Preface

Index

Section 1

 

Contents

Preface

1†† Section 1 : Is GŲdelís Platonist creation through definition valid?

 

††††††††††† 1-01†† GŲdelís Theorem V

††††††††††† 1-02†† GŲdelís reasoning in Theorem V

††††††††††† 1-03†† Applying GŲdelís reasoning to Ďx+yí

††††††††††† 1-04†† Ďsum(x, y)í cannot be directly expressed in S

††††††††††† 1-05†† Platonist creation through definition

††††††††††† 1-06†† Formal Number Theory

2†† Section 2 : Why did GŲdel ignore this reasoning?

 

††††††††††† 2-01†† GŲdelís Theorem VI

††††††††††† 2-02†† GŲdelís Theorem V

††††††††††† 2-03†† The formula Ď(R, r

††††††††††† 2-04†† Ď(R, r)í is not provable in S

††††††††††† 2-05†† Ď(R, r)í is provable in S

††††††††††† 2-06†† GŲdelís Theorem V is invalid

††††††††††† 2-07†† GŲdelís formula Ď(G, g

††††††††††† 2-08†† GŲdelís proof : Ď(G, g)í is not provable in S

††††††††††† 2-09†† GŲdelís proof : Ď(~G, g')í is not provable in S

††††††††††† 2-10†† In conclusion?

3††††† Section 3 : Is Mendelsonís use of the GŲdel β-function valid?

 

††††††††††† 3-01†† GŲdelís Theorem VI

††††††††††† 3-02†† Mendelsonís version of GŲdelís 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 Mendelsonís reasoning

4††††† Section 4 : Does GŲdelís implicit intuitionist meta-thesis demolish strong AI?

 

††††††††††† 4-01†† GŲdelís startling hypothesis

††††††††††† 4-02†† Significance of GŲdelís hypothesis

††††††††††† 4-03†† The ĎLiarí paradox

††††††††††† 4-04†† The ĎRussellí paradox

††††††††††† 4-05†† Creation through definition

††††††††††† 4-06†† GŲdelís constructive formal system S

††††††††††† 4-07†† GŲdelís arithmetisation of S

††††††††††† 4-08†† GŲdelís remarkable insight

††††††††††† 4-09†† GŲdelís explicit thesis

††††††††††† 4-10†† GŲdelís implicit intuitionist thesis

††††††††††† 4-11†† GŲdelís undecidable proposition

††††††††††† 4-12†† The path GŲdel ignored

††††††††††† 4-13†† Was GŲdel wrong?

††††††††††† 4-14†† Ďsum(x, y)í cannot be expressed directly in S

††††††††††† 4-15†† Platonist creation through definition

††††††††††† 4-16†† Formal Number Theory

††††††††††† 4-17†† Why did GŲdel choose the path he chose?

††††††††††† 4-18†† GŲdelís Theorems from a wider perspective

††††††††††† 4-19†† The relative significance of GŲdelís reasoning

††††††††††† 4-20†† So what does GŲdelís 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 GŲdel (2001)

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