Deeper than primes

[The Man]

If yis an axiom of X, then Gödel’s incompleteness theorems have no case.

There are axiomatic circumstances where “Gödel’s incompleteness theorems have no case”.

Would you like to guess where your notions fit among them?

Gödel’s incompleteness theorems have a case exactly because y is a true theorem by the axioms of X that cannot be proved or disproved (it is undecidable by the axioms of X, and we permanently have to extend X in order to deal with y theorem.

Nope.

As a result we get a consistent AND incomplete deductive framework, and this is exactly the result of Gödel’s incompleteness theorems, which you don’t grasp.

As usual, most people grasp it better than you.

Again the rest of your replies are of the same “quality”.

So far still better than the quality of your replies.

It is true if Membership is between elements of a set.

Who said anything about “between”? I think we continue to come upon this language barrier Doron and although I generally understand how different words in other languages might have exactly the same meaning in yours, that does not infer exactly the same meaning in those other languages.

It is not true if Membership is between atoms, and atoms are independent of each other, yet together they define a complex.

Again with the “between”. The word used was “share” and they do share membership otherwise they are simply not both, well, members.

ETA line : Are you now claiming that your “Independent Membership” does not share that, well, independence?

Again your weak reasoning can't get Independent Membership, and the rest of your post is based on this inability.

Your weak notions have meaning only for you and all of your posts are based on your inability to understand that.

No The Man, it is simple and therefore profound.

More conflation Doron?

Your use of “simply trivial” clearly demonstrates that you do not understand the fundamental difference between “Simple” and “Trivial”.

Your continually inconsistent assertions clearly demonstrate that you just are not serious about developing your notions.

And because you do not get this difference then your ill reasoning actually enables (1-D AND 0-D) to be 0-D in
the case of 0.999...[base 10]=1.000...

Obviously you still do not understand what dimension means.

Say no more.

You first.

 

[doronshadmi]

Are you now claiming that your “Independent Membership” does not share that, well, independence?

Again your local-only reasoning rising its limited head.

You simply can't get the idea of independent building-blocks that are gathered into a complex by Membership, where what enables that membership is the common properly of being atoms (no one of the bulling-blocks is an element of the other, under Membership).

As for “between” since you are unable to get Non-locality you are unenable to get “between” as simultaneous (common state) of different IDs, that are independent under “share” .

EDIT:

Your inability to get "Independent Membership" is equivalent to your inability to understand "Mutually Independent", where axioms that share the same framework are not derived from each other (they are mutually independent, where “mutual”=”share” and “do not derived from each other” = “independent”).

 

[jsfisher]

If yis an axiom of X, then Gödel’s incompleteness theorems have no case.

Absolute nonsense. You just drew a line and some circles, then said "See? See!" Gödel, on the other hand, actually proved something, building a case from the ground up.

Gödel’s incompleteness theorems have a case exactly because y is a true theorem by the axioms of X that cannot be proved or disproved (it is undecidable by the axioms of X, and we permanently have to extend X in order to deal with y theorem.

More nonsense. The Incompleteness Theorem doesn't require any extensions to any axiom set.

By the way, please stop with the phrase, true theorem. It is redundant.

As a result we get a consistent AND incomplete deductive framework, and this is exactly the result of Gödel’s incompleteness theorems, which you don’t grasp.

Project much? You picture of circles and a line doesn't establish a framework, let alone one that is consistent and incomplete. Moreover, the Incompleteness Theorem doesn't establish anything as consistent and incomplete, which you don't grasp.



You seem to be ducking my question about R_q(q), too. Why is that?

 

[jsfisher]

Your inability to get....

You make up words, don't tell anyone what they mean, then blame them for not understanding your gibberish. And you wonder why everyone laughs at you.

 

[zooterkin]

Do you understand that (1-D AND 0-D), which is a complex, cannot be only 1-D (which is an atom or building-block), or only 0-D (which is an atom or building-block)?

If you logically understand it, then the understanding that no amount of (1-D AND 0-D) complexities is 1-D or 0-D, is logically inevitable.

Have you got wheels on those goalposts?

 

[doronshadmi]

You seem to be ducking my question about R_q(q), too. Why is that?

If one (you, for example) thinks that un-decidable (cannot be proved of disproved) refers to some axiom of system X, then there is no use to reply to him, simply because the need of proof is clearly not related to axioms, but only to theorems.

Your supporting of The Man nonsense about this case, clearly mark you as an ignorant of Gödel’s incompleteness theorems.

There is no need to reply about X to an ignorant of X.

More nonsense. The Incompleteness Theorem doesn't require any extensions to any axiom set.

It is a consequence of these theorems and not a formal part of the theorems, but you can’t get it, do you jsfisher?

You also unable to get the symmetry between infinite extrapolation\interpolation that is based on the inability of (n-dim AND k-dim) to be only n-dim or only k-dim.

the Incompleteness Theorem doesn't establish anything as consistent and incomplete,

Axiomatic systems that are strong enough to deal with Arithmetic, cannot be consistent AND complete.

So, in order to save Consistency, such strong systems must be incomplete in order to be considered as consistent frameworks.

In other words, they are consistent AND incomplete.

 

[doronshadmi]

Have you got wheels on those goalposts?

What do you mean?

 

[zooterkin]

What do you mean?

If you don't get it, I don't think I can help you.

 

[doronshadmi]

Membership is entirely dependent on how one defines what constitutes (and thus does not constitute) a member.

Good. In the case of Independent Membership, the member is the shared property of the considered elements, and in the case of atoms’ Membership, the shared property is the absence of building-blocks.

Your inability to get your own words, in this case, is clearly seen in http://www.internationalskeptics.com/forums/showpost.php?p=5299295&postcount=6742.

There are axiomatic circumstances where “Gödel’s incompleteness theorems have no case”.

Would you like to guess where your notions fit among them?

Yes, the case that one claims that y is an axiom.

 

[dafydd]

Why, are you the Messiah of non paradigm-shifts?

?????????

 

[doronshadmi]

If you don't get it, I don't think I can help you.

Ya, I can't help you to get http://www.internationalskeptics.com/forums/showpost.php?p=5299131&postcount=6739.

 

[jsfisher]

...irrelevant straw man snipped...

Surely you can say something about R_q(q), can't you? No?


By the way, Doron, why do you even accept any of Gödel's proofs? They all rely on that upside-down A quantifier that you so ignorantly reject. His proofs can't be worth anything if they're riddled with "for all", now can they?

Also, Gödel clear rejects all your stuff. He insists the formal statement, A and not A, cannot be a theorem in a consistent system.

So, Doron, why do you keep referencing a brilliant mathematician like Gödel when he contradicts everything you stand for?

 

[jsfisher]

Axiomatic systems that are strong enough to deal with Arithmetic, cannot be consistent AND complete.

So, in order to save Consistency, such strong systems must be incomplete in order to be considered as consistent frameworks.

In other words, they are consistent AND incomplete.

No, Doron. That is a very stupid conclusion.

Arithmetic (and any formal system large enough to include arithmetic) cannot be both consistent and complete. That's pretty much all Gödel has to say on the subject of incompleteness.

What you choose to consider arithmetic to be is irrelevant.

It may be consistent or it may not. We don't know, and we have no way to tell other than eventually discovering some inconsistency (were there to be one).

 

[doronshadmi]

No, Doron. That is a very stupid conclusion.

Arithmetic (and any formal system large enough to include arithmetic) cannot be both consistent and complete. That's pretty much all Gödel has to say on the subject of incompleteness.

What you choose to consider arithmetic to be is irrelevant.

It may be consistent or it may not. We don't know, and we have no way to tell other than eventually discovering some inconsistency (were there to be one).

What you say is wrong, because if X is strong enough to include arithmetic and X is consistent, then X must be also incomplete.

 

[doronshadmi]

By the way, Doron, why do you even accept any of Gödel's proofs? They all rely on that upside-down A quantifier that you so ignorantly reject. His proofs can't be worth anything if they're riddled with "for all", now can they?

You still do not get it.

Gödel had to choose between Completeness and Consistency of strong systems because by Standard Math strong systems that are also complete can prove anything as true including A and its negation (exactly because "for all" quantifier).

So by Stndard Math strong systems must be incomplete in order to save their consistency.

OM gets the same conclusion form a novel point of view, which says that the very nature of consistent strong systems is their incompleteness, and this novel idea is based on the nature of Non-locality, in addition to Locality, which is not in the scope of Gödel’s work on this subject exactly because by using Non-locality we show (http://www.internationalskeptics.com/forums/showpost.php?p=5289082&postcount=6704) that "for all" quantifier does not hold in strong systems.

Gödel had to choose between Consistency and Completeness under the standard notion.

On the contrary OM shows that if X is a strong system and Consistent, then its very nature is to be Consistent AND Incomplete.

jsfisher, you see only the standard formal form and miss the notion, which is not limited to your local-only formalism.

 

[dafydd]

You still do not get it.

Gödel had to choose between Completeness and Consistency of strong systems because by Standard Math strong systems that are also complete can prove anything as true including A and its negation.

So by Stndard Math strong systems must be incomplete in order to save their consistency.

OM gets the same conclusion form a novel point of view, which says that the very nature of consistent strong system is their incompleteness, and this novel idea is based on the nature of Non-locality, in addition to Locality, which is not in the scope of Gödel’s work on this subject.

Gödel had to choose between Consistency and Completeness under the standard notion.

jsfisher, you see only the standard formal form and miss the notion, which is not limited to your local-only formalism.

On the contrary OM shows that if X is a strong system and Consistent, then its very nature is to be Consistent AND Incomplete.

Are you feeling alright?

 

[doronshadmi]

Are you feeling alright?

I am feeling alright even if I am alleft.

 

[laca]

I am feeling alright even if I am alleft.

Alleft? Is that some new mental condition that only you have? Would explain a lot...

 

[Skeptic]

(Sigh)

Like many people, Doron, when first encountering higher mathematics, got confused and did not understand certain concepts (such as that of a set, or a limit).

Most people either eventually understand after putting effort into it, or give up and decide math is not for them (a pity, but never mind.)

No so Doron. Like most cranks, he jumped to the conclusion that since he didn't understand something taught in first-year math courses, the only possible reason is that everybody else is wrong, that all of modern mathematics is based on flawed premises, and that everybody who disagrees is part of a giant conspiracy of mathematicians to hide the truth.

 

[The Man]

Again your local-only reasoning rising its limited head.

Again simply a result of your loco-only reasoning.

You simply can't get the idea of independent building-blocks that are gathered into a complex by Membership, where what enables that membership is the common properly of being atoms (no one of the bulling-blocks is an element of the other, under Membership).


As for “between” since you are unable to get Non-locality you are unenable to get “between” as simultaneous (common state) of different IDs, that are independent under “share” .

You simply can not understand that if your “membership is the common properly of being atoms” then your atoms are dependent on that “common properly” for that “membership”.

EDIT:

Your inability to get "Independent Membership" is equivalent to your inability to understand "Mutually Independent", where axioms that share the same framework are not derived from each other (they are mutually independent, where “mutual”=”share” and “do not derived from each other” = “independent”).

So you do claim they share that independence exactly as I said. “Mutually Independent” is dependent on that independence being, well, mutual. “Independent Membership” infers that their membership is independent and thus not dependent on the other one being also a member or that membership not being mutual.