Contents
Preface
* Chapter 1 : Introduction And Terminology
1-01 Introduction
1-02 Terminology : Standard
1-03 Terminology : Non-standard
* Chapter 2 : Every Primitive
Recursive Relation Is Not Expressible Formally
2-01 Introduction
2-02 The fallacy in Gödel’s reasoning
2-02 The fallacy in Gödel’s reasoning
2-03 The primitive recursive function ‘Sb(y : (v, x) )’
2-04 The primitive recursive function ‘xB(y)’
2-05 The primitive recursive function ‘Pr(n)’
2-06 Can Gödel’s proof be salvaged ?
2-07 Conclusions
* Chapter 3 : Every Primitive
Recursive Relation Is Not Decidable
3-01 Introduction
3-02 Gödel’s Theorems V and VI
3-03 Gödel’s
reasoning in Theorem VI
3-04 Implicit assumptions underlying Gödel’s meta-proof of Theorem VI
3-05 Is Q (x, y ) decidable ?
3-06 ‘r' is PROVABLE’ º M ‘r' is not PROVABLE’
3-07 Conclusions
3-08 Alternative Formal Structures
* Chapter 4 : The Significance
Of Gödel Numbering
In Formal Systems
4-01 Introduction
4-02 The symbolic meta-mathematical reasoning in M
4-03 The verbose meta-mathematical reasoning in M
4-04 Conclusions
* Chapter 5 : The Fallacy In Gödel’s Proof Of Undecidability
5-01 Gödel’s
Theorem V
5-02 Gödel’s
reasoning in Theorem V
5-03 A lemma
5-04 Applying Gödel’s
reasoning to x!
5-05 The basis of Gödel’s
induction
5-06 x! is not
expressible constructively
5-07 Gödel’s
reasoning is non-constructive
5-08 The fallacy in Gödel’s
reasoning
5-09 Applicability of Gödel’s Theorem V
5-10 Gödel’s
Theorem VI
5-11 Gödel’s
reasoning in Theorem VI
5-12 The breakdown of Gödel’s
proof
5-13 Conclusions
◄ Index ◄ Title ◄ Copyright ◄ Dedication ◄ Preface ▲ Contents Chapter 1
► Chapter
2 ►
Chapter 3
► Chapter
4 ► Chapter 5 ► References ► Roots
► Bibliography ► Web_links
►
◄ Questioning Gödel’s
Theorems (Dec 2000) ◄ Beyond Gödel
(Oct 2001)
(Updated : 10/18/01 9:48:48 AM by re@alixcomsi.com)