IR, 45 (cor), 46 Θ, 48 MT Θ ,47 MT Θ,48 M 0,48. B l (cor)mt Θ,49 M i,49 A, 50, 134. s, 53. MT,53 Q i,53. U i,53 U s,53 φ i : M i Q i,54 P,55 s,55

Transcription

1 References 1. G. Ludwig: Die Grundstrukturen einer physikalischen Theorie, 2nd edn (Springer-Verlag, Berlin Heidelberg New York, 1990). French translation by G. Thurler: Les structures de base d une théorie physique (Springer-Verlag, Berlin Heidelberg New York, 1990) 2. G. Ludwig: Einführung in die Grundlagen der theoretischen Physik, 4 vols. (Vieweg, Braunschweig, ) 3. E. Scheibe: Die Reduktion physikalischer Theorien. Teil I: Grundlagen und elementare Theorie (Springer-Verlag, Berlin Heidelberg New York, 1997) 4. E. Scheibe: Die Reduktion physikalischer Theorien. Teil II: Inkommensurabilität und Grenzfallreduktion (Springer-Verlag, Berlin Heidelberg New York, 1999) 5. E. Scheibe: Between Rationalism and Empiricism: Selected Papers in the Philosophy of Physics, Chapter III Reconstruction, Ed. by B. Falkenburg (Springer- Verlag, Berlin Heidelberg New York, 2001) 6. N. Bourbaki: Elements of Mathematics. Theory of Set (Springer-Verlag, Berlin Heidelberg New York, 1st edition 1968/2nd printing 2004) 7. W. Weidlich, G. Haag: Concepts and models of a quantitative sociology. In: Series of Synergetics, Vol. 14 (Springer-Verlag, Berlin Heidelberg New York, 1983) 8. G. Ludwig: An Axiomatic Basis for Quantum Mechanics, 2 vols. (Springer- Verlag, Berlin Heidelberg New York, 1986, 1987) 9. N. Bourbaki: Elements of Mathematics. General Topology, Chapters 1 4 (Springer-Verlag, Berlin Heidelberg New York, 1st edition 1989/2nd printing 1998) 10. N. Bourbaki: Elements of Mathematics. General Topology. Chapters 5 10 (Springer-Verlag, Berlin Heidelberg New York, 1st edition 1989/2nd printing 1998) 11. H.-J. Schmidt: Axiomatic Characterization of Physical Geometry, Lecture Notes in Physics, Vol. 111 (Springer-Verlag, Berlin Heidelberg New York, 1979) 12. P. Janich: Protophysik. In: Handbuch wissenschaftstheoretischer Begriffe, ed.by J. Speck (Hrsg.) (Vandenhoeck & Ruprecht, Göttingen, 1980) 13. P. Janich: Die Protophysik der Zeit (Suhrkamp, Frankfurt/Main, 1980) 14. G. Ludwig: The Relations between various Spacetime Theories in Semantical Aspect of Spacetime Theories, ed. by U. Majer, H.-J. Schmidt (BI- Wissenschaftsverlag, Mannheim, 1994)

2 List of Symbols W, 11, 14, 144 PT (also written PT ν), 12 A p (also written A pν ), 12, 44 ϱ, 12 G (also written G ν), 13, 60 W ν, 14, 144 MT,17, 18, 18 τ, 18, 18 τ x(b), 19, 23 ( x)r, 24 ( x)r, 24 =, 25, 26, 27, 27 /, 27, 27 Coll xr, 28 E x(r), 28 {x R(x)}, 28 {x, y}, 29 (x, y), 29 P, 30, 30 S(E 1,...,E n), 30 f 1,...,f n S,30, 34 B l,34 B lex, 40, 132 J, 44 Ã, 45 IR, 45 (cor), 46 Θ, 47 MT Θ,47 Θ, 48 MT Θ,48 M 0,48 s, 48 B l (cor)mt Θ,49 M i,49 A, 50, 134 MT ΘA, 50, 53 MT,53 Q i,53 s, 53 U i,53 U s,53 φ i : M i Q i,54 P,55 s,55 s,55 MT A, 56 Q i,73 s ν,73 MT Σ(Qi,s ν ), 73 (MT Σ),74 M i,74 ŝ ν,74 Σ, 74,74

3 176 List of Symbols, 74,74 MT P (also write P ), 75 N, 85 U,85 MT U,85 MT U A,85 H,96 MT ex, 113 MT ex, 113 PT ex, 113 PT ex PT, 114 B li, 114 PT β PT α, 116 appr, 117 PT appr, 117 W o(a), 124 A max, 124 W o(a max), 124 MTA, 125 Q is, 125 PT s, 125 Σ s, 126 E k, 131 u µ, 131 Σ new, 131 F, 132 T ( M1,...,IR), 132 F, 132 T (M 1,...,IR), 132 φ : F T ( M1,...,IR), 132 φ i : M i Mi, 132 F U, 132 E k, 132 u µ, 132 Ã ex, 133 H, 134 A, 135 H, 135 A, 137 G(A, H), 137 A h, 138 H h, 138 A h, 138 G h (A h, H h ), 138 G h (A, H), 138 G(A, H), 141 Ã tot, 143

4 Index application domain of a PT 12, 44 axiom 19 collectivizing 28, 47 explicit 19 finite set 48 implicit 20 axiomatic basis 73 simple 77 axiomatic relation 64 physically interpretable 77 axiomatic rule 20 basic language 34 extended 40, 132 initial 114 semantics of the 39 syntax of the 38 basic property 40 canonical extension of mappings 30 echelon 30 construction 30 scheme 30, 64 experiment hypothetical 96 fact 11 directly recordable 11 indirectly recordable 11 not stated 45 stated 45 finiteness of physics 52 fundamental domain of a PT 13, 60 hypotheses interpretation of 139 mathematical classification of 138 physical classification of 138 idealization process 53 imprecise mapping 54 indirect measurement 134 inaccuracy set of 137 classification of 140 mathematical 139 physical 140 interpretation of 141 law of nature idealized 75 idealized pure 77 pure 76 logics 21 mathematical structure 64 Mathematical Theory the basic 46 the standard 48 mathematical theory 17 constant of the 19 the idealized 53 enriched by A 56 the standard enriched by A 50 mathematization process 46 Measurement indirect 138 measurement

5 178 Index error of 44, 50 network of physical theories 118 norm 98 now 122 object 11 possible 131 property of 11 relation between 11 physical reality 12 physical system 128 physical theory 12 application domain of a 12, 44 approximation 117 closed 124 extended 113 fundamental domain of a 13, 60 new concept in a 131 new word in a 132 reality domain of a 14, 143 richer than another 116 skeleton 101 pre-theory 13, 112 proof 19 property 11 reality 11 possible 127, 131 new 131 structure of 11 reality domain of a PT 14, 143 all PTs 14, 144 recording process 34 recording rule 44 relation between objects 11 collectivizing 28 empirically allowed 97 empirically deductible 98 empirically refutable 98 possible 131 transportable 64 semantic compositionality 41 semantic relation 39 of denotation 43 of designation 41 of reference 42 of representation 42 sentence formal 46 compound 50 first kind 138 natural 34 compound 38, 45 extended 133 negation of a 38 set 27 auxiliary base 65 idealization of finite 54 idealized picture 53 inaccuracy 53, 85 possible 85 usable 87 physical 53 principal base 64 theory of 27 sign 18 equality 23 logical 18 relational 18 substantific 18 simple axiomatic basis 77 species of structures: 64, idealized 66 appr, approximation 117 ex, extended 113 Σ, basic 64 Σ new, related to new concepts 131 equally rich 66, 106 equivalent 66 poorer 66 procedure of deduction of a 68 representation of a 70 richer 66 theory of the 65 species of uniform structures 85 term intrinsic 68 picture 73 structure 64 theorem 20 truth of a proposition 43 typification 64 world formula 119