Mathematics, ideas and the physical real:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
London [u.a.]
Continuum
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XLII, 310 S. Ill. 20 cm |
| ISBN: | 9781441146564 1441146563 9781441123442 144112344X |
Staff View
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV037486418 | ||
| 003 | DE-604 | ||
| 005 | 20150609 | ||
| 007 | t | ||
| 008 | 110621s2011 a||| |||| 00||| eng d | ||
| 020 | |a 9781441146564 |c (hbk.) £60.00 |9 978-1-4411-4656-4 | ||
| 020 | |a 1441146563 |c (hbk.) £60.00 |9 1-4411-4656-3 | ||
| 020 | |a 9781441123442 |c (pbk.) £18.99 |9 978-1-4411-2344-2 | ||
| 020 | |a 144112344X |c (pbk.) £18.99 |9 1-4411-2344-X | ||
| 035 | |a (OCoLC)734086969 | ||
| 035 | |a (DE-599)OBVAC08501903 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 1 | |a eng |h fre | |
| 049 | |a DE-12 |a DE-384 |a DE-11 |a DE-355 | ||
| 084 | |a CC 2600 |0 (DE-625)17610: |2 rvk | ||
| 084 | |a CI 5400 |0 (DE-625)18471: |2 rvk | ||
| 100 | 1 | |a Lautman, Albert |d 1908-1944 |e Verfasser |0 (DE-588)13864179X |4 aut | |
| 240 | 1 | 0 | |a Les mathématiques, les idées et le réel physique |
| 245 | 1 | 0 | |a Mathematics, ideas and the physical real |c Albert Lautman. Transl. by Simon B. Duffy |
| 264 | 1 | |a London [u.a.] |b Continuum |c 2011 | |
| 300 | |a XLII, 310 S. |b Ill. |c 20 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 546 | |a Translated from the French | ||
| 650 | 0 | 7 | |a Mathematische Logik |0 (DE-588)4037951-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Philosophie |0 (DE-588)4045791-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 1 | |a Philosophie |0 (DE-588)4045791-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Mathematische Logik |0 (DE-588)4037951-6 |D s |
| 689 | 1 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Augsburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
Record in the Search Index
| _version_ | 1805079041953234944 |
|---|---|
| adam_text |
Contents
Translator's Note
ix
Acknowledgements
xi
Introduction, by Jacques Lautman
xiii
Secondary Bibliography on the Work of Albert Lautman
xx
Albert Lautman and the Creative Dialectic of
Modern Mathematics, by Fernando
Zalamea
xxiii
1.
Effective Mathematics
xxiv
2.
Structure and Unity
xxvi
3.
Mixes
xxviii
4.
Notions and Ideas
xxx
5.
Platonism
xxxii
6.
Category Theory
xxxiv
Preface to the
1977
Edition, by
Jean Dieudonné
xxxix
Considerations on Mathematical Logic
1
Mathematics and Reality
9
International Congress of the Philosophy of Science
13
On the Reality Inherent to Mathematical Theories
27
The Axiomatic and the Method of Division
31
1.
Equality
34
2.
Multiplication
35
3.
Unity
37
4.
Measure and the Integral
37
5.
The Absolute Value
39
Book I: Essay on the Unity of the Mathematical Sciences
in their Current Development
Introduction: Two Kinds of Mathematics
45
Chapter
1
The Structure of a Domain of Magnitudes and
the Decomposition of Its Elements: Dimensional
Considerations in Analysis
50
Chapter
2
The Domain and Numbers: Non-Euclidean Metrics
in the Theory of Analytic Functions
60
Chapter
3
The Algebra of Non-Commutative Magnitudes:
Pfaffian Forms and the Theory of Differential Equations
67
Chapter
4
The Continuous and the Discontinuous: Analysis and
the Theory of Numbers
73
Conclusion
80
Book II: Essay on the Notions of Structure and Existence
in Mathematics
Introduction: On the Nature of the Real in Mathematics
87
Section
1:
The
Schemas
of Structure
93
Chapter
1
The Local and the Global
95
1.
Differential Geometry and Topology
102
2.
The Theory of Closed Groups
105
3.
Approximate Representation of Functions
106
Chapter
2
Intrinsic Properties and Induced Properties
110
1.
Parallelism on a Riemann Manifold
113
2.
Structural Properties and Situational Properties
in Algebraic Topology
115
3.
Duality Theorems
118
4.
The Limitations of Reduction
124
Chapters The Ascent towards the Absolute
125
1.
Galois's Theory
126
2.
Class Field Theory
128
3.
The Universal Covering Surface
130
4.
The Uniformization of Algebraic Functions on
a Riemann Surface
133
Section
2:
The
Schemas
of Genesis
139
Chapter
4
Essence and Existence
141
1.
The Problems of Mathematical Logic
141
2.
Existence Theorems in the Theory of Algebraic
Functions
148
3.
Existence Theorems in Class Field Theory
151
4.
The Theory of the Representation of Groups
152
Chapter
5
'Mixes'
157
1.
Hilbert Space
160
2.
Normal Families of Analytic Functions
167
Chapter
6
On the Exceptional Character of Existence
171
1.
The Methods of
Poincaré
175
2.
The Singularities of Analytic Functions
178
Conclusion
183
Book III New Research on the Dialectical Structure of Mathematics
Foreword
197
Chapter
1
The Genesis of the Entity from the Idea
199
1.
The Genesis of Mathematics from the Dialectic
203
Chapter
2
The Analytic Theory of Numbers
207
1.
The Law of Reciprocity
208
2.
The Distribution of Primes and the Measurement
of the Increase to Infinity
213
3.
Conclusion
218
Letter to Mathematician Maurice
Fréchet
220
Book IV Symmetry and Dissymmetry in Mathematics and Physics
Chapter
1
Physical Space
229
Chapter
2 The Problem
of Time
241
1.
Sensible Time and Mathematical Physics
242
2.
The Theory of Partial Differential Equations
251
3.
The Theory of Differential Equations and Topology
258
Notes
263
Bibliography
281
Index
297
Albert Lautman
(1908-1944)
was a French philosopher
of mathematics whose work played a crucial role in the
history of contemporary French philosophy. His ideas
have had an enormous influence on key contemporary
thinkers including
Gilles Deleuze
and Alain Badiou,
for whom he is a major touchstone in the development
of their own engagements with mathematics. N
Mathematics, Ideas and the Physical Real presents
the first English translation of Lautman's published
works between
1933
and his death in
1944.
Rather than
being preoccupied with the relation of mathematics to
logic or with the problems of foundation, which have
dominated philosophical reflection on mathematics,
Lautman undertakes to develop an understanding of
thë^
broader structure of mathematics and its evolution. The two
powerful ideas that are constants throughout his work, and
which have dominated subsequent developments in mathematics,
are the concept of mathematical structure and the idea of the
essential unity underlying the apparent multiplicity of mathematical
disciplines. This collection of his major writings offers readers
a much-needed insight into his influence on the development of
mathematics and philosophy. |
| any_adam_object | 1 |
| author | Lautman, Albert 1908-1944 |
| author_GND | (DE-588)13864179X |
| author_facet | Lautman, Albert 1908-1944 |
| author_role | aut |
| author_sort | Lautman, Albert 1908-1944 |
| author_variant | a l al |
| building | Verbundindex |
| bvnumber | BV037486418 |
| classification_rvk | CC 2600 CI 5400 |
| ctrlnum | (OCoLC)734086969 (DE-599)OBVAC08501903 |
| discipline | Philosophie |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zc 4500</leader><controlfield tag="001">BV037486418</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150609</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110621s2011 a||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441146564</subfield><subfield code="c">(hbk.) £60.00</subfield><subfield code="9">978-1-4411-4656-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1441146563</subfield><subfield code="c">(hbk.) £60.00</subfield><subfield code="9">1-4411-4656-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441123442</subfield><subfield code="c">(pbk.) £18.99</subfield><subfield code="9">978-1-4411-2344-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">144112344X</subfield><subfield code="c">(pbk.) £18.99</subfield><subfield code="9">1-4411-2344-X</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)734086969</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)OBVAC08501903</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield></datafield><datafield tag="041" ind1="1" ind2=" "><subfield code="a">eng</subfield><subfield code="h">fre</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-384</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CC 2600</subfield><subfield code="0">(DE-625)17610:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CI 5400</subfield><subfield code="0">(DE-625)18471:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lautman, Albert</subfield><subfield code="d">1908-1944</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)13864179X</subfield><subfield code="4">aut</subfield></datafield><datafield tag="240" ind1="1" ind2="0"><subfield code="a">Les mathématiques, les idées et le réel physique</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematics, ideas and the physical real</subfield><subfield code="c">Albert Lautman. Transl. by Simon B. Duffy</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">London [u.a.]</subfield><subfield code="b">Continuum</subfield><subfield code="c">2011</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XLII, 310 S.</subfield><subfield code="b">Ill.</subfield><subfield code="c">20 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">Translated from the French</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Philosophie</subfield><subfield code="0">(DE-588)4045791-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Philosophie</subfield><subfield code="0">(DE-588)4045791-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Mathematische Logik</subfield><subfield code="0">(DE-588)4037951-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Augsburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Augsburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield></record></collection> |
| id | DE-604.BV037486418 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T06:38:41Z |
| institution | BVB |
| isbn | 9781441146564 1441146563 9781441123442 144112344X |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022637870 |
| oclc_num | 734086969 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-11 DE-355 DE-BY-UBR |
| owner_facet | DE-12 DE-384 DE-11 DE-355 DE-BY-UBR |
| physical | XLII, 310 S. Ill. 20 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Continuum |
| record_format | marc |
| spelling | Lautman, Albert 1908-1944 Verfasser (DE-588)13864179X aut Les mathématiques, les idées et le réel physique Mathematics, ideas and the physical real Albert Lautman. Transl. by Simon B. Duffy London [u.a.] Continuum 2011 XLII, 310 S. Ill. 20 cm txt rdacontent n rdamedia nc rdacarrier Translated from the French Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s DE-604 Mathematische Logik (DE-588)4037951-6 s Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Lautman, Albert 1908-1944 Mathematics, ideas and the physical real Mathematische Logik (DE-588)4037951-6 gnd Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4045791-6 (DE-588)4037944-9 |
| title | Mathematics, ideas and the physical real |
| title_alt | Les mathématiques, les idées et le réel physique |
| title_auth | Mathematics, ideas and the physical real |
| title_exact_search | Mathematics, ideas and the physical real |
| title_full | Mathematics, ideas and the physical real Albert Lautman. Transl. by Simon B. Duffy |
| title_fullStr | Mathematics, ideas and the physical real Albert Lautman. Transl. by Simon B. Duffy |
| title_full_unstemmed | Mathematics, ideas and the physical real Albert Lautman. Transl. by Simon B. Duffy |
| title_short | Mathematics, ideas and the physical real |
| title_sort | mathematics ideas and the physical real |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Mathematische Logik Philosophie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022637870&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lautmanalbert lesmathematiqueslesideesetlereelphysique AT lautmanalbert mathematicsideasandthephysicalreal |