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Reading Frege's Grundgesetze

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ISBN-10: 0199233705

ISBN-13: 9780199233700

Edition: 2012

Authors: Richard G. Heck, Richard G. Heck

List price: $78.00
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Description:

Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the moremathematical parts of the book have rarely been read. Richard G. Heck, Jr., aims to change that, and establish it as a neglected masterpiece that must be placed at the center of Frege's philosophy.Part I of Reading Frege's Grundgesetze develops an interpretation of the philosophy of logic that informs Grundgesetze, paying especially close attention to the difficult sections of Frege's book in which he discusses…    
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Book details

List price: $78.00
Copyright year: 2012
Publisher: Oxford University Press
Publication date: 11/29/2012
Binding: Hardcover
Pages: 288
Size: 6.38" wide x 9.45" long x 0.90" tall
Weight: 1.364
Language: English

Preface
Thank Yous
Editorial Notes
Acknowledgements
Introduction
The Genesis of Grundgesetze
The Fall and Rise of Grundgesetze
Frege on the Reals
Logic in Grundgesetze
The Centrality of Grundgesetze
Goals for the Book
The Logic Behind Frege's Logicism
Frege and Semantics
Frege and the Justification of Logical Laws
Formalism and the Significance of Interpretation
The Regress Argument
Grundgesetze I ��29-32 (I)
The Character of the Induction
Frege on Free Variables
The Induction Step
The Basis Case: The Logical Expressions
The Basis Case: The Smooth Breathing (I)
Grundgesetze I �10
Philosophical Aspects
Technical Aspects
Is Caesar a Value-Range?
The Second Problem, and Frege's Response
Are the Arguments in �10 Syntactic or Semantic?
Grundgesetze I ��29-32 (II)
The Basis Case: The Smooth Breathing (II)
Linnebo's Alternative
Final Remarks on ��29-32
The Cost of Frege's Response to the Caesar Problem
The Mathematics Behind Frege's Logicism
The Development of Arithmetic
Frege's Use of Basic Law V
Frege's Formulations of HP
Frege's Proofs of Axioms for Arithmetic
The Concept of Natural Number
The Basic Facts about the Ancestral
An Elegant Proof that Every Number has a Successor
The Strategy of the Proof
Theorem 154
An Important Lemma
Another Important Lemma
Completion of the Proof
Frege's Proofs of the Existence of Successor
HP in Grundgesetze
Definition by Recursion
Frege's Proof of Theorem 263
Frege's Use of Ordered Pairs
Definition by Recursion
The Definition of Relations by Recursion
Functionality and the n-Ancestral
Theorem 207
The Adequacy of Frege's Definition of the Ancestral
Theorem 263 in the Context of Frege's Development of Arithmetic
Frege on Finitude
Frege's Characterization of Finitude
Frege's Proof of Theorem 321
The Proof of Theorem 288
The Significance of Theorems 327 and 348
Finitude, the Least Number Principle, and Well-ordering
The Finite and the Infinite
Remarks on Volume II
Chapter Mu: There is No Cardinal Between the Finite Cardinals and Endlos
A Generalized Least Number Principle
Remarks on Frege's Proof of Theorem 359
The Proof of Theorem 428
The Significance of Theorem 428
Chapter Nu
The Definition of Addition
A Strengthened Version of HP
The Proof of Theorem 469
The Proof of Theorem 468
The Proof of Theorem 463
Remarks on Theorem 469
Cardinal Multiplication
Further unto the Infinite
The Theorems in Chapter Omicron
The Infinite and the Dedekind Infinite
Frege and the Axiom of Choice
Formalization and Frege's Conception of Logical Truth
Appendices
Outline of a Fregean Theory of Truth
Frege's Definitions
Theorems Concerning the Ancestral
Trees of Dependencies
Bibliography
Index