Deeper than primes

[jsfisher]

http://www.internationalskeptics.com/forums/showpost.php?p=4653568&postcount=2500

Yes, I agree. You were wrong in that post, too.

 

[doronshadmi]

You cite a reference for you latest vocabulary addition that clearly states the "empty fusion" is impossible, then you proceed to use this impossibility as an actual object. Not only that, you use it as a member of a member-less set.

Are you still confused why we regard many of your statements as contradictory?



I'll leave identifying the absurdities of this part of the statement as an exercise for the interested reader.

Yes, it is impossible on its own.

This is exactly why Emptiness or Fullness are not researchable on their own.

But if they are investigated under a collection framework, then they are researchable, for example: |{ }| = 0 where 0 is the cardinal of the empty fusion.

This time please do not ignore Organic Mathematics Framework:

[qimg]http://www.geocities.com/complementarytheory/OMF.jpg[/qimg]​

You also ignored this part of http://www.internationalskeptics.com/forums/showpost.php?p=4653568&postcount=2500 :

EDIT:

In other words collections are used to measure the existence of both collections or fusions.

On the contrary, fusions cannot be used to measure the existence of collections or fusions, because fusions' existence can be also too weak (in the case of Emptiness) or too strong (in the case of Fullness).

This is exactly the reason of why mathematicians are using collection (and not fusion) as a measurment tool.

http://www.internationalskeptics.com/forums/showpost.php...postcount=2500

Yes, I agree. You were wrong in that post, too.

In order to agree (or not) with X you first have to show that you understand X.

It is clearly shown above that you do not get X ( where X, in this case, is http://www.internationalskeptics.com/forums/showpost.php?p=4653568&postcount=2500 ).

This time please provide more details about X.

EDIT:

Some correction of http://www.internationalskeptics.com/forums/showpost.php?p=4653568&postcount=2500 :

Instead of:

Since cardinality measures the existence of things, it is used here to also measure their absence (as clearly shown above by using the independent existence of the ZF axiom of the empty set from the description of the axiom).

it has to be:

Since cardinality measures the existence of things, it is used here to also measure their absence (as clearly shown above by using the independent existence of the the empty set from the description of the ZF axiom of the empty set).

In this part I show that Cardinality's measurement (of fusions or collections, it does not matter) is possible only under the pre-existence of a collection, and the value of some cardinality is not equivalent to the measured thing (for example 0 is not equivalent to Emptiness), exactly as the empty set's existence does not depend on the description of the ZF axiom of the empty set (but the empty set's property depends on the description of the ZF axiom of the empty set).

Again, "the empty set's existence" is not the same as "the empty set's property", exactly as a collection (known by that name "Set") exists whether it is empty or not.

The ZF axiom of the empty set determinates only the property of the empty set.

If the ZF axiom of the empty set determinates the existence of the empty set, then a circular reasoning is used as follows:

Set A is empty iff any given set (including A) is not a member of A.

If the ZF axiom of the empty set determines the existence of A, then a circular reasoning is used because this axiom uses A in order to determine the existence of A, which is without a doubt a circular reasoning.

In order to avoid it, the ZF axiom of the empty set determinates only the property of the empty set and defiantly not its existence.

Jsfisher, if you cannot get this simple fact you do not understand the ZF axiom of the empty set.

 

[doronshadmi]

There's this English proverb containing the nouns "pearls" and "swine".

There is ddt that cannot support his own arguments.

 

[doronshadmi]

If the existence of a measurement tool is not available under research, then it cannot be used as a valid measurement tool.

This is exactly the case of fusions, for example:

fusion X – fusion X = Emptiness

In order to measure Emptiness (the result of fusion X – fusion X) we cannot use a fusion, because if fusion X – fusion X, then no measurement tool is available for the reseach of the magnitude of existence of Emptiness.

It can be done only indirectly by using collection as a measurement tool instead of fusion.

The reason of why it can be done by collection is based of the fact that the collection's existence is independent of it's investigated things (where these things can be collections or fusions).

The independency of existence from the researched things is a must have term for any measurement tool, which enables to determine the Cardinality (the magnitude of existence) of the researched (collections or fusions).

In the case of the empty set, the existing collection { } is used as a measurement tool in order to determine
the magnitude of existence of fusion X – fusion X = Emptiness = Empty fusion under collection, such that |{ }| = 0 where 0 is not the same as fusion X – fusion X = Emptiness.

One claims that also collection X – collection X = Emptiness. In this case one actually determines the existence of collection in terms of the existence of a fusion, so in this case we deal with a fusion that its name is 'collection' (which is not the same as collection).

Here is a quate, taken from Michael D. Potter's book "Set theory and its philosophy" page 21 in http://books.google.com/books?id=Fx...er&source=gbs_similarbooks_r&cad=4_2#PPA21,M1 :

... But the standard cases have a tendency to obscure the distinction between two quite different ways in which it has been taken that things can be aggregated – collection and fusion. Both are formed by bundling objects together, but a fusion is no more than the sum of its parts, whereas a collection is something more. ...

This "something more" is exactly the ability of a collection to be available (to exist) as a measurement tool during research (independently of the researched whether it is a collection –empty or not- or a fusion –empty or not-), which is an ability of existence that a fusion does not have.

Again, the term Empty fusion has a meaning only under the framework of collection , where the a collection is a measurement tool that its existence is independent of the measured things.

 

[jsfisher]

Yes, it is impossible on its own.

It is impossible, period. I notice, too, you fail to address your contradictory "member of a member-less set".

This is exactly why Emptiness or Fullness are not researchable on their own.

This is all unnecessary nonsense. You insist it must be so, but you can demonstrate no inadequacy it overcomes. Instead you introduce contradiction.

But if they are investigated under a collection framework, then they are researchable, for example: |{ }| = 0 where 0 is the cardinal of the empty fusion.

Figure out what cardinality really means and use the term correctly. This perpetual misunderstanding by you of all things mathematical doesn't lend much to your credibility as a great thinker.

This time please do not ignore Organic Mathematics Framework:

Your so-called framework is nothing close to a framework. Your treatise is a poorly written tour of unrelated constructs. It has its own battery of reasoning circles, contradictions, and gibberish. There is nothing organic about it, and certainly nothing that can be described as coherent Mathematics.

You also ignored this part of http://www.internationalskeptics.com/forums/showpost.php?p=4653568&postcount=2500

I didn't ignore it. It was just more repetition of nonsense you'd made up. Your fantastical ideas are without purpose, necessity, foundation, or consistency.

In order to agree (or not) with X you first have to show that you understand X.

This is precisely what you have failed to do. You disagree with Mathematics, yet you have demonstrated repeatedly you don't understand Mathematics.

It is clearly shown above that you do not get X...This time please provide more details about X.

As has been pointed out to you, Doron, your foundation is faulty. There is no point in considering where you think you end up when your starting point is all wrong.

EDIT:

Some correction of http://www.internationalskeptics.com/forums/showpost.php?p=4653568&postcount=2500 :

You have an interesting usage of the word, correction. It is still wrong for the reasons already given.

...
The ZF axiom of the empty set determinates only the property of the empty set.

Is it that reading comprehension thing? Which part of "There exists" from the Axiom of the Empty Set confuses you?

If the ZF axiom of the empty set determinates the existence of the empty set, then a circular reasoning is used as follows:

Set A is empty iff any given set (including A) is not a member of A.

If the ZF axiom of the empty set determines the existence of A, then a circular reasoning is used because this axiom uses A in order to determine the existence of A, which is without a doubt a circular reasoning.

The Axiom isn't what you say it is. You prove again you and Mathematics are complete strangers. Here it is again

[latex]$$$ \exists x\, \forall y\, \lnot (y \in x) $$$[/latex]​

Is it that universal qualifier that's tripping you up?

In order to avoid it, the ZF axiom of the empty set determinates only the property of the empty set and defiantly not its existence.

Jsfisher, if you cannot get this simple fact you do not understand the ZF axiom of the empty set.

Let's see: You can't even quote the Axiom correctly, but you accuse me of not understanding it. How curious.

 

[doronshadmi]

In other words jsfisher, you are not able to deal with mathematical stuff from a philosophical or fundamental reasoning points of view, as clealry written in http://www.internationalskeptics.com/forums/showpost.php?p=4655247&postcount=2522 and http://www.internationalskeptics.com/forums/showpost.php?p=4655517&postcount=2524 .

 

[The Man]

Ho yes it is.

" " is an existing (empty) description exactly as { } is an existing (empty) set.

Who are you calling a ‘Ho’?

“ “ is not a description it is a space in quotation marks, { } is not a description it is a space between brackets. Both of those are representations, what follows them in the previous statement are descriptions as this statement is also a description of that statement. Representations are not descriptions, but require descriptions in order to indicate exactly what it is you’re trying to represent. You have plenty of representations, Doron, and very few descriptions.

The axiom describes the property of the empty set, and it does not determine its existence.

You still do not have a clue as to what an axiom is, do you?

Exactly, and this meaning is achieved only by using the notion of fusion as a member of the empty set and not the notion of collection as the member of the empty set.

No Doron its meaning is archived by not ascribing to it, well, members. Whether you call them ‘fusion’ or 'collection'.

Empty fusion = = the absence of collections and\or fusions

No Doron an empty fusion only means that no fusion is possible, it says nothing about a collection.

Empty collection = { }

Now if you only understood what that represents.

It is clearly shown that the members of { } are defined in terms of Empty fusion and not in terms of Empty collection.

It is clearly shown that you have no idea what you are talking about and continue to misrepresent a set that has no members as, well, having members.

Did you forget this?

Empty collection = { }

That is you defining { } “in terms of Empty collection”. Again if you cannot even be bothered to agree with what you claim then why could you possibly expect anyone else to?

Cardinality value can be taken only by using a collection.

Well since Cardinality is the measure of size for a ‘collection’ or set that is rather trivial, but it is taken for a collection not so much by “using a collection”. For example your habit of taking the cardinality of a collection by making it a subset of another collection then taking the cardinality of that other collection is completely ludicrous and is simply a tool so you can lie to yourself that your minimum ‘measure of existence’ or ‘cardinality’ for a set or ‘collection’ is 1

A collection (whether it is empty or not, it does not matter) is first of all an existing thing, that in the case of Cardinality it is used as a tool to determine the magnitude of the existence of the possible members that belong to it. these members can be collections, fusions where fusions can be empty ({ }) or full( {_}_ }.

No Doron; empty set = empty collection = no members = cardinality 0 = { }. It is all quite trivial yet, you seem to have some extreme problems understanding that and have in fact created this whole fantasy ‘paradigm shift’ based on your inability to grasp such a simple concept.

Again, the value of a cardinal is determined by the magnitude of the existence of some set's members, so in the case of B={A}, |{A}| determinates the magnitude of the existence of A, which in this case it is the member of B.

If some set has more than a one existing member, then the velue of that cardinal is the sum of the the existing members.

Doron you have clearly demonstrated before that you have absolutely no grasp of the meaning of cardinality and there is no need to continue demonstrating that by such ridiculous, ludicrous and patently false statements.

I write my terms in simple and straight forward way right here on this thread.

Your history clearly demonstrates that your rough thinking cannot get the outcomes of a fine thinking.

What a crock of some mighty fine crap you’ve got going there. You should actually try to understand the concepts you are speaking of, before you injure your arm patting yourself on the back for your ‘fine thinking’.

 

[jsfisher]

In other words jsfisher, you are not able to deal with mathematical stuff from a philosophical or fundamental reasoning points of view, as clealry written in http://www.internationalskeptics.com/forums/showpost.php?p=4655247&postcount=2522 and http://www.internationalskeptics.com/forums/showpost.php?p=4655517&postcount=2524 .

Project much?

By the way, how's it coming with your explanation of what you mean by "distinction is a first order property"? Got anything, yet?

 

[doronshadmi]

Jsfisher I must admit that you are a skillful rough thinker.

Is it that reading comprehension thing? Which part of "There exists" from the Axiom of the Empty Set confuses you?

No it confuses you because you do not get the consequences if ZF axiom of the empty set actually creates the empty set.

If ZF axiom of the empty set is an axiom of creation, then we are using a circular reasoning because one of the terms of the creation of the empty set is that no set, including the empty set, is a member of the empty set.

For example: the case {{}} is also not {}

In order to show that {{}} is also not {}, {} must exist, but if it is created by the ZF axiom of the empty set, then this very axiom cannot show the case where {{}} is also not {}, because {} cannot simultaneously be created and also used in order to determine the case that {{}} is also not {}, because in that case we are using {} as a member of {{}} in order to determine something during the creation of {}.

If {} is used to determine something about {} during the creation of {}, it is called circular reasoning.

In order to avoid such circularity, the ZF axiom of the empty set is taken as an axiom of description (and not of creation).

As an axiom of description "There exists" is understood as a declaration about an already existing object that its properties (but not it existence) are determined by this axiom.

The Axiom isn't what you say it is. You prove again you and Mathematics are complete strangers. Here it is again

[latex]$$$ \exists x\, \forall y\, \lnot (y \in x) $$$[/latex]​

Is it that universal qualifier that's tripping you up?

The axiom is exactly what I say if we wish to avoid circular reasoning.

EDIT:

In general, X cannot simultaneously be created and used in order to determine its existence, if we wish to avoid circular reasoning.

Let's see: You can't even quote the Axiom correctly, but you accuse me of not understanding it. How curious.

Really?

You are invited to show in details how the ZF axiom of the empty set is an axiom of creation AND not based on circular reasoning.

 

[doronshadmi]

empty set = empty collection = no members = cardinality 0 = { }

Wrong.

Empty set = empty collection = no members = {}

cardinality 0 = |{ }|

The rest of your post is based on the wrong notion that |{ }| = { }

You do not distingush between the ability of X to exist, and some of its proprties that cannot be meaured unless X exists.

 

[jsfisher]

No it confuses you because you do not get the consequences if ZF axiom of the empty set actually creates the empty set.

More proof you don't understand what an axiom is. The Axiom of the Empty Set does not create anything. Here it is again:

[latex]$$$ \exists x\, \forall y\, \lnot (y \in x) $$$[/latex]​

You should note a complete lack of creating going on in there.

You are again trying to force action verbs onto simple declarations. It doesn't work. You end up twisting yourself into a knot trying to reach ridiculous conclusions.

If ZF axiom of the empty set is an axiom of creation...

...which it isn't, so the rest of your argument is without basis.

...
As an axiom of description...

...which it isn't.

"There exists" is understood as a declaration about an already existing object that its properties (but not it existence) are determined by this axiom.

So, what you are saying is that "there exists" doesn't mean "there exists". I suppose that makes things very easy for you if can be that arbitrary with language.

...
You are invited to show in details how the ZF axiom of the empty set is an axiom of creation AND not based on circular reasoning.

As pointed out, above, you have mischaracterized the Axiom.

 

[The Man]

Wrong.

Empty set = empty collection = no members = {}

cardinality 0 = |{ }|

The rest of your post is based on the wrong notion that |{ }| = { }

So you are simply unable to distinguish between…

Cardinality of the empty set = |{ }| = 0

And

The empty set = { } = no members = cardinality 0 = empty collection?

What happened to ‘distinction’ being a ‘first order property’ of your ‘new paradigm’?

You do not distingush between the ability of X to exist, and some of its proprties that cannot be meaured unless X exists.

Well, just what properties of X do you think you can measure if X does not exist?

 

[doronshadmi]

So you are simply unable to distinguish between…

Cardinality of the empty set = |{ }| = 0

And

The empty set = { } = no members = cardinality 0 = empty collection?

What happened to ‘distinction’ being a ‘first order property’ of your ‘new paradigm’?

No The Man, you are the one that does not distinguish betweem cardinality 0 and { }.

Cardinality 0 = |{ }|

The empty set = { }

{ } is not the same as |{ }|.

Well, just what properties of X do you think you can measure if X does not exist?

|{ }| = 0 which is the magnutude of existence of Emptiness.

Again, it is possible only if { } exists independently of its measurments.

 

[jsfisher]

So you are simply unable to distinguish between...

He's misinterpreting the phrase, cardinality 0. It is a subtle thing, and ordinarily I'd be inclined to explain the nuances to him. Unfortunately, if he can't understand a blatantly obvious phrase like there exists, it would be pointless to take on cardinality 0.

 

[The Man]

No The Man, you are the one that does not distinguish betweem cardinality 0 and { }.

Cardinality 0 = |{ }|

Zero has a cardinality? Perhaps you mean the cardinality of a set containing “0”? In that case it would be 1.

|{ }| = cardinality { } = The cardinality of the empty set = 0

The empty set = { }

{ } is not tha same as |{ }|.

I never said it was, distinction and reading comprehension certainly do not seem to be properties of your new ‘paradigm’, in any order.

|{ }| = 0 which is the magnutude of existence of Emptiness.

Ah so now besides researching what you claim to be un-reachable and thinking when you claim to be thoughtless, you now claim cardinality for something you assert does not exist.

 

[The Man]

He's misinterpreting the phrase, cardinality 0. It is a subtle thing, and ordinarily I'd be inclined to explain the nuances to him. Unfortunately, if he can't understand a blatantly obvious phrase like there exists, it would be pointless to take on cardinality 0.

Indeed, and of course it is the responsibility of the writer to make themselves clear (a responsibility Doron clearly abdicates). ‘0 cardinality’ would have been a better ordering on my part, but for most the point was clear (and unnecessary). Likewise I would normally have no problem in clarifying as I am now, but for Doron, as you say it is pointless. He will simply continue to take the meaning he wants and run with it as long as he can.

 

[doronshadmi]

So, what you are saying is that "there exists" doesn't mean "there exists".

No, I say that "there exists" is a declaration about an already existing thing.

The ZF axiom of the empty set only describes the properties of already existing thing, and I see that you agree with me that this is the case.

Empty fusion is possible (it is measurable) only under collection's framework, and the magnitude of existence of it is exactly 0.

It is impossible if we try to say something directly about Emptiness, but under collection this impossible fusion has a magnitude of existence symbolized as 0, where the existence of the empty set (the tool that enables this measurement) does not depend on the magnitude of existence of its muasured things if they = 0 or ∞ , exactly as its existence is not based on the axiom that only describes (but not create) it.

"No members" = "Empty fusion" under collection's (existing) framework.

A set is an existing thing that its magnitude of existehce is > 0 and < ∞

 

[doronshadmi]

Zero has a cardinality? Perhaps you mean the cardinality of a set containing “0”? In that case it would be 1.

|{ }| = cardinality { } = The cardinality of the empty set = 0



I never said it was, distinction and reading comprehension certainly do not seem to be properties of your new ‘paradigm’, in any order.





Ah so now besides researching what you claim to be un-reachable and thinking when you claim to be thoughtless, you now claim cardinality for something you assert does not exist.

You don't wish to get the difference between fusion and collection, and how they are measurable under collection.

It is ok with me, but then keeping silence or talking with you is the same.

EDIT:

Who are you calling a ‘Ho’?

“ “ is not a description it is a space in quotation marks, { } is not a description it is a space between brackets. Both of those are representations, what follows them in the previous statement are descriptions as this statement is also a description of that statement. Representations are not descriptions, but require descriptions in order to indicate exactly what it is you’re trying to represent. You have plenty of representations, Doron, and very few descriptions.

I am talking on the level that tries to get the very existence of things (ontology), you are talking on the level that tries to get the descriptions of already existing things (their definitions).

From the level of ontology " " is an existing (empty) description exactly as { } is an existing (empty) set.

 

[doronshadmi]

He's misinterpreting the phrase, cardinality 0. It is a subtle thing, and ordinarily I'd be inclined to explain the nuances to him. Unfortunately, if he can't understand a blatantly obvious phrase like there exists, it would be pointless to take on cardinality 0.

Indeed, and of course it is the responsibility of the writer to make themselves clear (a responsibility Doron clearly abdicates). ‘0 cardinality’ would have been a better ordering on my part, but for most the point was clear (and unnecessary). Likewise I would normally have no problem in clarifying as I am now, but for Doron, as you say it is pointless. He will simply continue to take the meaning he wants and run with it as long as he can.

So by your jargon Cardinality and Cardinal are not the same thing, ok got it.

Cardinality X = the object that has X as its cardinal.

In this case Cardinality 0 = { } = the object that has 0 as its cardinal.

But you see The Man, since I use Cardinal as the measurement unit of existence of the measured things, where a set is nothing but the measurement tool, then the resulted value is not about the measurement tool but about the measured things.

This is exacly the case of |{ }|, which is the measurment unit of what belongs to { }.

Again you do not follow my arguments, and in this case I am in my yard you are in your yard, and there is silence between us.

 

[jsfisher]

No, I say that "there exists" is a declaration about an already existing thing.

Axioms don 't have a time reference. There is no "already existing" with them. If you actually understood first-order logic, this would all make sense to you.

The ZF axiom of the empty set only describes the properties of already existing thing, and I see that you agree with me that this is the case.

No, and no.

Empty fusion is possible (it is measurable) only under collection's framework, and the magnitude of existence of it is exactly 0.

No, and no.