Deeper than primes - Continuation

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The case of the not so truthful speaking Doron:

Exhibit A:
doronshadmi said:
"There exists a set X (this is the part that uses set's platonic level of existence) such that (this is the part that uses set's non-platonic level of existence (the level of members, which defines set's identity, but not set's platonic level of existence)) {} is a member of X and, whenever a set y is a member of X, then S(y) is also a member of X."
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Exhibit B:
doronshadmi said:
This is my last post to you on this subject.

Please look at http://www.internationalskeptics.com/forums/showpost.php?p=10039964&postcount=3903.

Now take
doronshadmi said:
"There exists a set X (this is (a) part of the axiom) such that (this is (b) part of the axiom) {} is a member of X and, whenever a set y is a member of X, then S(y) is also a member of X."
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and omit what is written in italic letters within the brackets

( http://en.wikipedia.org/wiki/Zermelo...om_of_infinity )
... 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(y) is also a member of X.
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and here it is.
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Yeah, well... not really. Shadmi fumbles again and loses the ball...

Doron, even you can see that what you are doing here is silly...

You started out claiming Exhibit A was exactly what the ZFC definition was, and in Exhibit B you just write something else...

The question was, where did you get the quote for Exhibit A from? Nowhere, that's where. You just made it up.

This one is also for your upcoming error post.
 
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doronshadmi said:
If one reads http://www.internationalskeptics.com/forums/showpost.php?p=10041415&postcount=3920 he\she can easily realize that the first quote is titled by my name (which means that it is not the original Wikipedia quote, as appears in http://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory#7._Axiom_of_infinity).

End of discussion on this case.
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So, what took you *so* long to admit this? Hmmm?

To the casual onlooker it would seem that you wanted to confuse matters by acting as if something you claim was actually in a real definition.

This is not the first time you have been caught redhanded. Nor will it be the last.

By no means end of discussion since I guess some other people and me might discuss your dishonest looking tactics in more detail with pointers to where you did the same thing and maybe with some speculation as to why you need to resort to these methods....
 
jsfisher said:
Great! So there will be no more pretense on your part that any of this shadmized philosophy is in any way part of ZFC. It is all just doron-fantasy.
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No. The end of the discussion is about Little 10 Toes request ( http://www.internationalskeptics.com/forums/showpost.php?p=10041415&postcount=3920 ), as also explained in http://www.internationalskeptics.com/forums/showpost.php?p=10042281&postcount=3923.

It does not mean that Philosophically is not part of ZFC.

Since your basic notion is based on complete separation between Philosophy and Mathematics, your quote above is the best you can get.
 
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doronshadmi said:
It does not mean that Philosophically is not part of ZFC.
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Oh, but it does. The only way you have been able to "show" that your odd philosophy is part of ZFC is by you cramming it in in an attempt to displace the real philosophic basis for ZFC then pretending it was there all along.

You've admitted as much in your response to Little 10 Toes. Are you now recanting your recant?
 
jsfisher said:
Oh, but it does.
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Please support your "Oh, but it does" by explicitly demonstrate how what you call real philosophic basis is an actual part of ZFC framework.

jsfisher said:
the real philosophic basis for ZFC
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It is no more than the currently accepted point of view of one level reasoning.

jsfisher said:
You've admitted as much in your response to Little 10 Toes. Are you now recanting your recant?
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No. The notions of your one level reasoning are ineffective if used to deduce finer resolutions of Philosophical AND Mathematical framework like ZFC.
 
doronshadmi said:
Please support your "Oh, but it does" by explicitly demonstrate how what you call real philosophic basis is an actual part of ZFC framework.
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Gee, Doron, your very next sentence admits ZFC has a philosophic basis that isn't the latest confusion you've been peddling:

It is no more than the currently accepted point of view of one level reasoning.
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Now, I am not endorsing the accuracy of your statement; I'm just observing that it acknowledges a foundation to ZFC that isn't at all like yours.

No. The notions of your one level reasoning are ineffective if used to deduce finer resolutions of Philosophical AND Mathematical framework like ZFC.
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If true, then you should be able to point to where ZFC is influenced by the basis you claim it has. Then again, that would require you actually nail down what this philosophy of yours really is, and that will never happen. It would be too much like defining your terms, only harder.
 
jsfisher said:
Gee, Doron, your very next sentence admits ZFC has a philosophic basis that isn't the latest confusion you've been peddling:
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jsfisher, I talking about a framework which is logically Philosophical AND mathematical. So please try once again to demonstrate your "Oh, but it does" by using your one level reasoning.

Edit:
jsfisher said:
Now, I am not endorsing the accuracy of your statement;
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You can't say any useful thing about two levels reasoning by using a one level reasoning. But the other way around is possible, because it includes one level reasoning as some special case of it.

Edit:
jsfisher said:
I'm just observing that it acknowledges a foundation to ZFC that isn't at all like yours.
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You are using weaker foundation, such that Philosophy is not an integral factor of any given mathematical framework.

jsfisher said:
If true, then you should be able to point to where ZFC is influenced by the basis you claim it has.
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By using Philosophy AND Mathematics it has be pointed out in http://www.internationalskeptics.com/forums/showpost.php?p=10039964&postcount=3903.

jsfisher said:
... and that will never happen.
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It indeed will never happen if one insists that Philosophy AND Mathematics is logically false framework.
 
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doronshadmi said:
jsfisher, I talking about a framework which is logically Philosophical AND mathematical. So please try once again to demonstrate your "Oh, but it does" by using your one level reasoning.
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You didn't understand it the first time, and I see no point in repeating it. Besides, this is all a distraction with you trying to shift the burden. Your claim; your burden.

You can't say any useful thing about two levels reasoning by using a one level reasoning. But the other way around is possible, because it includes one level reasoning as some special case of it.
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Yeah, we've seen this nonsense from you before. You have special powers of perception and reasoning no one else (and I literally mean no one else) can match, and no one else can possibly understand your genius.

Or, you are completely confused.

The latter seems more likely. [The latest AAH'ed posts from Jabba's immortality thread pay tribute to your confusion, Doron.]


All that aside, though. What point are you honestly hoping to make? Not the little picky bits you dwell on; what's the real conclusion you want to present?
 
jsfisher said:
The latter seems more likely. [The latest AAH'ed posts from Jabba's immortality thread pay tribute to your confusion, Doron.]
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I missed a Jabba & Doron thread! Just for the entertainment I read the AAH!

As for the conclusions... I think all of us 'veterans' know deep in our heart that Doron will never go beyond claiming something that is 'bickerworthy'.

We tried the 'ok, if everyone would agree, then what?' route already and that got us nowhere.

Whatever claim is ever made the algorithm for processing it will be this:

1 - Doron makes a claim
2 - If someone disagrees, then Doron will present endless arguments and will respond to any counter argument until it gets to the 'you don't get it' stage.
3 - If everyone agrees, then Doron will ignore that and post, out of the blue, completely new claims that have not advanced the whole concept or philosophy of Doron one iota. Go to 2.

Doron is extremely predictable. I wonder if I can make a claim for the $1.000.000 by predicting the course of Doron's progress with his philosophy over the next 5 years....
 
jsfisher said:
You didn't understand it the first time,
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You don't understand it at all times when one level reasoning and separation between Philosophy and Mathematics are the fundamental notions of your mathematical framework, now please explicitly demonstrate your "Oh, but it does" Philosophical AND Mathematical framework.

jsfisher said:
You have special powers of perception and reasoning no one else
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Ridiculous drama, that is played by a person that avoids the linkage among two levels of existence, where one level is logically tautological existence, and the other level is logically non-tautological existence as shown in http://www.internationalskeptics.com/forums/showpost.php?p=10039964&postcount=3903, which is philosophical AND mathematical framework.
 
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By set theory like ZFC, there exits a set whether it is empty or non-empty.

It means that set's existence is independent of its minimal identity, which is being empty or non-empty.

By using Logic, one easily understands that the independence of set's existence from its minimal identity (identified as empty or non-empty), is as follows:

1) Set's existence is always true (tautology).

2) Members' existence is not always true (it is not a tautology).

In other words, the essential notion of set is logically involved with two levels of existence, where one level is always true (tautology), and the other level is not always true (it is not a tautology).

These logical terms are so easily deduced, yet they can't be captured by any notion that does not distinguish between tautological existence and non-tautological existence.
 
doronshadmi said:
By set theory like ZFC, there exits a set whether it is empty or non-empty.
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By ZFC, there is an empty set. By ZFC, there are non-empty sets. By ZFC, there are finite sets, and there are infinite sets.

It means that set's existence is independent of its minimal identity, which is being empty or non-empty.
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Identity, minimal or otherwise, is not a ZFC concept. So, the above and everything that followed have nothing to do with ZFC. Instead, they are Doronshadmi fantasy concepts.
 
jsfisher said:
By ZFC, there is an empty set.
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A set is identified as empty, by defining members' existence as logically always false.
jsfisher said:
By ZFC, there are non-empty sets. By ZFC, there are finite sets, and there are infinite sets.
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Sets are identified as non-empty, by defining members' existence, which is generally not a tautological existence, where this non-tautological existence is emptiness (derived from contradiction, which is the opposite (or one may use the word "complement") of tautology), finite or potentially infinite (actual infinity is logically an existence that is always true, and this is logically not the case about members' existence).
jsfisher said:
Identity, minimal or otherwise, is not a ZFC concept.
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Identity, minimal or otherwise, is definitely a ZFC concept (what comes after "such that" part (or its equivalent expression) of ZFC axioms).
 
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doronshadmi said:
1) Set's existence is always true (tautology).

2) Members' existence is not always true (it is not a tautology).
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The error here is, by using logic, this:

The members' existence is always true (tautology), but their relation to the set (belonging to that set) is not.

Whether an element belongs or does not belong to a set has no bearing on it's existence.

In fact, this is clear by the notion that a member can be belong to another set, or no set at all.

Furthermore, you could say that all elements that are not member of a set are always member of the set 'not member of set X'.

Therefore this whole tautology/non-tautology talk is wrong.

There, I have used logic.
 
realpaladin said:
Furthermore, you could say that all elements that are not member of a set are always member of the set 'not member of set X'.
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Be careful with that. You need to enforce limited comprehension or some hierarchy set scheme to steer clear of Russel's Paradox.
 
There are persons that have troubles to understand that something cannot be considered as a member unless it belongs to some set.

This is not the case about a set, it exists also if it is not a member of some set, for example:

{} exits, and this existence is independent of {{}}, which is being a member of a given set.
 
jsfisher said:
And this is why it is some important we nag you to define your terms. Lest you continue to equivocate among nuances of meaning, you must define what you mean by "identified."
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Again, given The Axiom Of Infinity, X existence is independent of what comes after "such that", which define X identity but does not define X existence (X existence is defined by "There exists").

Please this time reply in details to all of what is written in http://www.internationalskeptics.com/forums/showpost.php?p=10045682&postcount=3938.
 
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doronshadmi said:
Again, given The Axiom Of Infinity, X existence is independent of what comes after "such that", which define X identity but does not define X existence (X existence is defined by "There exists").
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That's nice. Now, care to actually respond to the post you quoted?
 
doronshadmi said:
There are persons that have troubles to understand that something cannot be considered as a member unless it belongs to some set.
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Well, I could quibble about the word, belongs, but that aside, where are these persons to which you refer? Who has trouble understanding that set membership means member of a set?

This is not the case about a set, it exists also if it is not a member of some set, for example:

{} exits, and this existence is independent of {{}}, which is being a member of a given set.
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Is this some special meaning of "independent" known only to you, Doron? Were there no empty set, there'd be no set of the empty set, and vice versa. This is not the sort of independence with which I am familiar.
 
jsfisher said:
you must define what you mean by "identified."
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By "identified" I mean that X property is given, where this property has no impact on X tautological existence (X exits whether X property is given or not).

An example (without loss of generality):

Given The Axiom Of Infinity, X existence is independent of what comes after "such that", which define X identity but does not define X existence (X existence is defined by "There exists", but not by "such that").
 
doronshadmi said:
By "identified" I mean that X property is given, where this property has no impact on X tautological existence (X exits whether X property is given or not).
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That would confirm that your "identified" is not part of ZFC. Thanks for clearing that up.

An example (without loss of generality)...
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You really need to figure out what "without loss of generality" means.
 
jsfisher said:
Were there no empty set, there'd be no set of the empty set, and vice versa. This is not the sort of independence with which I am familiar.
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You are still missing it, a set (as a tautological existence) is notated by the the outer "{" and "}" and it has members (in the case of {{}} or not (in the case of {}).

So sets' existence is independent of members existence, but not vice versa.
 
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jsfisher said:
That would confirm that your "identified" is not part of ZFC.
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Only of you do not distinguish between "there exits" and "such that".

By ZFC there is set (defined by "there exists").

By using the tautological existence of set, each given ZFC axiom defines its property as empty, finite or potentially infinite (the property is only potentially infinite, because it is given by set's members (or their absence) that do not have tautological existence (notated by the outer "{" and "}" of any given set, no matter what property is related to it).

jsfisher said:
You really need to figure out what "without loss of generality" means.
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You really have to figure out that the example that was given by The Axiom Of Infinity holds for any axiom which deals with sets.
 
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jsfisher said:
Your content has been growing ever more distant from the context.
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No, it stays as finer resolution of ZFC that can't be deduced by your monolithic reasoning.

Some analogy:

X is called an atom because a given resolution can't define any complexity in it.

A finer resolution is used and defines complexity in X, so by the finer resolution X can't be considered as an atom anymore.

But the one that uses the previous resolution insists that X is an atom.

No matter what the one that uses the finer resolution says, the one that uses the previous resolution rejects it (for example: http://www.internationalskeptics.com/forums/showpost.php?p=10046314&postcount=3951).
 
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jsfisher said:
Be careful with that. You need to enforce limited comprehension or some hierarchy set scheme to steer clear of Russel's Paradox.
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I know, but the thing is, if I just act like Doron and provide no rigorous context, all manner of BS Logic is possible.

Doron spouting nonsense about people being able to comprehend this or that is so utterly worthless because there is nothing to comprehend until he starts off from square one.

He never did, so *anything* he proclaims is of the same ilk as to what I wrote; in need of a rigorous background, context and limitation.
 
doronshadmi said:
No, it stays as finer resolution of ZFC that can't be deduced by your monolithic reasoning.

Some analogy:

X is called an atom because a given resolution can't define any complexity in it.

A finer resolution is used and define complexity in X, so by the finer resolution X can't be considered as an atom anymore.

But the one that uses the previous resolution insists that X is an atom.

No matter what the one that uses the finer resolution says, the one that uses the previous resolution rejects it.
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Old hat; truth is locally consistent but globally inconsistent.

When do we get to something new?
 
jsfisher said:
That remains a doronism, as are your meaningless attempts to partition first-order predicates.
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The finer resolution is very simple, as follows:

Given some ZFC axiom, "There exists set X" is the first-order expression of it, where any further expression of it is not the first-order expression of it (for example: "such that ...").

Logically the first-order expression is a tautological existence, where the non first-order expression is not a tautological existence.

The first-order expression of set's notion is notated by the outer "{ and "}"

The non first-order expression of set's notion is notated by that is between the outer "{ and "}" (or its absence, which is not notated at all).
 
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doronshadmi said:
jsfisher said:
That remains a doronism, as are your meaningless attempts to partition first-order predicates.
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You spend a day and a half of quality time with google trying to figure out what I meant, and this is all you came up with???

The finer resolution is very simple, as follows:

Given some ZFC axiom, "There exists set X" is the first-order expression of it, where any further expression of it is not the first-order expression of it (for example: "such that ...").
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First-order predicate, as in first-order predicate calculus or first-order logic. It has a precise meaning, and the meaning does not agree with what you posted.

Go back to googling the Intertubes. See if you can find how well-formed formulae may be constructed and come to understand why "there exists set X" isn't one. Then, you may even get a glimpse at why nothing of what you have been recently alleging as part of ZFC is part of ZFC.
 
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