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Phenomenology and Mathematics

:	Mirja Hartimo
:	Mirja Hartimo
:	Phenomenology and Mathematics
:	Springer-Verlag
:	9789048137299
:	1
:	CHF 139.30
:

:	20. und 21. Jahrhundert
:	English

:	216
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

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^th century figures (Boole, Schröder, Weierstrass) as well as the 20^th 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?'

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 asSynthese, Journal of History and Philosophy of Logic,andSouthern 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