Deeper than primes - Continuation

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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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