Analysis Without Measurement

319 Pages·2009·3.202 MB·English

by  Donald W. Katzner

Analysis without measurement

Analysis without measurement
DONALD W. KATZNER
University of Massachusetts at Amherst
CAMBRIDGE UNIVERSITY PRESS
Cambridge
London New York New Rochelle
Melbourne Sydney
CAMBRIDGE UNIVERSITY PRESS
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Cambridge University Press
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Published in the United States of America by Cambridge University Press, New York
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Information on this title: www.cambridge.org/9780521102902
© Cambridge University Press 1983
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 1983
This digitally printed version 2009
A catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Katzner, Donald W., 1938-
Analysis without measurement.
Includes bibliographies and index.
1. Economics - Methodology. 2. Economics-
Mathematical models. 3. Social sciences -
Methodology. 4. Social sciences - Mathematical
models. I. Title.
HB131.K37 330'.0724 82-4469
ISBN 978-0-521-24847-1 hardback
ISBN 978-0-521-10290-2 paperback
for
J.B.

Contents
Preface page xi
1 Introduction 1
1.1 Purpose 1
1.2 A reader's guide 11
1.3 Philosophical setting 17
1.4 The idea of a system 25
References 29
2 Notes on measurement 33
2.1 Types 33
2.2 Numerical scales 37
References 49
Part I: Theoretical methods 51
3 Basic concepts 53
3.1 Sets, relations, and functions 53
3.2 Topology, convergence, and closeness 59
3.3 Uniformities 69
3.4 Fixed sets and points 74
References 77
4 Algebraic structure 79
4.1 Semigroups of partial transformations 79
4.2 A particular specification 83
References 88
5 Analysis of specific systems 89
5.1 Simultaneous relations 90
5.2 Periodic relations 95
5.3 The finite case 100
Vll
li Contents
5.4 Maximization 106
5.5 Choice systems 109
References 112
6 General systems 113
6.1 Definition of a system 113
6.2 Causality 118
6.3 Connection and feedback 124
6.4 Control 128
6.5 Categories of systems 131
References 136
7 Some epistemological considerations 137
7.1 Dialectical analysis 138
7.2 Infinity 141
7.3 Change 147
7.4 The geometry of space 150
References 154
Part II: Applications to theoretical problems 157
Prologue 159
8 Political systems 161
8.1 Political structure 163
8.2 Solutions and cycles 165
References 169
9 Planning 171
9.1 A planner's view of society 175
9.2 Change over time 179
9.3 Operational planning 181
References 184
10 Simultaneous change and modernization 185
10.1 Society 188
10.2 Evolution 192
10.3 An alternative perspective 197
10.4 Modernization 199
References 203
Contents ix
11 Profits, optimality, and the social division of labor
in the firm 205
(With H. GINTIS)
11.1 A model of the production process 207
11.2 Conditions for Pareto optimality 214
11.3 Conditions for profitability 221
11.4 Conclusion 223
Appendix 225
References 229
Part III: Empirical verification 231
12 Statistical background 233
12.1 Preliminaries 234
12.2 Probability 235
12.3 Hypothesis testing and estimation 243
12.4 Dependence 246
References 251
13 Empirical relations among variables 253
13.1 Identification 254
13.2 Dummy variates 261
13.3 Models with both quantifiable and nonquantifiable
elements 270
References 273
14 An empirical application: occupational preferences
and the quality of life 275
(with J. E. RUSSO)
14.1 The model 276
14.2 Empirical analysis 278
14.3 Income and happiness 288
14.4 Conclusion 289
References 290
15 Getting on without measures 291
References 295
Index 297