(Ebook PDF) Essays on Frege’s basic laws of arithmetic 1st Edition by Philip Ebert, Marcus Rossberg 0191020052 9780191020056 full chapters

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ISBN-10 :  0191020052 

ISBN-13 :  9780191020056

Author : Philip A. Ebert, Marcus Rossberg 

The volume is the first collection of essays that focuses on Gottlob Frege’s Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege’s magnum opus. It brings together twenty-two renowned Frege scholars whose contributions discuss a wide range of topics arising from both volumes of Basic Laws of Arithmetic. The original chapters in this volume make vivid the importance and originality of Frege’s masterpiece, not just for Frege scholars but for the study of the history of logic, mathematics, and philosophy.

Essays on Frege’s : basic laws of arithmetic 1st Table of contents:

1: The Basic Laws of Cardinal Number
1.1 THE PROOF OF HP
1.2 THE AXIOMS OF ARITHMETIC
1.3 THE INFINITE
1.4 THE FINITE
1.5 THE FINITE AND THE INFINITE
1.6 FURTHER UNTO THE INFINITE
1.7 CONCLUSION
REFERENCES
2: Axioms in Frege
2.1 CONSISTENCY AND INDEPENDENCE OF AXIOMS
2.1.1 Conceptual Analysis and Logical Entailment
2.1.2 Independence and Independence-Demonstrations
2.1.3 Frege’s Complaints
2.1.4 Consistency and Implicit Definitions
2.2 THE AXIOMS OF ARITHMETIC
2.2.1 The Content of the Axioms
2.2.2 The Independence of the Axioms
2.2.3 Frege on Defining Conditions
2.3 CONCLUSION
REFERENCES
3: When Logic Gives Out. Frege on Basic Logical Laws
3.1 INTRODUCTION
3.2 THE ARCHITECTURAL ARGUMENT
3.2.1 The Marks of the Logical
3.2.2 BLL and the Absence of Proof
3.3 SELF-EVIDENCE
3.4 SENSE-BASED UNDERSTANDING
3.5 THE CONSTITUTIVITY OF LOGIC
3.6 FREGE’S PRAGMATIC FOUNDATIONALISM
3.7 A DYNAMIC FOUNDATIONALISM?
3.7.1 The Dual Character of BLL
3.7.2 Content-Recarving and Justification
REFERENCES
4: The Context Principle in Frege’s Grundgesetze
4.1 INTRODUCTION
4.2 HOW ARE THE NUMBERS “GIVEN TO US”?
4.3 THE CONTEXT PRINCIPLE IN THE GRUNDLAGEN
4.4 THE “REPRODUCTION” OF MEANING
4.5 THE CONTEXT PRINCIPLE IN THE GRUNDGESETZE
4.6 DEVELOPING FREGE’S EXPLANATORY STRATEGY
4.6.1 Our Test Case in More Detail
4.6.2 Holophrastic Reductionism
4.6.3 Semantically Constrained Content Recarving
4.6.4 Towards a Metasemantic Interpretation
4.7 CONCLUSION
REFERENCES
5: Why Does Frege Care Whether Julius Caesar is a Number? Section 10 of Basic Laws and the Context P
5.1 JULIUS CAESAR
5.2 WHY DON’T WE NEED A DEFINITION OF THE NOTION OF EXTENSION OF A CONCEPT?
5.3 THE STANDARD INTERPRETATION AND THE METAPHYSICAL REQUIREMENT
5.4 DEFINING THE NUMBERS IN BASIC LAWS
5.5 SECTION 10 OF BASIC LAWS
5.6 SECTION 10 AND THE STANDARD INTERPRETATION: THREE DIFFICULTIES
5.7 THE CONTEXT PRINCIPLE
5.8 CONCLUSION
REFERENCES
6: Grundgesetze and the Sense/Reference Distinction
6.1 INTRODUCTION
6.2 SENSE AND REFERENCE AND THE CHANGES TO FREGE’S LOGICAL LANGUAGE
6.3 PRINCIPLES OF COMPOSITION: THE ISSUE
6.4 FOUR VIEWS ON THE STRUCTURE OF THOUGHTS
6.4.1 The Coarse-Grained View: Logical Equivalence
6.4.2 Intermediate Views: Concepts, their Extensions and Recarvings
6.4.3 The Fine-Grained View: Language-Proposition Isomorphism
6.4.4 The Ultra-Fine-Grained View
6.5 THE OVERABUNDANT THIRD REALM
REFERENCES
7: Double Value-Ranges
7.1 INTRODUCTION
7.2 FUNCTIONS IN GENERAL
7.3 GRAMMAR
7.4 WHY VALUE-RANGES?
7.5 THE APPLICATION FUNCTION
7.6 VALUE-RANGES FOR BINARY FUNCTIONS
7.7 FEATURES OF DOUBLE VALUE-RANGES
7.8 SIMULTANEOUS SATURATION
7.9 CONCLUDING REMARKS
REFERENCES
8: The Proof of Hume’s Principle
8.1 INTRODUCTION
8.2 WHAT DOES FREGE PROVE?
8.3 THE PROOF
8.4 WHY NO PROOF OF HUME’S PRINCIPLE
8.5 BEGRIFFSSCHRIFT, NATURAL DEDUCTION STYLE
8.6 THE FORM OF (49)
8.7 DEFINITION AND RECOGNITION
8.8 FINISHING REMARK
REFERENCES
9: Frege’s Theorems on Simple Series
9.1 INTRODUCTION
9.2 LANGUAGE AND SYMBOLISM
9.3 THE MEANING OF ‘SIMPLE SERIES’
9.4 FREGE’S PROOF OF THEOREM 207. DENUMERABLE VERSUS SIMPLY INFINITE
9.5 BOUNDED SIMPLE SERIES. CARDINAL AND ORDINAL NUMBERS
APPENDIX: UNIQUENESS OF PREDECESSOR WITHIN A SERIES
REFERENCES
10: Infinitesimals, Magnitudes, and Definition in Frege
10.1 INTRODUCTION: INFINITESIMALS, OBJECTS, AND CONTEXTUAL DEFINITION
10.2 HANKEL, GAUSS AND NEGATIVES: A CAUTIONARY VIGNETTE
10.3 A PERENNIAL SCHOLARLY PUZZLE: FREGE ON CONTEXTUAL DEFINITIONS IN GRUNDLAGEN AND LATER
10.4 THE NARROW PROBLEM: WHAT, PRECISELY, IS FREGE’S ATTITUDE TO INFINITESIMALS?
10.5 PRESENTING OBJECTS AND “EXTENT OF VALIDITY”: THE RIEMANN INTEGRAL
10.6 GRUNDLAGEN ’S DISCUSSION REVISITED: RESTRICTED DEFINITIONS AND INTRODUCING OBJECTS
10.7 IDENTITIES FIXING SENSE WITHOUT PROVIDING REFERENCE: AN EXAMPLE FROM FREGE’S ENVIRONMENT
10.8 IN SHORT
REFERENCES
11: Frege’s Relation to Dedekind: Basic Laws and Beyond
11.1 INTRODUCTION
11.2 A BRIEF SUMMARY OF DEDEKIND’S FOUNDATIONAL CONTRIBUTIONS
11.3 COMPARING FREGE’S AND DEDEKIND’S RECEPTIONS
11.4 AN OVERVIEW OF FREGE’S COMMENTS ON DEDEKIND
11.5 DEDEKIND’S REMARKS ABOUT FREGE—AND POSSIBLE LINES OF INFLUENCE
11.6 FREGE’S MINOR CRITICISMS—AS WELL AS SOME ABSENT ONES
11.7 FREGE’S MORE CENTRAL AND LASTING CRITICISMS
11.8 TOWARDS A RECONCILIATION OF FREGE AND DEDEKIND
REFERENCES
12: Frege on Creation
12.1 INTRODUCTORY
12.2 THE STATEMENT OF THE CRITICISM IN THE GRUNDGESETZE
12.2.1 Contra Dedekind
12.2.2 Contra Hankel
12.2.3 Contra Stolz and Cantor
12.3 THE FIRST PROBLEM: THE ARBITRARINESS OF “LAWS”
12.4 THE SECOND PROBLEM: CONSISTENCY
12.5 CONTRA HILBERT
12.6 NON-UNIQUENESS
12.7 EXISTENTIAL ASSUMPTIONS AND HUME’S PRINCIPLE
12.8 CONCLUSION
REFERENCES
13: Mathematical Creation in Frege’s Grundgesetze
13.1 FREGE’S PLATONISM: THE PUZZLE
13.2 DUMMETT, SCHIRN, LINNEBO, AND HECK ON §§146–147
13.3 TWO KINDS OF CREATION: §146 AND §147
13.4 FREGE’S UNUSUAL CONCESSIVE TONE: HIS OPPONENTS
REFERENCES
14: Frege on the Real Numbers
14.1 INTRODUCTION
14.2 FREGE’S THEORY OF THE REAL NUMBERS IN THE GRUNDGESETZE
14.2.1 Objections to Contemporaries
14.2.2 Frege’s Informal Account
14.2.3 Formal Developments
14.3 FREGE’S ONTOLOGICAL DISTINCTION
14.3.1 Motivating the Ontological Distinction
14.3.2 Some Questions
14.4 THE METAPHYSICS OF MAGNITUDES
14.5 IDEALIZATION AND METAPHYSICS: THE APPLICATION CONSTRAINT
REFERENCES
15: Frege’s Little Theorem and Frege’s Way Out
15.1 INTRODUCTION
15.2 FREGE’S LITTLE THEOREM AND BASIC LAW V′
15.3 FINITE EXCEPTIONS
15.4 SINGLETONS, MONISM, AND CONTRADICTION
15.5 RECONSTRUCTING ARITHMETIC
REFERENCES
16: “How did the serpent of inconsistency enter Frege’s paradise?”
16.1 NAÏVETÉ OR INSOUCIANCE?
16.2 INDEFINITE EXTENSIBILITY: THE PROBLEM OF CHARACTERIZATION
16.3 INDEFINITE EXTENSIBILITY AND THE ORDINALS: RUSSELL’S CONJECTURE AND “SMALL” CASES
16.4 INDEFINITE EXTENSIBILITY EXPLICATED
16.5 INDEFINITE EXTENSIBILITY: BURALI-FORTI
16.6 INDEFINITE EXTENSIBILITY: CANTOR
16.7 BASIC LAW V
16.8 CODA
REFERENCES
17: Second-Order Abstraction Before and After Russell’s Paradox
17.1 INTRODUCTION
17.2 THE FOUNDATIONAL PROJECT: INITIAL DOUBTS AND ALLEGED IRREFUTABILITY
17.3 FREGE’S PARADIGMS OF SECOND-ORDER ABSTRACTION: HUME’S PRINCIPLE AND AXIOM V
17.4 AXIOMS IN GENERAL AND AXIOM V IN PARTICULAR: THE REQUIREMENT OF SELF-EVIDENCE
17.5 A CLOSER EXAMINATION OF THE TWO SIDES OF BASIC LAW V: IDENTITY OR DIFFERENCE OF SENSE?
17.6 THE CHOICE OF AN ABSTRACTION PRINCIPLE AS AN AXIOM OF A THEORY T : FREGE’S EPISTEMIC DILEMMA
17.7 FREGE’S REACTIONS TO RUSSELL’S PARADOX IN THE PERIOD 1902–1906
REFERENCES
18: Formal Arithmetic Before Grundgesetze
18.1 FIRST- AND SECOND-LEVEL EXTENSIONS
18.2 VALUE-RANGES VERSUS EXTENSIONS
18.3 FREGE’S CHANGING VIEWS ABOUT FUNCTIONS
18.4 THE WAGES OF UNSATURATEDNESS
18.5 EXTENSIONS
18.6 NUMERICAL EQUALITY
18.7 HP AND THE EXPLICIT DEFINITION OF NUMBER
18.8 CLOSING
REFERENCES
19: Definitions in Begriffsschrift and Grundgesetze
19.1 INTRODUCTION
19.2 THE BEGRIFFSSCHRIFT DEFINITIONS
19.3 TYPE A DEFINITIONS: FREGE’S COMMENTARY CONTRASTED WITH SOME MODERN INTERPRETATIONS
19.4 DEFINITIONS OR ELUCIDATIONS? PRIMITIVE VOCABULARY OR DEFINED SIGNS?
19.5 THE PROBLEM OF THE CORRESPONDING FUNCTION
19.6 HECK AND MAY ON THE DEVELOPMENT OF FREGE’S CONCEPTION OF FUNCTIONS AND QUANTIFIERS
19.7 TYPE B DEFINITIONS: FREGE’S COMMENTARY AND PETER SIMONS’S INTERPRETATION
19.8 THE BS CONCEPTS IN GG, AND THE PROBLEM OF THE CORRESPONDING FUNCTION ONCE AGAIN
19.9 HOW ALL THIS IS AVOIDED IN GG THROUGH THE USE OF VALUE-RANGES
19.10 HECK’S ELIMINATION OF VALUE-RANGES FROM GG
19.11 REMNANTS OF THE BS PERSPECTIVE: FREGE’S PIECEMEAL CONCEPTION OF VARIABLE-BINDING
19.12 CONCLUSION: A GLIMPSE OF THE FUTURE?
REFERENCES
Works by Frege
Other works
20: A Brief History of English Translations of Frege’s Writings
20.1 INTRODUCTION
20.2 PHASES IN THE TRANSLATION OF FREGE’S WRITINGS
20.3 THE FIRST TRANSLATION OF THE OPENING PAGES OF THE GRUNDGESETZE (1915–1917)
20.4 THE FIRST TWO BOOKS IN ENGLISH (1948–1956)
20.5 THE DEVELOPMENT OF INTEREST IN FREGE’S LOGICAL SYSTEM (1964–1972)
20.6 THE TRILOGY OF COLLECTED WRITINGS (1977–1984)
20.7 THE FREGE READER (1997)
20.8 THE COMPLETE TRANSLATION OF GRUNDGESETZE(2013)
20.9 CONCLUSION
REFERENCES
21: Translating ‘Bedeutung’ in Frege’s Writings: A Case Study and Cautionary Tale in the Histo
21.1 INTRODUCTION
21.2 RUSSELL’S TRANSLATION IN 1903
21.3 RUSSELL’S TRANSLATION IN 1905
21.5 WITTGENSTEIN’S TRANSLATION—AND THE TRANSLATION OF WITTGENSTEIN—IN 1913–1914
21.6 INTERLUDE: ANSCOMBE’S TRANSLATION OF WITTGENSTEIN’S NOTEBOOKS 1914–1916
21.7 OGDEN AND RICHARD’S THE MEANING OF MEANING
21.8 CARNAP’S TRANSLATION IN MEANING AND NECESSITY
21.9 BLACK’S TRANSLATION IN 1948
21.10 FEIGL’S TRANSLATION IN 1949
21.11 AUSTIN’S TRANSLATION OF DIE GRUNDLAGEN DER ARITHMETIK IN 1950
21.12 GEACH AND BLACK’S TRANSLATIONS 1952, 1960, AND 1980
21.13 FURTH’S TRANSLATION IN 1964
21.14 DONNELLAN’S DISTINCTION BETWEEN DENOTATION AND REFERRING
21.15 DUMMETT’S FIRST TRANSLATION OF ‘BEDEUTUNG’ AS ‘MEANING’
21.16 TUGENDHAT’S SUGGESTED TRANSLATION OF ‘BEDEUTUNG’ AS ‘SIGNIFICANCE’
21.17 REVERTING TO ‘REFERENCE’
21.18 THE DECISION TO TRANSLATE ‘BEDEUTUNG’ BY ‘MEANING’
21.19 THE DISPUTE BETWEEN BELL AND THE TRANSLATORS OF POSTHUMOUS WRITINGS
21.20 THE FREGE READER
21.21 THE COMPLETE TRANSLATION OF THE GRUNDGESETZE
21.22 BEDEUTUNG: ONE RELATION OR THREE RELATIONS?
21.23 BENDING TERMS IN TRANSLATION
21.24 TOWARDS A LINGUISTIC PHENOMENOLOGY OF “REFERRING” VERBS
21.25 CONCLUSION
REFERENCES
22: Contemporary Reviews of Frege’s Grundgesetze
22.1 INTRODUCTION
22.2 TRANSLATIONS

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