Introduction to the theories of measurement and meaningfulness and the use of symmetry in science:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Mahwah, NJ [u.a.]
Erlbaum
2007
|
| Schriftenreihe: | The LEA series in scientific psychology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 173 S. |
| ISBN: | 0805862021 9780805862027 9781410615985 1410615987 |
Internformat
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| 245 | 1 | 0 | |a Introduction to the theories of measurement and meaningfulness and the use of symmetry in science |c Louis Narens |
| 264 | 1 | |a Mahwah, NJ [u.a.] |b Erlbaum |c 2007 | |
| 300 | |a IX, 173 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a The LEA series in scientific psychology | |
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Datensatz im Suchindex
| _version_ | 1804136613607899136 |
|---|---|
| adam_text | Contents
1
The Need for Theories of Measurement and
Meaningfulness
1
1.1
Plateau s Theory
2
1.2
Derivation of Plateau s Power Law
4
1.3
Issues Raised by Plateau s Theory
8
1.4
Additional Lemmas and Proofs
10
1 Measurement
15
2
Representational Measurement Theory
17
2.1
Introduction
17
2.2
Preliminaries
18
2.2.1
Basic Notation
18
2.2.2
Isomorphisms
18
2.3
Cantor s Characterization of the Continuum
20
2.4
Continuous Structures
22
2.5
Scale Types
28
2.6
Representational Meaningfulness
32
3
Symmetries and the
Erlanger
Program
35
3.1
Symmetries
35
3.2 Erlanger
Program
40
3.3
Comparison of Geometric and
Measurement-Theoretic Concepts
43
4
Threshold Measurement
47
4.1
Continuous Threshold Structures
48
4.2
Weber s and Fechners Laws
52
4.3
Threshold Structures with Only Psychological Primitives
56
4.4
Meaningfulness Considerations
57
і
CONTENTS
Magnitude
Production
61
5.1
Stevens
Methods of Magnitude Estimation and Production
61
5.2
Narens
1996
Theory
63
5.3
Empirical Tests
68
5.4
Continuous Ratio Production
69
5.5
Conclusions
70
Torgerson s Conjecture
73
6.1
Bisection Data
73
6.2
Torgerson s Conjecture
77
6.3
An Experimental Test of Torgerson s Conjecture
79
6.4
Theoretical Considerations
81
6.5
Proof of Lemma
6.1 82
II Meaningfulness
87
7
Meaningfulness Concepts from Measurement Theory
89
7.1
Quantitative «S-Meaningfulness
89
7.2
Qualitative iS-Meaningfulness
95
7.3
Endomorphism
Invariance
97
8
Preliminary Set Theory
101
8.1
Introduction
101
8.2
The Language
L
(Є, А)
101
8.3
Basic Set Theory
105
8.4
The Sets V and
P
109
8.5
First-Order and Higher-Order Relations
112
9
Scientific Topics
115
9.1
Principles for Scientific Topics
115
9.2
Pure Mathematics
117
9.3
Set-Theoretic Interpretation
118
10
Theories of Meaningfulness
121
10.1
Axiom of Measurement
121
10.2
Axiom System TSJ
126
10.3
Meaningfulness and the
Erlanger
Program
127
10.3.1
Invariance
under Extensions of Permutations
127
10.3.2
Є
-Symmetries
129
10.3.3
Axiom System
£ 131
10.4
Additional Proofs
135
CONTENTS ix
11 Applications,
Limitations,
and Generalizations of
Axiom System FST
143
11.1
An Epistemology for a Rule Based on
Invariance
143
11.2
Limitations of Axiom System TST
150
11.3
Intrinsicness
151
11.4
Possible Psychophysical Laws
155
11.5
Distinguishing Empirical and Meaningful Relations
161
References
163
Index
169
|
| adam_txt |
Contents
1
The Need for Theories of Measurement and
Meaningfulness
1
1.1
Plateau's Theory
2
1.2
Derivation of Plateau's Power Law
4
1.3
Issues Raised by Plateau's Theory
8
1.4
Additional Lemmas and Proofs
10
1 Measurement
15
2
Representational Measurement Theory
17
2.1
Introduction
17
2.2
Preliminaries
18
2.2.1
Basic Notation
18
2.2.2
Isomorphisms
18
2.3
Cantor's Characterization of the Continuum
20
2.4
Continuous Structures
22
2.5
Scale Types
28
2.6
Representational Meaningfulness
32
3
Symmetries and the
Erlanger
Program
35
3.1
Symmetries
35
3.2 Erlanger
Program
40
3.3
Comparison of Geometric and
Measurement-Theoretic Concepts
43
4
Threshold Measurement
47
4.1
Continuous Threshold Structures
48
4.2
Weber's and Fechners Laws
52
4.3
Threshold Structures with Only Psychological Primitives
56
4.4
Meaningfulness Considerations
57
і
CONTENTS
Magnitude
Production
61
5.1
Stevens'
Methods of Magnitude Estimation and Production
61
5.2
Narens'
1996
Theory
63
5.3
Empirical Tests
68
5.4
Continuous Ratio Production
69
5.5
Conclusions
70
Torgerson's Conjecture
73
6.1
Bisection Data
73
6.2
Torgerson's Conjecture
77
6.3
An Experimental Test of Torgerson's Conjecture
79
6.4
Theoretical Considerations
81
6.5
Proof of Lemma
6.1 82
II Meaningfulness
87
7
Meaningfulness Concepts from Measurement Theory
89
7.1
Quantitative «S-Meaningfulness
89
7.2
Qualitative iS-Meaningfulness
95
7.3
Endomorphism
Invariance
97
8
Preliminary Set Theory
101
8.1
Introduction
101
8.2
The Language
L
(Є, А)
101
8.3
Basic Set Theory
105
8.4
The Sets V and
P
109
8.5
First-Order and Higher-Order Relations
112
9
Scientific Topics
115
9.1
Principles for Scientific Topics
115
9.2
Pure Mathematics
117
9.3
Set-Theoretic Interpretation
118
10
Theories of Meaningfulness
121
10.1
Axiom of Measurement
121
10.2
Axiom System TSJ
126
10.3
Meaningfulness and the
Erlanger
Program
127
10.3.1
Invariance
under Extensions of Permutations
127
10.3.2
Є
-Symmetries
129
10.3.3
Axiom System
£ 131
10.4
Additional Proofs
135
CONTENTS ix
11 Applications,
Limitations,
and Generalizations of
Axiom System FST
143
11.1
An Epistemology for a Rule Based on
Invariance
143
11.2
Limitations of Axiom System TST
150
11.3
Intrinsicness
151
11.4
Possible Psychophysical Laws
155
11.5
Distinguishing Empirical and Meaningful Relations
161
References
163
Index
169 |
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| index_date | 2024-07-02T17:59:16Z |
| indexdate | 2024-07-09T20:59:11Z |
| institution | BVB |
| isbn | 0805862021 9780805862027 9781410615985 1410615987 |
| language | English |
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| physical | IX, 173 S. |
| publishDate | 2007 |
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| series2 | The LEA series in scientific psychology |
| spelling | Narens, Louis Verfasser (DE-588)1084236524 aut Introduction to the theories of measurement and meaningfulness and the use of symmetry in science Louis Narens Mahwah, NJ [u.a.] Erlbaum 2007 IX, 173 S. txt rdacontent n rdamedia nc rdacarrier The LEA series in scientific psychology Measurement Symmetry (Mathematics) Threshold logic Messtheorie (DE-588)4169537-9 gnd rswk-swf Symmetrie (DE-588)4058724-1 gnd rswk-swf Messtheorie (DE-588)4169537-9 s Symmetrie (DE-588)4058724-1 s DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015717759&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Narens, Louis Introduction to the theories of measurement and meaningfulness and the use of symmetry in science Measurement Symmetry (Mathematics) Threshold logic Messtheorie (DE-588)4169537-9 gnd Symmetrie (DE-588)4058724-1 gnd |
| subject_GND | (DE-588)4169537-9 (DE-588)4058724-1 |
| title | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science |
| title_auth | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science |
| title_exact_search | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science |
| title_exact_search_txtP | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science |
| title_full | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science Louis Narens |
| title_fullStr | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science Louis Narens |
| title_full_unstemmed | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science Louis Narens |
| title_short | Introduction to the theories of measurement and meaningfulness and the use of symmetry in science |
| title_sort | introduction to the theories of measurement and meaningfulness and the use of symmetry in science |
| topic | Measurement Symmetry (Mathematics) Threshold logic Messtheorie (DE-588)4169537-9 gnd Symmetrie (DE-588)4058724-1 gnd |
| topic_facet | Measurement Symmetry (Mathematics) Threshold logic Messtheorie Symmetrie |
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