Goddard / Routley .:. The Logic of Significance and Context

Goddard, Leonard and Richard Routley,
The Logic of Significance and Context. Vol. 1. Edinburgh, London: Scottish Academic Press, 1973. x, 641 Seiten mit Literaturverzeichnis. Pappband (gebunden). Grossoktav. 233 x 155 mm. 1023 g

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* Leicht gebräunt, Schnitt schwach fleckig, der Buchblock hängt leicht durch.
Bestell-Nr.159813

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Goddard Routley | Philosophie | Philosophy | Logik | Logic

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Contents of Volume I

INTRODUCTION
Historical Background 1
The Need for a Logic of Significance 5
Nonsignificance, Falsity and The Ungrammatical 8
The Proposed Logic 15

PART I
CONTEXT LOGIC
CHAPTER 1 THE SEMANTIC THEORY
1.1 Initial Problems 21
1.2 Sentences and their Use 23
1.3 True and False Sentences 24
1.4 Significant and Nonsignificant Sentences 29
1.5 Incomplete Sentences 32
1.6 Comparable Semantic Values 34
1.7 The Meaning of Sentences 35
§1 The Background Language 35
§2 The Context 39
1.8 Criteria of Nonsignificance 42

CHAPTER 2 ELEMENTS OF THE SENTENTIAL THEORY
2.1 Sentential Variables and Constants 44
2.2 Connectives and Semi-well-formed Formulae 46
2.3 Context Variables and Constants 47
2.4 The Sentential Quotation Function 49
2.5 The Relation between Sentences and Statements 54
2.6 The Logic of Statements, SL 62
2.7 The Logic of Statement-yielding Sentences, RSL 68
2.8 Extended Statement Logic, ESL 73
2.9 The Basic Well-formed Formulae of Context Logic, CL 76
2.10 The Nature of the Basic Formulae 79
2.11 The Formal Basis of CL 81
2.12 Properties of Sentences 90
2.13 The Statement-yielding Relation, Statement Identity and the Statement Function 92
2.14 Truth and Falsity 104
2.15 The Valuation Function and the Derived Sentential Range 110
2.16 The Reduced Sentential Range 117
2.17 Strong Extensional Equivalence 118
2.18 Further Developments 119

CHAPTER 3 ELEMENTS OF THE PREDICATE AND QUANTIFICATION
THEORY
3.1 Syntactical and Semantical Preliminaries 120
3.2 Constants, Subjects and Predicates 123
3.3 Place-holders, Arguments, Parameters and Variables: Their Values and Ranges 134
3.4 Operators: Quantifiers and Descriptions
3.5 The Syntax of Context Logic, and Identity 152
3.6 Aboutness and Items, and other Contractions 172
3.7 Predicates, Properties and Universals 191
3.8 Derived Ranges and Significance Essentialism
§l Significance Ranges 201
§2 Truth and Falsity Ranges 204
§3 Secondary Item Ranges 205
§4 Significance Essentialism 208
3.9 Separating Incompleteness from the Varieties of Nonsense 212

PART II
THE PRINCIPLES OF SIGNIFICANCE
CHAPTER 4 TOWARDS A L0GIC OF SIGNIFICANCE
4.1 The Method to be Adopted 219
4.2 The Standard Method 223
4.3 Deficiencies of the Standard Method 225
4.4 Ideal Languages 231
4.5 The Scope of Logic and the Anti-Logic Campaign 234
4.6 The Irreducibility of Nonsignificance 237
4.7 Degrees of Significance 246
4.8 Conventionalist and Contingency Objections 248

CHAPTER 5 SENTENTIAL SIGNIFICANCE LOGIC I:
THE MATRIX APPROACH
5.1 Extensional Connectives 256
5.2 Extended Classical Connectives 258
5.3 Classical Significance Connectives 260
5.4 Strong Regular Significance Connectives 265
5.5 Designated Values: S and C Logics 273
5.6 The Problem of Consistency for Matrix Logics 276
5.7 Sorted Variables 293
5.8 Stage 0: The Logics So and Co 295
5.9 Stage 1: The Logics Sl and Cl 305
5.10 stage 2. The Logics S2 and C2 312
5.11 stage 3. The Logics Sg and cs 323
5.12 stage 4: Alternative Interpretations of Sg and G, 335
and the 4-Logics
5.13 stage 5: The Logics Sö and Cb 345
5.14 Stage 6: The Logics SG and Cd 355

CHAPTER 6 SENTENTIAL SIGNIFICANCE LOGICS II:
THE AXIOMATIC APPROACH
6.1 stage O. Axiomatic Formulations of 0-Systems 368
6.2 Stage 1: Axiomatic Formulations of I-Systems 373
6.3 Stage 2. Axiomatic Formulations of 2-Systems 391
6.4 Stage 3: Axiomatic Formulations of 3-Systems 406
6.5 Stage 4: Axiomatic Formulations of 4-Systems 409
6.6 Stage 5: Axiomatic Formulations of 5-Systems 413
6.7 Stage 6: Axiomatic Formulations of 6-Systems 415

CHAPTER 7 INTENSIONAL AND QUANTIFIED SIGNIFICANCE LOGICS
7.1 Extending Sentential Significance Logics 431
7.2 Intensional Superstructures 435
§1 Inadequacies of Extensional Significance Logics: Non-value-functional Connectives 435
§2 Set-up and Situational Semantics 442
§3 Accounting for Specific Properties of Intensional Connectives 448
§4 Multiply Modal Significance Logics 452
§5 Soundness and Completeness Theorems 457
§6 Decidability
§7 Generalizations, and the Intensionality of Connectives 463
§8 The Context Interpretation of Set-ups and the Addition 466
of Context
7.3 Quantified Significance Logics: the Interpretation of 469
Quantifiers
7.4 Kinds of Quantified Significance Logics 475
7.5 On the Quantification Logic of Principia Mathematica 477
§1 The Logic PMI 479
§2 The Logic PM2 481
§3 The Criteria of Significance in Principia Mathematica 482
§4 Significance Semantics for PM2 483
§5 The Logic PSI 485
7.6 Many-sorted Significance Logics 485
7.7 The Quantificational System QS6 493
§1 The Syntax and Contractional Semantics
§2 The Postulational Theory 496
§3 Skolem-Löwenheim and Completeness Theorems 502
§4 Compatibility and Interpolation Theorems 510
§5 Generalized Quantified Significance Theories 517
7.8 Quantification Logics with Alternative Sentential Bases 518
§1 The Quantification Logic QS4 518
§2 The Restricted Quantification Logics QS5 and QSa 520
§3 The Restricted Quantification Logic QS2 522
§4 The Quantification Logic QL with alternative quantifiers 525
7.9 Developments of Quantified Significance Logics 528
§1 SA, a Significance Arithmetic; and the Theory of Partial Recursive Functions 528
§2 Significant Subjects, Special Subjects and Existence: QS6E 529
§3 Quantified Significance Logic with Leibniz Identity: QS6E z 533
§4 Contextually Defined Definite Descriptions in QS6E 537
§5 The Logic of Classes and Relations in QS6E 538
§6 Restricted Variables and Restricted Quantifiers 541
7.10 Quantified Multiply Modal Significance Logics 545
7.11 Further Enlarged Quantified Significance Logics 553
§1 Logics Based on an Any-Operator: 553
§2 Definite Descriptions in SCS6E 558
§3 Modalisation: CIS6, etc. 560
§4 General Intensional Logics, Context and Pragmatics 563
7.12 Second-Stage Quantified Significance Logics 566
§1 Interpretational Problems 566
§2 A Semantics for 2QSg 576
§3 The Postulational Theoryfor 2QS6 577
§4 Soundness, Completeness and Löwenheim-Skolem Theorems 579
for 2QS6
§5 The Extended Assertoric Logic ES6, and the Consistency of2QS6 584
7.13 Developments of Second-Stage Quantified Significance Logics 587
§1 Further Second-Stage Logics 587
§2 The Weakness of Completeness: Extensions of 2QS6 by Abstraction 589
§3 Extensions of Second-Stage Logics 592
§4 Reductions of Second-Stage Logics to Many-Sorted Significance Logics 598
§5 Applications of Normally Interpreted Second-Stage Logics and their Extensions: Class Theory and Number Theory 602
§6 On Identity 606
7.14 The Structure of Categories 614

BIBLIOGRAPHY 637

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