questfortruth
Well-Known Member
Demonstrated in an alternative way, that the Theorems of Gödel are true, and hold not only for some special mathematical problems but in general (for any kind of statement in any kind of system/situation). As applications: Hilbert’s Second Problem Solved. Agnosticism is solved. The burden of Disproof is given to atheists. Andrew Wiles’s proof of Fermat’s Last Theorem (which is a hypothesis) uses unproven hypothesis-es of set theory (not the axioms of set theory), thus, the proof is debunked.
Proof of the Second Incompleteness Theorem
The set of axioms produces statements. Some are decidable, some are undecidable. To prove in full range the consistency of mathematics is to prove the validity of all statements, including undecidable ones. Latter to do is impossible by definition. Thus, it is not possible to prove, that mathematics is consistent.
Another way to prove the Gödel’s Second Theorem:
The axioms are defined not as assumptions, but as undecidable but obvious things. Indeed, some axioms can be logically demonstrated [thus, gaining the status of theorems or facts].
More in the viXra:
Wiles Has not Proven the Fermat’s Last Theorem, viXra.org e-Print archive, viXra:2005.0209
Proof of the Second Incompleteness Theorem
The set of axioms produces statements. Some are decidable, some are undecidable. To prove in full range the consistency of mathematics is to prove the validity of all statements, including undecidable ones. Latter to do is impossible by definition. Thus, it is not possible to prove, that mathematics is consistent.
Another way to prove the Gödel’s Second Theorem:
- Axioms are defined as undecidable things.
- Such things are true.
- Thus, axioms are true, and, thus, the set of axioms are without self-contradiction, i.e. consistent.
The axioms are defined not as assumptions, but as undecidable but obvious things. Indeed, some axioms can be logically demonstrated [thus, gaining the status of theorems or facts].
More in the viXra:
Wiles Has not Proven the Fermat’s Last Theorem, viXra.org e-Print archive, viXra:2005.0209
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