◄ Preface

◄ Index

Section 1 ►

Contents

Preface

1 Section 1 : Is Gödel’s Platonist creation through definition valid?

1-01 Gödel’s Theorem V

1-02 Gödel’s reasoning in Theorem V

1-03 Applying Gödel’s reasoning to ‘x+y’

1-04 ‘sum(x, y)’ cannot be directly expressed in S

1-05 Platonist creation through definition

1-06 Formal Number Theory

2 Section 2 : Why did Gödel ignore this reasoning?

2-01 Gödel’s Theorem VI

2-02 Gödel’s Theorem V

2-03 The formula ‘(R, r)’

2-04 ‘(R, r)’ is not provable in S

2-05 ‘(R, r)’ is provable in S

2-06 Gödel’s Theorem V is invalid

2-07 Gödel’s formula ‘(G, g)’

2-08 Gödel’s proof : ‘(G, g)’ is not provable in S

2-09 Gödel’s proof : ‘(~G, g')’ is not provable in S

2-10 In conclusion?

3 Section 3 : Is Mendelson’s use of the Gödel β-function valid?

3-01 Gödel’s Theorem VI

3-02 Mendelson’s version of Gödel’s proof

3-03 Why is this reasoning ignored?

3-04 The inconsistency in S

3-05 Every primitive recursive formula is not expressible formally in a consistent S

3-06 Conclusion : The fallacy in Mendelson’s reasoning

4 Section 4 : Does Gödel’s implicit intuitionist meta-thesis demolish strong AI?

4-01 Gödel’s startling hypothesis

4-02 Significance of Gödel’s hypothesis

4-03 The ‘Liar’ paradox

4-04 The ‘Russell’ paradox

4-05 Creation through definition

4-06 Gödel’s constructive formal system S

4-07 Gödel’s arithmetisation of S

4-08 Gödel’s remarkable insight

4-09 Gödel’s explicit thesis

4-10 Gödel’s implicit intuitionist thesis

4-11 Gödel’s undecidable proposition

4-12 The path Gödel ignored

4-13 Was Gödel wrong?

4-14 ‘sum(x, y)’ cannot be expressed directly in S

4-15 Platonist creation through definition

4-16 Formal Number Theory

4-17 Why did Gödel choose the path he chose?

4-18 Gödel’s Theorems from a wider perspective

4-19 The relative significance of Gödel’s reasoning

4-20 So what does Gödel’s reasoning actually achieve?

4-21 Addressing Platonism : What is Mathematics?

4-22 In conclusion?

References

Roots

Bibliography

Web_links

◄ Index ◄ Title ◄ Preface ▲ Contents Section 1 ► Section 2 ►

Section 3 ► Section 4 ► References ► Roots ► Bibliography ► Web_links ►

◄ Beyond Gödel (2001)

(Updated : 10/11/01 1:57:50 AM by re@alixcomsi.com)