Godels theorem is invalid as his G statement is banned by an axiom of the system he uses to prove his theorem

[anne]

Godels theorem is invalid as his G statement is banned by an axiom of the system he uses to prove his theorem

http://gamahucherpress.yellowgum.com/wp ... GODEL5.pdf

a flaw in theorem Godels sentence G is outlawed by the very axiom he uses to prove his theorem
ie the axiom of reducibiilty AR -thus his proof is invalid


http://www.enotes.com/topic/Axiom_of_reducibility

russells axiom of reducibility was formed such that impredicative statements were banned


but godels uses this AR axiom in his incompleteness proof ie axiom 1v
and formular 40

and as godel states he is useing the logic of PM ie AR

"P is essentially the system obtained by superimposing on the Peano axioms the logic of PM [ ie AR axiom of reducibility]"

now godel constructs an impredicative statement G which AR was meant
to ban

The impredicative statement Godel constructs is
http://en.wikipedia.org/wiki/G%C3%B6del ... theorems#F...

the corresponding Gödel sentence G asserts: G cannot be proved to be true within the theory T

now godels use of AR bans godels G statement

thus godel cannot then go on to give a proof by useing a statement his own axiom bans
but in doing so he invalidates his whole proof

[Logik]

Gödel simply recognised how constructive mathematics works, but he was +-35 years too early to make his proof much simpler than it needs to be.
There are many foundational axioms in intuitionistic logic following Brouwer's footsteps.

Let us not forget that the term "exists" in the context of logic/mathematics simply means "does not contradict any axiom".

https://en.wikipedia.org/wiki/G%C3%B6de ... ical_proof

More precisely, it presupposes the notion of positive and negative properties, and proves the necessary existence of an object which each positive property, but no negative property, applies to.

Let me demonstrate the meaning of the bold text in practice.

Let there be an object such that it has the following positive properties:

1. It has four sides. A, B, C, D.
1.1 Each side is a line: AB, BC, CD, DA
2. Each line has equal length: AB = BC = CD = DA = L

What would you call that object?
Would you say such an object exists?

ANY and all squares fit the criteria above.

Suppose that we defined negative properties:
1. The distance from the centre of the figure (at the intersections of AC and BD) to any point on the perimeter cannot be less than N meters.
e.g AC = BD < 2N

And now we have an exclusionary criterion. This allows us to sort all squares into two categories.

Those which are included by the criterion of AC = BD < 2N e.g where the inequality is valid
Those which are excluded by the criterion of AC = BD < 2N e.g where the inequality is invalid

[Eodnhoj7]

Gödel simply recognised how constructive mathematics works, but he was +-35 years too early to make his proof much simpler than it needs to be.
There are many foundational axioms in intuitionistic logic following Brouwer's footsteps.

Let us not forget that the term "exists" in the context of logic/mathematics simply means "does not contradict any axiom".

https://en.wikipedia.org/wiki/G%C3%B6de ... ical_proof

More precisely, it presupposes the notion of positive and negative properties, and proves the necessary existence of an object which each positive property, but no negative property, applies to.

Let me demonstrate the meaning of the bold text in practice.

Let there be an object such that it has the following positive properties:

1. It has four sides. A, B, C, D.
1.1 Each side is a line: AB, BC, CD, DA
2. Each line has equal length: AB = BC = CD = DA = L

What would you call that object?
Would you say such an object exists?

ANY and all squares fit the criteria above.

Suppose that we defined negative properties:
1. The distance from the centre of the figure (at the intersections of AC and BD) to any point on the perimeter cannot be less than N meters.
e.g AC = BD < 2N

And now we have an exclusionary criterion. This allows us to sort all squares into two categories.

Those which are included by the criterion of AC = BD < 2N e.g where the inequality is valid
Those which are excluded by the criterion of AC = BD < 2N e.g where the inequality is invalid

All axioms are simultaneously thetical and antithetical and Godel fails in taking this into account as an axiom.

The 13 prime directives, I was arguing, already addresses this.

[Logik]

All axioms are simultaneously thetical and antithetical and Godel fails in taking this into account as an axiom.

That they are. Relative to the observer.

Which moves the point if inquiry simply into "what is the meaning of truth?'

When you abolish this distinction in your mind you have arrived at Monism.

[Eodnhoj7]

All axioms are simultaneously thetical and antithetical and Godel fails in taking this into account as an axiom.

That they are. Relative to the observer.

Which moves the point if inquiry simply into "what is the meaning of truth?'

When you abolish this distinction in your mind you have arrived at Monism.

If all axioms are thetical and antithetical, then the central point as neutrality effectively is the centerpoint through "sythesis" or "joining" as a pure axiomatic state.

Monism results in dualism, as monism still necessitates "nonbeing" as a form of approximation synonymous to parmenides and the antithetical atomists. The result is a triadic state mirroring the pythagorean interpretation where "3" is the first number.

All is one and three and three in one.

[Logik]

"3" is the first number.

That's an axiomatic assumption...

You can start there and you will produce valid mathematics.

Or you can start with bounded rationality (all numbers exist between 0 and 1).

You will still end up with valid mathematics.

[Eodnhoj7]

"3" is the first number.

That's an axiomatic assumption...

You can start there and you will produce valid mathematics.

Or you can start with bounded rationality (all numbers exist between 0 and 1).

You will still end up with valid mathematics.

1) All axioms are origin points and as such are 1 in themselves.

2) Bounded rationality is observed on another thread where all fractions/fractals are simultaneously whole numbers/lines in themselves.

3) 1 exists if and only if it progresses to 2.

2 exists if and only if it progresses back to 1 as 3 where 3 is 1 progressing to itself and through itself.

A. 3 exists if it progresses to 1 as 4 and 2 as 5. Etc.

B. 1 in turn progresses to 3 as 4 and 2 progresses to 3 as 5. Etc.

All whole numbers are composed of 3 numbers (1,2,3) as 1 continual line.

All numbers exists as extensions of 1 through (1,2,3) as 3 cycling quantities (see points A and B).

The number line is subject to the fallacy of circularity as that is its premise.

[Logik]

"3" is the first number.

That's an axiomatic assumption...

You can start there and you will produce valid mathematics.

Or you can start with bounded rationality (all numbers exist between 0 and 1).

You will still end up with valid mathematics.

1) All axioms are origin points and as such are 1 in themselves.

2) Bounded rationality is observed on another thread where all fractions/fractals are simultaneously whole numbers/lines in themselves.

3) 1 exists if and only if it progresses to 2.

2 exists if and only if it progresses back to 1 as 3 where 3 is 1 progressing to itself and through itself.

A. 3 exists if it progresses to 1 as 4 and 2 as 5. Etc.

B. 1 in turn progresses to 3 as 4 and 2 progresses to 3 as 5. Etc.

All whole numbers are composed of 3 numbers (1,2,3) as 1 continual line.

All numbers exists as extensions of 1 through (1,2,3) as 3 cycling quantities (see points A and B).

The number line is subject to the fallacy of circularity as that is its premise.

You will reach different conclusions by meta-analysis of your own axioms and their consequences.

Metametaphysics.

But you need to develop the framework first before you can do meta-analysis on it.

[Eodnhoj7]

That's an axiomatic assumption...

You can start there and you will produce valid mathematics.

Or you can start with bounded rationality (all numbers exist between 0 and 1).

You will still end up with valid mathematics.

1) All axioms are origin points and as such are 1 in themselves.

2) Bounded rationality is observed on another thread where all fractions/fractals are simultaneously whole numbers/lines in themselves.

3) 1 exists if and only if it progresses to 2.

2 exists if and only if it progresses back to 1 as 3 where 3 is 1 progressing to itself and through itself.

A. 3 exists if it progresses to 1 as 4 and 2 as 5. Etc.

B. 1 in turn progresses to 3 as 4 and 2 progresses to 3 as 5. Etc.

All whole numbers are composed of 3 numbers (1,2,3) as 1 continual line.

All numbers exists as extensions of 1 through (1,2,3) as 3 cycling quantities (see points A and B).

The number line is subject to the fallacy of circularity as that is its premise.

You will reach different conclusions by meta-analysis of your own axioms and their consequences.

Metametaphysics.

But you need to develop the framework first before you can do meta-analysis on it.

"Death of philosophy thread", general section, point 2.

• All axioms are subject to a progressive variation, including this statement as this statement is an axiom. This statement through points 2 and 3.

• This progressive variation, due to its extra dimensional nature of moving away from an origin axiom, is linearly progressive or regressive relative to a point of origin as a starting point. This statement exists through the first point, above, while existing in accords to it's own nature as stated here and the third point below.

• As a variation of an original axiom, due to its linear progressive/regressive nature, all axioms exist as connected when taking into account progress/regress as simultaneous entities with their individual status as progress and/or regress being relativistic and hence an approximation of the original axiom. This point exists according to its own state while subject to points 1 and 2.

Anyone who understands this section will understand it existing "as is" while being fully rational and irrational.

[Logik]

"Death of philosophy thread", general section, point 2.

• All axioms are subject to a progressive variation, including this statement as this statement is an axiom. This statement through points 2 and 3.

• This progressive variation, due to its extra dimensional nature of moving away from an origin axiom, is linearly progressive or regressive relative to a point of origin as a starting point. This statement exists through the first point, above, while existing in accords to it's own nature as stated here and the third point below.

• As a variation of an original axiom, due to its linear progressive/regressive nature, all axioms exist as connected when taking into account progress/regress as simultaneous entities with their individual status as progress and/or regress being relativistic and hence an approximation of the original axiom. This point exists according to its own state while subject to points 1 and 2.

Anyone who understands this section will understand it existing "as is" while being fully rational and irrational.

I don't know if I can parse all the language, so how about an experiment instead?

What can you predict from the above?

[Eodnhoj7]

"Death of philosophy thread", general section, point 2.

• All axioms are subject to a progressive variation, including this statement as this statement is an axiom. This statement through points 2 and 3.

• This progressive variation, due to its extra dimensional nature of moving away from an origin axiom, is linearly progressive or regressive relative to a point of origin as a starting point. This statement exists through the first point, above, while existing in accords to it's own nature as stated here and the third point below.

• As a variation of an original axiom, due to its linear progressive/regressive nature, all axioms exist as connected when taking into account progress/regress as simultaneous entities with their individual status as progress and/or regress being relativistic and hence an approximation of the original axiom. This point exists according to its own state while subject to points 1 and 2.

Anyone who understands this section will understand it existing "as is" while being fully rational and irrational.

I don't know if I can parse all the language, so how about an experiment instead?

What can you predict from the above?

1. Entropy.
2. Reproductive variation.
3. Branch effect in all abstract and empirical science ranging from schools in philosophy, math, chemistry, language, physics, etc.
4. Number Line.
5. Language Variation through synonyms.
6. Evolution/devolution.
7. Fractals/fractions.
8. Linear Change through time line
9. Chaos theory
10. Personality change over time.
11. Change in axioms of metaphysics/philosophy/sciences.
12. Mental change.
13. Emotional change.
14. Physical change.
15. Variation in empirical object from one moment to the next.
16. Variation in abstract ideal and its interpretation from one moment to the next.
17. Sequences (number line, etc.)
18. This list...

[Logik]

"Death of philosophy thread", general section, point 2.

• All axioms are subject to a progressive variation, including this statement as this statement is an axiom. This statement through points 2 and 3.

• This progressive variation, due to its extra dimensional nature of moving away from an origin axiom, is linearly progressive or regressive relative to a point of origin as a starting point. This statement exists through the first point, above, while existing in accords to it's own nature as stated here and the third point below.

• As a variation of an original axiom, due to its linear progressive/regressive nature, all axioms exist as connected when taking into account progress/regress as simultaneous entities with their individual status as progress and/or regress being relativistic and hence an approximation of the original axiom. This point exists according to its own state while subject to points 1 and 2.

Anyone who understands this section will understand it existing "as is" while being fully rational and irrational.

I don't know if I can parse all the language, so how about an experiment instead?

What can you predict from the above?

1. Entropy.
2. Reproductive variation.
3. Branch effect in all abstract and empirical science ranging from schools in philosophy, math, chemistry, language, physics, etc.
4. Number Line.
5. Language Variation through synonyms.
6. Evolution/devolution.
7. Fractals/fractions.
8. Linear Change through time line
9. Chaos theory
10. Personality change over time.
11. Change in axioms of metaphysics/philosophy/sciences.
12. Mental change.
13. Emotional change.
14. Physical change.
15. Variation in empirical object from one moment to the next.
16. Variation in abstract ideal and its interpretation from one moment to the next.
17. Sequences (number line, etc.)
18. This list...

Well, there's an easy way to test this claim. Coins predict also. They are wrong only 50% of the time.

If your error rate is lower than a coin - then you have a useful hypothesis.

[Eodnhoj7]

I don't know if I can parse all the language, so how about an experiment instead?

What can you predict from the above?

1. Entropy.
2. Reproductive variation.
3. Branch effect in all abstract and empirical science ranging from schools in philosophy, math, chemistry, language, physics, etc.
4. Number Line.
5. Language Variation through synonyms.
6. Evolution/devolution.
7. Fractals/fractions.
8. Linear Change through time line
9. Chaos theory
10. Personality change over time.
11. Change in axioms of metaphysics/philosophy/sciences.
12. Mental change.
13. Emotional change.
14. Physical change.
15. Variation in empirical object from one moment to the next.
16. Variation in abstract ideal and its interpretation from one moment to the next.
17. Sequences (number line, etc.)
18. This list...

Well, there's an easy way to test this claim. Coins predict also. They are wrong only 50% of the time.

If your error rate is lower than a coin - then you have a useful hypothesis.

19. Coin toss.
20. All dualisms in respect to alternating through time.
21. Interpretations of the above perspective.


All axioms as change, necessitates any objective or subjective state inside or outside the observer as subject to variation with this variation, when observed in reverse simultaneously, necessitating an inherent connection of all axioms.

The above law is 100 percent correct, x percent correct and 0 percent correct as it is subject to the same variation. As 0 percent correct it is observed as correct though another set of axioms, such as the examples provided.

[Logik]

19. Coin toss.
20. All dualisms in respect to alternating through time.
21. Interpretations of the above perspective.


All axioms as change, necessitates any objective or subjective state inside or outside the observer as subject to variation with this variation, when observed in reverse simultaneously, necessitating an inherent connection of all axioms.

The above law is 100 percent correct, x percent correct and 0 percent correct as it is subject to the same variation. As 0 percent correct it is observed as correct though another set of axioms, such as the examples provided.

The objective standard you need to exceed is the error rate of a coin toss.

Make a yes/no prediction. Record it. Test/validate it. 10 times
If your error rate is 50% or more - it's just a coincidence.

[Eodnhoj7]

19. Coin toss.
20. All dualisms in respect to alternating through time.
21. Interpretations of the above perspective.


All axioms as change, necessitates any objective or subjective state inside or outside the observer as subject to variation with this variation, when observed in reverse simultaneously, necessitating an inherent connection of all axioms.

The above law is 100 percent correct, x percent correct and 0 percent correct as it is subject to the same variation. As 0 percent correct it is observed as correct though another set of axioms, such as the examples provided.

The objective standard you need to exceed is the error rate of a coin toss.

Make a yes/no prediction. Record it. Test/validate it. 10 times
If your error rate is 50% or more - it's just a coincidence.

Then all dualistic measurements set the foundation for coincidence when changing the number of times over a given course before an even split is observed.

There is no law which necessitates 10 as the number of times without reverting this to 10, then that to ten, and that to ten, etc.