Deeper than primes

[epix]

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.

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.

 

[epix]

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.

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?

 

[The Man]

Right, exactly as True is specified to be False, see? I also know to use this kind of trick.

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

Yes, by using the name "level" in The Man's flat-land.

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

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

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

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.

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

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.

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.

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

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

Ho, I truly like infinite collections exactly as they are, well, infinite.

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

Once again stop simply trying to posit aspects of the currently agreed flat-land reasoning onto others.

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

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

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.

The assertions of a person that does not get the concept of different levels, do not hold water.

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.

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.

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?

 

[The Man]

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?

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.

 

[doronshadmi]

Remember that a set is always a subset of itself,

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.

 

[doronshadmi]

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

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.

So now you have no problem with a set being a member of itself

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.

Three valued logic in “Simple True\False Logic:”?

No, only Simple True\False Logic.

 

[doronshadmi]

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.

So now you are an expert of "dark ages" and "modern" ideas.

How "fascinating".

 

[doronshadmi]

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

No epix, by your "reasoning" Local = Non-local, which is always false (a contradiction).

 

[epix]

No epix, by your "reasoning" Local = Non-local, which is always false (a contradiction).

"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.

 

[doronshadmi]

If Exclusion=True and Inclusion=True, then Exclusion=Inclusion,

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:

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.

 

[The Man]

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.

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.

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.

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.

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.

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.

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

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.

No, only Simple True\False Logic.

So you are not confused or just some other third alternative, but simply just lying?

 

[The Man]

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.

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”.

 

[epix]

Originally Posted by epix
If Exclusion=True and Inclusion=True, then Exclusion=Inclusion,

Nonsense.

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.

 

[jsfisher]

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

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.

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.

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.

 

[epix]

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.

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.

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.

 

[doronshadmi]

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.

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.

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

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.

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.

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.

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.

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.

So you are not confused or just some other third alternative, but simply just lying?

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:

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

Jsfisher response was:

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

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]

 

[doronshadmi]

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

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.

 

[doronshadmi]

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”.

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.

 

[The Man]

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.

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.

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.

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?

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.

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.

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.

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.

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.

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”

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]

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”.

 

[The Man]

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.

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.