The Topos of Music: Geometric Logic of Concepts, Theory, and Performance
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2002
|
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-0348-8141-8 |
| Beschreibung: | Man kann einen jeden BegrifJ, einen jeden Titel, darunter viele Erkenntnisse gehoren, einen logischen Ort nennen. Immanuel Kant [258, p. B 324] This book's title subject, The Topos of Music, has been chosen to communicate a double message: First, the Greek word "topos" (r01rex; = location, site) alludes to the logical and transcendental location of the concept of music in the sense of Aristotle's [20, 592] and Kant's [258, p. B 324] topic. This view deals with the question of where music is situated as a concept and hence with the underlying ontological problem: What is the type of being and existence of music? The second message is a more technical understanding insofar as the system of musical signs can be associated with the mathematical theory of topoi, which realizes a powerful synthesis of geometric and logical theories. It laid the foundation of a thorough geometrization of logic and has been successful in central issues of algebraic geometry (Grothendieck, Deligne), independence proofs and intuitionistic logic (Cohen, Lawvere, Kripke). But this second message is intimately entwined with the first since the present concept framework of the musical sign system is technically based on topos theory, so the topos of music receives its top os-theoretic foundation. In this perspective, the double message of the book's title in fact condenses to a unified intention: to unite philosophical insight with mathematical explicitness |
| Umfang: | 1 Online-Ressource (XCVI, 1344 p) |
| ISBN: | 9783034881418 9783034894548 |
| DOI: | 10.1007/978-3-0348-8141-8 |
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| 500 | |a Man kann einen jeden BegrifJ, einen jeden Titel, darunter viele Erkenntnisse gehoren, einen logischen Ort nennen. Immanuel Kant [258, p. B 324] This book's title subject, The Topos of Music, has been chosen to communicate a double message: First, the Greek word "topos" (r01rex; = location, site) alludes to the logical and transcendental location of the concept of music in the sense of Aristotle's [20, 592] and Kant's [258, p. B 324] topic. This view deals with the question of where music is situated as a concept and hence with the underlying ontological problem: What is the type of being and existence of music? The second message is a more technical understanding insofar as the system of musical signs can be associated with the mathematical theory of topoi, which realizes a powerful synthesis of geometric and logical theories. It laid the foundation of a thorough geometrization of logic and has been successful in central issues of algebraic geometry (Grothendieck, Deligne), independence proofs and intuitionistic logic (Cohen, Lawvere, Kripke). But this second message is intimately entwined with the first since the present concept framework of the musical sign system is technically based on topos theory, so the topos of music receives its top os-theoretic foundation. In this perspective, the double message of the book's title in fact condenses to a unified intention: to unite philosophical insight with mathematical explicitness | ||
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Datensatz im Suchindex
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| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:10:45Z |
| institution | BVB |
| isbn | 9783034881418 9783034894548 |
| language | English |
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| spellingShingle | Mazzola, Guerino The Topos of Music Geometric Logic of Concepts, Theory, and Performance Mathematics Geometry, algebraic Visualization Geometry Topology Applications of Mathematics Algebraic Geometry Mathematics, general Mathematik Mathematische Methode (DE-588)4155620-3 gnd Musiktheorie (DE-588)4040876-0 gnd Tonalität (DE-588)4185654-5 gnd |
| subject_GND | (DE-588)4155620-3 (DE-588)4040876-0 (DE-588)4185654-5 |
| title | The Topos of Music Geometric Logic of Concepts, Theory, and Performance |
| title_alt | With contributions by numerous experts |
| title_auth | The Topos of Music Geometric Logic of Concepts, Theory, and Performance |
| title_exact_search | The Topos of Music Geometric Logic of Concepts, Theory, and Performance |
| title_full | The Topos of Music Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola |
| title_fullStr | The Topos of Music Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola |
| title_full_unstemmed | The Topos of Music Geometric Logic of Concepts, Theory, and Performance by Guerino Mazzola |
| title_short | The Topos of Music |
| title_sort | the topos of music geometric logic of concepts theory and performance |
| title_sub | Geometric Logic of Concepts, Theory, and Performance |
| topic | Mathematics Geometry, algebraic Visualization Geometry Topology Applications of Mathematics Algebraic Geometry Mathematics, general Mathematik Mathematische Methode (DE-588)4155620-3 gnd Musiktheorie (DE-588)4040876-0 gnd Tonalität (DE-588)4185654-5 gnd |
| topic_facet | Mathematics Geometry, algebraic Visualization Geometry Topology Applications of Mathematics Algebraic Geometry Mathematics, general Mathematik Mathematische Methode Musiktheorie Tonalität |
| url | https://doi.org/10.1007/978-3-0348-8141-8 |
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