Deeper than primes

[The Man]

Yes. I know that all your makeup-logic gets is trivial.

Since you are unable to get the notion of an atom, you also unable to get the notion of a complex.

Well you’ve apparently got a complex of some kind that much is clear. As dafydd noted before most likely just a Messiah Complex.

An axiomatic framework is a complex; exactly as a ray or a segment are complexities.

For example:

Non-connected points are totally independent (isolated) of each other.

If a point is equivalent to an axiom, than no axiomatic framework exists if each axiom is totally independent (isolated) of the other axioms.

Such “frameworks” are referred to as being independently axiomatizable, but that has already been explained to you.

Also a segment has a line in addition to the endpoints (the axioms), where the line is the connector of the points. This property is the mutual aspect to the segment which is not total connectivity as an endless (edgeless) straight line is.

So an axiomatic framework is not total isolation (only point-like) or total connectivity (only line-like), but it is a complex where this complex is not totally connected (because of the independency of the axioms of each other) and not totally isolated (because of the mutuality (line-like property) that enables the compassion of the axioms with each other.

In other words, any axiomatic framework is a complex, which is at least mutual AND independent.

This beauty is beyond your makeup-logic.

Well thanks again Doron for so clearly demonstrating that you simply do not have a clue to what you are talking about. Again learn the actual concepts you are trying to base your arguments upon or at the very least pay attention when things like an independently axiomatizable “framework” is explained to you.


ETA:

I think part of your problem Doron is that perhaps you still do not understand that all independence is not mutual. To try and explain this to you again, mutual independence refers to A not depending on B and B not depending on A. If A does not depend on B but B depends on A then they are not mutually independent of each other. Now considering “framework” F based on Axioms A, B, C, D and E. The Axioms can be mutually independent of each other. That is E can not be proven from any or all of the remaining axioms A,B,C and D in F. Likewise A can not be proven from any or all of the remaining axioms B,C,D and E in F, so on and so fourth for each of the axioms. Thus the axioms are (in this example) mutual independent of each other and F is then independently axiomatizable. Also the axioms are simply independent of the “framework” F since F can not prove any of those axioms with those axioms and it is technically not F without any of those axioms. However since F is based on those axioms, F is dependent on those axioms (again since it is technically not F without any of those axioms). So the axioms (in this example) are mutually independent of each other and they are independent of the “framework” F, but F and its axioms are not mutually independent of each other, since F is specifically dependent upon those axioms.

 

[Little 10 Toes]

Doronshadmi, is there a reason why you don't answer my questions?

 

[jsfisher]

If you can cite any evidence to contradict my statements, please do so. Knock yourself out.

But you can't, can you? You just make crap up, and you can't even convince yourself that any of your crap is real. Proof is your inability to define anything.

So, instead, you blame everyone else because your notions are a failure.

Very simple:

If it is so simple, why can't you actually cite anything to support your statements? Instead you just make up crap or spew gibberish. Lack of content on your part does not support your case.

Since according to Gödel's incompleteness theorems (and because of the use of "for all" quantifier in strong systems that are able to deal with arithmetic)

Stricken part just more of your lack of understanding of what words mean...

...axiomatic system X cannot be Consistent AND Complete

True so far (except for that stricken part)...

then any mathematician that wishes to works with such strong system like X, has to choose between Consistency and Completeness.

This part, not so true. Mathematicians do not choose what is true and what is not.

Mathematicians working with any system that includes arithmetic understand that arithmetic may not be consistent, and it not, their work may be invalidated.

Most of (if not all) the mathematicians choose Consistency because strong AND complete axiomatic systems can prove A and not-A as true, and we get a non-interesting framework, which is naturally rejected by mathematicians.

I don't these words you used mean what you think they mean. The important point, though, is that mathematicians do not decide consistency based on a simple matter of choice.

 

[doronshadmi]

Evasion noted.

Misunderstanding noted.

If I have two points, are they local or non-local to each other?

Local. please see http://www.scribd.com/doc/21954566/NXOR-XOR page 9.

 

[doronshadmi]

I don't these words you used mean what you think they mean. The important point, though, is that mathematicians do not decide consistency based on a simple matter of choice.

No, you do not understand what you read.

If strong axiomatic system X cannot be both consistent AND complete, then any reasonable mathematician accepts the incompleteness of such a system, in order to save its consistency, simply because complete strong axiomatic systems prove that A AND its negation are both true, which are non-interesting systems.

Mathematicians do not choose what is true and what is not

Mathematicians do choose between the intersting and the non-interesting.

If it is so simple, why can't you actually cite anything to support your statements? Instead you just make up crap or spew gibberish. Lack of content on your part does not support your case.

You are ignorant about the consequences of Godel's incompleteness theorems.

 

[doronshadmi]

Well you’ve apparently got a complex of some kind that much is clear. As dafydd noted before most likely just a Messiah Complex.






Such “frameworks” are referred to as being independently axiomatizable, but that has already been explained to you.



Well thanks again Doron for so clearly demonstrating that you simply do not have a clue to what you are talking about. Again learn the actual concepts you are trying to base your arguments upon or at the very least pay attention when things like an independently axiomatizable “framework” is explained to you.


ETA:

I think part of your problem Doron is that perhaps you still do not understand that all independence is not mutual. To try and explain this to you again, mutual independence refers to A not depending on B and B not depending on A. If A does not depend on B but B depends on A then they are not mutually independent of each other. Now considering “framework” F based on Axioms A, B, C, D and E. The Axioms can be mutually independent of each other. That is E can not be proven from any or all of the remaining axioms A,B,C and D in F. Likewise A can not be proven from any or all of the remaining axioms B,C,D and E in F, so on and so fourth for each of the axioms. Thus the axioms are (in this example) mutual independent of each other and F is then independently axiomatizable. Also the axioms are simply independent of the “framework” F since F can not prove any of those axioms with those axioms and it is technically not F without any of those axioms. However since F is based on those axioms, F is dependent on those axioms (again since it is technically not F without any of those axioms). So the axioms (in this example) are mutually independent of each other and they are independent of the “framework” F, but F and its axioms are not mutually independent of each other, since F is specifically dependent upon those axioms.

From your long post it is clearly shown that you simply unable to get complex (mutuality AND independency) such that the mutuality property of complex (mutuality AND independency) prevents from (mutuality AND independency) to be independency-only, and the independency property of complex (mutuality AND independency) prevents from (mutuality AND independency) to be mutuality-only.

It is all based on your inability to distinguish between complex and atom.

 

[jsfisher]

No, you do not understand what you read.

Project much?

If strong axiomatic system X cannot be both consistent AND complete , then any reasonable mathematician accepts the incompleteness of such a system, in order to save its consistency

You continue to present this as an option for the mathematician. Utter bollocks. Naive Set Theory failed to be consistent, and no amount of choice or acceptance by mathematicians was able to overcome that little defect.

...simply because complete strong axiomatic systems prove that A AND its negation are both true, which are non-interesting systems.

Too bad for you, then, isn't it? Contradiction is the cornerstone of your Doronetics.

 

[The Man]

From your long post it is clearly shown that you simply unable to get complex (mutuality AND independency) such that the mutuality property of complex (mutuality AND independency) prevents from (mutuality AND independency) to be independency-only, and the independency property of complex (mutuality AND independency) prevents from (mutuality AND independency) to be mutuality-only.

It is all based on your inability to distinguish between complex and atom.

From the superfluous repetition in your post it is clearly shown that you are simply going to ignore the fact that your claim…

If a point is equivalent to an axiom, than no axiomatic framework exists if each axiom is totally independent (isolated) of the other axioms.

is utterly and completely wrong.

It is all based on your unwillingness to actually learn the concepts you base your arguments upon and your refusal to apply any semblance of consistency to your notions.

 

[The Man]

…simply because complete strong axiomatic systems prove that A AND its negation are both true, which are non-interesting systems.

Too bad for you, then, isn't it? Contradiction is the cornerstone of your Doronetics.

As I have always said the staunchest opponent to Doron’s notions is Doron himself in expressing his notions.

I choose Non-locality as a fundamental principle of strong axiomatic frameworks, such that there exist y with respect to framework X, such that y belongs (it is true under X) AND does not belong (it is un-provable under X) to X.

So now we have by Doron’s own assertions that his ‘belongs to AND does not belong to’ claim brands his OM “system” as “non-interesting”. Take your time Doron; come back when you actually have something that at least you can claim is interesting.

 

[doronshadmi]

The Man,

OM is non-interesting exactly because you cannot distinguish between atom and complex.

As long as you do not get that difference, your posts do not even scratch OM.

 

[doronshadmi]

Naive Set Theory failed to be consistent, and no amount of choice or acceptance by mathematicians was able to overcome that little defect.

Strong axiomatic theory (which deals with Arithmetic) failes to be consistent (and no amount of choice or acceptance by mathematicians was able to overcome that little defect) if one insists that it is also complete.

 

[zooterkin]

OM is non-interesting exactly because you cannot distinguish between atom and complex.

A rare moment of insight? Though I don't think that's the only reason it's non-interesting.

 

[doronshadmi]

A rare moment of insight? Though I don't think that's the only reason it's non-interesting.

Please provide some details.

 

[doronshadmi]

The Man,

OM is non-interesting exactly because you cannot distinguish between atom and complex.

As long as you do not get that difference, your posts do not even scratch OM.

You also still do not get http://www.scribd.com/doc/16542245/OMPT page 20.

 

[zooterkin]

Please provide some details.

After you.

 

[doronshadmi]

After you.

http://www.internationalskeptics.com/forums/showpost.php?p=5299131&postcount=6739

 

[ddt]

A rare moment of insight? Though I don't think that's the only reason it's non-interesting.

Apparently, according to doron it's so interesting it even has its place in a literature discussion forum (online-literature.com).

 

[jsfisher]

Strong axiomatic theory (which deals with Arithmetic) failes to be consistent (and no amount of choice or acceptance by mathematicians was able to overcome that little defect) if one insists that it is also complete.

First, no one here except you, doron, is insisting The Arithmetic is or is not consistent or that it is or is not complete.

Second, what you insist Mathematics to be is independent of what Mathematics is. As the thread has demonstrated, it is actually generally the exact opposite of what you insist.

 

[doronshadmi]

First, no one here except you, doron, is insisting The Arithmetic is or is not consistent or that it is or is not complete.

Yes I know jsfisher, you refuse to get Gödel’s result about the impossibility of strong axiomatic systems to be both consistent AND complete, according to classical mathematics.

But this is your personal problem, not mine.

Second, what you insist Mathematics to be is independent of what Mathematics is.

There is no fixed object called Mathematics. Anyone that claims such a thing (for example: jsfisher, that clealry takes Math as some fixed object) does not understand the nature of developed science.

 

[The Man]

The Man,

OM is non-interesting exactly because you cannot distinguish between atom and complex.

No Doron, it is “non-interesting exactly because” it is useless, undefined and self contradictory. Even as you yourself note, it claims a proposition and its negation are both true, so it is “non-interesting” just by your own standard.

As long as you do not get that difference, your posts do not even scratch OM.

What ever OM itch you have Doron it is yours to scratch, but you just have to make up your mind where you think that itch is and what think you need to scratch it. Otherwise you’ll just continue scratching the inside of your Arse with your head.