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E-raamat: Introduction to the Theories of Measurement and Meaningfulness and the Use of Symmetry in Science

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This book is designed to be an introduction to the theories of measurement and meaningfulness, and not a comprehensive study of those topics. A major theme of this book is the psychophysical measurement of subjective intensity. This has been a subject of intense interest in psychology from the very beginning of experimental psychology. And from that beginning to the present day, it has continuously generated major controversies involving measurement and meaningfulness.

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
I 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 Fechner's Laws
52
4.3 Threshold Structures with Only Psychological Primitives
56
4.4 Meaningfulness Considerations
57
5 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
6 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 S-Meaningfulness
95
7.3 Endomorphism Invariance
97
8 Preliminary Set Theory
101
8.1 Introduction
101
8.2 The Language L(E, A)
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 .TST
126
10.3 Meaningfulness and the Erlanger Program
127
10.3.1 Invariance under Extensions of Permutations
127
10.3.2 E-Symmetries
129
10.3.3 Axiom System E
131
10.4 Additional Proofs
135
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 FST
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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