Deeper than primes - Continuation

[doronshadmi]

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???

I did not spend any "quality time with google trying to figure out what" you "meant".

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.

"there exists set X" is logically a tautology (set's existence is always true) and (whether you agree with it, or not) it is wff (∃ is taken as unary connective).

By using the wff of set's tautological existence (for example: ∃X), one enables to deduce the rest expressions about set X.

 

[Little 10 Toes]

Wtf is wff?

 

[jsfisher]

I did not spend any "quality time with google trying to figure out what" you "meant".

Clearly not.

"there exists set X" is logically a tautology (set's existence is always true) and (whether you agree with it, or not) it is wff (∃ is taken as unary connective).

Ah! You've added "wff" to your lexicon of the misunderstood. Well, at least your google experience for today got you something. Be that as it may, you don't get to re-define first-order predicate calculus. Existential quantifiers are just that, and not "unary connectives". ∃x is not a well-formed formula.

 

[jsfisher]

Wtf is wff?

Well-formed formula.

There is a simple set of rules for how all valid first-order logic formulae may be constructed. Doron has, unsurprisingly, been coloring outside the lines.

 

[doronshadmi]

Existential quantifiers are just that, and not "unary connectives"

jsfisher, I do not ask your permission to define ∃ as a unary connective on X.

∃X is the wff "X existence is always true", and on the basis of this wff additional properties are given, for example: "empty", "non-empty", etc.

 

[jsfisher]

jsfisher, I do not ask your permission to define ∃ as a unary connective on X.

Doron, if you consider a dog's tail to be a leg, how many legs does a dog have?

Four.

As much as you'd like things to be otherwise, existential qualifiers do not accede to your authority.

∃x is not a well-formed formula.

 

[doronshadmi]

As much as you'd like things to be otherwise, existential qualifiers do not accede to your authority.

∃x is not a well-formed formula.

As much as you'd like things to be otherwise, existential qualifiers do not accede to your authority.

∃x is wff, that if translated to English we get "x existence is always true" and on the basis of this wff additional properties are given, for example: "empty", "non-empty", etc.

 

[jsfisher]

As much as you'd like things to be otherwise, existential qualifiers do not accede to your authority.

I'm not the one pretending to have the authority to redefine mathematical terminology to suit my whim.

∃x is not a well-formed formula.

So, how many legs does the dog have?

 

[sympathic]

jsfisher, I do not ask your permission to define ∃ as a unary connective on X.

For someone who seems desperate for communication and recognition/approval you sure are going the wrong way dude.

 

[realpaladin]

For someone who seems desperate for communication and recognition/approval you sure are going the wrong way dude.

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...

 

[doronshadmi]

EDIT:

I'm not the one pretending to have the authority to redefine mathematical terminology to suit my whim.

∃x is not a well-formed formula.

Your balded reply is an example of how you pretending to have the authority to reject new notions that are useful for mathematical development, and in this case the development is as follwos:

The existence of set is logically a tautology and this tautological existence is logically modified to express multiple properties of it, for example: "empty", "non-empty" etc., where no one of the multiple properties is tautological existence.

So logically and mathematically we get a logical common source to many expressions of it.

For someone who seems desperate for communication and recognition/approval you sure are going the wrong way dude.

Please do not reflect your (possibly) hidden desires on me, I do not need any external authority in order to logically define the notion of set as the common source for many expressions of it, where beaning a common source (which is logically a tautological existence) is actually the fulfillment of communication among any mathematical framework that uses the notion of set.

-----------------

One may claim: "There exists set X such that it is empty AND non-empty" contradicts the existence of X.

My answer: ∃X is a tautological existence that its property is undefined, or if "empty AND non-empty" is taken as a contradiction, then X is after all empty.

In both cases ∃X is a tautological existence.

 

[jsfisher]

Your balded reply...

The word is 'bolded'.

...is an example of how you pretending to have the authority to reject new notions that are useful for mathematical development

New notions? You aren't introducing new notions. You are simply claiming things mean something different than they actually mean. What a strange and contradictory world you are trying to create in which 2+2=5 today because you find it convenient, and tomorrow, 2+2=banana split to satisfy a certain craving.

∃x is not a well-formed formula.​

 

[doronshadmi]

The word is 'bolded'.



New notions? You aren't introducing new notions. You are simply claiming things mean something different than they actually mean. What a strange and contradictory world you are trying to create in which 2+2=5 today because you find it convenient, and tomorrow, 2+2=banana split to satisfy a certain craving.

∃x is not a well-formed formula.​

∃x is wff, where this wff is simply "x existence is always true".

your "2+2=5" or "2+2=banana split" examples are irrelevant in this case.

Moreover, your "actually mean" is no more than the current agreement among mathematicians about ∃x, which according to it ∃x is not taken as "x existence is always true".

The only way to show that I am wrong is to logically show that ∃x can't be "x existence is always true".

So, you are invited to logically show it.

------------------------

Once again, by defining ∃x as a wff, the existence of set is logically a tautology and this tautological existence is logically modified to express multiple properties of it, for example: "empty", "non-empty" etc., where no one of the multiple properties is a tautological existence (exactly because x properties are y or not-y (where y is, for example, the expression "empty")).

So logically and mathematically we get a logical common source to many expressions of it, which are not tautologies.

------------------------

In terms of notations, ∃x as a wff is notated by the outer "{" and "}", so you also have to explicitly show that given any set (empty or not) it can't be expressed by using the outer "{" and "}".

 

[jsfisher]

The only way to show that I am wrong is to logically show that ∃x can't be "x existence is always true".

No need. The meaning of the existential quantifier is well-established. Its meaning fully discredits your desperate attempts to present it as something else.

∃x is not a well-formed formula.

 

[doronshadmi]

No need. The meaning of the existential quantifier is well-established. Its meaning fully discredits your desperate attempts to present it as something else.

∃x is not a well-formed formula.

The meaning of existential quantifier is well-agreed, that's all.

The only way to show that I am wrong is given in http://67.228.115.45/showpost.php?p=10049923&postcount=3973

As long as you can't logically show it

∃x is a well-formed formula.

 

[jsfisher]

The meaning of existential quantifier is well-agreed, that's all.

Yes, that is the essence of meaning and usage.

Moreover, if you insist on using the existential quantifier to mean something else, than you are talking about a completely different thing than what's found in ZFC.

Either way, the result is the same: The nonsense you are alleging as part of ZFC is not a part of ZFC.

 

[doronshadmi]

Yes, that is the essence of meaning and usage.

All you have is a common agreement among persons, that is not based on any logic that clearly demonstrates that ∃x can't be "x existence is always true" within ZFC.

EDIT:

Sorry but common agreement that is not logically supported (where this logical support clearly demonstrates that ∃x as "x existence is always true" can't logically be within ZFC) , is not enough.

 

[jsfisher]

All you have is a common agreement among persons, that is not based on any logic that clearly demonstrates that ∃x can't be "x existence is always true" within ZFC.

Sorry but common agreement that is not logically supported, is not enough.

Please prove by detailed logic that "sorry" as you used it, above, cannot mean, "Yes, I know I am completely wrong on this and what follows the word 'but' is a complete lie".

 

[doronshadmi]

Please prove by detailed logic that "sorry" as you used it, above, cannot mean, "Yes, I know I am complete wrong on this and what follows the word 'but' is a complete lie".

Since, unlike the common agreement, it is logically shown that ∃x is a wff ("x existence is always true") within ZFC, then ("Yes, I know I am complete wrong on this and what follows the word 'but' is a complete lie") is logically false.

The only way to show that I am wrong, is to show that "x existence is always true" can be logically false within ZFC, and common agreement is not enough in this case.

 

[jsfisher]

Since, unlike the common agreement, it is logically shown that ∃x is a wff

You have yet to show that. All well-formed formulae, by their very definition, can be constructed from a small set of rules. ∃x cannot be constructed from those rules, and so ∃x is not a well-formed formula.

Or, perhaps it can, but that would be for you to demonstrate. Last I checked, the only rule in the set that included the existential quantifier was this: If Ψ is a formula and x is a set, then ∃x Ψ is a formula.