Luce Foundations of Measurement

Volume 3
1. Auflage 2014
ISBN: 978-1-4832-9504-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 356 Seiten, Web PDF

From the Foreword is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or unhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the earth, including in it all the seas and the hollows of the earth filled up to a height equal to that of the highest mountains, would be many times further still from recognizing that any number could be expressed which exceeded the multitude of the sand so taken. But I will try to show you by means of geometrical proofs, which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in magnitude to the earth filled up in the way described, but also that of a mass equal in magnitude to the universe.:See Table of Contents and MAQ.

Autoren/Hrsg.

Luce, R Duncan

Inhaltsverzeichnis

1;Front Cover;1
2;Representation, Axiomatization, and Invariance;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;14
7;Acknowledgments;16
8;Chapter 18. Overview;18
8.1;18.1 NONADDITIVE REPRESENTATIONS (CHAPTER 19);20
8.2;18.2 SCALE TYPES (CHAPTER 20);24
8.3;18.3 AXIOMATIZATION (CHAPTER 21);28
8.4;18.4 INVARIANCE AND MEANINGFULNESS (CHAPTER 22);31
9;Chapter 19. Nonadditive Representations;35
9.1;19.1 INTRODUCTION;35
9.2;19.2 TYPES OF CONCATENATION STRUCTURE;42
9.3;19.3 REPRESENTATIONS OF PCSs;54
9.4;19.4 COMPLETIONS OF TOTAL ORDERS AND PCSs;65
9.5;19.5 PROOFS ABOUT CONCATENATION STRUCTURES;73
9.6;19.6 CONNECTIONS BETWEEN CONJOINT AND CONCATENATION STRUCTURES;92
9.7;19.7 REPRESENTATIONS OF SOLVABLE CONJOINT AND CONCATENATION STRUCTURES;104
9.8;19.8 PROOFS;106
9.9;19.9 BISYMMETRY AND RELATED PROPERTIES;118
9.10;EXERCISES;121
10;Chapter 20. Scale Types;125
10.1;20.1 INTRODUCTION;125
10.2;20.2 HOMOGENEITY, UNIQUENESS, AND SCALE TYPE;129
10.3;20.3 PROOFS;143
10.4;20.4 HOMOGENEOUS CONCATENATION STRUCTURES;159
10.5;20.5 PROOFS;173
10.6;20.6 HOMOGENEOUS CONJOINT STRUCTURES;197
10.7;20.7 PROOFS;201
10.8;EXERCISES;209
11;Chapter 21. Axiomatization;212
11.1;21.1 AXIOM SYSTEMS AND REPRESENTATIONS;213
11.2;21.2 ELEMENTARY FORMALIZATION OF THEORIES;221
11.3;21.3 DEFINABILITY AND INTERPRETABILITY;235
11.4;21.4 SOME THEOREMS ON AXIOMATIZABILITY;242
11.5;21.5 PROOFS;246
11.6;21.6 FINITE AXIOMATIZABILITY;248
11.7;21.7 THE ARCHIMEDEAN AXIOM;263
11.8;21.8 TESTABILITY OF AXIOMS;268
11.9;EXERCISES;282
12;Chapter 22. Invariance and Meaningfulness;284
12.1;22.1 INTRODUCTION;284
12.2;22.2 METHODS OF DEFINING MEANINGFUL RELATIONS;286
12.3;22.3 CHARACTERIZATIONS OF REFERENCE INVARIANCE;302
12.4;22.4 PROOFS;307
12.5;22.5 DEFINABILITY;309
12.6;22.6 MEANINGFULNESS AND STATISTICS;311
12.7;22.7 DIMENSIONAL INVARIANCE;324
12.8;22.8 PROOFS;343
12.9;22.9 REPRISE: UNIQUENESS, AUTOMORPHISMS, AND CONSTRUCTABILITY;346
12.10;EXERCISES;353
13;References;355
14;Author Index;364
15;Subject Index;368