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Aug 30, 2023, 9:07:20 PM8/30/23

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Gödel incompleteness is more aptly construed as the non-sequitur error

in the same way that the conclusion {the Moon orbits the Earth} is not a

logical consequence of the premise {cats are mammals}.

Provability ONLY validates logical consequence. Whenever a conclusion is

not provable from its premises we have the non-sequitur error. This

remains true when the only premises are the axioms of the formal system.

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

in the same way that the conclusion {the Moon orbits the Earth} is not a

logical consequence of the premise {cats are mammals}.

Provability ONLY validates logical consequence. Whenever a conclusion is

not provable from its premises we have the non-sequitur error. This

remains true when the only premises are the axioms of the formal system.

--

Copyright 2023 Olcott "Talent hits a target no one else can hit; Genius

hits a target no one else can see." Arthur Schopenhauer

Aug 30, 2023, 9:22:19 PM8/30/23

to

On 8/30/23 9:07 PM, olcott wrote:

> Gödel incompleteness is more aptly construed as the non-sequitur error

> in the same way that the conclusion {the Moon orbits the Earth} is not a

> logical consequence of the premise {cats are mammals}.

>

> Provability ONLY validates logical consequence. Whenever a conclusion is

> not provable from its premises we have the non-sequitur error. This

> remains true when the only premises are the axioms of the formal system.

>

>

What is "non-squitur" about it?
> Gödel incompleteness is more aptly construed as the non-sequitur error

> in the same way that the conclusion {the Moon orbits the Earth} is not a

> logical consequence of the premise {cats are mammals}.

>

> Provability ONLY validates logical consequence. Whenever a conclusion is

> not provable from its premises we have the non-sequitur error. This

> remains true when the only premises are the axioms of the formal system.

>

>

Do you enen understand what you are saying?

What doesn't follow?

You don't seem to understand how logic works.

The statment of G in F is TRUE, as has been proven in Meta-F, which has

been constructed in a manner that statements shown to be true in Meta-F

that don't contain any references to things that only exist in Meta-F

(and G doesn't contain such a reference) are also true in F.

The statement G has also been proven (with logic Meta-F) to not be

provable in F.

Thus G is proven to be an example of a statement True in F, and not

provable in F.

The Definition of "completness" for a logic system is that ALL True

statements in the system are provable, and a system is Incomplete if

there exists a True statement that is not provable.

Since G meets that criteria, F is not complete.

The proof applies to ALL system with sufficient axioms to provide the

needed basics of Natural Numbers, thus all such system are, by

necessity, and so proven, to be incomplete.

Your denial just shows your ignorance.

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