Logical physics

301 Pages·1983·5.26 MB·English

by  Zinov'ev A. A. (Зиновьев Александр Александрович)

BOSTON STUDIES IN THE PHILOSOPHY
OF SCIENCE
EDITED BY ROBERTS. COHEN AND MARX W. WARTOFSKY
VOLUME 74
A. A. ZINOV'EV
LOGICAL PHYSICS
Translated from the Russian by O. A. Germogenova
Edited by
ROBERT S. COHEN
D. REIDEL PUBLISHING COMPANY
A MEMBER OF THE KLUWER K B ACADEMIC PUBLISHERS GROUP
DORDRECHT / BOSTON / LANCASTER
Library of Congress Cataloging in Publication Data
Zinoviev, Aleksandr, 1922-
Logical physics.
(Boston studies in the philosophy of science; v. 74)
Translation of: Logicheskaia fizika.
Includes index.
1. Logic. 2. Physics-Philosophy. I. Cohen, Robert Sonne.
II. Title. III. Series.
Q174.B67 vol.74 [BC57] 001'Ols [530'.01] 83-15970
ISBN 90-277-0734-0
Published by D. Reidel Publishing Company,
P.O. Box 17, 3300 AA Dordrecht, Holland.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers
190 Old Derby Street, Hingham, MA 02043, U.S.A.
In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, Holland.
Originally published in Russian by Nauka under the title: Logiceskaja fizika
All Rights Reserved
© 1983 by D. Reidel Publishing Company
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner
Printed in The Netherlands
TABLE O F C O N T E N T S
EDITORIAL PREFACE xi
PREFACE XV
CH A P T E R O N E / THE G E N E R A L T H E O R Y O F I N F E R E N C E AND TERM S
1. The Rules of Logic 1
2. Terms 2
3. Two Types of Terms 4
4. Simple and Complex Terms 4
5. Complex Terms 5
6. Occurrence of Terms and Statements in Other Terms and
Statements 6
7. Metaterms and Metastatements 6
8. The Meaning of Terms 8
9. Terms Including Statements 9
10. Definitions 9
1. Statements 1
12. The Meaning of Statements 13
13. Definitions with Statements 13
14. The Definition of Predicates 15
15. The Truth Values of Statements 16
16. The Number of Truth Values 17
17. The Cordinates of Statements 18
18. Truth Value for Statements with Conjunction, Disjunction
and Negation Operators 20
19. Truth Values of Other Forms of Statements 21
20. Tautology, Contradictions, Realizable Statements 24
21. Deduction 25
2. Logical Inference 26
23. The General Theory of Deduction 28
24. Classical and Non-Classical Cases in the Theory of
Inference 31
25. The Rules of Inference and the Truth Values of Statements 32
VI TABLE OF C O N T E N T S
26. Identity by Meaning and Entailment 3
27. The General Theory of Terms 3
28. The Cordinates of Statements 41
29. Consequences of Definitions 4
30. Implicit Definitions 45
31. Incomplete Definitions 46
32. Pseudodefmitions 47
3. Operational Definitions 48
34. Intuitively Obvious Statements 49
35. Variables 49
36. Definitions with Variables 53
37. The Multiple Meanings of Linguistic Expressions 54
38. Explication 5
39. Consistency of Terms 56
CHAPTER TWO / THE SPECIAL THEORY OF INFERENCE AND TERMS
1. The Logical Explication of Terms 57
2. Empirical and Abstract Objects 57
3. Individuals 59
4. Clases (Sets) 60
5. Clusters 63
6. States, Events 65
7. Existence 65
8. Quantifiers and Existence 68
9. Modal Predicates 69
10. Posibility 70
1. Contingent Events 73
12. Fatalism 75
13. Modal Operators 7
14. The Actual, the Existential, the Potential 77
15. The Measurement of Posibility 78
16. Relations 80
17. Comparison Relations 80
18. Order Relations 83
19. The Relation 'Betwen' 85
20. The Existence of Relations 85
21. Ordered Series 86
2. Contact 8
TABLE OF CONTENTS Vl
23. Continuity and Discontinuity of an Empirical Series 89
24. The Begining and End of a Series 89
25. Interval 92
26. Length 92
27. Abstract Series 95
28. Finite and Infinite Series 96
29. Structure , 97
30. Existence of a Structure 101
31. The Dimensions and Order of Structures 102
32. Corespondence 102
33. Corespondence of Clases 104
34. Functions 105
35. Ordered States 106
36. Conditional Statements with an Order-Relation 107
37. Functional Dependence 107
38. Conections 108
39. Ordering of Clases 10
CHAPTER THREE / NUMBER, MAGNITUDE, QUANTITY
1. Numbers in the Language 112
2. Numbers as Terms 13
3. Base Arithmetic 15
4. The Abbreviated Form of NB 117
5. The Universal Nature of Arithmetic 117
6. Expanded Arithmetic (EA) 118
7. Infinite Numbers 19
8. Formal Arithmetic with Metastatements 120
9. Formal Arithmetic and the Theory of Numbers 121
10. Number-Terms 123
11. The Existence of Numbers 123
12. Number as a Part of a Subject 125
13. Quantity 125
14. The Degrees and Range of Truth 127
15. Measurement and Definition 128
16. Number-Quantifiers 128
17. Amount 129
18. The Standard Classes of Numbers 129
19. The Cardinality of Classes of Numbers 130
Vlll TABLE OF CONTENTS
20. Comparison of Cardinalities of Classes 131
21. Other Definitions 132
22. Reducibility to Logic 133
23. A Remark on the Class of Positive Integers 134
24. A Remark on a Paradox with the Number Terms 135
CHAPTER FOUR / LOGICAL PHYSICS
1. On the Method of Presentation of Logic 136
2. Empirical Individuals 137
3. Variation 138
4. The Transition State 140
5. Space and Time 140
6. Spatial and Temporal Relations 142
7. The Time and Space' of Existence of an Empirical
Individual 146
8. The Existence of Space and Time 149
9. The Spatial and Temporal Location of an Individual 151
10. One and the Same Individual 151
11. Change in Space and Time 155
12. The Ireversibility of Time 159
13. On the Relation of Generation 161
14. The Continuity of Space and Time 162
15. In variance of Space and Time 164
16. Identity and Difference of Location and Time 164
17. The Predication of Variations 165
18. Translation, Change of Place (Movement) 167
19. The Paradox of Motion 168
20. Proces 170
21. Minimal Dimensions 171
22. On Infinite Dimensions 176
23. Rate 181
24. Zeno's Paradoxes 185
25. Quanta of Space, Time and Motion 186
26. The Relativity of Motion 186
27. On the Existence and Motion of Clusters 191
28. The Beam 193
29. The Universe as a Whole 194
30. Empirical Geometry 197
TABLE OF CONTENTS IX
31. Empirical Connections 204
32. The Predicates of Tendencies 205
33. Paradoxes of Connections 207
34. Conditional Predicates 209
35. Influence 210
36. Cause 214
37. Forms of Causal Relations , 219
38. Determinism and Indeterminism 222
39. Other Forms of Connections 224
40. On the Logical Situation in Microphysics 225
41. The Wave-Particle Duality 232
42. The Trajectory 235
43. The Part and the Whole 235
4. Forecasts 237
45. The Hypothetical Ontology 239
46. General Assertions Concerning the Universe and Physical
Asumptions 247
47. Generalizations of the Results of Science 249
APPENDIX
I. Epistemic Expresions 251
I. On the Concept of Belief 259
I. On the Notion of Preference 259
IV, On the Logic of Norms and Questions 262
V. On the Logic of Estimates 262
VI. On the Theory of Proof 265
VI. On Complete (Rigorous) Induction 266
VI. On Logical Consistency 270
IX. On the Systems of the Logic of Classes 274
GLOSARY OF SYMBOLS 279
SUBJECT INDEX 280