Deeper than primes

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doronshadmi said:
Slowly but surely OM notions are spread http://adsabs.harvard.edu/abs/2010AIPC.1232..299K .
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Are OM notions spreading? If so, then the Harvard folks got a surprise when attempting to partition an integer where the number of elements is set finite, like 3, for example. Let's start . . .

7 = 0 + 0 + 7

But since the non-zero element of the partition is identical to the integer to be partitioned, which is also the definiens, a "regression" emerges:

7 = 0 + 0 + 0 + 0 +7

Now the partition has 5 elements, and the recurrence let the process of partitioning approach infinity.

You can use a general form and partition integer g this way:

g = {0 + 0 + g}

which is a form very similar to the troublesome

G = {A, A, G}

There surely must be some difference between '=' and '='.
 
doronshadmi said:
The Man, I see that also jsfisher does not agree with you about the identity of a member of set A to set A.
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And again, a lie!! Doron, where did I either agree--which you said I did--or disagree--which you said I did--with this statement you attribute to The Man?

Is it compulsive, Doron, that you have to fabricate things?

Most children learn the difference between telling the truth and lying before kindergarten. Did you forget, or do they just not teach anything about honesty where you are?
 
zooterkin said:
Really? This would be the same Moshe Klein who you chased away when he tried to understand OM, but in fact showed that even you did not understand it?
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Yes really.

This is the same Moshe Klein, which wrote an article together with Prof. Andrei Khrennikov and Prof. Tal Mor about sub-partitions, which is based on the strict case of Organic Numbers.
 
Little 10 Toes said:
Isn't that the same article that was not peer reviewed?

Edit: I also notice, your name isn't listed as an author. Funny since you're the one that "invented" the idea. Also, no mention in the abstract of OM.
Click to expand...

Please register to http://scitation.aip.org/getabs/ser...0001000299000001&idtype=cvips&gifs=yes&ref=no , open the article and you will find my name together with Moshe’s name, which refers to http://www.scribd.com/doc/18453171/International-Journal-of-Pure-and-Applied-Mathematics-Volume-49 .
 
epix said:
Are OM notions spreading? If so, then the Harvard folks got a surprise when attempting to partition an integer where the number of elements is set finite, like 3, for example. Let's start . . .

7 = 0 + 0 + 7

But since the non-zero element of the partition is identical to the integer to be partitioned, which is also the definiens, a "regression" emerges:

7 = 0 + 0 + 0 + 0 +7

Now the partition has 5 elements, and the recurrence let the process of partitioning approach infinity.

You can use a general form and partition integer g this way:

g = {0 + 0 + g}

which is a form very similar to the troublesome

G = {A, A, G}

There surely must be some difference between '=' and '='.
Click to expand...

Please register to http://scitation.aip.org/getabs/ser...0001000299000001&idtype=cvips&gifs=yes&ref=no in order to read its content, before you reply.
 
jsfisher said:
And again, a lie!! Doron, where did I either agree--which you said I did--or disagree--which you said I did--with this statement you attribute to The Man?

Is it compulsive, Doron, that you have to fabricate things?

Most children learn the difference between telling the truth and lying before kindergarten. Did you forget, or do they just not teach anything about honesty where you are?
Click to expand...

Evasion noted.

It must be stressed that in this case jsfisher has only two options:

1) A set is identical to its member.

2) A set is not identical to its member.

He chose Evasion.
 
doronshadmi said:
Yes really.

This is the same Moshe Klein, which wrote an article together with Prof. Andrei Khrennikov and Prof. Tal Mor about sub-partitions, which is based on the strict case of Organic Numbers.
Click to expand...

I find that hard to believe, since you've yet to provide an adequate description, let alone a strict definition, of what an Organic Number actually is.
 
zooterkin said:
not a link to yet another PDF with pretty pictures
Click to expand...
An Organic Number is a conceptual form that is derive from the linkage among Non-locality and Locality, which enables to deal with parallel (uncertain) and serial (certain) information under a one framework.

The logical reasoning of Non-locality and Locality is defined as follows:

X is a placeholder of a given element.

Membership is the relation of X w.r.t Inclusion\Exclusion.

The non-local aspect of Membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are the same w.r.t Inclusion\Exclusion, then X Membership is called non-local w.r.t Inclusion\Exclusion.

The local aspect of membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are different w.r.t Inclusion\Exclusion, then X Membership is called local w.r.t Inclusion\Exclusion.


Here is a 2-valued view of these definitions:

Code: 
Inclusion\Exclusion 
  F            F          [ ]    (Non-locality)  (NOR)

  T            F          [.]    (Locality)--|
                                             |-- (XOR) 
  F            T          [ ].   (Locality)--|

  T            T          [[u] ][/u]_   (Non-locality)  (AND)

NOR+AND ---> NXOR so we are dealing here with NXOR\XOR Logic, where both Non-local and Local Memberships are logically defined.

Edit:

http://www.internationalskeptics.com/forums/showpost.php?p=5837358&postcount=954

http://www.internationalskeptics.com/forums/showpost.php?p=5974148&postcount=9988
 
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doronshadmi said:
An Organic Number is a conceptual form that is derive from the linkage among Non-locality and Locality, which enables to deal with parallel (uncertain) and serial (certain) information under a one framework.

The logical reasoning of Non-locality and Locality is defined as follows:

X is a placeholder of a given element.

Membership is the relation of X w.r.t Inclusion\Exclusion.

The non-local aspect of Membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are the same w.r.t Inclusion\Exclusion, then X Membership is called non-local w.r.t Inclusion\Exclusion.

The local aspect of membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are different w.r.t Inclusion\Exclusion, then X Membership is called local w.r.t Inclusion\Exclusion.


Here is a 2-valued view of these definitions:

Code: 
Inclusion\Exclusion 
  F            F          [ ]    (Non-locality)  (NOR)

  T            F          [.]    (Locality)--|
                                             |-- (XOR) 
  F            T          [ ].   (Locality)--|

  T            T          [[u] ][/u]_   (Non-locality)  (AND)

NOR+AND ---> NXOR so we are dealing here with NXOR\XOR Logic, where both Non-local and Local Memberships are logically defined.

http://www.internationalskeptics.com/forums/showpost.php?p=5837358&postcount=954
Click to expand...


You seem to have overlooked (although you did go to the trouble of snipping them) the key words in my request:
zooterkin said:
B) That doesn't answer my point at all. Please give a clear definition (here, not a link to yet another PDF with pretty pictures) of what an Organic Number is, and what you can do with it.
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zooterkin said:
You seem to have overlooked (although you did go to the trouble of snipping them) the key words in my request:
Click to expand...
It is a clear definition that is based on clear Logic.

All you have to do is get out of your box, where in this box a line is made by points.
 
doronshadmi said:
Any given member that is included in set A, is not identical to set A.
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Again, it is when the member is specified to be that set.


doronshadmi said:
The maneuvering with names like “subset” and “set” has no significance, because these names are actually the same object.
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Doron, you’re the only one trying to ‘maneuver’ with names.


doronshadmi said:
I see you’ve missed the point. Set A and A as a member of set A are not identical, because set A has an additional level that A as a member of set A does not have, ad infinitum ...
Click to expand...

I see you’ve missed your own point about “maneuvering with names”, again.

doronshadmi said:
In that case you get a set that is based on infinite regression, and infinite regression does not have strict identity. Again, any given set is identical to itself, also any given member is identical to itself, but no member of a given set is identical to that set.
Click to expand...

Again this “infinite regression” is only in your imagination because you seem to have some sort of “identity” crisis about how you represent set “A”.

doronshadmi said:
You still miss the difference between “define by” or “defined as” and “identical to”.
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Nope, you still miss that your own failed reasoning is still only yours no matter how much you want to ascribe it to someone else.

doronshadmi said:
The “strict” one (which asserts that a given member of a given set is identical to that set) is exactly the naive notion that leads to fantasies like Russell’s Paradox and proper classes.
Click to expand...

Once again you clearly demonstrate that you have no idea what you are talking about.

Here is the non-truncated quote again.

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B not contained in A), then
• A is also a proper (or strict) subset of B; this is written as
or equivalently
• B is a proper superset of A; this is written as
Click to expand...




doronshadmi said:
It is all derived from the fantasy that the magnetite of existence of infinite collected members is identical to the magnitude of existence of a given collector, which leads to the inability to distinguish between “define by” or “defined as” and “identical to”.
Click to expand...

Once again stop simply trying to posit aspects of your own failed reasoning onto others.

doronshadmi said:
Set is a collector\collected framework that enables the existence of collections, whether they are empty or not.
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In this case the “collected” is the “collector”.

doronshadmi said:
Evidently the notion of “Set is a collector\collected framework that enables the existence of collections, whether they are empty or not”, is simply beyond you.
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Nope, just your usual dichotomistic nonsense.

doronshadmi said:
The traditional one.
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So you don’t know what that “traditional one” is or how to express it accurately?

doronshadmi said:
And this fact prevents a member of that set to be identical to that set.
Click to expand...

The fact that it is still just set “A” prevents it from not being, well, set “A”, so they are in fact identical by that fact.

doronshadmi said:
A set is defined by its members, but it does not mean that any of these members is identical to that set.
Click to expand...

Once again it does if that set is defined as one of its members.

doronshadmi said:
The “crisis” is your fantasy that can’t distinguish between “Identical to” and “defined by” or defined as”.
Click to expand...

Doron, I’m not the one claiming some “identity” changes just because you use a different representation that you still equate to your set “A”. The crisis and ignorance remains entirely yours.

doronshadmi said:
Organic Mathematics has no “crisis” about the notion of the incompleteness of infinite collections.
Click to expand...

Actually it does, since you simply don’t like “infinite collections” it leaves your OM extremely restricted.


doronshadmi said:
On the contrary, the traditional notion has a “crisis” about this subject because it can’t distinguish between “Identical to” and “defined by” or defined as”.
Click to expand...

Once again stop simply trying to posit aspects of your own failed reasoning onto others.



doronshadmi said:
The traditional notion uses frameworks like ZF(C) in order to avoid paradoxes that do not exist, and it also using a garbage can called “proper classes”.
Click to expand...

Doron you keep going on about the problems and paradoxes resulting from a set including itself as a member, so who are you trying to kid with this “do not exist” nonsense (other than just yourself)?

doronshadmi said:
The fact that Set A is defined by these iterations, does not mean that any of these iterations is identical to set A.
Click to expand...

Doron you equated them to set “A” yourself, so stop kidding yourself.

doronshadmi said:
Once again stop simply trying to posit aspects of currently agreed failed reasoning onto others.
Click to expand...

I have asserted and continue to assert that you don’t even agree with yourself, so don’t kid yourself about me trying to posit some or any ‘agreement’ upon you or anyone else.

doronshadmi said:
The Man, I see that also jsfisher does not agree with you about the identity of a member of set A to set A.
Click to expand...

How about actually linking the quote, as it seems evident that he was simply not agreeing with your assertion that he agreed to something and I would agree with him. As you often simply assert nonsense claiming people agree with it.
 
epix said:
Doron can actually do this due to the definition of an element A of a set S: A is an element of S if and only if A is not an element of A.

Here is a tautology that deals with a similar situation:

y = 2x - 5y

y + 5y = 2x
6y = 2x
y = (2x)/6

If the tautology doesn't tolerate 'y' on both sides, then there could be a problem with A = {A, B, C}, as it was, coz Godel got busy with it.
Click to expand...


As I said before…

The Man said:
Doron a letter does not define a set it is simply used to represent a set and you equate your letter (set “A”) to all your various instances of different “bracketed notation”, thus asserting them as, well, equal. All you have is set “A” so your “different levels of a given set” are all just set “A”. Your “infinite regression” is just in your imagination as there is nowhere for you to regress to, you only have set “A”. Sure, in this case, it is both the set and the element of that set, you can go around that circle as many times as you like but you just end up back were you started with only set “A”.
Click to expand...

Since “(2x)/6” = “y”, technically ‘y’ is on both sides (more specifically both sides are equally representative of ‘y’). The technical name for this is ‘term rewriting’ (which we have been over with Doron before). You can represent ‘y’ or set “A” any number of different ways, but you are still simply representing ‘y’ or set “A” in either given case.
 
doronshadmi said:
Evasion noted.

It must be stressed that in this case jsfisher has only two options:

1) A set is identical to its member.

2) A set is not identical to its member.

He chose Evasion.
Click to expand...

Evasion? Of your misinterpretation of The Man's statement? --Not hardly.

The issue -- which you are evading -- is your continued out-right lying about what other people said or meant.

You are a proven dishonest person, Doron. You have destroyed your own credibility and your integrity. It sucks to be you.


By the way, the text quoted above is an example of a false dichotomy. Doron gets nothing right.
 
The Man said:
Again, it is when the member is specified to be that set.
Click to expand...
Right, exactly as True is specified to be False, see? I also know to use this kind of trick.

The Man said:
I see you’ve missed your own point about “maneuvering with names”, again.
Click to expand...
Yes, by using the name "level" in The Man's flat-land.

The Man said:
Again this “infinite regression” is only in your imagination because you seem to have some sort of “identity” crisis about how you represent set “A”.
Click to expand...
Crisis ?? no way, I like infinite regression of infinite levels after it is one of the possible ways to express Complexity.

The Crisis is a direct result of forcing completeness on such an expression, because in flat-land there can't be levels and as a result we get the illusion that a member of X is identical to X, which of course is resulted by fantasy illusion like Russell's paradox and garbage can like proper classes.

The Man, imagination is good, because it can help you to see beyond flat-land, illusion is bad because you keeps you locked under flat-land.

The Man said:
you still miss that your own failed reasoning
Click to expand...
You still miss your own flat-land reasoning.

The Man said:
In this case the “collected” is the “collector”.
Click to expand...
I know, this is a normal day in flat-land.

The Man said:
Nope, just your usual dichotomistic nonsense.
Click to expand...
Another normal experience in flat-land, which naturally gets different levels as dichotomy.

The Man said:
The fact that it is still just set “A” prevents it from not being, well, set “A”, so they are in fact identical by that fact.
Click to expand...
It is the best reasoning that you can get in flat-land, you are right.

The Man said:
Once again it does if that set is defined as one of its members.
Click to expand...
Yes I know, also a line segment is identical to the end-points that define it, isn't it The Man from flat-land?

The Man said:
Actually it does, since you simply don’t like “infinite collections” it leaves your OM extremely restricted.
Click to expand...
Ho, I truly like infinite collections exactly as they are, well, infinite.

The Man said:
Once again stop simply trying to posit aspects of your own failed reasoning onto others.
Click to expand...
Once again stop simply trying to posit aspects of the currently agreed flat-land reasoning onto others.

The Man said:
Doron you keep going on about the problems and paradoxes resulting from a set including itself as a member, so who are you trying to kid with this “do not exist” nonsense (other than just yourself)?
Click to expand...
The Man you keep going on about the problems and paradoxes that do not exist, because no member is identical to its set.

The Man said:
I have asserted and continue to assert that you don’t even agree with yourself
Click to expand...
The assertions of a person that does not get the concept of different levels, do not hold water.

The Man said:
How about actually linking the quote, as it seems evident that he was simply not agreeing with your assertion that he agreed to something and I would agree with him. As you often simply assert nonsense claiming people agree with it.
Click to expand...

Simple True\False Logic:

jsfisher said:
doronshadmi said:
Closed box reasoning has been noted.

Your agreed reasoning, which asserts that a member is identical to its set, does not hold water.
Click to expand...

Where did I agree to that? You are lying again, Doron.
Click to expand...

By jsfisher's reply I am lying if I assert that jsfisher agrees that a member is identical to its set.

So since I am lying, then by True\False Logic jsfisher does not agree that a member is identical to its set, which is the assertion that you, The Man, are using.

Jsfisher clearly does not use here Ternary Logic, because he claims that I am lying.
 
jsfisher said:
You are a proven dishonest person, Doron. You have destroyed your own credibility and your integrity. It sucks to be you.
Click to expand...
It was shown time after time that your "you are lying" does not hold water, exactly as it does not hold water in your last "you are laying" case:

The Man said:
How about actually linking the quote, as it seems evident that he was simply not agreeing with your assertion that he agreed to something and I would agree with him. As you often simply assert nonsense claiming people agree with it.
Click to expand...

Simple True\False Logic:

jsfisher said:
doronshadmi said:
Closed box reasoning has been noted.

Your agreed reasoning, which asserts that a member is identical to its set, does not hold water.
Click to expand...

Where did I agree to that? You are lying again, Doron.
Click to expand...

By jsfisher's reply I am lying if I assert that jsfisher agrees that a member is identical to its set.

So since I am lying, then by True\False Logic jsfisher does not agree that a member is identical to its set, which is the assertion that The Man using.

Jsfisher clearly does not use here Ternary Logic, because he claims that I am lying.
 
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doronshadmi said:
An Organic Number is a conceptual form that is derive from the linkage among Non-locality and Locality, which enables to deal with parallel (uncertain) and serial (certain) information under a one framework.

The logical reasoning of Non-locality and Locality is defined as follows:

Code: 
Inclusion\Exclusion 
  T            T          [[u] ][/u]_   (Non-locality)  (AND)
Click to expand...
The reasoning is not logical; it's a dogmatic and unsupported declaration.

Inclusion and exclusion compared as above: a nut N is inside the nut shell {} AND at the same time it is not. That's hard to believe, but seeing is believing:

N = {N}

What do you see, Bernie?

I see two nuts: one is outside the nutshell and the other is inside the nutshell.

You see wrong: there is only one nut: ONE is local to the shell {} and ONE is non-local to the shell.


Too bad that for the total lack of necessary awarness of your own ideas, you defined the result of Inclusion(True) and Exclusion(True) in such a sorrowful, dogmatic way.

Do PARrot and PARadox share the same etymology? PAR=PAR, afterall.
 
doronshadmi said:
Please register to http://scitation.aip.org/getabs/ser...0001000299000001&idtype=cvips&gifs=yes&ref=no in order to read its content, before you reply.
Click to expand...
Doron, the only reason why you get any replies here at all is that this site is partly dedicated to moping after ideas that were born during the dark ages and somewhat survived. If you take your goodies elsewhere, as you did many times before you knocked on this door, the age of your thread won't exceed ten reply posts, as it turned to be the case. All I need to do is to google up some of your fancy terms and count.
 
The Man said:
As I said before…

Since “(2x)/6” = “y”, technically ‘y’ is on both sides (more specifically both sides are equally representative of ‘y’). The technical name for this is ‘term rewriting’ (which we have been over with Doron before). You can represent ‘y’ or set “A” any number of different ways, but you are still simply representing ‘y’ or set “A” in either given case.
Click to expand...
I can't read all posts in a detail, so I would like to make dead sure about your initial position on A = {A, B, C}. That example is an invalid definition of the set, right?
 
doronshadmi said:
Right, exactly as True is specified to be False, see? I also know to use this kind of trick.
Click to expand...

Well that’s you OM for you and you've been tricking only yourself with it for quite some time.

doronshadmi said:
Yes, by using the name "level" in The Man's flat-land.
Click to expand...

Ah, a new aspect of your own failed reasoning for you to simply ascribe to others.

doronshadmi said:
Crisis ?? no way, I like infinite regression of infinite levels after it is one of the possible ways to express Complexity.
Click to expand...

What “Complexity”? Again by your own assertions your “infinite regression of infinite levels” only ‘expressed’ your set “A”.


doronshadmi said:
The Crisis is a direct result of forcing completeness on such an expression, because in flat-land there can't be levels and as a result we get the illusion that a member of X is identical to X, which of course is resulted by fantasy illusion like Russell's paradox and garbage can like proper classes.
Click to expand...

Doron, I did not ‘force’ anything, you equated all your “levels” to your set “A” yourself.

doronshadmi said:
The Man, imagination is good, because it can help you to see beyond flat-land, illusion is bad because you keeps you locked under flat-land.


You still miss your own flat-land reasoning.


I know, this is a normal day in flat-land.


Another normal experience in flat-land, which naturally gets different levels as dichotomy.


It is the best reasoning that you can get in flat-land, you are right.
Click to expand...

Doron you simply imagining what you would like others to claim or ‘agree’ is an illusion and keeps you locked in your own nonsensical fiat-land.


doronshadmi said:
Yes I know, also a line segment is identical to the end-points that define it, isn't it The Man from flat-land?
Click to expand...

Who ever claimed such a ridiculous thing, other than just you?

doronshadmi said:
Ho, I truly like infinite collections exactly as they are, well, infinite.
Click to expand...

Who are you calling a “Ho”? Excellent, so now you have no problems with an infinite set?

doronshadmi said:
Once again stop simply trying to posit aspects of the currently agreed flat-land reasoning onto others.
Click to expand...

Once again Doron I have certainly never tried to posit any kind of “agreement” (with or without you) on to anyone.

doronshadmi said:
The Man you keep going on about the problems and paradoxes that do not exist, because no member is identical to its set.
Click to expand...

So now you have no problem with a set being a member of itself as it is one of those “problems and paradoxes that do not exist”? Oh, wait you claim “no member is identical to its set” even though you equated your “infinite regression of infinite levels” to your set “A”. Looks like, as usual your “problems and paradoxes” are just with yourself.


doronshadmi said:
The assertions of a person that does not get the concept of different levels, do not hold water.
Click to expand...

Well when you finally get to that ‘level’ where you actually agree with just yourself, please let us know. As ‘Dante’s Inferno’ will most likely have becomes ‘Dante’s Ice Capades’ by then.


doronshadmi said:
Simple True\False Logic:


By jsfisher's reply I am lying if I assert that jsfisher agrees that a member is identical to its set.


So since I am lying, then by True\False Logic jsfisher does not agree that a member is identical to its set, which is the assertion that you, The Man, are using.

Jsfisher clearly does not use here Ternary Logic, because he claims that I am lying.
Click to expand...

Three valued logic in “Simple True\False Logic:”? Looks like you still haven’t reached that ‘level’ where you agree with yourself. Are you claiming that you are simply confused or some other third alternative to simply accurately representing the assertions of others or just lying about them?
 
epix said:
I can't read all posts in a detail, so I would like to make dead sure about your initial position on A = {A, B, C}. That example is an invalid definition of the set, right?
Click to expand...

Sorry to hear that, but as always I’m more than willing to try to answer any questions as best I can. Remember that a set is always a subset of itself, just not a proper subset. So in that regard I would say that the set, as defined above, is not a proper family of subsets equivilent to set "A", as “A” can not be a proper subset of itself.
 
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The Man said:
Remember that a set is always a subset of itself,
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The Man uses different names for the same object.

This is not the case with "member of set X" and "set X", which are different things, because no member of set X has the same levels as set X has.
 
The Man said:
Who are you calling a “Ho”? Excellent, so now you have no problems with an infinite set?
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You have a problem with actual infinity, which is the non-locality beyond the incompleteness (potential infinity w.r.t actual infinity) of any given collection, which is the result of collector/collected different levels.

The Man said:
So now you have no problem with a set being a member of itself
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Sure, the infinite regression is exactly a proof of the incompleteness of an infinite collection, which prevents the possibility that a member of set X is identical to set X.

As a result Russell's paradox or proper classes do not exist, and any infinite collection is incomplete w.r.t Non-locality (the collector level), which is actual infinity.

Only in flat-land (your universe, The Man) the collector and the collected has no difference, because the concept of levels do not exist.

The Man said:
Three valued logic in “Simple True\False Logic:”?
Click to expand...
No, only Simple True\False Logic.
 
epix said:
Doron, the only reason why you get any replies here at all is that this site is partly dedicated to moping after ideas that were born during the dark ages and somewhat survived. If you take your goodies elsewhere, as you did many times before you knocked on this door, the age of your thread won't exceed ten reply posts, as it turned to be the case. All I need to do is to google up some of your fancy terms and count.
Click to expand...
So now you are an expert of "dark ages" and "modern" ideas.

How "fascinating".
 
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doronshadmi said:
No epix, by your "reasoning" Local = Non-local, which is always false (a contradiction).
Click to expand...

"My reasoning" was based on your reasoning that came up with Exclusion=True and Inclusion=True, which you mindlessly demonstrated. Anyone except you can see that if Exclusion and Inclusion are opposites, then so must be Local and Non-Local -- with all insane consequences in tow. Why do you call a contradiction Non-locality and not Locality?

If Exclusion=True and Inclusion=True, then Exclusion=Inclusion, and therefore Local=Non-Local, Yes=No, Left=Right, and so on all the way to the funny farm.

We can live with one monster. No need for another.
 
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epix said:
If Exclusion=True and Inclusion=True, then Exclusion=Inclusion,
Click to expand...
Nonsense.

By defining domain [ ], Inclusion is what is internal w.r.t the given domain and Exclusion is what is external w.r.t the the given domain.


X is a placeholder.


XOR holds if the input truth values (T or F) are different.

NXOR holds if the input truth values (T or F) are the same.



If X is internal XOR external w.r.t [ ], then X is called local w.r.t [ ]

If X is internal NXOR external w.r.t [ ], then X is called non-local w.r.t [ ]


Here is a 2-valued view of these definitions:

Code: 
Inclusion\Exclusion 
  F            F          [ ]    (Non-locality)  (NOR)

  T            F          [.]    (Locality)--|
                                             |-- (XOR) 
  F            T          [ ].   (Locality)--|

  T            T          [[u] ][/u]_   (Non-locality)  (AND)

NOR+AND ---> NXOR so we are dealing here with NXOR\XOR Logic, where both Non-local and Local Memberships are logically defined.
 
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doronshadmi said:
You have a problem with actual infinity, which is the non-locality beyond the incompleteness (potential infinity w.r.t actual infinity) of any given collection, which is the result of collector/collected different levels.
Click to expand...

Nope, your nonsense is not a problem for anyone but you.

Once again you seem to be engaging in some kind of anthropomorphism where a set (the collection itself) becomes some kind of “collector” requiring some activity like actually having to collect the elements of the set.

doronshadmi said:
Sure, the infinite regression is exactly a proof of the incompleteness of an infinite collection, which prevents the possibility that a member of set X is identical to set X.
Click to expand...

So you do still have a problem with a set being a member of itself and more specifically an infinite collection being complete.

Once again you equated your own “infinite regression” to your set “A” yourself, so your only problem remains with just yourself.

doronshadmi said:
As a result Russell's paradox or proper classes do not exist, and any infinite collection is incomplete w.r.t Non-locality (the collector level), which is actual infinity.
Click to expand...

Again you seem to be confusing a set which is always “complete” as defined and an infinite list or infinite activity like a collector collecting elements, which can not be completed.

We have been over this before Doron, a set simply defines what constitutes its members. That definition is complete, in and of itself (it includes all the members of that set). Other than simply defining the set, there is no activity like collecting, comparing or listing the elements (or even adding more brackets) that needs to be completed.

doronshadmi said:
Only in flat-land (your universe, The Man) the collector and the collected has no difference, because the concept of levels do not exist.
Click to expand...

Only in fiat-land (your universe, Doron) do you simply continue to assert what you would like others to ‘agree’ with regardless of what they keep telling you.

doronshadmi said:
No, only Simple True\False Logic.
Click to expand...

So you are not confused or just some other third alternative, but simply just lying?
 
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doronshadmi said:
The Man uses different names for the same object.

This is not the case with "member of set X" and "set X", which are different things, because no member of set X has the same levels as set X has.
Click to expand...

Once again Doron you specifically equated all of your “levels” of your “infinite regression” to your set “A” yourself, making them, by your own assertions, just “different names for the same object”.
 
Originally Posted by epix
If Exclusion=True and Inclusion=True, then Exclusion=Inclusion,
Click to expand...

doronshadmi said:
Nonsense.
Click to expand...

Euclid came up with five Common Notions, which are basically in effect till today. For some reason, he decided that this one goes first:

C.N. 1. Things which equal the same thing also equal one another.

That's the Common Notion also known as the transitive property that you decided to violate and regard it as "nonsense." Your reasoning is profoundly unsound and it is going to stay that way, coz axioms cannot be proven -- they rely on common sense. Hence Common Notions.
 
doronshadmi said:
By jsfisher's reply I am lying if I assert that jsfisher agrees that a member is identical to its set.
Click to expand...

I see your reading comprehension skills are suffering again. You were lying because you claimed I'd made a statement I had not made. You have done that twice recently, in fact, and for contradictory statements.

So since I am lying, then by True\False Logic jsfisher does not agree that a member is identical to its set, which is the assertion that you, The Man, are using.
Click to expand...

You get nothing right, do you? You were when you stated that I made a certain statement or two. Nowhere, however, does that provide you a basis for what statement I would have made, had I made one.

Jsfisher clearly does not use here Ternary Logic, because he claims that I am lying.
Click to expand...

You were lying. You made a deliberate, false statement. That fully encompasses the meaning of lying.

You are a liar. You make deliberate, false statements.

It is something you seem to do very naturally, perhaps compulsively.
 
Oopsy-toopsy.

From: epix
To: The Man

When I scrolled back to see once again Doron's transformations, I realized that they and the conclusion are more absurd than I anticipated. If there is a field of mathematics that may find the accomodation in "Philosophy & Religion" motel somewhat acceptable, then it is the set theory. But Doron's insistence on "Turbulent Transformational Paganism" with [.], []. , [_]_ and all those demigods non-local to Christianity flying around makes any modest link impossible.

There is a practical branch of the set theory that enables to shuffle items around for various purposes, such as a comparison of the string of elements. There is a kind of set called a "list" that is defined and implemented differently then the set itself. The list is the practical part, whereas the set is used more or less for logical manipulations. Some languages, such as Java, allow implementation of both forms: sets and lists.

Some calculators, such as TI-89 allow only a list manipulation as a part of the computational hierarchy. That means there had to be the "thou shall not . . ." and one of them is the "Circular definition":

Example 1.
Code: 
Define a = {a, b, c}
Error: Circular definition

The attempt to define a list with three elements, for example, results in an error message when the defining term is also a part of the expression to be defined. It follows that the story would be the same in the next example:

Example 2.
Code: 
Define y = 2x - 6y
Error: Circular definition

Some believe in "thou shall not," and some don't. So let's override the error to see what happens in the case of Example 2:

Define y = 2x - 6y => 2x - 62x - 6y... and the substitution of y goes to infinity -- if the calculator could concatenate the function with itself.

Here is the fun part:
Q: What is Circular definition?
A: Circular definition is a definition that is circular.

Quite "illuminating answer," but that's what circular definition is all about in a practical example.

It's dark and you leave point A for point B. You get disoriented and walk in circles around point A forever and ever ad infinitum -- if you happen to be a non-omniscient, immortal deity. So that's the "etymology" of the term Circular definition (See Doron's renditions of those trips nowhere.)

How he relates the Russell's paradox to the infinite regression is a mystery to me -- if he does it at all. Once you expand a set to include identical elements, the set is no longer a set but a list by definition and becomes "non-local" to the set theory that Russel's paradox is a part of.

But there is a funny extension, a set of arguments that actually takes the pure abstract, or the philosophy of the Russell paradox to the religion territory through a remarkable coincidence. It's a very strange stuff, coz it comes to light only when you try to explain to Doron his absurd mistakes that only a few are capable of making, and that's not that easy, coz it's like trying to find a grammar mistake in a text written in French when you barely speak that language.
 
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The Man said:
Once again you seem to be engaging in some kind of anthropomorphism where a set (the collection itself) becomes some kind of “collector” requiring some activity like actually having to collect the elements of the set.
Click to expand...
The “activity” is a direct result of your flat reasoning, which can’t comprehend the concept of different levels that stands at the basis of any given collection, the notion of different level is expressed as collector\collected hierarchy of existence, where the level of collector’s magnitude of existence is stronger than the level of the collected magnitude of existence.

The Man said:
So you do still have a problem with a set being a member of itself and more specifically an infinite collection being complete.
Click to expand...
So you do still have a flat-land reasoning problem with a set not being identical to any of its member s and more specifically, the fact that an infinite collection being incomplete, which is a straightforward result that is derived from the different magnitude of existence of collector\collected w.r.t each other.

The Man said:
We have been over this before Doron, a set simply defines what constitutes its members. That definition is complete, in and of itself (it includes all the members of that set). Other than simply defining the set, there is no activity like collecting, comparing or listing the elements (or even adding more brackets) that needs to be completed.
Click to expand...
The notion of “an activity that is needed to complete something” is a direct result of your flat reasoning, that can’t get the he different magnitude of existence of collector\collected w.r.t each other. But this is your flat level-less reasoning problem, that has nothing to do with OM’s reasoning about the considered subject.

The Man said:
Only in fiat-land (your universe, Doron) do you simply continue to assert what you would like others to ‘agree’ with regardless of what they keep telling you.
Click to expand...
You tell me nothing The Man, as long as you speck form a universe that has no different levels of existence, known as flat-land.

The Man said:
So you are not confused or just some other third alternative, but simply just lying?
Click to expand...
If I am lying it means that jsfisher does not agree with your assertion that a set is identical to its member.

Simple as that.

The rest mambo jambo jsfisher ‘s replies on this subject, do not hold water.
Let us do some demonstration of his mambo jambo reply:

I wrote to jsfisher:
doronshadmi said:
Your agreed reasoning, which asserts that a member is identical to its set, does not hold water.
Click to expand...

Jsfisher response was:
jsfisher said:
Where did I agree to that? You are lying again, Doron.
Click to expand...
It must be stressed that the “agreed reasoning” is the traditional reasoning, which accepts the notion that a member of set X is identical to set X.

If I am lying by claiming that jsfisher agrees with the traditional reasoning about the considered subject, then jsfisher's reply (“Where did I agree to that?) actually reinforces my argument that he does not agree with the traditional (agreed) reasoning about this subject.

By using jsfisher’s reply on that subject, it is clearly understood that if I am lying, then jsfisher has at least two alternatives, which are different than the traditional (agreed) reasoning about this subject, as follows:

Alternative 1: jsfisher does not agree with the traditional (agreed) reasoning about the considered subject, by taking the opposite notion, which claims that no member of set X is identical to set X.

Alternative 2: jsfisher does not agree with both alternatives, which are:

1) OM’s reasoning: There can’t be a member of set X, which is identical to set X.

2) Traditional (agreed) reasoning: There can be a member of set X, which is identical to set X.

So as you see, even disagreement with (1) and (2) is an option for jsfisher.

In order to clarify jsfisher's reasoning about this subject let us ask him a simple question:

jsfisher please choose one and only one of the given options:

1) OM’s reasoning: There can’t be a member of set X, which is identical to set X.

2) Traditional (agreed) reasoning: There can be a member of set X, which is identical to set X.

3) I disagree with (1) and (2) and my reasoning about this subject is: [please write your reasoning]
 
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epix said:
C.N. 1. Things which equal the same thing also equal one another.
Click to expand...
In that case there is a thing which is identical to itself, and the twisted definition of "Things which equal the same thing" is just playing with words.
 
The Man said:
Once again Doron you specifically equated all of your “levels” of your “infinite regression” to your set “A” yourself, making them, by your own assertions, just “different names for the same object”.
Click to expand...

The considered object, called set A, is exactly infinite levels, where no given level is identical to set A, which is a notion that can't be grasped in flat-land.
 
doronshadmi said:
The “activity” is a direct result of your flat reasoning, which can’t comprehend the concept of different levels that stands at the basis of any given collection, the notion of different level is expressed as collector\collected hierarchy of existence, where the level of collector’s magnitude of existence is stronger than the level of the collected magnitude of existence.
Click to expand...

Nope, again the only activity required is defining the set, the set is the collection. What do you think is this “collector” and how does it collect anything.

doronshadmi said:
So you do still have a flat-land reasoning problem with a set not being identical to any of its member s and more specifically, the fact that an infinite collection being incomplete, which is a straightforward result that is derived from the different magnitude of existence of collector\collected w.r.t each other.
Click to expand...

Nope, I have no “problem with a set not being identical to any of its member s” when it is not defined as “being identical to any of its member s” and as you have yet to show any defined member of an infinite set that is not a member of that set (hence that set being incomplete), the problem of a “ an infinite collection being incomplete” remains simply yours.

Your simply fiat-land reasoning does not imbue anyone with “flat-land reasoning” just because you would like to label them as such.

What is this “magnitude of existence” you keep referring to?

doronshadmi said:
The notion of “an activity that is needed to complete something” is a direct result of your flat reasoning, that can’t get the he different magnitude of existence of collector\collected w.r.t each other. But this is your flat level-less reasoning problem, that has nothing to do with OM’s reasoning about the considered subject.
Click to expand...

Indeed it does have everthing to do with “OM’s reasoning about the considered”, as you can not show any element that is lacking in an infinite set. Your claims of an infinte set being incomplte are simply the result of you requiring some infinite acticitve like collecting, listing or ‘visiting’ each member of that set.

doronshadmi said:
You tell me nothing The Man, as long as you speck form a universe that has no different levels of existence, known as flat-land.
Click to expand...

You tell yourself nothing Doron as your “OM’s reasoning” is simply based upon your own, usually self-contradictory edicts, known as Doron’s fiat-land.

doronshadmi said:
If I am lying it means that jsfisher does not agree with your assertion that a set is identical to its member.

Simple as that.
Click to expand...

No Doron it just means that you deliberately misrepresent the assertions and statements of others and even just make up your own to ascribe to them.

“Simple as that”

doronshadmi said:
The rest mambo jambo jsfisher ‘s replies on this subject, do not hold water.
Let us do some demonstration of his mambo jambo reply:

I wrote to jsfisher:


Jsfisher response was:

It must be stressed that the “agreed reasoning” is the traditional reasoning, which accepts the notion that a member of set X is identical to set X.

If I am lying by claiming that jsfisher agrees with the traditional reasoning about the considered subject, then jsfisher's reply (“Where did I agree to that?) actually reinforces my argument that he does not agree with the traditional (agreed) reasoning about this subject.

By using jsfisher’s reply on that subject, it is clearly understood that if I am lying, then jsfisher has at least two alternatives, which are different than the traditional (agreed) reasoning about this subject, as follows:

Alternative 1: jsfisher does not agree with the traditional (agreed) reasoning about the considered subject, by taking the opposite notion, which claims that no member of set X is identical to set X.

Alternative 2: jsfisher does not agree with both alternatives, which are:

1) OM’s reasoning: There can’t be a member of set X, which is identical to set X.

2) Traditional (agreed) reasoning: There can be a member of set X, which is identical to set X.

So as you see, even disagreement with (1) and (2) is an option for jsfisher.

In order to clarify jsfisher's reasoning about this subject let us ask him a simple question:

jsfisher please choose one and only one of the given options:

1) OM’s reasoning: There can’t be a member of set X, which is identical to set X.

2) Traditional (agreed) reasoning: There can be a member of set X, which is identical to set X.

3) I disagree with (1) and (2) and my reasoning about this subject is: [please write your reasoning]
Click to expand...

Again what ““agreed reasoning” is the traditional reasoning“, be specific and cite a reference. Evidently you have never considered the alternative that you are simply wrong about there being some “agreed” or “traditional reasoning” and how certain non-naive set theories actually deal with the possibility of “set X” being defined as a member of “set X”.
 
doronshadmi said:
The considered object, called set A, is exactly infinite levels, where no given level is identical to set A, which is a notion that can't be grasped in flat-land.
Click to expand...


Evidently it is just a notion that you simply can’t grasp in your self-contradictory fiat-land, as you equated each and every one of your ‘levels’ to your set “A”.

Since you now specifically assert “set A, is exactly infinite levels,” (as you alluded to before) then that infinite set of levels you ascribe to “A” is complete.
 
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