Logic, Methodology and Philosophy of Science, Proceeding of the 1960 International Congress (eBook)

Front Cover 1
Logic, Methodology and Philosophy of Science 4
Copyright Page 5
Contents 8
Preface 6
SECTION I MATHEMATICAL LOGIC 12
Symposiuam on Decision Problems 12
Chapter 1 On a Decision Method in Restricted Second Order Arithmetic 12
Chapter 2 The Undecidability of Exponential Diophantine Equations 23
Chapter 3 On a Theorem of Cobham Concerning Undecidable Theories 25
Symposiuam on the Notion of Recursiveness 37
Chapter 4 The Theory of Hierarchies 37
Chapter 5 Turing-Machine Computable Functionals of Finite Types I 49
Chapter 6 Recursive Equivalence Types and Combinatorial Functions 57
Chapter 7 Some Applications of Degrees 67
SECTION II FOUNDATIONS OF MATHEMATICAL THEORIES 71
Chapter 8 Recent Developments in Model Theory 71
Symposium on Foundations of Set Theory 91
Chapter 9 Some Applications of the Theory of Models to Set Theory 91
Chapter 10 On The Principles of Reflection in Axiomatic Set Theory 98
Chapter 11 Two Contributions to The Foundations of Set Theory 105
Chapter 12 Quine's Individuals 122
Chapter 13 Typical Ambiguity 127
Chapter 14 Some Problems and Results Relevant to the Foundations of Set Theory 136
Chapter 15 Common Extension in Equational Classes 147
Symposium on Metamathematics of Algebra and Geometry 154
Chapter 16 Metamathematics and Algebra: an Example 154
Chapter 17 Diophantine Equations and Non-Standard Models of Arithmetic 162
Chapter 18 On Completeness and Decidability and Some Non-Definable Notions of Elementary Hyperbolic Geometry 170
Chapter 19 New Foundations of Absolute Geometry 179
SECTION III PHILOSOPHY OF LOGIC AND MATHEMATICS 187
Chapter 20 Remarks About Formalization and Models 187
Chapter 21 Mathematics and Logic 192
Chapter 22 Nominalistic Analysis of Mathematical Language 198
Chapter 23 After Thirty Years 205
Chapter 24 Foundations of Intuitionistic Logic 209
SECTION IV GENERAL PROBLEMS OF METHODOLOGY AND PHILOSOPHY OF SCIENCE 222
Chapter 25 Praxiological Sentences and How They are Proved 222
Symposium on Models in the Empiricl Sciences 235
Chapter 26 Models in the Empirical Sciences 235
Chapter 27 On the Structural Form of Interdependent Systems 243
Chapter 28 What Theories are Not 251
Chapter 29 Models of Data 263
Chapter 30 Determinism and Indeterminism in a New "level" Conception of Matter 273
Symposium on Theoretical and Empirical Aspects of Science 276
Chapter 31 The Controversy: Deductivism Versus Inductivism 276
Chapter 32 The Theoretical and the Empirical Aspects of Science 286
Chapter 33 Some Comments on Truth and the Growth of Knowledge 296
Chapter 34 Abstraction in Natural Science 304
SECTION V FOUNDATIONS OF PROBABILITY AND INDUCTION 314
Chapter 35 The Aim of Inductive Logic 314
Symposium on Current Views of Subjective Probability 330
Chapter 36 Subjective Probability as the Measure of a Non-Measurable Set 330
Chapter 37 Remarks on the Epistemology of Subjective Probability 341
SECTION VI METHODOLOGY AND PHILOSOPHY OF PHYSICAL SCIENCES 351
Symposium on the Role of Mathematics in the Formulution of Physical Theories 351
Chapter 38 Analyse Mathématique du "Principe de Continuité" en Physique 351
Chapter 39 Is the Mathematical Explanation of Physical Data Unique? 359
Chapter 40 The Pernicious Influence of Mathematics on Science 367
Chapter 41 Curved Empty Space-Time as the Building Material of the Physical World: an Assessment 372
SECTION VII METHODOLOGY AND PHILOSOPHY OF BIOLOGICAL AND PSYCHOLOGICAL SCIENCES 386
Chapter 42 The Scientific Status of Psychoanalysis 386
Symposium on Alternative Approaches to the Theoy of Choice 402
Chapter 43 A Stochastic Model for the Act of Choice 402
Chapter 44 Response Strengths and Choice Probability: A Consideration of two Combination Rules 411
Chapter 45 Theories of Choice and the Stimulus-Response Framework 424
Chapter 46 A Descriptive Approach to the Dynamics of Choice Behavior 435
Chapter 47 "Brain-Computer" Approach to the Theory of Choice 445
SECTION VIII METHODOLOGY AND PHILOSOPHY OF SOCIAL SCIENCES 453
Chapter 48 Models for the Analysis of Balance of Power in Society 453
Chapter 49 Philosophy of Science and Empirical Social Research 474
Symposium on Macro- and Microeconomics 485
Chapter 50 Microeconomics and Macroeconomics 485
Chapter 51 Résultats et Directions de Recherche Dans la Théorie De l'Agrégation 495
Chapter 52 Three Models of Economic Growth 505
Chapter 53 Alternative Approaches to the Aggregation Problem 518
SECTION IX METHODOLOGY AND PHILOSOPHY OF LINGUISTICS 539
Chapter 54 Explanatory Models in Linguistics 539
Smposium on Models in Linguistics 562
Chapter 55 Some Recent Results in Theoretical Linguistics 562
Chapter 56 Models in Linguistics and Models in General 569
Chapter 57 Lists in Grammars 578
Chapter 58 Criteria for a Model of Language 588
SECTION X METHODOLOGY AND PHILOSOPHY OF HISTORICAL SCIENCES 595
Chapter 59 Scientific Method and the Work of the Historian 595
Chapter 60 The Historian's Problem of Selection 606
SECTION XI HISTORY OF LOGIC, METHODOLOGY, AND PHILOSOPHY OF SCIENCE 615
Chapter 61 Remarks on the Role of Quantity, Quality, and Relations in the History of Logic, Methodology and Philosophy of Science 615
Chapter 62 The Main Trends in the Foundations of Geometry in the 19th Century 624
Chapter 63 Modality de Dicto and de Re 633
Chapter 64 Contraposition in Indian Logic 645
Chapter 65. Program of the Proceedings 664