concessive Negative or Skeptical Solutions 109
III. Benacerrafs Dilemma and Kantian Structuralism 45
IV. The HW Theory 48
V. Conclusion: Benacerrafs Dilemma Again and Recovered Paradise 48
References 204
IX On Referring to Gestalts 206
I. Introduction 31
II. R-Structured Wholes 32
1. Preliminaries 105
2. The Part-of Relation 109
3. One Sort of Structured Wholes: R-Structured Wholes 114
4. Questions of Identify 217
III. On Relations 220
IV. Mereological Semantics: Logig As Philosophy? 229
References 232
INDEX 235