Kurt Gödel and the foundations of mathematics: horizons of truth
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2011
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke "This volume commemorates the life, work, and foundational views of Kurt Gödel (1906-1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers"-- Provided by publisher. |
| Beschreibung: | XXIII, 515 S. Ill., graph. Darst. |
| ISBN: | 9780521761444 9781107677999 |
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Datensatz im Suchindex
| _version_ | 1804147963515109376 |
|---|---|
| adam_text | Contents
Contributors page
xi
Foreword
-
Gaisi Takeuti
xiii
Preface
xv
Acknowledgments
xvii
Short Biography of Kurt
Godei
xix
I Historical Context:
Gödel s
Contributions and Accomplishments
GodeVs Historical, Philosophical, and Scientific Work
1
The Impact of
Gödel s
Incompleteness Theorems on Mathematics
3
Angus Macintyre
2
Logical Hygiene, Foundations, and Abstractions: Diversity among
Aspects and Options
27
Georg Kreisel
Godeľs
Legacy: A Historical Perspective
3
The Reception of
Gödel s 1931
Incompletability Theorems by
Mathematicians, and Some Logicians, to the Early
1960s 57
Ivor Grattan-Guinness
4 Dozent
Godei
Will Not Lecture
75
Karl Sigmund
5 Gödel s
Thesis: An Appreciation
95
Juliette Kennedy
6 Lieber Herr
Bernaysl
Lieber Herr
Gò dell Godei
on Finitism,
Constructivity, and Hubert s Program 111
Solomon Feferman
The Past and Future of Computation
1
Computation and Intractability: Echoes of Kurt
Godei
137
Christos
H. Papadimitriou
8
From the
Entscheidungsproblem
to the Personal Computer
-
and Beyond
151
B. Jack Copeland
Go delian Cosmology
9
Godei,
Einstein,
Mach,
Gamow, and Lanczos:
Gödel s
Remarkable
Excursion into Cosmology
185
Wolfgang Rindler
10
Physical Unknowables
213
Karl
Svozil
II A Wider Vision: The Interdisciplinary, Philosophical,
and Theological Implications of
Gödel s
Work
On the Unknowables
11
Godei
and Physics
255
John D. Barrow
12
Godei,
Thomas Aquinas, and the Unknowability of God
277
Deny
s
Α..
Turner
Godei
and the Mathematics of Philosophy
13 Gödel s
Mathematics of Philosophy
299
Piergiorgio
О
difreddi
Godei
and Philosophical Theology
14 Gödel s Ontological
Proof and Its Variants
307
Petr Hájek
Godei
and the Human Mind
15
The
Godei
Theorem and Human Nature
325
Hilary W. Putnam
16
Godei,
the Mind, and the Laws of Physics
339
Roger Penrose
III New Frontiers: Beyond
Gödel s
Work in Mathematics
and Symbolic Logic
Extending
Gödel s
Work
17 Gödel s
Functional Interpretation and Its Use in
Current Mathematics
361
Ulrich Kohlenbach
18
My Forty Years on ffis Shoulders
399
Harvey M. Friedman
The Realm of Set Theory
19
My Interaction with Kurt
Godei:
The Man and His Work
435
Pauli
Cohen
Godei
and the Higher Infinite
20
The
Transfinite
Universe
449
W. Hugh Woodin
Godei
and Computer Science
21
The
Godei
Phenomenon in Mathematics: A Modern View
475
Avi
Wigderson
Index
509
This volume commemorates the life, work, and foundational views of Kurt
Godei
(1906-1978),
most famous for his hallmark works on the completeness of first-order
logic, the incompleteness of number theory, and the consistency
-
with the other widely
accepted axioms of set theory
-
of the axiom of choice and of the generalized continuum
hypothesis. It explores current research, advances, and ideas for future directions not only
in the foundations of mathematics and logic but also in the fields of computer science,
artificial intelligence, physics, cosmology, philosophy, theology, and the history of science.
The discussion is supplemented by personal reflections
írom
several scholars who knew
Godei
personally, providing some interesting insights into his life. By putting his ideas
and life s work into the context of current thinking and perceptions, this book will extend
the impact of
Gödel s
fundamental work in mathematics, logic, philosophy, and other
disciplines for future generations of researchers.
|
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| callnumber-subject | QA - Mathematics |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik Philosophie |
| edition | 1. publ. |
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| spelling | Kurt Gödel and the foundations of mathematics horizons of truth ed. by Matthias Baaz ... 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2011 XXIII, 515 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke "This volume commemorates the life, work, and foundational views of Kurt Gödel (1906-1978), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances, and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology, and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy, and other disciplines for future generations of researchers"-- Provided by publisher. Gödel, Kurt Gödel, Kurt 1906-1978 (DE-588)11869569X gnd rswk-swf Mathematik Philosophie Gödel's theorem Mathematics Philosophy MATHEMATICS / Logic bisacsh Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf (DE-588)4143413-4 Aufsatzsammlung gnd-content Gödel, Kurt 1906-1978 (DE-588)11869569X p Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 Baaz, Matthias 1960- Sonstige (DE-588)135812003 oth Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024147538&sequence=000005&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024147538&sequence=000006&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Kurt Gödel and the foundations of mathematics horizons of truth Gödel, Kurt Gödel, Kurt 1906-1978 (DE-588)11869569X gnd Mathematik Philosophie Gödel's theorem Mathematics Philosophy MATHEMATICS / Logic bisacsh Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)11869569X (DE-588)4045791-6 (DE-588)4037944-9 (DE-588)4143413-4 |
| title | Kurt Gödel and the foundations of mathematics horizons of truth |
| title_auth | Kurt Gödel and the foundations of mathematics horizons of truth |
| title_exact_search | Kurt Gödel and the foundations of mathematics horizons of truth |
| title_full | Kurt Gödel and the foundations of mathematics horizons of truth ed. by Matthias Baaz ... |
| title_fullStr | Kurt Gödel and the foundations of mathematics horizons of truth ed. by Matthias Baaz ... |
| title_full_unstemmed | Kurt Gödel and the foundations of mathematics horizons of truth ed. by Matthias Baaz ... |
| title_short | Kurt Gödel and the foundations of mathematics |
| title_sort | kurt godel and the foundations of mathematics horizons of truth |
| title_sub | horizons of truth |
| topic | Gödel, Kurt Gödel, Kurt 1906-1978 (DE-588)11869569X gnd Mathematik Philosophie Gödel's theorem Mathematics Philosophy MATHEMATICS / Logic bisacsh Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
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