Deeper than primes - Continuation

[Little 10 Toes]

I see what you did there…

 

[doronshadmi]

EDIT:

The parenthetical comments in italics are your fantasy, not anything in ZFC. You simply are making stuff up, as you so frequently do.

jsfisher, fantasy is only at the subjective level of existence, which is dependent on the objective level of existence (which is independent on any given identity, or fantasy).

By using again and again "making stuff up", "fantasy" etc., I think that this is your way to describe the non-useful aspect of the subjective (b.t.w identity is a very useful aspect of the subjective, as seen, for example, in ZFC).

Your reasoning simply can't deal with the objectivity of the discovered, which is independent on the subjectivity of the invented.

You post also relates in no way to the post of mine you quoted. So there is no evidence you understood my post at all. This lends further support to the conclusion your reading comprehension issues are at the root of why you fabricate instead of understand.

There is a clear evidence that can't grasp the objective level of set's existence, which is independent on any given identity exactly because identities are subjective inventions.

Also, I note your continued parroting of "S" in your posts as if you believed it has meaning stripped from its original context. Even more evidence of failures in understanding.

Nothing was stripped from its original context. On the contrary, I address the dependency of the invented (the subjective level of members like "S") on the discovered (the objective level of set's existence ("there exists set X")).

In ZFC there is an hierarchy of dependency (which means that both X existence and X identity are used), where X identity depends on X existence, but X existence does not depend on X identity.

For example, nothing was stripped or "slightly hacked" from ZFC by post http://www.internationalskeptics.com/forums/showpost.php?p=10017698&postcount=3731, only in your one level imagination.

ETA:
By the way, in what way is "the empty set {}" different from "the empty set" or from "{}"? Or do you just feel compelled to restate things redundantly by repeating things?

My mistake (I used what is written in http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory without first checking it) the correct one is "the empty set ({})". Thank you for your remark.

 

[doronshadmi]

I see what you did there…

What?

 

[jsfisher]

I see what you did there…

What?

Don't look up, what ever you do.

 

[jsfisher]

...<non sequitur sequence snipped>...

Nothing was stripped from its original context. On the contrary, I address the dependency of the invented (the subjective level of members like "S") on the discovered (the objective level of set's existence ("there exists set X")).

It surprises me not at all that you cannot see that your continual re-presentation of "S" is without its context.

In ZFC there is an hierarchy of dependency (which means that both X existence and X identity are used), where X identity depends on X existence, but X existence does not depend on X identity.

And, yet, you cannot point to that anywhere in the ZFC axioms.

...
My mistake (I used what is written in http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory without first checking it) the correct one is "the empty set ({})". Thank you for your remark.

You must get a different version of Wikipedia in Isreal. What does it show for Axiom of infinity^WP?

 

[realpaladin]

@JSFisher: what is the angle this time?

 

[realpaladin]

Doron,

just waiting for a long time and then suddenly starting all over does not work.

You still fail to show how any of this connects with the questions stated before you rebooted this thread...

And really, if I would accept your 'reboot' statement, can you show how this helps in your roadmap, or in the two islands thought experiment?

 

[jsfisher]

@JSFisher: what is the angle this time?

One of his favorites: There really is no infinity, except there sort of is, but you never get there, because everything is a process, and you can always take one more step, and by God! those braces have feelings, too!

And anyone who thinks otherwise doesn't get it.

 

[doronshadmi]

It surprises me not at all that you cannot see that your continual re-presentation of "S" is without its context.

It surprises me not at all that you cannot see that "S" is an invention that is dependent on the discovered, but not vice versa.

And, yet, you cannot point to that anywhere in the ZFC axioms.

And, your one level reasoning is not useful in order to point to that anywhere in the ZFC axioms, so?

You must get a different version of Wikipedia in Isreal. What does it show for Axiom of infinity^WP?

http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory is the English version of Wikipedia all over the internet.

Moreover, in http://www.internationalskeptics.com/forums/showpost.php?p=10011797&postcount=3709 you use an expression that appears in http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory, so for better communication with you I used what comes before this expression, which is:

"...there exists a set X such that the empty set Ø is a member of X and, whenever a set y is a member of X, then S is also a member of X."

So, the mistake is in the English version of Wikipedia all over the internet, but your reply about this case clearly expose how you actually ignore the details my replies, and in this case my reply was

My mistake (I used what is written in http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory without first checking it) the correct one is "the empty set ({})". Thank you for your remark.

that simply ignored by you.

No wonder that by systematically using such an attitude, you reinforce your misunderstanding of my replies.

 

[doronshadmi]

One of his favorites: There really is no infinity, except there sort of is, but you never get there, because everything is a process, ...

This is another demonstration of how you systematically ignore what I write (http://www.internationalskeptics.com/forums/showpost.php?p=10023528&postcount=3756):

It has to be stressed that level of members is an invention that is defined in some moment in time, but it does not mean that, for example, "whenever a set y is a member of X, then S is also a member of X" is a process in time, it simply demonstrates the inaccessibility of the invented (subjective) level of members of a given set, to the discovered (objective) level of set.

No wonder that you have no clew of what I am talking about, and you are not in any position to explain what I write (except in your own fantasies).

 

[jsfisher]

...<non sequitur sequence snipped>...

http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory is the English version of Wikipedia all over the internet.

Yes, I know. My comment was steeped in sarcasm. If you look carefully at what is written, not simply what you imagine you'd like to be there, the character sequence "{}" does not appear where you claimed.

More lack of attention to detail on your part, Doron. It only undermines your position.

 

[jsfisher]

This is another demonstration of how you systematically ignore what I write

Discount, not ignore. Must I continually remind you?

 

[doronshadmi]

"There exists ..." is the discovered (objective) level of existence, which is independent on the invented (subjective) level of existence.

In other words, identification (which is done at the invented (subjective) level of existence) needs the discovered (objective) level of existence, in order to exits, but the discovered (objective) level of existence does not need identification in order to exists.

This notion of shown in the following:

Now, by following these notions as the basis of cardinal numbers (which are based on ZFC set-theory level, but they are not at ZFC set-theory level), the right way to express cardinal numbers is shown in the following example:

{||}=0 , {|{}|}=1 , {|{},{{}}|}=2 etc. , or {|{}, {{}}, {{},{{}}}, ... |} < aleph0 (where aleph0 is at the objective level (notated here by the outer "{" and "}"), where no number of members (where members are at the subjective level) is accessible to it).

As can be seen, the subjective (invented) level of members is inaccessible to the objective (discovered) level of a given set (where this objectivity is expressed by the outer "{" and "}", whether a given set is empty or non-empty).

In other words, given a set with infinitely many members, they are inherently under construction (where "inherently under construction" is not a processes) (for example: "whenever a set y is a member of X, then S is also a member of X") since the subjective level of members (which provide the identity of a given set) is inaccessible to the objective level of a given set (where this objectivity is expressed here by the outer "{" and "}", whether a given set is empty or non-empty).

More generally, Mathematics (abstract or non-abstract) is useful exactly because it is discovered and invented, where the invented depends on the discovered, but not vice versa.

 

[Little 10 Toes]

There are no levels of existence in ZFC. That is something that you made up.

That is what jsfisher is trying to tell you.

(Or at least that is my understanding.)

 

[realpaladin]

So, Doron, at which point do we get somewhere in the roadmap from this to the world-peace?

Again, it appears that all Organic Mathematics has to offer is strife and misunderstanding.

But I probably misunderstand all of that

 

[realpaladin]

This is another demonstration of how you systematically ignore what I write (http://www.internationalskeptics.com/forums/showpost.php?p=10023528&postcount=3756):

No wonder that you have no clew of what I am talking about, and you are not in any position to explain what I write (except in your own fantasies).

Doron, first: "attack the argument, not the arguer" as per contract with this forum.

Second, if JSFisher is in no position to explain what you write, then please be so civil to refrain from taking a position that explains what he writes, whether it be his fantasies or not.

Finally, where in ZFC, I use the Wolfram pages; they are better suited for mathematics than Wikipedia, can you find any support for your claims? Here is the link: http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

 

[jsfisher]

Nostalgia, but appropriate nostalgia.

 

[realpaladin]

I'm lovin' it.

 

[doronshadmi]

There are no levels of existence in ZFC.

According to his one level reasoning, so?

 

[doronshadmi]

"There exists AND does not exist set X" is a contradiction at the objective (platonic) level of discovery (or in other words, the objective (platonic) level is not discovered, which has no impact on the objective (platonic) existence of set X).

"There exists set X" such that "it is AND it is not its own member" is a contradiction at the subjective (non-platonic) level of invention, which has an impact on X's subjective invented identity, but it does not have any impact on X objective level of discovery (X exists as a platonic object even if its non-platonic subjective level is not well-defined).

By understanding this hierarchy of dependency, any Mathematics that is based on sets, is useful exactly because it is discovered (this is its objective platonic level) AND invented (this is its subjective non-platonic level), such that the invented depends on the discovered, but not vice versa.

The non-platonic subjective level of set is inaccessible to the platonic objective level of set, where this inaccessibly provides the room for unlimited subjective non-platonic interpretations (inventions) that are based on the platonic objective level of set, but not vice versa.

More details are given, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=10025797&postcount=3773.