Deeper than primes - Continuation

[realpaladin]

Originally Posted by jsfisher

You need to add, "Why do you ignore..." to it. Then, if and when he ever responds to it, you change it to "Please read the entire post before responding." Then, you have to link to the link, then you, well, you know already.

LOL. That is correct.

And a new trick our old dog learnt is to use badly hidden indirect references like 'white noise'...

I keep wondering *why* he would still respond to any of this if he really is ignoring... I still call OCD.

[doronshadmi]

Originally Posted by sympathic

Thanks for you support. Indeed it takes perseverance to have some sort of dialog with Doron. It is encouraging that he sees his responses thrown back to him as attacks -- maybe he will learn something from this.

sympathic, I do not see your replies as attacks, my response was about the white noise ( http://forums.randi.org/showpost.php...postcount=1330 ).

Take for example the white noise about Moshe Klein and me, lies have to be exposed even if they are expressed by white noise.

I think that you enable to distinguish between in-vitro and in-vivo as a novel view of Set.

What do you think?

[realpaladin]

Originally Posted by doronshadmi

The white noise ( http://forums.randi.org/showpost.php...postcount=1330 ) can't agree with itself if I can create new notions or only grab notions from others.

Score yet another point for my predictions!!!

Why do you ignore "Edit: Let's act like a total Doron about it and keep including the link to my predictions: http://forums.randi.org/showpost.php...postcount=1499"?


Not a single answer in over 5 pages to a question that has been asked.

I know for this board it is not anywhere near a record, but it must tell casual onlookers something about the skill level in math that Doron posesses.

[Little 10 Toes]

Originally Posted by doronshadmi

Try again to understand that 2 is not a member unless it is an object of a wider environment, which is notated by the outer "{" and "}" of a given set, where the the outer "{" and "}" are not members.

Try to understand what I am asking for. I do not want examples. I have asked:

Originally Posted by Little 10 Toes

Please show exactly where in "Set-Theory" that objects are considered as members as they belong to a wider environment. Your claim, your proof.

[realpaladin]

Here I predict that the answer will be in the vein of: "Your mathematical branches of verbal-non-verbal limited to something or other does not get..."
That is with about 75% confidence.

With 100% confidence I predict that you will not get the only correct answer "It says nowhere in Set-Theory".

That answer may be given, but with an addition that will again bring it into the domain of the first prediction, like "Your limited set-theory does not grasp <word-salad>"

Let's see how I am doing here.

[doronshadmi]

Originally Posted by Little 10 Toes

Try to understand what I am asking for. I do not want examples. I have asked:

Originally Posted by Little 10 Toes

Please show exactly where in "Set-Theory" that objects are considered as members as they belong to a wider environment. Your claim, your proof.

Try to understand my answer to you, which is not understood in terms of the standard notion of Set.

Here it is again, and please this time do not try to force the standard view on it, otherwise you are going to miss it again.

1) NOthing (is not notated by any symbol) is below membership.

2) YESthing (notated by the outer "{" and "}") is above membership.

3) Membership can have infinitely many levels, where each level is wider (or higher) than the previews levels.

4) The smallest level of membership is level 0, and examples of level 0 are: {}, 2, 236.67, etc...

5) The next level of membership is level 1, and examples of level 1 are: {{}, 2, 236.67}, {{}}, {2}, {236.67}, etc...

6) The next level of membership is level 2 , and examples of level 2 are: {{{}, 2, 236.67}}, {{{}}}, {{2}}, {{236.67}}, etc...

7) No level of membership is reducible into NOthing or extensible into YESthing.

8) There can be several different levels of membership in a given expression, for example: {}, {{}, 2, 236.67}, 2 ,{{{}}}, {{{{{236.67}}, 2}}} , etc ...

(1) to (8) are not understood in terms of the standard notion of Set but they are easily understood in terms of the novel notion of Set, as shown in http://forums.randi.org/showpost.php...postcount=1440.

Level 0 of membership can't be but in-vitro (since NOthing is below membership).

The wider (or higher) levels of membership can be in-vivo w.r.t lower levels, or in-vitro w.r.t higher levels.

[realpaladin]

Originally Posted by doronshadmi

Try to understand my answer to you, which is beyond the standard understanding of Set.

Here it is again, and please this time do not try to force the standard view on it, otherwise you are going to miss it again.

1) NOthing is below membership.

2) YESthing (notated by the outer "{" and "}") is above membership.

3) Membership can have infinitely many levels, where each level is wider (or higher) than the previews levels.

4) The smallest level of membership is level 0, and examples of level 0 are: {}, 2, 236.67, etc...

5) The next level of membership is level 1, and examples of level 1 are: {{}, 2, 236.67}, {{}}, {2}, {236.67}, etc...

6) The next level of membership is level 2 , and examples of level 2 are: {{{}, 2, 236.67}}, {{{}}}, {{2}}, {{236.67}}, etc...

7) No level of membership is reducible into NOthing or extensible into YESthing

8) (1) to (7) are not understood in terms of standard notion of Set.

And I score another point. In no circumstance will Doron answer your question. He will answer a self-provided strawman of a question.

1) No explanation why this is, and it has NOTHING to do with Set Theory. Therefore Doron already fails to answer the original question.
2) Again, no explanation on why this is. There is no coherent reason why this is so other than Doron thinking it a neat way to evade the unmasking of his insufficient knowledge.
3) Again, no explanation why this is.
4) etc...

This has absolutely NOTHING to do with any theory, because if you will go the route of asking what you can do with it, or what it is good for, you end up with bovine coprolites about people's awareness and not nuking each other.

Nothing there defines any causal reasoning, neither on a verbal level, a non-verbal level or any other conscious level.

[jsfisher]

It is getting to be about time for another Shadmi Side Shuffle^TM wherein Doron renames everything. It is mostly just rearranging the deck chairs while pretending to introduce yet another deep thought, but sometimes it introduces new contradiction.

His local\non-local complementation has also been XOR\NAND reasoning, not to mention the verbal/visual nonsense in his lastest spewage. My favorite Shadmi Side Shuffle, though, was distinction becoming unity.

This yesthing/nothing pun has worn itself out. Time for some fresh material.

ETA:
Shame on me. I had dismissed this whole in-vitro/in-vivo nonsense as especially silly, even for Doron, and ended up forgetting about it entirely. The Shadmi Side Shuffle is currently in progress with this new in-viagra set theory.

[doronshadmi]

There is a difference at the level of membership between an object that is not a member of a given set, and the same object as a member of a given set, as rigorously shown at http://forums.randi.org/showpost.php...postcount=1526 .

By understanding the different levels of membership S={...} is a lower level of membership than {{...}}.

Let {...} be the set of all sets that are not members of themselves.

{...} as a member of itself is done at a wider (or higher) level of membership {{...}}, or in other words {...} ≠ {{...}}, and as a result there is no paradox, without any need of special axioms, as done by ZF(C).

By using the principle of Occam's razor, the novel notion of levels of membership provides a simpler solution to Russell's Paradox than ZF(C) solution, and also enables to deal with objects (for example, non-local numbers) that that are not found by ZF(C).

Furthermore, the notion of levels of membership and the fact that NOthing is below membership and YESthing is above membership, enables novel understanding of Entropy (both as abstract and\or physical concept).

[zooterkin]

Originally Posted by doronshadmi

There is a difference at the level of membership between an object that is not a member of a given set, and the same object as a member of a given set,

Next contestant, Mrs. Sybil Fawlty from Torquay. Specialist subject - the bleeding obvious.

Quote:

rigorously

Hah!

[realpaladin]

Originally Posted by doronshadmi

There is a difference at the level of membership between an object that is not a member of a given set, and the same object as a member of a given set, as rigorously shown at http://forums.randi.org/showpost.php...postcount=1526 .

Extreme emphasis mine:

Anyone with half a brain does not need more than that highlighted word and the post-link to have it trivially demonstrated that:

Doron Shadmi knows absolutely NOthing about science, let alone math.

[doronshadmi]

Originally Posted by zooterkin

Next contestant, Mrs. Sybil Fawlty from Torquay. Specialist subject - the bleeding obvious.

Hah!

If you have a trauma, than maybe http://www.smd.qmul.ac.uk/Documents/Research/50687.pdf can help you.

I also like http://uncyclopedia.wikia.com/wiki/S...din%27_obvious

[jsfisher]

It is bleeding obvious he had to google "bleeding obvious". This amuses me. I'm reasonably certain he googled "Pakleds", too, but hasn't come up with a clever response, yet, to impress his imaginary friends from the playground.

[doronshadmi]

Let's do it even simpler, by using the notion that the outer "{" and "}" of a given set are not used by any member of that set, in order to avoid Russell's paradox.

By this notion no member of a given set is equivalent to that set, and since Russell's paradox holds only if a member of a given set is equivalent to that set, we can conclude that Russell's paradox does not hold.

For example, {2} is not equivalent to {2,{2}}.

[jsfisher]

Originally Posted by doronshadmi

Let's do it even simpler, by using the notion of outer "{" and "}" that do not belong to any member of any set, in order to avoid Russell's paradox.

Well, there ya go. Solve paradoxes through notation. That is simple...and absolutely incompetent.

[doronshadmi]

Traditional Mathematicians sometimes do not comprehend the notions that are expressed by notations, since they do not use spatial brain's skills (where the term spatial is not restricted only to Geometry) as a significant factor of their reasoning.

For example: (by not using the notion of different levels of membership, exactly as done by Traditional Mathematicians) member {2} is not equivalent to set {{2}} or set {2,{2}}, etc ...

[jsfisher]

Originally Posted by doronshadmi

For example: (by not using the notion of different levels of membership, exactly as done by Traditional Mathematicians) member {2} is not equivalent to set {{2}} or set {2,{2}}, etc ...

So, according to Doron, {2} is equivalent to {{2}} and {2. {2}}.

This Doronetics sure proves itself worthless at ever turn.

[doronshadmi]

Also Traditional Mathematicians wrongly interpret the term "not using the notion of different levels of membership" as if, for example, member {2} is equivalent to set {{2}} or set {2,{2}}, etc...

Once again the lack of spatial reasoning, air its non-view.

[jsfisher]

Originally Posted by doronshadmi

Also Traditional Mathematicians wrongly interpret the term "not using the notion of different levels of membership" as if, for example, member {2} is equivalent to set {{2}} or set {2,{2}}, etc...

Once again the lack of spatial reasoning, air its non-view.

You say stupid things, Doron, you can expect to be called on them. Your reading-comprehension difficulties are evident, again, also. You said:

Originally Posted by doronshadmi

For example: (by not using the notion of different levels of membership, exactly as done by Traditional Mathematicians) member {2} is not equivalent to set {{2}} or set {2,{2}}, etc ...

You said that "Traditional Mathematicians" would NOT see {2}. {{2}}. and {2, {2}} as equivalent, and this you attribute to NOT using your ridiculous "different levels of membership" concept. Let me add that only a moron would consider those three as equivalent. Even Doronetics couldn't possibly consider them equivalent, now could it? Your "different levels of membership" concept isn't that lost from reality, now is it?

[doronshadmi]

Let's look at the Barber case, as written in wikipedia ( http://en.wikipedia.org/wiki/Barber_paradox ):

Quote:

The barber shaves only those men in town who do not shave themselves.

All this seems perfectly logical, until we pose the paradoxical question:

Who shaves the barber?

This question results in a paradox because, according to the statement above, he can either be shaven by:

1. himself, or
2. the barber (which happens to be himself).

However, none of these possibilities are valid! This is because:

• If the barber does shave himself, then the barber (himself) must not shave himself.

• If the barber does not shave himself, then the barber (himself) must shave himself.

In this story the barber is equivalent to the outer "{" and "}" or in other words, it is the considered set.

In that case any attempt to define the barber in terms of a member of that set (belongs , does not belong), is misleading.

[jsfisher]

Originally Posted by doronshadmi

Let's look at the Barber case, as written in wikipedia ( http://en.wikipedia.org/wiki/Barber_paradox ):



In this story the barber is equivalent to the outer "{" and "}" or in other words, it is the considered set.

In that case any attempt to define the barber in terms of a member of that set (belongs , does not belong), is misleading.

The barber is the "considered set"? Doron, you have really lost it. You are trying so very hard to cling to your confused concepts that you have to grasp at utter insanity like this.

The "Barber paradox" is a paradox, and neither the power of Greyskull nor the power of braces can make it go away.

[realpaladin]

If he is ignoring JSFisher... then to him this thread would now look at someone who mumbles to himself.

Can I get an "Oh yeah!" for my diagnosis of OCD in Doron?

[realpaladin]

Originally Posted by jsfisher

You say stupid things, Doron, you can expect to be called on them. Your reading-comprehension difficulties are evident, again, also.
<snippety for brevity>
Even Doronetics couldn't possibly consider them equivalent, now could it? Your "different levels of membership" concept isn't that lost from reality, now is it?

I am getting the feeling that he glimpses things beyond his understanding, but simply is too lazy to do a real study on them.

Without Moshe Klein all Doron Shadmi can do is to revert to his pillpul skills of kibitzing until the opponent gives in.

[sympathic]

Originally Posted by realpaladin

I am getting the feeling that he glimpses things beyond his understanding, but simply is too lazy to do a real study on them.

Without Moshe Klein all Doron Shadmi can do is to revert to his pillpul skills of kibitzing until the opponent gives in.

Doron obsessively tries to apply his OM gibberish to everything that comes to mind whether it is related or not. It is a true illness.

The sad fact is that he refuses to admit that this whole OM gibberish is a balloon filled with hot air. It has no real substance.

His OM ramblings stem out of a graphical representation of the primary numbers 1 and 2, which he then assembles graphically to form all natural numbers. From this he tries to pull out explanations to just about anything known to mankind.

[realpaladin]

Originally Posted by sympathic

Doron obsessively tries to apply his OM gibberish to everything that comes to mind whether it is related or not. It is a true illness.

The sad fact is that he refuses to admit that this whole OM gibberish is a balloon filled with hot air. It has no real substance.

His OM ramblings stem out of a graphical representation of the primary numbers 1 and 2, which he then assembles graphically to form all natural numbers. From this he tries to pull out explanations to just about anything known to mankind.

And beyond... where no Man has gone before...

(since I don't 'get it' I was trying to get secondaries or even tertiary effects... but even those do not seem to exist or anything they point to can be achieved quite effectively with current and past knowledge)

[doronshadmi]

It is important to expose the lack of traditional mathematicians to understand Set also in terms of visual_spatial brain's skills.

By not being restricted only to Geometry, visual_spatial brain's skills enable to understand that the outer "{" and "}" of a given set are not taken in terms of membership (in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).

This post has 3 parts, but first let us use also visual_spatial brain's skills in order to minimally express the fundamental notion of Ploychotomy, which is the dichotomy of NOthing and YESthing complement opposites, as follows:

The definition (and the minimal needed symbolic expression) of the dichotomy of complement opposites:

NOthing (not notated by any symbol) is that has no predecessor.

YESthing (notated by the outer "{" and "}" symbols) is that has no successor.

According to these definitions (and the minimal needed symbolic expression), the empty set (notated as {}) is the minimal expression of NOthing and YESthing complement opposites, where:

1) NOthing (not notated by any symbol) is below membership (it is not understood in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).

2) YESthing (notated by the outer "{" and "}") is above membership (it is not understood in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).

(The complementarity of NOthing and YESthing is derived from Unity (thing) among them, and it is discussed in part 3 of this post).

By following the notions as described above, the empty set {} expression is understood as follows:

The outer "{" "}" represent YESthing, no symbols between the outer "{" "}" represent NOthing, where both NOthing and YESthing are not understood in terms of membership ("belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).

By dealing also with the concept of non-empty set (according to the notions above) the universe of members is between YESthing and NOthing, where NOthing and YESthing are not understood in terms of membership ("belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).

An example: The considered universe, in the case of members 2 and {2}, is {2,{2}}, where the outer "{" "}" is above membership (it is not understood in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).


------------------------------------------------------------

Part 1:

In this part we are using the novel notion of outer "{" and "}" (as described above) in order to understand the relations among sets and members, by translating the Barber story into sets and members.

First, here is the story as quoted from Wikipedia ( http://en.wikipedia.org/wiki/Barber_paradox ):

Quote:

The barber shaves only those men in town who do not shave themselves.

All this seems perfectly logical, until we pose the paradoxical question:

Who shaves the barber?


This question results in a paradox because, according to the statement above, he can either be shaven by:

1. himself, or
2. the barber (which happens to be himself).

However, none of these possibilities are valid! This is because:

• If the barber does shave himself, then the barber (himself) must not shave himself.
• If the barber does not shave himself, then the barber (himself) must shave himself.

Let us translate this story into the concept of sets and members, by using the novel relation between these concepts.

"The barber shaves" is equivalent to the outer "{" and "}" (YESthing), where the outer "{" "}" (YESthing) is above membership (it is not understood in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).

"only those men in town who do not shave themselves." is equivalent to the members, which are (below the outer "{" "}" (YESthing), which is above membership (it is not understood in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic)) AND (above NOthing (not notated by any symbol), which is below membership (it is not understood in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic)).

So "the Berber shaves" can't be below the outer "{" "}" (YESthing), which is above membership (it is not understood in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic)).

The "paradox" is artificially derived from the attempt to define "The barber shaves" is terms of membership by missing the fact that it is above membership ("The barber shaves" can't be defined in terms of "belong to" , "does not belong to" or partial belonging as done by Fuzzy logic).

By understanding the difference of being a set and being a member of a given set, Russell's paradox is naturally avoided, without any need of special axioms (as done, for example, by ZF(C)).

------------------------------------------------------------

Part 2:

In this part we are using the novel notion of different level of membership, such that no member is reducible into NOthing or extensible into YESthing, as follows:

1) NOthing (not notated by any symbol) is below membership.

2) YESthing (notated by the outer "{" and "}") is above membership.

3) Membership can have infinitely many levels, where each level is wider (or higher) than the previews levels.

4) No level of membership is reducible into NOthing or extensible into YESthing.

5) The smallest level of membership is level 0, and examples of level 0 are: {}, 2, 236.67, etc...

6) The next level of membership is level 1, and examples of level 1 are: {{}, 2, 236.67}, {{}}, {2}, {236.67}, etc...

7) The next level of membership is level 2 , and examples of level 2 are: {{{}, 2, 236.67}}, {{{}}}, {{2}}, {{236.67}}, etc...

8) There can be several different levels of membership in a given expression, for example: {}, {{}, 2, 236.67}, 2 ,{{{}}}, {{{{{236.67}}, 2}}} , etc ...

(1) to (8) are not understood in terms of the standard notion of Set (which does not distinguish between the difference of being a set and being a member of a given set) but they are easily understood in terms of the novel notion of Set, as shown in part 3 of this post.

Level 0 of membership can't be but in-vitro (since NOthing is below membership).

The wider (or higher) levels of membership can be in-vivo w.r.t lower levels, or in-vitro w.r.t higher levels.

The terms in-vitro (the object is isolated from a wider environment, for example: 2) and in-vivo (the object is not isolated from a wider environment, for example: {2} or {2,{2}} etc...) are not restricted here only to biological systems.

------------------------------------------------------------

Part 3:

In this part we define the considered framework in terms of Unity, as follows:

Let's use a cross-section of Riemann sphere through its 0 and ∞ poles.

The concept of Set is closed under the polychotomy of YESthing and NOthing.

That is among polychotomy is thing (known also as Unity), as follows:

http://farm8.staticflickr.com/7043/6...c426828a_z.jpg

NOthing is weaker than any tool that is used to measure it.

YESthing is stronger than any tool that is used to measure it.

Unity (thing) is among NO,SOME,EVERY,YES ploychotomy.

-----------------------------

By following the notions above the outer "{" "}" represent YESthing, no symbols between the outer "{" "}" represent NOthing, and between these extremes we have SOMEthing and EVERYthing.

According to these notions the universe of members is between YESthing and NOthing, where NOthing and YESthing are not one of the members (members that are not at level 0 can have outer "{" "}", which are always below the outer "{" "}" of a given set).

(An example: The considered universe in the case of 2 and {2} is {2,{2}}, where the outer "{" "}" is above membership).

[realpaladin]

[doronshadmi]

By understanding http://forums.randi.org/showpost.php...postcount=1546 let's use it in order to get the notions of some notations.

2 is some level 0 membership, or in other words, it is only in-vitro.

If 2 is understood as |{{},{{}}}| or |{{{}}}|, then 2 is a measurement tool of level 2 membership in the case of {{{}}}, or the mixing of level 1 and level 2 memberships in the case of {{},{{}}}, where the internal "{" and "}" are in-vitro w.r.t the external "{" and "}" and the external "{" and "}" are in-vivo w.r.t internal "{" and "}".

By not using 2 as a measurement tool, it is only in-vitro, as already shown above.

If we use in-vivo on {1,2,3} (where the in-vivo is done by the outer "{" and "}"), then it is possible to define {2} as the in-vivo w.r.t 2 (which is in-viteo w.r.t {2}).

In no way any given member is complete, since it is not reducible into NOthing and\or it is not extensible into YESthing.

Furthermore, by understanding Unity (thing) among Polychotomy, NO,SOME,EVERY,YES are incomplete w.r.t Unity.

[realpaladin]

[doronshadmi]

"The set of all ideas" is in itself an idea.

If the "The set of all ideas" is one of its members, then by not ignoring the levels of membership we get "The set of all ideas (of all ideas)", which is not "The set of all ideas".

"The set of all ideas (of all ideas)" is in itself an idea.

If the "The set of all ideas (of all ideas)" is one of its members, then by not ignoring the levels of membership we get "The set of all ideas (of all ideas (of all ideas))", which is not "The set of all ideas (of all ideas)".

Etc... ad infinitude ... , such that "The set of all ideas (of all ideas (of all ideas (of all ideas (of all ideas))))..." is inherently incomplete.

-----------------------

In the case of the Barber story, since a set and a member of that set are not at the same level, then what is true for the set is not necessarily true for being a member of that set, for example:

In order to be a member in the Barber story, each member must be shaved by the barber, which does not change the fact that parsons that shave themselves are also resulted by a shaved face.

So we get two sets of persons with shaved faces, which is not necessarily true for the barber, because by being at the level of set he can have, for example, a beard, or in other words, it is not a member of both sets of persons with shaved faces.

In this case the question "Who shaves the barber's face?" is irrelevant to the true condition of the barber's face.

[zooterkin]

Originally Posted by doronshadmi

"The set of all ideas" is in itself an idea.

If the "The set of all ideas" is one of its members, then by not ignoring the levels of membership we get "The set of all ideas (of all ideas)", which is not "The set of all ideas".

"The set of all ideas (of all ideas)" is in itself an idea.

If the "The set of all ideas (of all ideas)" is one of its members, then by not ignoring the levels of membership we get "The set of all ideas (of all ideas (of all ideas))", which is not "The set of all ideas (of all ideas)".

Etc... ad infinitude ... , such that "The set of all ideas (of all ideas (of all ideas (of all ideas (of all ideas))))..." is inherently incomplete.

-----------------------

In the case of the Barber story, since a set and a member of that set are not at the same level, then what is true for the set is not necessarily true for being a member of that set, for example:

In order to be a member in the Barber story, each member must be shaved by the barber, which does not change the fact that parsons that shave themselves are also resulted by a shaved face.

So we get two sets of persons with shaved faces, which is not necessarily true for the barber, because by being at the level of set he can have, for example, a beard, or in other words, it is not a member of both sets of persons with shaved faces.

In this case the question "Who shaves the barber's face?" is irrelevant to the true condition of the barber's face.

Perhaps the barber is a woman?

[laca]

Originally Posted by zooterkin

Perhaps the barber is a woman?

Oh, snap!

[doronshadmi]

Originally Posted by zooterkin

Perhaps the barber is a woman?

This non-paradoxical joke can be found in ( http://en.wikipedia.org/wiki/Barber_paradox ).

I am talking about these claims, taken from ( http://en.wikipedia.org/wiki/Barber_paradox ):

Quote:

Notice that the paradox still occurs if we claim that the barber is a man in our town with a beard. In this case, the barber does not shave himself (because he has a beard); but then according to his claim (that he shaves all men who do not shave themselves), he must shave himself.

In a similar way, the paradox still occurs if the barber is a man in our town who cannot grow a beard. Once again, he does not shave himself (because he has no hair on his face), but that implies that he does shave himself.

Both claims are wrong, since the act of shaving one's face is true at the level of a member of a given set, but it is not necessarily true at the level of a set, and the barber is equivalent to the level of a set (it is not necessarily true about the barber's face), as shown in part 1 of http://forums.randi.org/showpost.php...postcount=1546 .

In my opinion, Humor is the taste of life as long as it feeds life's development.

[jsfisher]

Originally Posted by doronshadmi

"The set of all ideas" is in itself an idea....

Yes, and this is way the naive set theory is, well, naive. It isn't suitable for any formal result that admits this sort of self-reference.

Why do you insist on deriving Doronetics from something known not to work?

[doronshadmi]

Traditional mathematicians do not understand that the inherent incompleteness of the concept of Set is the inability of its members to be reducible into NOthing (not notated by any symbol) or to be extensible into YESthing (notated by the outer "{" and "}" symbols).

This inability is significant in order to understand Non-Entropic (naturally open) abstract or physical frameworks.

The attempt to define completeness at the level of membership, actually prevents the understanding of Non-Entropic (naturally open) abstract or physical frameworks.

It has to be stressed the understanding of Non-Entropic (naturally open) abstract or physical frameworks, is essential for further development of living creatures.

[doronshadmi]

Good luck K. Ghosh.

http://ijpam.eu/contents/2012-76-2/11/11.pdf

[doronshadmi]

A 1-dimensional element along the edges of 2-dimensional Möbius strip, is a single reflexive element in 3-dimensional space (as can be seen in the following picture):

Any partial observation along the 2-dimensional Möbius strip is resulted by 2 opposite 1-dimensional elements along its edges.

Without a loss of generality, the given example is a visual_spatial proof that the sum of partial observations is not the same as the whole observation.

This result is equivalent to the inability of some collection of lower (abstract or physical) spaces to fully cover a given higher (abstract or physical) space.

[zooterkin]

Originally Posted by doronshadmi

This result is equivalent to the inability of some collection of lower (abstract or physical) spaces to fully cover a given higher (abstract or physical) space.

No.

[doronshadmi]

Originally Posted by zooterkin

No.

Yes. A collection of lower spaces is not the same as the whole higher space, according to http://forums.randi.org/showpost.php...postcount=1557 .

[jsfisher]

Originally Posted by doronshadmi

Without a loss of generality

We can only hope that someday Doron learns what that phrase really means and how it is used. Today is not that day.

Quote:

...the given example is a visual_spatial proof that the sum of partial observations is not the same as the whole observation.

In fact, it is not a proof of any sort, but it is a fine demonstration of just the opposite of what Doron claims as true.

So, once again, Doron attempts to make his point by contradicting himself.