Deeper than primes

[jsfisher]

You can't blame him for trying. There's something attractive about finding a way to objectify qualities and subjectify quantities.
Objectify qualities and we can have an objective morality where what's right can in a sense be calculated.
Subjectify quantities and we're not mere statistics. I'm not a number but a free man.
Doron has his own answer to Dualism.
It's not the only way out oif the dillema, but it's his, his very own religion.

Unfortunately the cost of it is to sogg mathematics.

That it is a religions is very clear. As for it warping Mathematics, it didn't have to be so. Had Doron explored his notions as a philosophic point of view and then looked towards how that might influence a new branch of Mathematics, he'd have been fine. He didn't do that. Instead, his took them as not a view, but the view, the only possible view which in turn led to contradiction with most of Mathematics.

More unfortunate is that it appears Doron's notions are not based on any sort of new insight, but on a complete misunderstandings of some basic principals.

 

[doronshadmi]

Wow! Talk about biting the hand....

Oh, well. Now, back to an earlier question. You'd said your notion of between was "derived directly form the must have property of any collection of all distinct objects (the standard mathematical notion)." What property of any collection would that be?

Its completeness (the tarm all is used at http://www.internationalskeptics.com/forums/showpost.php?p=4722270&postcount=2875 ).

 

[doronshadmi]

That it is a religions is very clear.

You are right, weak emergence became the dogma of the mathematical science.

It is about time to change this dogma, in order to avoid this beautiful science to be some kind of a religion (which is the exact state of Standard Math).

Instead, his took them as not a view, but the view, the only possible view ...

This is the very notion of the Organic view, to gather different mathematical branches into a one framework, where each current or future developed branches, will be developed without disconnected from The Tree of Mathematics.

By your alternative, where each mathematical framework is totally disconnected, you cannot use the term "Brach", because it has a meaning only under a one organic framework, exactly as Organic Mathematics claims.

More unfortunate is that it appears Doron's notions are not based on any sort of new insight, but on a complete misunderstandings of some basic principals.

This is the typical conclusion of a person that uses weak emergence as a dogma.

 

[Apathia]

It is a simple and a qualitative distinction.

a) Relation is always non-local.

Of course. But you do see don't you that we speak of relations of relations, so that one realtion is in the Local slot and the other in the Non-Local slot?
I guess not.

Also you do not get Singularity's self reference as the bridging between the local AND the non-local.

I see what you do with this. It's a fascinating device.
But the trouble comes down to your making of the non-local a domain.
Yes, I know, there's Non-Local in its "self state." and then non-local as one end of the bridge. But these two keep getting conflated with each other.
And that makes for confusing contradictions.

BTW I like the "Bridging" metaphor much better than this "between" business that makes instant inconsistancy.

What you call Mathematics is the limited case of weak emergence, where the Whole is the sum of its parts.

Organic Mathematics is a non-standard Strong Emergence Theory, where the Whole is greater than the sum of the (not its, but the) Parts.

Math people, is there such a thing in mathematics as to deal with emerging properties?

I'm inclined to give Doron the point here if mathematics has no way to describe emergence.
Though I'm not keen on some kind of retrofit to arithmetic and algebra such that sums are indeterminate or a range of different values.

In order to start to get it please read at least http://www.geocities.com/complementarytheory/OMPT.pdf page 17.

In other words Apathia, your criticism is based on a fundamental misunderstanding, and therefore it is not relevant, in this case.

First make your homework before you air your view about OM.

I've probably spent more time wit your various .pdfs than anyone here.
As the others have expirenced, when I go to the pages you cite, I find merely a repeat of the same dense verbage without any clarifying definitions or information.

I've had to grope my way through hitting, but mostly missing the intent of your presentation.

As the others, I am unable to find an ultimate coherence to your ideas.

Some example: = + (what you call Relation Relation) is meaningless at OM.

Some example: 1 __ ((what you call element element) is meaningless at OM.

Only relation element or element relation can have a meaning at OM.

Are the combos Local/Local and Non-Local/Local also meaningless?
Are relation element and element relation the same thing?
I kind of hope not.

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

On the contrary to Obama's slogan:

NO, YOU CAN'T!

[/QUOTE]

I sure can't argue with that.

 

[doronshadmi]

Again,

Your fandametal mistake Apathia is that you have a "crisp notion" of what Math is not.

There is no difference between you, jsfisher or The Man that have a "crisp notion" of what Math is.

Your both "crisp notions" are wrong, because you do not get that OM is a non-standard Strong Emeregence, that cannot be understood by using Standard or Weak Strong Emeregence.

Are the combos Local/Local and Non-Local/Local also meaningless?

Your question is meaningless.

Are relation element and element relation the same thing?

From parallel observation yes, from serial observation no.

As the others, I am unable to find an ultimate coherence to your ideas.

Because you try to get a non-standard Strong Emergence Reasoning in terms of Standard or Weak Strong Emergence.

BTW I like the "Bridging" metaphor much better than this "between" business that makes instant inconsistancy.

It is not a metaphor, it is a rigorous mathematical definition.

This time please read very carefully all of http://www.geocities.com/complementarytheory/OMPT.pdf .

Be aware of the fact that I improve it all the time.

Math people, is there such a thing in mathematics as to deal with emerging properties?

Yes, but only in terms of Standard Strong Emergence, where the Whole is greater than the sum of its Parts.

 

[jsfisher]

First off, I need to make a correction. The "must have property" in question related to immediate successor and immediate predecessor, not between. I mistyped.

That said...

Its completeness

This is very surprising, Doron, since completeness is not a collection property.

Did you mean something else? The only restriction you'd imposed on the original "some collection" was that it have a cardinality > 1 (and that all its members be distinct objects, but that's already a given).

 

[doronshadmi]

This is very surprising, Doron, since completeness is not a collection property.

Yes I know, the term all is used only as a decoration, isn't it jsfisher?

 

[jsfisher]

Math people, is there such a thing in mathematics as to deal with emerging properties?

I'm inclined to give Doron the point here if mathematics has no way to describe emergence.

In a context sensitive way, yes, Mathematics deals with emergence (at least insofar as I understand the term). If I may borrow Doron's necklace analogy, the necklace exceeds the sum of the beads and string separately. The beads have order and binding in the necklace they didn't have alone.

If I understand weak and strong emergence correctly, it isn't that the whole may exceed the sum of its parts (which is the only way I think Doron has used it), but that the whole can be different from its parts. The parts can lose their separate identity. In a real sense, 1 + 2 = 3 is an example of this in that two things are united into one thing, and the one thing has no distinguishable parts.

Again, it depends on context. Emergence consequences can appear or disappear depending on what's under consideration.

 

[jsfisher]

Yes I know, the term all is used only as a decoration, isn't it jsfisher?

Either way, completeness is not a collection property.

But let's also consider just how you used the term, all:

it is derived directly form the must have property of any collection of all distinct objects (the standard mathematical notion).

Your use of all is somewhat ambiguous.

You could have meant "any collection of all possible distinct objects", except then the word "any" jumps out as odd since there shouldn't be more than one of these things. Moreover, this wouldn't be a collection, either, but a proper class. You didn't say "the proper class of all distinct objects."

No, that interpretation doesn't work.

Doron, how often have you said something like "a set where all the members are distinct and order is not important"? Everything after "a set" is redundant. With you history of expression, it seemed more reasonable to assume you meant "any collection in which all members are distinct objects."

Not only was this second interpretation consistent with your style, it is also consistent with the original requirement, that the collection need only have cardinality > 1.

So, that was the interpretation of your words I used. Is there some other interpretation you intended that still maintains consistency with the cardinality requirement?

And where is this completeness property requirement coming from?

 

[Little 10 Toes]

"magnitude of existence" definition

Do you really do not get that Emptiness has the least magnitude (where "magnitude" is a measurement unit) of existence, and its opposite, called Fullness has the most magnitude of existence?

It is a straightforward notion.

So in the phrase "magnitude of existence", you say that magnitude is a measurement unit. What is it measuring?

 

[doronshadmi]

Again, it depends on context.

Just tell to a mathematician that Cantor's second diagonal argument is not a proof of non-countability, but it is a proof of the incompleteness of any non-finite given collection, and you immediately see his ability to be opened to new ideas.

Just ask a mathematician to define a line in terms of dragging a point, and you will find that he uses this term without understand the consequences if this claim.

Just show to a mathematician that any collocation that he uses obeys the use of the universal quantifier "for all" that determined by him, and as a result of his determination there must be, for example, an immediate predecessor to y in the case of [x,y), and you will see that he does not understand the consequences if his own determinations.

Things first must be notions' dependent.

Without notions there is no context, and the notion that stands at the basis of the world "context" is exactly the string\bead bridging where the "con" is the string aspect and the "text" is the bead aspect of the bridging.

As long as the mathematicians do not get the notions of their own frameworks, this science will stay notionless mechanic action.

You could have meant "any collection of all possible distinct objects", except then the word "any" jumps out as odd since there shouldn't be more than one of these things. Moreover, this wouldn't be a collection, either, but a proper class.

Look how twisted and complicated is the notion of this mathematician.

Instead of simply get the consequences of using the universal quantifier in [x,y) case (and as a result, there must be an immediate predecessor to y, that actually cannot be found and leads to contradiction) the mathematician will use a complicated maneuver in order to avoid the straightforward consequences of his own determinations.

a proper class

This is the nice word that the mathematicians invented in order to avoid the contradictions of their own the determinations.

Instead of face them they through them to the pinky garbage can, called by them "proper class", and everybody are happy (but stay notationless).

And where is this completeness property requirement coming from?

From your own determinations and use of the the universal quantifier in [x,y) case.

 

[doronshadmi]

So in the phrase "magnitude of existence", you say that magnitude is a measurement unit. What is it measuring?

This is a beautiful question.

As I get it, Measuring is the notion that stands at the basis of the determination to understand many things by using a common principle that help us to compare them with each other.


According to http://en.wikipedia.org/wiki/Measure_theory the common principle is a collection of distenct elements (a set).

 

[jsfisher]

Just tell to a mathematician that Cantor's second diagonal argument is not a proof of non-countability, but it is a proof of the incompleteness of any non-finite given collection, and you immediately see his ability to be opened to new ideas.

You have previously alleged defects in Cantor's proof. As stated before, allegation doesn't equal fact. When pressed for fact, you fell flat. All you were able to demonstrate was your lack of understanding of Cantor's proof.

Just ask a mathematician to define a line in terms of dragging a point, and you will find that he uses this term without understand the consequences if this claim.

You seem hung up on this poetic aside (and not my aside, by the way). Perhaps you should discuss it with its author to better understand what he meant rather than hound me with this straw man. No, wait, understanding isn't your goal, is it?

Just show to a mathematician that any collocation that he uses obeys the use of the universal quantifier "for all" that determined by him, and as a result of his determination there must be, for example, an immediate predecessor to y in the case of [x,y), and you will see that he does not understand the consequences if his own determinations.

Multiple instances of nonsense, here. For starters, collocation? Did you really misspell collection that badly? Also, the original statement only required a collection have cardinality > 1. The ambiguous all (not for all, by the way) was introduced later as either movement of the goal posts or an irrelevant redundancy -- an ambiguity you have not yet resolved, by the way, Doron.

Then again, since understanding isn't your goal, I doubt you will address the ambiguity. Instead you will leave your grand string of relevance and poorly worded statements to lay cover for your bogus proclamation that completeness is a "must have" collection property.

...<gibberish>...
Instead of simply get the consequences of using the universal quantifier in [x,y) case (and as a result, there must be an immediate predecessor to y, that actually cannot be found and leads to contradiction) the mathematician will use a complicated maneuver in order to avoid the straightforward consequences of his own determinations.

Again, you allege something, but you can not provide any proof. And again, instead of demonstrating your point, you display you lack of understanding of a simple construct, the universal qualifer in this case.

Be that as it may, here again for everyone's reference is Doron's original claim that's now under fire:

for any given immediate successor of some collection that its cardinal > 1 there must be an immediate predecessor, and for any given immediate predecessor of some collection that its cardinal > 1 there must be an immediate successor.

Note that the word all appears nowhere in the claim. Note also that Doron cannot support the claim.

 

[The Man]

In other words Apathia, your criticism is based on a fundamental misunderstanding, and therefore it is not relevant, in this case.

First make your homework before you air your view about OM.

Your fandametal mistake Apathia is that you have a "crisp notion" of what Math is not.

There is no difference between you, jsfisher or The Man that have a "crisp notion" of what Math is.

Your both "crisp notions" are wrong, because you do not get that OM is a non-standard Strong Emeregence, that cannot be understood by using Standard or Weak Strong Emeregence.

Did I not tell you it was only a matter of time before we were accused of being entirely too ‘crisp’.

 

[doronshadmi]

an ambiguity you have not yet resolved, by the way, Doron.

An ambiguity you have not yet resolved, by the way, jsfisher, which is a direct result of your limited Weak Emergence viewpoint, which is also a notionless mechanic action.

 

[doronshadmi]

Did I not tell you it was only a matter of time before we were accused of being entirely too ‘crisp’.

It is "crisp notion" in terms of a notionless mechanic action, something like dragging a point.

 

[Little 10 Toes]

"magnitude of existence" definiton

This is a beautiful question.

As I get it, Measuring is the notion that stands at the basis of the determination to understand many things by using a common principle that help us to compare them with each other.


According to http://en.wikipedia.org/wiki/Measure_theory the common principle is a collection of distenct elements (a set).

Too bad you don't actually answer the question directly.

I'll make it simple, when you say "magnitude of exsistence", are you measuring the number of distinct objects in a collection?

[ ] Yes
[ ] No

 

[doronshadmi]

Too bad you don't actually answer the question directly.

I'll make it simple, when you say "magnitude of exsistence", are you measuring the number of distinct objects in a collection?

[ ] Yes
[ ] No

[v]Yes (but instead of "distinct objects" I use "the existence of objects")

0 magnitude = no existing objects (Emptiness (the totality of non-existence)).

∞ magnitude = beyond existing objects (Fullness (the totality of existence)).

0 < n < ∞ , n magnitude = existing objects (the non-total existence).

 

[The Man]

It is "crisp notion" in terms of a notionless mechanic action, something like dragging a point.

Now you are claiming a “notionless” “notion”, how uncharacteristic of you.

 

[The Man]

An ambiguity you have not yet resolved, by the way, jsfisher, which is a direct result of your limited Weak Emergence viewpoint, which is also a notionless mechanic action.

Ah the interaction of the credulous with the gullible, you just provide the ambiguities and expect those gullible enough to resolve them for themselves.