The Man
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Once again you simply misrepresent the notion of Cardinality.
Deeper than primes
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Once again you simply misrepresent the notion of Cardinality.
doronshadmi
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The Man,
Contradiction has two forms:
Form 1: If Y is local w.r.t X then Y (belongs to X) AND (does not belong to X) is a contradiction (and your reasoning is limited only to this form).
The Man said:
Form 2: If Y is non-local w.r.t. X then (Y belongs to X) XOR (does not belong to X) is a contradiction (and this reasoning is beyond your limitation).
So as you see, the existence of domain is relevant to Non-locality, but you can't get it because your reasoning is local-only.
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The Man
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By all reasoning a contradiction is limited to that form, that both the proposition and its negation are considered to be true.
That is not a contradiction in that either the proposition or its negation is considered to be true.
Oh so now your "non-locality" does “care about the existence of any given domain” how consistently contradictory of you.
jsfisher
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No, let's not. Until such time as you can demonstrate any real utility for your word salad with contradictory garnish and complementary inconsistencies, I'm not interested in you repeating yourself.
No matter how much to cycle repeatedly through your nonsense, it gains no functional value.
doronshadmi
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1) If X is an atom, then it is an existing thing that does not include sub-existing things.
2) By (1) X is an existing AND empty thing.
3) By (1) not-X is an existing AND non-empty thing.
4) Sub-existing things are included XOR not-included with respect to not-X, such that not-X has at least one included sub-thing.
5) By (4) sub-existing things are local with respect to not-X.
6) If X is not sub-existing thing with respect to not-X, then X is included AND not-included with respect to not-X.
7) By (6) X is non-local with respect to not-X.
Generally, not-X is an existing thing that enables to define the properties of the things with respect to it, exactly because it is a non-atomic thing that enables to research Membership with respect to it.
Furthermore, not-X is the essence of deduction, where a set of axioms determinates what is true (included) within not-X and what is false (does not included within not-X).
Godel showed that in not-X systems that are strong enough to deal with arithmetic, there are truths of not-X that are not provable within not-X.
This can easily be understood by researching X with respect to non-X, where X is included AND not-included with respect to not-X.
As a result X is true with respect to not-X (included in not-X) but cannot be proven by not-X because it is included AND not-included with respect to not-X.
2) By (1) X is an existing AND empty thing.
3) By (1) not-X is an existing AND non-empty thing.
4) Sub-existing things are included XOR not-included with respect to not-X, such that not-X has at least one included sub-thing.
5) By (4) sub-existing things are local with respect to not-X.
6) If X is not sub-existing thing with respect to not-X, then X is included AND not-included with respect to not-X.
7) By (6) X is non-local with respect to not-X.
Generally, not-X is an existing thing that enables to define the properties of the things with respect to it, exactly because it is a non-atomic thing that enables to research Membership with respect to it.
Furthermore, not-X is the essence of deduction, where a set of axioms determinates what is true (included) within not-X and what is false (does not included within not-X).
Godel showed that in not-X systems that are strong enough to deal with arithmetic, there are truths of not-X that are not provable within not-X.
This can easily be understood by researching X with respect to non-X, where X is included AND not-included with respect to not-X.
As a result X is true with respect to not-X (included in not-X) but cannot be proven by not-X because it is included AND not-included with respect to not-X.
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doronshadmi
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It is a contradiction if Y is non-local w.r.t X.
It cares, but in the opposite way of how local things exist w.r.t to a given domain.
doronshadmi
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jsfisher,
As long as you are unable to understand that traditional Cardinality is a partial measurement of existing complexity, there is no use to talk with you about any utility that is not limited to this partial measurement.
jsfisher
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Whether I accept your corruption of well-established terms like cardinality is irrelevant. Whether I understand your obsession with trivialities like this thing you call complexity is irrelevant. The reason there is no point discussing utility of your mythical mathematics is very simple. It does not have any.
Little 10 Toes
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No it's not. And no I don't. Why do you keep complaining that Cardinality isn't what you think it means?
The Man
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Simply gibberish.
It is simply not a contradiction unless the proposition and its negation are both considered to be true. With the proposition of ‘belonging to’ or its negation of ‘not belonging to’ it is just not a contradiction. That your notion of non-local is self inconsistent and thus a contradiction in and of itself is beside the point. Once you define what classifies as ‘belonging to’ and there by ‘not belonging to’ in a self consistent fashion then apply that consideration consistently the consideration of that proposition or its negation being true is not a contradiction. That you insist it is one simply demonstrates that the contradiction is in your notion of “non-local” and has nothing to do with that particular proposition or its negation.
More gibberish
doronshadmi
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The proposition "Y belongs AND does not belong to X" is true if Y is non-local w.r.t X.
Again:
There exists X such that X is empty (X is an atom).
There exists not-X such that not-X is not-empty (not-X is not an atom).
X AND not-X is a contradiction.
For any given not-X there exists X such that if X belongs AND does not belong to not-X, then X is called non-local with respect to not-X, and it is notated as Y.
For any given not-X there exists X such that if X belongs XOR does not belong to not-X, then X is called local with respect to not-X, and it is notated as Z.
Y belongs XOR does not belong to not-X, is a contradiction.
Z belongs AND does not belong to not-X, is a contradiction.
Y and Z are two different atoms.
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The Man
Unbanned zombie poster
That is simply a contradiction as you are asserting both “Y belongs” and its negation ‘Y does not belong’ to be true. You simply cannot seem to make up your mind what you mean by “belongs” in any self consistent fashion.
Again simply gibberish
doronshadmi
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Again simply limited mind.
The Man
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Well whenever you can actually make up your mind about what you want your references to represent (like "belongs to") in any self consistent manor then please get back to us. Again take as much time as you feel your need.
doronshadmi
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The reference is not-X (which is not and atom) and there are two kinds of X (atoms) with respect to it, which are:
a) Non-local atom Y , which belongs AND does not belong to non-atom not-X.
b) Local atom Z, which belongs XOR does not belong to non-atom not-X.
When you get (a) in addition to (b), then please get beck to me. Again take as much time as you feel your need.
Meanwhile let us add more knowledge to your limited local-only reasoning, for example:
1) Membership between atoms.
Since atoms are existing AND empty things, then Y "belongs to X" means" "on X" such that Y is not a sub-thing of X, but it is how X exists as an atom, for example:
Y (which is a non-local atom) is "on AND not on" Z (which is a local atom).
Z (which is a local atom) is "on XOR not on" Y (which is a non-local atom).
Things become more interesting if Membership is researched between two non-local atoms. In that case they can be local OR non-local with respect to each other (as can be seen in page 23 of http://www.scribd.com/doc/16542245/OMPT , where =, < and > are used as relations which define the membership between the considered elements.)
2) Membership between atoms AND non-atoms.
These are cases (a) or (b) where in this case Y or Z are sub-things of not-X such that Y is "included AND not included" in not-X, and Z is "included XOR not included" in not-X.
3) Membership between non-atoms.
In this case Membership is a Z-only type, and this is all your limited reasoning gets.
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Little 10 Toes
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Not what? Please work on your English. (Refer to bolded portion of the quote)
doronshadmi
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"which is not an atom"
doronshadmi
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About the extension of Membership, it is already written in (at least) pages 1-5 of http://www.geocities.com/complementarytheory/TOUM.pdf
The Man
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Obviously you need more time as your reference of “belongs AND does not belong to” is still not used in any self consistent fashion. Using the reference “on AND not on” or "included AND not included" in an equally self inconsistent fashion still does not imbue your reference of “belongs AND does not belong to” with any consistency. As long as your references include the propositions like “belong” , “on” or “included” along with their respective negations as both being true for an indivisible “atom” then it is simply a contradiction.
Meanwhile let’s try to add some knowledge to you contradictory reasoning. In the U.S. police vehicles are often referred to as a “black and white”. Now the vehicle as a whole can not be entirely black and entirely white as that is simply a contradiction. However, some portions of the vehicle are entirely black and other portions of it are entirely white, thus the vehicle as a whole, being a collection of those black potions and white portions, is then black and white without contradiction. That lack of contradiction specifically comes from the vehicle as a whole being considered to be comprised of entirely black portions and entirely white portions. The same applies to your “belongs AND does not belong” it specifically partitions your professed “atom” into those opposing considerations. You can maintain that it is still an “atom” with such partitioning, but that is simply contradictory. Or you can accept that in such a consideration of partitioning it is simply not an “atom”, but specifically divided into, and by, those “belongs” as well as “does not belong” ascriptions.
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doronshadmi
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The self inconsistent fashion is a direct result of your inability to get the difference between membership between atoms and non-atoms.The Man said:
By using your example, the vehicle as a whole is non-local w.r.t its black or white aspects, where black or white aspects are local w.r.t the vehicle.The Man said:
Let us go deeper than that, and ask ourselves, what do we wish to achieve by using some tool.
Mathematics is a tool that is considered as interesting if it is found useful by its users\developers.
Currently Ethics and Logical reasoning are considered as disjoint systems according to the current paradigm of the mathematical science.
Jsfisher asked about OM’s utility and I already said that OM’s aim is to find the bridge between Ethics and Logics under a one comprehensive framework, where Ethics and logical reasoning are not disjoint concepts anymore.
The way to achieve this goal goes through our understanding of Complexity, where Complexity is the result invariant (non-local rules) AND variant (local expressions of non-local rules) under a one comprehensive framework, such that Complexity is survived and developed by using this framework, both by its quantitative aspects and qualitative aspects that are derived from the relations between the elements of a given complex.
Mathematical definitions do not create the things that are defined by them, and it can easily be demonstrated by ZF axiom of the Empty set:
"There is a set such that no set is a member of it." ( http://en.wikipedia.org/wiki/Axiom_of_empty_set )
“there is” is called Existential quantification that is a statement about the existence of the considered thing, and in the case of the Empty set, one of the already existing things that are not members of the considered set, is the empty set itself.
OM uses the same fashion by defining the minimal exiting terms that enable the existence of Complexity. By using this knowledge right at the foundations of some framework, we are able to penetrate better to the core of the researched concept, and by using the bridging between Non-locality and Locality OM clearly shows that traditional Cardinality is a partial case Complexity such that the number of the internal existing structures of a considered member, are ignored.
It can be done according to our purpose, but by OM we are aware of our wish to limit the number of the existing things of some collection, and we are aware of the fact that traditional Cardinality is a partial measurement of an existing Complexity.
OM has a very clear gaol, which is:
To define the best framework for Complexity’s survival AND development, and I think that this gaol the most important goal for complex systems like us, in the near and long run.
By using the current paradigm, where Ethics and logical reasoning are disjoint frameworks and Complexity is not a fundamental concept of the current mathematical science, I do not think that we will achieve the mentioned most important goal.
On the contrary, as things are done nowadays, we are going to fulfil the disjoint state between our Ethical and Logical\Technological skills, simply because we do nothing in order to understand Complexity, which is exactly what we are both mentally and physically.
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