Deeper than primes - Continuation

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jsfisher said:
If Ψ is a formula and x is a set, then ∃x Ψ is a formula.
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EDIT:

∃x is the formula "There exits set x"

Ψ is the formula "such that it is empty"

If Ψ is ""such that it is empty AND non-empty" , it does not have any impact on ∃x since x existence is a tautology (x exists even if some property of it is not clearly defined).

Another example:

∃x is the formula "There exits car x"

Ψ is the formula "such that it is all-blue"

If Ψ is "such that it is all-blue AND not all-blue" , it does not have any impact on ∃x since x existence is a tautology (x exists even if some property of it is not clearly defined).

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Let's return to ZFC.

Within ZFC members do not have tautological existence, because at least one set has no members at all.

This is not the case about set's existence within ZFC (a set has a tautological existence within ZFC, no matter if it does not have any member, its members are not clearly defined (and within ZFC it is the same as no members at all), or it has members).
 
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doronshadmi said:
EDIT:

∃x is the formula "There exits set x"

Ψ is the formula "such that it is empty"

If Ψ is ""such that it is empty AND non-empty" , it does not have any impact on ∃x since x existence is a tautology (x exists even if some property of it is not clearly defined).

Another example:

∃x is the formula "There exits car x"

Ψ is the formula "such that it is all-blue"

If Ψ is "such that it is all-blue AND not all-blue" , it does not have any impact on ∃x since x existence is a tautology (x exists even if some property of it is not clearly defined).
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This is all wrong.

The whole *notion* of the formula is a *selection* of *elements* that *may or may not exist*.

It is not *first we claim existence* and then we add properties.

You are not playing with objects which are first instanciated and then enriched by properties, you are playing with a mathematical formula.

The whole 'there exists' is not an existential 'existence', but a selective 'existence'.

How hard is comprehending language for you? Really!
 
jsfisher said:
If Ψ is a formula and x is a set, then ∃x Ψ is a formula.
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"x is a set" is the same as "there exists set x"

So what you wrote above is the same as "If Ψ is a formula and ∃x, then ∃x Ψ is a formula."

In other words, what you wrote above has no meaning if ∃x is not wff.
 
Does anyone can select an element that does not exist (even in the abstract sense)?
 
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doronshadmi said:
"x is a set" is the same as "there exists set x"
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Silly me. I was thinking in context it was clear that "x is a set" should be taken to mean "x is a variable serving to represent a hypothetical object from the domain of discourse, which for the instant discussion would be ZFC Set Theory".

Sorry for the confusion.
 
doronshadmi said:
Does anyone can select an element that does not exist (even in the abstract sense)?
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Yes. (Hint: we, and I mean most mathematical apt people had a discourse with you on that... it involves square roots and it has it's own set of numbers... though it might be a bit complex).

This question demonstrates Doron's grasp on philosophic matters as well as his aptitude in mathematics...

It is left as an excercise to the reader to determine whether this is good or bad... (hint: it ain't very good)
 
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realpaladin said:
LOL.

Do you know I spent an entire page writing up things like 'but the rapuctor does not blabargle!' and he *still* could bicker with that?

Bickering is his goal, because that looks so 'sciency', you know...
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Yeah... his tragedy is that he seems to be trapped in his own nonsense. He could not escape even if he truly wanted to. He genuinely strives for communication and recognition but his insistence on providing his own meaning to well accepted terms make communication with him impossible. While we find some of his rambles amusing and entertaining to an extent, I think for him this is truly painful.
 
realpaladin said:
LOL.

Do you know I spent an entire page writing up things like 'but the rapuctor does not blabargle!' and he *still* could bicker with that?

Bickering is his goal, because that looks so 'sciency', you know...
Click to expand...

double entry
 
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jsfisher said:
Silly me. I was thinking in context it was clear that "x is a set" should be taken to mean "x is a variable serving to represent a hypothetical object from the domain of discourse, which for the instant discussion would be ZFC Set Theory".

Sorry for the confusion.
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There is no confusion, as clearly demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=10050314&postcount=3981.

Moreover, if the domain of discourse is ZFC, then ∃x is not for any particular set, but it is about the tautological existence of "hypothetical object from the domain of discourse" (where in the case of ZFC, it is known as set).
 
It is nice to know that some people think that the set of real numbers does not exist (even in the abstract sense).:rolleyes:
 
doronshadmi said:
There is no confusion, as clearly demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=10050314&postcount=3981.
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Your mastery of the non sequitur is what legends are made of.

Moreover, if the domain of discourse is ZFC, then ∃x is not for any particular set, but it is about the tautological existence of "hypothetical object from the domain of discourse" (where in the case of ZFC, it is known as set).
Click to expand...

You have no idea what 'domain of discourse' means, do you? Still, x is a variable, and ∃ is a quantifier. Don't know what 'quantifier' means either, do you?
 
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jsfisher said:
No, actually, no. Remember that non sequitur thing?
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Yes, actually, yes. Remember that non sequitur thing about selecting things that do not exist (even in the abstract sense, where real numbers are one of the possible members of such abstract sense, which is "hypothetical object from the domain of discourse" (where in the case of ZFC, it is known as set))?
 
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