Godel's 2nd theorem ends in paradox

[anne]

Godel's 2nd theorem ends in paradox
Godel's 2nd theorem is about


http://gamahucherpress.yellowgum.com/w ... ODEL5.pdf
"If an axiomatic system can be proven to be consistent and complete from
within itself, then it is inconsistent.”


But we have a paradox

Gödel is using a mathematical system
his theorem says a system cant be proven consistent


THUS A PARADOX

Godel must prove that a system cannot be proven to be consistent based upon the premise that the logic he uses must be consistent . If the logic he uses is not consistent then he cannot make a proof that is consistent. So he must assume that his logic is consistent so he can make a proof of the impossibility of proving a system to be consistent. But if his proof is true then he has proved that the logic he
uses to make the proof must be consistent, but his proof proves that
this cannot be done
THUS A PARADOX

[Logik]

Godel's 2nd theorem ends in paradox
Godel's 2nd theorem is about


http://gamahucherpress.yellowgum.com/w ... ODEL5.pdf
"If an axiomatic system can be proven to be consistent and complete from
within itself, then it is inconsistent.”


But we have a paradox

Gödel is using a mathematical system
his theorem says a system cant be proven consistent


THUS A PARADOX

Godel must prove that a system cannot be proven to be consistent based upon the premise that the logic he uses must be consistent . If the logic he uses is not consistent then he cannot make a proof that is consistent. So he must assume that his logic is consistent so he can make a proof of the impossibility of proving a system to be consistent. But if his proof is true then he has proved that the logic he
uses to make the proof must be consistent, but his proof proves that
this cannot be done
THUS A PARADOX

Down this line of reasoning you will end up with the epistemic problems of criterion and justification and David Hilbert's https://en.wikipedia.org/wiki/Entscheidungsproblem which directly relates to the decidability criterion in logic.

https://en.wikipedia.org/wiki/Decidability_(logic)

IF you value consistency then for any logical system one can ask "Is this system consistent?".
IF you value completeness then for any logical system one can ask "Is this system complete?".

For any "proof" you provide to answer the above one can ask "Is this a valid proof?"
How would you go about justifying the validity of a proof?
How would you go about justifying the truth of any of your premises?

Whichever way you look at it you end up with the Münchhausen trilemma.

Whichever way you look at it you end up a decision problem and thus, it's subject to Turing's halting problem.

We've been thinking about logic wrong for a few millenia...

[Eodnhoj7]

Godel's 2nd theorem ends in paradox
Godel's 2nd theorem is about


http://gamahucherpress.yellowgum.com/w ... ODEL5.pdf
"If an axiomatic system can be proven to be consistent and complete from
within itself, then it is inconsistent.”


But we have a paradox

Gödel is using a mathematical system
his theorem says a system cant be proven consistent


THUS A PARADOX

Godel must prove that a system cannot be proven to be consistent based upon the premise that the logic he uses must be consistent . If the logic he uses is not consistent then he cannot make a proof that is consistent. So he must assume that his logic is consistent so he can make a proof of the impossibility of proving a system to be consistent. But if his proof is true then he has proved that the logic he
uses to make the proof must be consistent, but his proof proves that
this cannot be done
THUS A PARADOX

Down this line of reasoning you will end up with the epistemic problems of criterion and justification and David Hilbert's https://en.wikipedia.org/wiki/Entscheidungsproblem which directly relates to the decidability criterion in logic.

https://en.wikipedia.org/wiki/Decidability_(logic)

IF you value consistency then for any logical system one can ask "Is this system consistent?".
IF you value completeness then for any logical system one can ask "Is this system complete?".

For any "proof" you provide to answer the above one can ask "Is this a valid proof?"
How would you go about justifying the validity of a proof?
How would you go about justifying the truth of any of your premises?

Whichever way you look at it you end up with the Münchhausen trilemma.

Whichever way you look at it you end up a decision problem and thus, it's subject to Turing's halting problem.

We've been thinking about logic wrong for a few millenia...

Again, she is right.

Circularity and regress/progress are criterion as the munchauseen trillema, applied to the muchanusseen trillema results in a contradictory state where all contradictions exist as truth statements.

1. Russell linear based ZFC theory results in Godel's Incompleteness.
2. Godel's completeness requires a progressive linearism.
3. Russell cycles to Godel and Godel progresses to Russel.

They are two sides of the same coin and as both observe number as effectively a point of origin.

Proof is in "the death of philosophy thread" which effectively is the trillema canceling itself out into a truth statement (all axioms are points of origin, exist as linear definition, and are maintained through cycles) with the truth statement in turn following the same contradiction causing it to exist through infinite variation by contradiction acting as a form of logical atomism.