Ludwig / Thurler A New Foundation of Physical Theories

1. Auflage 2007
ISBN: 978-3-540-30833-1
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 178 Seiten

Currently not available, will follow before Dec 30.

Autoren/Hrsg.

Ludwig, Günther

Thurler, Gérald

Inhaltsverzeichnis

1;Foreword;5
2;Vorwort;6
3;Preface;7
3.1;Acknowledgments;8
4;Contents;9
5;Intention of the Book;12
5.1;Motivation and Problem Setting;12
5.2;Current State of Art;14
5.3;Main Ideas of Our Approach;14
5.4;Outline of the Book;16
6;Part I A New Form of Physical Theory;19
6.1;1 Reality;20
6.1.1;1.1 The Structure of Reality;20
6.1.2;1.2 The Physical Reality;21
6.1.3;1.3 Fairy Tales;25
6.2;2 Building of a Mathematical Theory;26
6.2.1;2.1 Formal Language;26
6.2.2;2.2 Axioms and Proofs;28
6.2.3;2.3 Logics;30
6.2.4;2.4 Set Theory;36
6.3;3 From Reality to Mathematics;41
6.3.1;3.1 Recording Process;42
6.3.2;3.2 Mathematization Process;54
6.3.3;3.3 Idealization Process;61
6.4;4 Species of Structures and Axiomatic Basis of a PT;70
6.4.1;4.1 Mathematical Structures;71
6.4.2;4.2 Deduction of Structures;74
6.4.3;4.3 Axiomatic Basis and Fairy Tales;80
6.4.4;4.4 Pure Laws of Nature;83
6.4.5;4.5 Change of the Mathematical Form of an Axiomatic Basis;85
6.4.6;4.6 Inaccuracy Sets and Uniform Structures;92
6.4.7;4.7 Do the Laws of Nature” Describe Realities?;99
6.4.8;4.8 Classi.cation of Laws of Nature;103
6.4.9;4.9 Skeleton and Uninterpreted Theories;108
6.5;5 Relations Between Various PTs;112
6.5.1;5.1 Relations Between Two PTs with the Same Application Domain;113
6.5.2;5.2 Relations Between Two PTs with a Common Part of an Application Domain;118
6.5.3;5.3 Pre-theories;119
6.5.4;5.4 Relations Between PTs with Di.erent Application Domains;123
6.5.5;5.5 Approximation Theories;124
6.5.6;5.6 The Network of PTs;125
6.6;6 Real and Possible as Physical Concepts;128
6.6.1;6.1 Closed Theories;131
6.6.2;6.2 Physical Systems;135
6.6.3;6.3 New Concepts in a PT;138
6.6.4;6.4 Indirect Measurements;140
6.6.5;6.5 Classi.cations and Interpretations;145
6.6.6;6.6 The Reality Domain of a PT;150
7;Part II Examples of Simple Theories;152
7.1;A A Description of the Surface of the Earth, or of a Round Table;153
7.1.1;The Physical Reality;153
7.1.2;The Basic Language Bl;153
7.1.3;The Application Domain Ap;153
7.1.4;The Text A;154
7.1.5;The Basic Mathematical Theory MT;154
7.1.6;The Standard Mathematical Theory MTT;154
7.1.7;The Enrichment of MTT by A;155
7.1.8;The Idealized Mathematical Theory MT.;155
7.1.9;The Enrichment of MT. by A;156
7.1.10;The Fundamental Domain G;157
7.1.11;The Axiomatic Basis MT;158
7.1.12;The Inaccuracy Sets and Uniform Structures;159
7.1.13;The Description of the Reality;160
7.1.14;A Closed Theory;161
7.1.15;New Concepts;162
7.1.16;Classifications and Interpretations of the New Concepts;162
7.2;B A Simpli.ed Example of Newton’s Mechanics;164
7.2.1;The Physical Reality;164
7.2.2;The Basic Language Bl;164
7.2.3;The Basic Mathematical Theory MT;166
7.2.4;The Standard Mathematical Theory MTT;166
7.2.5;The Idealized Mathematical Theory MT.;166
7.3;C The Structure of the Human Species;171
7.3.1;The Standard Mathematical Theory MTT;172
7.3.2;The Idealized Mathematical Theory MT.;173
8;References;176
9;List of Symbols;177
10;Index;179