Deeper than primes

[The Man]

"False under X" is a direct result of your Local-only reasoning.

No it is just a direct result of the negation of your statement “True under X”. You might actually know that if not for your Loco-only reasoning.

By using also Non-local reasoning y is a true statment under axiomatic system X (it belongs to X) but axiomatic system X is too weak in order to prove it, because y is also beyond axiomatic system X (it also does not belong to X).

You still haven’t learned what axiomatic means yet, but of course that is obvious and self-evident.

Your Local-only reasoning is too weak, The Man.

Your Loco-only reasoning is just self-contradictory, Doron.

Once again you clearly show above that you are simply using self-inconsistent criteria for your “belongs to X” as well as your “does not belong to X” ascription. As opposed to the self consistency of criteria for “belongs to X” along with its negation for “does not belong to X”. As usual your problem is that you simply can not make up your mind what your notions are.


On the one hand you claim that “it belongs to X” because it is an axiom of that system. Conversely the very same principle that makes it an axiom of that system, that it requires no or is accepted without poof under the system, is your stated reason for claiming it “does not belong to X”. As I have said before you are unlikely to get anyone to agree with your notions until you can at least demonstrate that you agree with yourself within your own notions.

Changing names does not help you to understand what you read.

Writing nonsense does not help you to demonstrate that you have any clue what you are talking about.

 

[doronshadmi]

Once again you clearly show above that you are simply using self-inconsistent criteria for your “belongs to X” as well as your “does not belong to X” ascription. As opposed to the self consistency of criteria for “belongs to X” along with its negation for “does not belong to X”. As usual your problem is that you simply can not make up your mind what your notions are.

No The Man, you take a local reasoning where (y belongs to X) XOR (y does not belong to X) is consistent, and (y belongs to X) AND (y does not belong to X) is non-consistent, and force it on non-local reasoning, where (y belongs to X) AND (y does not belong to X) is consistent, and (y belongs to X) XOR (y does not belong to X) is non-consistent.

You simply can’t get it all along this thread, because you are closed under Locality and can’t get any reasoning beyond it.

On the one hand you claim that “it belongs to X” because it is an axiom of that system.

y is not an axiom of X, but is a true statement that is derived from the axioms of X, but cannot be proved by the axioms of X.

Again, you show your fundamental misunderstanding of what you read, so instead of using your energy in order to “invent” poor names to my system in order to cover your misunderstanding of it, try to get it.

 

[doronshadmi]

No, the axiom is based on a wrong notion, which is something that you do not get from your mechanic-formal training.

Forcing wrong notion, does not make some determination an axiom.

 

[doronshadmi]

In addition to post http://www.internationalskeptics.com/forums/showpost.php?p=5288525&postcount=6702 here is a diagram that shows how y statement is true under axiomatic system X (or any extension of it) but it is unproved by X (or any extension of it) because it is also does not belong to X (or any extension of X):

Infinitely many X extensions cannot prove y.

y is not any particular statement, but it is used here to generally demonstrate the inability of axiomatic systems, which are strong enough to deal with arithmetic, to fully capture (to prove) y.

In other words, y is non-local (belongs AND does not belong) w.r.t X.

 

[The Man]

No The Man, you take a local reasoning where (y belongs to X) XOR (y does not belong to X) is consistent, and (y belongs to X) AND (y does not belong to X) is non-consistent, and force it on non-local reasoning, where (y belongs to X) AND (y does not belong to X) is consistent, and (y belongs to X) XOR (y does not belong to X) is non-consistent.

No Doron, it is just the result of non-loco reasoning. You simply try to force your loco-only reasoning on everything and everyone else

You simply can’t get it all along this thread, because you are closed under Locality and can’t get any reasoning beyond it.

Once again Doron, you simply labeling your self-contradictory assertions as “non-local reasoning” does not magically make them any less (or more) than just your self-contradictory assertions.

y is not an axiom of X, but is a true statement that is derived from the axioms of X, but cannot be proved by the axioms of X.

Again with the self contradictions Doron? “a true statement that is derived from the axioms of X” is provable as true “by the axioms of X” (that is how it is “derived” as true “from the axioms of X”). Your only argument about the general validity of “y” then only stems from the axiomatic nature of “X” in that those axioms of “X” from which “y” can be derived and proven as true within are themselves not proven or considered to require no proof within “X” (which is of course what makes them axioms of “X” and “X” an axiomatic system in the first place). Once again you are unlikely to get anyone to seriously consider your arguments or notions unless you first demonstrate that you are seriously considering your arguments or notions.

Again, you show your fundamental misunderstanding of what you read,

Again you show your fundamental misunderstanding of, well, everything that you write about.

so instead of using your energy in order to “invent” poor names to my system in order to cover your misunderstanding of it,

It is not a name of your “system”, Doron (that name was given before as Capricious References Annunciating Pomposity or C.R.A.P.). It is just an accurately descriptive term of your reasoning processes which covers your misunderstanding of your own “system”.

try to get it.

You first.

 

[jsfisher]

In other words, y is non-local (belongs AND does not belong) w.r.t X.

Apparently "non-local" can be understood in terms of belonging. Unfortunately, your diagrams, Doron, much like your analogies tend towards the vacuous. It suggests intersection of Y with X, but no sense of a belonging (or conversely, not belonging) relationship between the two.

Doron, please be so kind as to define your term, belong.

 

[Little 10 Toes]

http://www.internationalskeptics.com/forums/showpost.php?p=5283576&postcount=6686

First of all, that post does not even have the word dimension in it.

Let n=1 to ∞ and let k=0 to n-1, where n or k are atoms (they are existing AND empty things, exactly as {} is an existing AND empty thing).

Definition1: Given n it belongs NXOR does not belong to k.

Definition 2: Given k it belongs XOR does not belong to n.

Since n or k are atoms, they are not elements of each other, such that they are independent under Membership.

Independent Membership enables the existence of atoms as building-blocks of some complex, where a complex is the result n AND k atoms (no complex is only n or only k).

Since you have defined n and k as numbers I can chose n = 99 and k = 0. That fulfills your requirements. But then you declare that they are atoms. So atoms mean the same as urelements (alt. spelling is ur-elements).

Wikipedia describes urelements^WP: In set theory, a branch of mathematics, an urelement or ur-element (from the German prefix ur-, 'primordial') is an object (concrete or abstract) which is not a set, but that may be an element of a set. Urelements are sometimes called "atoms" or "individuals."

This destroys your claim of n belonging to k and k belonging to n. It also makes the term "Independent Membership" and "complex" meaningless since your ideas are based on the sets of n and k, which you already have defined as urelements and therefore not sets.

http://en.wikipedia.org/wiki/Atom_(disambiguation): Atom, a Ur-element in set theory

 

[doronshadmi]

This destroys your claim of n belonging to k and k belonging to n. It also makes the term "Independent Membership" and "complex" meaningless since your ideas are based on the sets of n and k, which you already have defined as urelements and therefore not sets.

http://en.wikipedia.org/wiki/Atom_(disambiguation): Atom, a Ur-element in set theory

No, Independent Membership is a novel notion that holds between atoms, where atoms are existing AND empty things.

The result of the Independent Membership is a complex, where a complex is (Atom-A AND atom-B), such that the Atom-B property of (Atom-A AND atom-B) prevents from (Atom-A AND atom-B) to be only Atom-A, and Atom-A property of (Atom-A AND atom-B) prevents from (Atom-A AND atom-B) to be only Atom-B.

You will not find this novel notion in wikipedia, because wikipedia deals with already agreed things.

Do not try to find the key in order to get OM under the already agreed street light.

In order to get OM you have to go beyond the already agreed, and this is the essence of a paradigm-shift, which in this case is inevitable.

The Man and jsfisher and The Man do not make the inevitable step to OM, and as a result they are not there and stay closed under the current paradigm, which is too weak in order to get OM’s reasoning.

Their failure to get OM is spread all along this thread.

 

[doronshadmi]

Apparently "non-local" can be understood in terms of belonging. Unfortunately, your diagrams, Doron, much like your analogies tend towards the vacuous. It suggests intersection of Y with X, but no sense of a belonging (or conversely, not belonging) relationship between the two.

Doron, please be so kind as to define your term, belong.

Again "y statment belongs AND does not belong to X" is the exact proprty of the non-locality of y w.r.t to X (or any X extension).

Your Local-only reasoning is to weak in order to deal with y.

 

[doronshadmi]

“y” can be derived and proven as true within are themselves not proven or considered to require no proof within “X” (which is of course what makes them axioms of “X”

Thank you for providing the information, which clearly shows that you do not understand Gödel’s incompleteness theorems.

The rest of your post is of the same “quality”.

 

[doronshadmi]

Here is a part of Gödel’s paper (the end of page 3) http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf :

From the remark that Rq(q) states its own improvability it immediately follows that Rq(q) is correct, since Rq(q) is in fact unprovable (because it is undecidable). The theorem which is undecidable within the system PM has hence been decided by metamathematical considerations. The exact analysis of this strange fact leads to surprising results about consistency proofs for formal systems, which will be discussed in section 4 (theorem XI).

Only an ignorant of Godel's incompleteness theorems, thinks that y (which is a theorem of X) is an axiom of X.

 

[jsfisher]

Apparently "non-local" can be understood in terms of belonging. Unfortunately, your diagrams, Doron, much like your analogies tend towards the vacuous. It suggests intersection of Y with X, but no sense of a belonging (or conversely, not belonging) relationship between the two.

Doron, please be so kind as to define your term, belong.

Again "y statment belongs AND does not belong to X" is the exact proprty of the non-locality of y w.r.t to X (or any X extension).

Your Local-only reasoning is to weak in order to deal with y.

Doron, I know my post was very long, so that must be why you completely missed the question I was asking. For your convenience, I have high-lighted it. Please respond to the question.

 

[doronshadmi]

Doron, I know my post was very long, so that must be why you completely missed the question I was asking. For your convenience, I have high-lighted it. Please respond to the question.

Pealse see http://www.scribd.com/doc/22312161/...s-Various-Degrees-of-the-Numbers’-Distinction pages 4-5.

"Belong" between atoms is a membership between A and B such that A or B are not building-blocks of each other (nevertheless the result is a complex).

EDIT:

If they share a common proprty, then they belong to each other by this common proprty without derived from each other.

Atoms (which are existing things) have a common property, called the absence of building-blocks.

In that case they are independent of each other, such that if atom X belongs XOR does not belong to Atom Y then atom X is local w.r.t atom Y.

Also if atom X belongs NXOR does not belong to atom Y then atom X is non-local w.r.t atom Y.

 

[doronshadmi]

The result of the membership between atoms is a complex, such that no complex is an atom.

Standard Math's membership is the local-only version where X belongs XOR does not belong to Y.

 

[The Man]

Thank you for providing the information, which clearly shows that you do not understand Gödel’s incompleteness theorems.

The rest of your post is of the same “quality”.

Try actually reading the whole sentence instead of just the part you quoted. Just to try and give you a clue “y” is referred to in the singular and the “axioms of “X”’ in the plural in that sentence.

Your only argument about the general validity of “y” then only stems from the axiomatic nature of “X” in that those axioms of “X” from which “y” can be derived and proven as true within are themselves not proven or considered to require no proof within “X” (which is of course what makes them axioms of “X” and “X” an axiomatic system in the first place).

Here is a part of Gödel’s paper (the end of page 3) http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf :


Only an ignorant of Godel's incompleteness theorems, thinks that y (which is a theorem of X) is an axiom of X.

Doron, deliberately truncating the statements of others that you quote to simply affirm your own ignorance of what was written, will still just convince people that you are not serious about your arguments and notions.

 

[jsfisher]

"Belong" between atoms is a membership between A and B such that A or B are not building-blocks of each other (nevertheless the result is a complex).

Ok, so non-local is based on belong, and belong is based on membership. However, since it is membership between atoms, this is not the normal set membership. So, Doron, all you have done is jumped from one term to the next without defining anything. Well done!

Unfortunately, that leaves your terms as still meaning nothing. Is that really what you wanted? Is it really all that hard to given some semblance of meaning to any of your words?

 

[Nonpareil]

Why is this thread not dead yet?

Doron, again, go take your theory to the professional mathematicians out there. If you're correct, they'll back you up, and you can come back and laugh at everyone here.

 

[jsfisher]

Here is a part of Gödel’s paper (the end of page 3) http://www.research.ibm.com/people/h/hirzel/papers/canon00-goedel.pdf :

From the remark that Rq(q) states its own improvability it immediately follows that Rq(q) is correct, since Rq(q) is in fact unprovable (because it is undecidable). The theorem which is undecidable within the system PM has hence been decided by metamathematical considerations. The exact analysis of this strange fact leads to surprising results about consistency proofs for formal systems, which will be discussed in section 4 (theorem XI).

Only an ignorant of Godel's incompleteness theorems, thinks that y (which is a theorem of X) is an axiom of X.

Doron, just how do you figure this excerpt relates to anything recently posted in this thread? I wager you can't even explain the significance of R_q(q).

 

[dafydd]

Why is this thread not dead yet?

Doron, again, go take your theory to the professional mathematicians out there. If you're correct, they'll back you up, and you can come back and laugh at everyone here.

What qualifications does Doron have?

 

[Nonpareil]

What qualifications does Doron have?

No idea, but it really doesn't matter. Whether he's a fisherman or a Ph.D., if his theory is correct, then it will be accepted by professional mathematicians. I really see no reason for him to be here, since he's obviously not convincing anyone.