| Document Type
|
:
|
BL
|
| Record Number
|
:
|
873759
|
| Main Entry
|
:
|
Heck, Richard G.
|
| Title & Author
|
:
|
Frege's Theorem.
|
| Publication Statement
|
:
|
Oxford :: OUP Oxford,, 2011.
|
| Page. NO
|
:
|
1 online resource (322 pages)
|
| ISBN
|
:
|
0191619655
|
|
|
:
|
: 9780191619656
|
|
|
:
|
019870898X
|
|
|
:
|
9780198708988
|
| Contents
|
:
|
Cover; Contents; Preface; Editorial Notes; Origin of the Chapters; 1 Frege's Theorem: An Overview; 1.1 Frege on Frege's Theorem; 1.2 The Caesar Problem; 1.3 What Does HP Have To Do With Arithmetic?; 1.4 Logicism and Neo-Logicism; 2 The Development of Arithmetic in Frege's: Grundgesetze der Arithmetik; 2.1 Basic Law V in Grundgesetze; 2.2 HP and Fregean Arithmetic; 2.3 Frege's Derivation of the Axioms of Arithmetic; 2.4 Frege's Derivation of the Axioms of Arithmetic, continued; 2.5 An Elegant Proof that Every Number has a Successor; 2.6 Frege's Axiomatization of Arithmetic; 2.7 Closing.
|
|
|
:
|
12 A Logic for Frege's Theorem12.1 Predecession; 12.2 Ancestral Logic; 12.3 Schemata in Schematic Logic: A Digression; 12.4 Arché Logic; 12.5 Frege's Theorem; 12.6 Philosophical Considerations; Appendix: Proof of Begriffsschrift, Proposition 124; Bibliography; Index; A; B; C; D; E; F; G; H; I; K; L; M; N; P; Q; R; S; T; U; V; W.
|
|
|
:
|
5.3 The Caesar Problem and the Apprehension of Logical Objects5.4 Closing; 6 The Julius Caesar Objection; 6.1 Why the Caesar Objection Has To Be Taken Seriously; 6.2 The Caesar Objection and the Feasibility of the Logicist Project; 6.3 Avoiding the Caesar Objection; 6.4 Closing; 7 Cardinality, Counting, and Equinumerosity; 7.1 Technical Preliminaries; 7.2 Frege and Husserl; 7.3 Counting and Cardinality; 7.4 Counting and Ascriptions of Number; 7.5 Closing; 8 Syntactic Reductionism; 8.1 Motivating Nominalism; 8.2 Taking Reductionism Seriously.
|
|
|
:
|
8.3 The Ineliminability of Names of Abstract Objects8.4 Where Do We Go From Here?; 9 The Existence (and Non-existence) of Abstract Objects; 9.1 Two Problems; 9.2 Semantic Reductionism and Projectible Predicates; 9.3 Ideology, Existence, and Abstract Objects; 9.4 The Julius Caesar Problem; 10 On the Consistency of Second-order Contextual Definitions; Postscript; 11 Finitude and Hume's Principle; 11.1 The Systems; 11.2 On the Philosophical Significance of These Results; 11.3 The Relative Strengths of the Systems; 11.4 PAF is equivalent to FAF; 11.5 Closing; Postscript.
|
|
|
:
|
Postscript3 Die Grundlagen der Arithmetik 82-83; Appendix: Counterparts in Grundgesetze of Some Propositions of Die Grundlagen; Postscript; 4 Frege's Principle; 4.1 Numbers as Extensions of Concepts; 4.2 The Importance of HP in Frege's Philosophy of Arithmetic; 4.3 The Role of Basic Law V in Frege's Derivation of Arithmetic; 4.4 Frege's Derivations of HP; 4.5 HP versus Frege's Principle; 4.6 Frege's Principle and the Explicit Definition; 4.7 The Caesar Problem Revisited; 4.8 Closing; Postscript; 5 Julius Caesar and Basic Law V; 5.1 The Caesar Problem; 5.2 The Caesar Problem in Grundgesetze.
|
| Abstract
|
:
|
Frege's Theorem collects eleven essays by Richard G Heck, Jr, one of the world's leading authorities on Frege's philosophy. The Theorem is the central contribution of Gottlob Frege's formal work on arithmetic. It tells us that the axioms of arithmetic can be derived, purely logically, from a single principle: the number of these things is the same as the number of those things just in case these can be matched up one-to-one with those. But that principle seems so utterlyfundamental to thought about number that it might almost count as a definition of number. If so, Frege's Theorem shows that a.
|
| Subject
|
:
|
Frege, Gottlob,1848-1925.
|
|
|
:
|
Frege, Gottlob,1848-1925.
|
| Subject
|
:
|
Arithmetic-- Philosophy.
|
| Subject
|
:
|
Logic, Symbolic and mathematical.
|
| Subject
|
:
|
Logic, Symbolic and mathematical.
|
| Subject
|
:
|
PHILOSOPHY-- History Surveys-- General.
|
| Subject
|
:
|
PHILOSOPHY-- History Surveys-- Modern.
|
| Dewey Classification
|
:
|
190513.01
|
| LC Classification
|
:
|
B29 .A2465 2009
|