Atjaunināt sīkdatņu piekrišanu

Essays on Godels Reception of Leibniz, Husserl, and Brouwer 2015 ed. [Hardback]

4.67/5 (6 ratings by Goodreads)
  • Formāts: Hardback, 328 pages, height x width: 235x155 mm, weight: 6387 g, XIV, 328 p., 1 Hardback
  • Sērija : Logic, Epistemology, and the Unity of Science 35
  • Izdošanas datums: 05-Dec-2014
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319100300
  • ISBN-13: 9783319100302
Citas grāmatas par šo tēmu:
  • Hardback
  • Cena: 127,23 €*
  • * ši ir gala cena, t.i., netiek piemērotas nekādas papildus atlaides
  • Standarta cena: 149,69 €
  • Ietaupiet 15%
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Daudzums:
  • Ielikt grozā
  • Piegādes laiks - 4-6 nedēļas
  • Pievienot vēlmju sarakstam
Essays on Godels Reception of Leibniz, Husserl, and Brouwer 2015 ed.Palielināt
  • Formāts: Hardback, 328 pages, height x width: 235x155 mm, weight: 6387 g, XIV, 328 p., 1 Hardback
  • Sērija : Logic, Epistemology, and the Unity of Science 35
  • Izdošanas datums: 05-Dec-2014
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319100300
  • ISBN-13: 9783319100302
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783319100302.html
Keywords:
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage.

The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism.

The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe

d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not.

The remaining essays provide further context.  The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.

Recenzijas

Mark van Atten in this author-edited volume brings together eleven previously published or at time of writing about to independently appear essays in the history of the phenomenology of mathematics. Van Attens studies are extraordinarily rich in exploring the books chosen topics. reader is strongly recommended to take up this detailed examination of Gödels selective reading in logic-related branches of phenomenological philosophy, as much for the questions it provokes as its detailed authoritative analysis of historical-philosophical themes. (Dale Jacquette, Phenomenological Reviews, reviews.ophen.org, April, 2016)

If van Atten is right on this, and he sets out a strong case for it, then the combination of Gödels ideas and phenomenology was ... still born. (Prof. Dr.Manuel Bremer, Phenomenological Reviews, reviews.ophen.org, January, 2016)

The book collects together most of the essays on Kurt Gödel that Mark van Atten has either authored or co-authored. Attens work is a remarkably rich, careful and detailed scholarly masterpiece. The chapters form a unified philosophical picture in which the chapters necessitate each other, hence a collection of the articles is well justified. The book will be a classic, worth returning to time and again. (M. Hartimo, History and Philosophy of Logic, October, 2015)

This book is a beautiful example of genuine Gödel scholarship by an author who is quite rightly recognized as an authority in the field, and thus it is an important contribution that cannot be ignored. (Jean Paul Van Bendegem, Notre Dame Philosophical Reviews, ndpr.nd.edu, July, 2015)

1 Introduction
1(22)
Mark van Atten
1.1 Subject and Aim
2(3)
1.2 Godel's Commitment to Phenomenology
5(4)
1.3 The Religious Component in Phenomenology
9(5)
1.4 The Pragmatic Value of Husserl's and Godel's Historical Turn
14(1)
1.5 Overview of the Essays
15(8)
References
18(5)
Part I Godel and Leibniz
2 A Note on Leibniz's Argument Against Infinite Wholes
23(10)
Mark van Atten
2.1 Introduction
23(1)
2.2 Leibniz's Argument and Its Refutation
24(4)
2.3 The Consistency of Cantorian Set Theory
28(1)
2.4 The Part-Whole Axiom
29(1)
2.5 Concluding Remark
30(3)
References
31(2)
3 Monads and Sets: On Godel, Leibniz, and the Reflection Principle
33(32)
Mark van Atten
3.1 Introduction
33(1)
3.2 Fitting Cantor's Sets into Leibniz' Metaphysics
34(5)
3.3 The Reflection Principle
39(4)
3.4 Godel's Analogy Argument for the Reflection Principle
43(17)
3.4.1 Presentation of the Argument
43(4)
3.4.2 The Analogy Is Ineffective
47(11)
3.4.3 'Medieval Ideas'
58(2)
3.5 Concluding Remark
60(5)
References
4 Godel's Dialectica Interpretation and Leibniz
65(12)
Mark van Atten
References
73(4)
Part II Godel and Husserl
5 Phenomenology of Mathematics
77(18)
Mark van Atten
5.1 Connecting Phenomenology and Mathematics
77(3)
5.1.1 Mathematics as Part of Husserl's Motivation to Develop Phenomenology
77(2)
5.1.2 Mathematics and Phenomenology can be Described as Two (Different) Types of Science, with Correspondingly Different Types of Knowledge and of Reasoning
79(1)
5.1.3 Phenomenology of Mathematics
79(1)
5.2 Transcendental Phenomenology as a Foundation of Mathematics
80(5)
5.3 Examples
85(10)
5.3.1 Intuitionistic Logic
86(1)
5.3.2 Choice Sequences
87(1)
5.3.3 The Bar Theorem
88(1)
5.3.4 Hilbert's Program
89(1)
5.3.5 Incompleteness and Intuition
90(1)
5.3.6 The Dialectica Interpretation
90(2)
References
92(3)
6 On the Philosophical Development of Kurt Godel
95(52)
Mark van Atten
Juliette Kennedy
6.1 Introduction
95(3)
6.2 Godel's Position in the 1950s: A Stalemate
98(9)
6.2.1 Inconclusive Arguments
98(1)
6.2.2 Realism and Rationalism
99(4)
6.2.3 Epistemological Parity
103(3)
6.2.4 A Way Out?
106(1)
6.3 Godel's Turn to Husserl's Transcendental Idealism
107(17)
6.3.1 Varieties of Idealism
107(1)
6.3.2 Godel and German Idealism
108(4)
6.3.3 The Turn to Husserl's Transcendental Idealism
112(10)
6.3.4 Godel's Criticisms of Husserl's Idealism
122(2)
6.4 How Is the Turn Related to Leibniz?
124(6)
6.4.1 Phenomenology as a Methodical Monadology
124(3)
6.4.2 Searching for the Primitive Terms
127(3)
6.5 Comparison with Earlier Interpretations
130(3)
6.6 Influence from Husserl on Godel's Writings
133(5)
6.6.1 On the Schools in the Foundations of Mathematics
133(1)
6.6.2 The Given
134(2)
6.6.3 Revisions in the Main Text of the Cantor Paper
136(2)
6.7 Godel's Assessment of His Philosophical Project
138(9)
References
140(7)
7 Godel, Mathematics, and Possible Worlds
147(10)
Mark van Atten
References
154(3)
8 Two Draft Letters from Godel on Self-Knowledge of Reason
157(8)
Mark van Atten
References
162(3)
Part III Godel and Brouwer
9 Godel and Brouwer: Two Rivalling Brothers
165(8)
Mark van Atten
Reference
171(2)
10 Mysticism and Mathematics: Brouwer, Godel, and the Common Core Thesis
173(16)
Mark van Atten
Robert Tragesser
10.1 Introduction
173(3)
10.2 Brouwer's Mysticism
176(3)
10.3 Godel's Mysticism
179(2)
10.4 Comparison of Brouwer and Godel: Mathematics and the Good
181(4)
10.5 A Partial Argument Against CCT
185(1)
10.6 Closing Remarks
185(4)
References
186(3)
11 Godel and Intuitionism
189(48)
Mark van Atten
11.1 Introduction
189(1)
11.2 Personal Contacts
190(4)
11.2.1 Godel and Brouwer
190(1)
11.2.2 Godel and Heyting
191(3)
11.3 Philosophical Contacts
194(43)
11.3.1 The Incompleteness Theorem
194(1)
11.3.2 Weak Counterexamples
195(1)
11.3.3 Intuitionistic Logic as a Modal Logic
195(1)
11.3.4 Continuity Arguments in Set Theory
196(1)
11.3.5 Around the Dialectica Interpretation
196(31)
Appendix: Finitary Mathematics and Autonomous Transfinite Progressions
227(2)
References
229(8)
Part IV A Partial Assessment
12 Construction and Constitution in Mathematics
237
Mark van Atten
12.1 Introduction
237(2)
12.2 Intuitionistic Mathematics Is Part of Transcendental Phenomenology
239(29)
12.2.1 Husserl: Pure Mathematics as Formal Ontology
239(5)
12.2.2 Brouwer: Mathematics as Mental Constructions
244(2)
12.2.3 A Systematic Comparison
246(17)
12.2.4 Discussion of Some Remaining Objections
263(5)
12.3 Beyond Intuitionistic Mathematics?
268(10)
12.4 A Historical Note
278(1)
12.5 Concluding Remark
278
Appendix: Null on Choice Sequences
279(3)
References
282
Erratum 1(288)
Bibliography 289(20)
Original Publications 309(2)
Author and Citation Index 311(8)
Name and Subject Index 319
Mark van Atten is senior researcher at the Centre national de la recherche scientifique in France. His research interests are philosophy of mathematics and idealism.