Logos and alogon: thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns
This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earl...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham, Switzerland
Springer
[2022]
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035249203&sequence=000001&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=035249203&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Zusammenfassung: | This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the books title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields |
| Umfang: | xvi, 294 Seiten 25 cm |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV049910429 | ||
| 003 | DE-604 | ||
| 005 | 20241127 | ||
| 007 | t| | ||
| 008 | 241016s2022 xx |||| 00||| eng d | ||
| 015 | |a GBC2F5284 |2 dnb | ||
| 020 | |z 3031136772 |9 3-031-13677-2 | ||
| 020 | |z 9783031136771 |9 978-3-031-13677-1 | ||
| 035 | |a (OCoLC)1372366184 | ||
| 035 | |a (DE-599)BVBBV049910429 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 | ||
| 084 | |a SG 700 |0 (DE-625)143071: |2 rvk | ||
| 100 | 1 | |a Plotnitsky, Arkady |d 1949- |e Verfasser |0 (DE-588)113760426 |4 aut | |
| 245 | 1 | 0 | |a Logos and alogon |b thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns |c Arkady Plotnitsky |
| 264 | 1 | |a Cham, Switzerland |b Springer |c [2022] | |
| 300 | |a xvi, 294 Seiten |c 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 520 | |a This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the books title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields | ||
| 650 | 4 | |a Mathematics / Philosophy | |
| 650 | 4 | |a Mathematics, Ancient | |
| 650 | 4 | |a Thought and thinking / Mathematics | |
| 650 | 4 | |a Mathématiques / Philosophie | |
| 650 | 4 | |a Mathématiques anciennes | |
| 650 | 4 | |a Pensée / Mathématiques | |
| 650 | 7 | |a Mathematics, Ancient |2 fast | |
| 650 | 7 | |a Mathematics / Philosophy |2 fast | |
| 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 |
| 650 | 0 | 7 | |a Geschichte |0 (DE-588)4020517-4 |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 | 2 | |a Geschichte |0 (DE-588)4020517-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035249203&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035249203&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035249203 | |
Datensatz im Suchindex
| _version_ | 1822520866769993728 |
|---|---|
| adam_text |
Contents 1 Introduction. 1.1 Prologue: Logos and Alogon in the Tragic Age of the Greeks. 1.2 Modern Mathematics and Radical Pythagorean Mathematics: Abstraction and Alogon. 13 1.3 Thinking Mathematical Thinking: From History to Philosophy. References. 26 31 2 The Spirit of Pythagoreans Against Platonism: From Logos to Alogon, and from Alogon to Logos, in Mathematical Thinking. 33 2.1 Introduction. 2.2 Radical Pythagorean Mathematics andthe Nature of Reality. 2.3 What Is a Mathematical Concept?. 2.4 Modern Mathematics Between Geometry and Algebra. . . 2.5 Radical Pythagorean Thinking. 2.6 Conclusion. References. 33 35 52 76 83 95 95 3 “Comprehending the Connection of Things”: Bernhard Riemann and Conceptual Thinking in Mathematics. 3.1 Introduction. 3.2 Philosophy of Spatiality, from Kant toRiemann and Beyond. 3.3 Manifolds, Spaces, and
Geometries. 3.4 Space-Time-Matter. 3.5 Conclusion. References. 1 1 99 99 100 108 118 132 133 4 What Is a Curve?: A Pythagorean Essay. 137 4.1 Introduction. 137 4.2 Curves as Algebra: Descartes/Fermat/Diophantus. 144 4.3 Curves as Surfaces, Surfaces as Curves: Riemann/Riemann/Riemann. 147 XV
Contents xvi 5 4.4 Curves as Discrete Manifolds: . 4.5 Conclusion. References. 150 156 157 Create More Worlds”: Mathematical Practice as Philosophy. . . Introduction. Algebra: Abel and Galois. Geometry: Lobachevsky and Riemann. Algebraic Geometry: Weiland Grothendieck. Conclusion: Technology Against Ontology in Mathematical Practice as Philosophy. 179 References. 159 159 161 166 174 “To 5.1 5.2 5.3 5.4 5.5 184 6 Who Thinks Abstractly?: From Modern Geometry to Modern Algebra with Emmy Noether. 187 6.1 Introduction. 187 6.2 Philosophy (with Mathematics): Abstract Thinking, Algebraic and Geometrical, in Mathematics. 191 6.3 Geometry (with Algebra): Noether’s Theorems and Noether’s Noether’s
Theorems. 203 6.4 Algebra (with Algebra): Abstract Algebra from Galois to Noether. . . 210 6.5 Topology (with Algebra): FromStructuresto Morphisms. 213 6.6 Conclusion. . . . 216 References. 218 7 Physics as Modern Mathematics: From Relativity to Quantum Theory, and Beyond. 221 7.1 Introduction. 221 7.2 Modern Mathematicsin Relativityand Quantum Theory. 222 7.3 “The Heisenberg Method”: Algebra and Alogon. 235 7.4 Matrices, Spinors, and Group Representations: Algebra, Geometry, and Symmetry in QuantumTheory. 253 7.5 Platonic Solids, Galois Atoms, and theCosmic Galois Group. 260 7.6 From Physics to Mathematics: The Yang-Mills Theory and Differential Topology. 274 7.7 Conclusion. 279 References. 282 Name Index. . 285 Subject
Index. 289
This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the book’s title, an alogon in the logos of mathematics'. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields. |
| any_adam_object | 1 |
| author | Plotnitsky, Arkady 1949- |
| author_GND | (DE-588)113760426 |
| author_facet | Plotnitsky, Arkady 1949- |
| author_role | aut |
| author_sort | Plotnitsky, Arkady 1949- |
| author_variant | a p ap |
| building | Verbundindex |
| bvnumber | BV049910429 |
| classification_rvk | SG 700 |
| ctrlnum | (OCoLC)1372366184 (DE-599)BVBBV049910429 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV049910429</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20241127</controlfield><controlfield tag="007">t|</controlfield><controlfield tag="008">241016s2022 xx |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">GBC2F5284</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">3031136772</subfield><subfield code="9">3-031-13677-2</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="z">9783031136771</subfield><subfield code="9">978-3-031-13677-1</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1372366184</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV049910429</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SG 700</subfield><subfield code="0">(DE-625)143071:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Plotnitsky, Arkady</subfield><subfield code="d">1949-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)113760426</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Logos and alogon</subfield><subfield code="b">thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns</subfield><subfield code="c">Arkady Plotnitsky</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cham, Switzerland</subfield><subfield code="b">Springer</subfield><subfield code="c">[2022]</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xvi, 294 Seiten</subfield><subfield code="c">25 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="520" ind1=" " ind2=" "><subfield code="a">This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the books title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics / Philosophy</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics, Ancient</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Thought and thinking / Mathematics</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathématiques / Philosophie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathématiques anciennes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Pensée / Mathématiques</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematics, Ancient</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Mathematics / Philosophy</subfield><subfield code="2">fast</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="650" ind1="0" ind2="7"><subfield code="a">Geschichte</subfield><subfield code="0">(DE-588)4020517-4</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="2"><subfield code="a">Geschichte</subfield><subfield code="0">(DE-588)4020517-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Passau - ADAM Catalogue Enrichment</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=035249203&sequence=000001&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 Passau - ADAM Catalogue Enrichment</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=035249203&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Klappentext</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-035249203</subfield></datafield></record></collection> |
| id | DE-604.BV049910429 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-28T19:09:01Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035249203 |
| oclc_num | 1372366184 |
| open_access_boolean | |
| owner | DE-739 |
| owner_facet | DE-739 |
| physical | xvi, 294 Seiten 25 cm |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer |
| record_format | marc |
| spelling | Plotnitsky, Arkady 1949- Verfasser (DE-588)113760426 aut Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns Arkady Plotnitsky Cham, Switzerland Springer [2022] xvi, 294 Seiten 25 cm txt rdacontent n rdamedia nc rdacarrier This book is a philosophical study of mathematics, pursued by considering and relating two aspects of mathematical thinking and practice, especially in modern mathematics, which, having emerged around 1800, consolidated around 1900 and extends to our own time, while also tracing both aspects to earlier periods, beginning with the ancient Greek mathematics. The first aspect is conceptual, which characterizes mathematics as the invention of and working with concepts, rather than only by its logical nature. The second, Pythagorean, aspect is grounded, first, in the interplay of geometry and algebra in modern mathematics, and secondly, in the epistemologically most radical form of modern mathematics, designated in this study as radical Pythagorean mathematics. This form of mathematics is defined by the role of that which beyond the limits of thought in mathematical thinking, or in ancient Greek terms, used in the books title, an alogon in the logos of mathematics. The outcome of this investigation is a new philosophical and historical understanding of the nature of modern mathematics and mathematics in general. The book is addressed to mathematicians, mathematical physicists, and philosophers and historians of mathematics, and graduate students in these fields Mathematics / Philosophy Mathematics, Ancient Thought and thinking / Mathematics Mathématiques / Philosophie Mathématiques anciennes Pensée / Mathématiques Mathematics, Ancient fast Mathematics / Philosophy fast Philosophie (DE-588)4045791-6 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Geschichte (DE-588)4020517-4 gnd rswk-swf Mathematik (DE-588)4037944-9 s Philosophie (DE-588)4045791-6 s Geschichte (DE-588)4020517-4 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035249203&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035249203&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Plotnitsky, Arkady 1949- Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns Mathematics / Philosophy Mathematics, Ancient Thought and thinking / Mathematics Mathématiques / Philosophie Mathématiques anciennes Pensée / Mathématiques Mathematics, Ancient fast Mathematics / Philosophy fast Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd |
| subject_GND | (DE-588)4045791-6 (DE-588)4037944-9 (DE-588)4020517-4 |
| title | Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns |
| title_auth | Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns |
| title_exact_search | Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns |
| title_full | Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns Arkady Plotnitsky |
| title_fullStr | Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns Arkady Plotnitsky |
| title_full_unstemmed | Logos and alogon thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns Arkady Plotnitsky |
| title_short | Logos and alogon |
| title_sort | logos and alogon thinkable and the unthinkable in mathematics from the pythagoreans to the moderns |
| title_sub | thinkable and the unthinkable in mathematics, from the Pythagoreans to the moderns |
| topic | Mathematics / Philosophy Mathematics, Ancient Thought and thinking / Mathematics Mathématiques / Philosophie Mathématiques anciennes Pensée / Mathématiques Mathematics, Ancient fast Mathematics / Philosophy fast Philosophie (DE-588)4045791-6 gnd Mathematik (DE-588)4037944-9 gnd Geschichte (DE-588)4020517-4 gnd |
| topic_facet | Mathematics / Philosophy Mathematics, Ancient Thought and thinking / Mathematics Mathématiques / Philosophie Mathématiques anciennes Pensée / Mathématiques Philosophie Mathematik Geschichte |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035249203&sequence=000001&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=035249203&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT plotnitskyarkady logosandalogonthinkableandtheunthinkableinmathematicsfromthepythagoreanstothemoderns |