A hidden assumption

[nathan]

Popositional logic is

ah, here's your problem. Pixy's talking about propositional logic. Popositional logic is some kind of new fangled logic of popularity.

 

[nathan]

Completeness = atomic state = that has no parts.

Although it looks like one is an adjective and one is a noun, you're claiming they are the same thing. Why is that? Surely it would be clearer to use one name for one thing, rather than two names?

Also, if 'completeness' and 'atomic state' are the same thing, doesn't that make:

... the completeness of the atomic state, ...

tautalogical?

 

[ArmillarySphere]

You forgot to specify "final member". And "parts".

And if a complete set has no parts, how can it be a set?

 

[Bodhi Dharma Zen]

I'm still waiting doronshadmi...

 

[PixyMisa]

Wrong wrong.

Depends on what form of set theory you're using. Certainly, the claim that S cannot be {S} is not universal.

And both of us are using our cognitions all along this thread (something that is beyond your awarness).

False and irrelevant.

Please show how S is also {S}.

Example: We define S as the set of all sets.

S={S}

Some forms of set theory don't allow this. Others do.

 

[doronshadmi]

Example: We define S as the set of all sets.

S={S}

Some forms of set theory don't allow this. Others do.

S={S} is possible if {}={{}} is possible.

 

[doronshadmi]

Ignoring for a moment how completely wrong that is, there is no logical connection among the three statements.

Logic does not hold without Symmetry\Asymmetry complementation as its universal principle, as clearly shown in http://www.internationalskeptics.com/forums/showpost.php?p=3595037&postcount=366 .

 

[doronshadmi]

You forgot to specify "final member". And "parts".

And if a complete set has no parts, how can it be a set?

A set is a result of Symmetry\Asymmetry complementation.

This result is incomplete by definition if compared to the atomic state, which is not a set because it is ∈ (or its negation) itself, where ∈ (or its negation) is not a member of any set, but no set exists without it.

A set is the result of ∈ (or its negation)\not (∈ (or its negation)) complementation.

 

[doronshadmi]

ah, here's your problem. Pixy's talking about propositional logic. Popositional logic is some kind of new fangled logic of popularity.

 

[doronshadmi]

Although it looks like one is an adjective and one is a noun, you're claiming they are the same thing. Why is that? Surely it would be clearer to use one name for one thing, rather than two names?

Also, if 'completeness' and 'atomic state' are the same thing, doesn't that make:


tautalogical?

Yes.

Both expressions are the same, and it is not researchable at its self state.

Symmetry is the invariant aspect of the atomic state (total unity) and Asymmetry is the variant aspect of the atomic state (total isolation).

The researchable is the complementation of these aspects, and no result of this complementation is total, and therefore incomplete, if compared to the totality of the atomic state itself (which is not reseachable at its self state, but used as the fundamental point of view of the reseachable).

You may ask: How an atom has more than a one aspect, after all it is an atom?

My answer: Indeed an atom at its self state does not have anything to talk about (it is not researchable) but by using the self state as the fundamental point of view of itself, we get the researchable, which is the atomic state as its own element.

The atomic state as its own element does not have the totality of the atomic state itself, and this non-totality is understood as a complementation of two opposite aspects of the atomic state, which are not equivalent to the atomic state at its self state.

Furthermore this complementation and any result that is deduced from it, do not have the totality (the completeness) of the atomic self state. In other words, any researchable thing is incomplete by definition if compared to the non-researchable (the atomic state itself).



As about adjective\noun, That's my English problem.

 

[PixyMisa]

S={S} is possible if {}={{}} is possible.

Wrong. You're still confusing notation with meaning.

Update: Hmm. Okay, on further consideration, I'm not certain on this one. It requires a different form of set theory that I'm less familiar with. Anyone else?

And everything else you've said is still nonsensical or wrong.

 

[nathan]

S={S} is possible if {}={{}} is possible.

Please clarify:
*) do you mean 'if' or do you mean 'iff'?
*) is 'S' any set, or a specific set (such as the set of all sets)?

 

[PixyMisa]

It's slightly weird, because {S}∈S, S∈{S} and S∈S. But I can't establish to my own satisfaction that this necessarily implies that S={S}. Brain hurt now.

 

[doronshadmi]

Please clarify:
*) do you mean 'if' or do you mean 'iff'?
*) is 'S' any set, or a specific set (such as the set of all sets)?

Does the set of all sets must be a member?

 

[doronshadmi]

It's slightly weird, because {S}∈S, S∈{S} and S∈S. But I can't establish to my own satisfaction that this necessarily implies that S={S}. Brain hurt now.

Because you are using ∈ (or its negation) without understanding (you try to research collections by using collections). This is impossible because in order to research X it must be compared with not-X.

Furthermore, what unable to compare between X and not-X must be not any one of them.

The generalization is to get the researchable by using the non-researchable as the fundamental point of view.

In other words, the researchable cannot be understood from a point of view of the researchable, and the non-researchable cannot be understood in terms of the researchable.

 

[ArmillarySphere]

It's slightly weird, because {S}∈S, S∈{S} and S∈S. But I can't establish to my own satisfaction that this necessarily implies that S={S}. Brain hurt now.

Not really - there are other sets that are members of S, but which are not members of {S}. Putting it otherwise, {S} has a cardinality of 1, and as for S itself, I'd make a wild guess at infinity.

 

[PixyMisa]

Because you are using ∈ (or its negation) without understanding (you try to research collections by using collections). This is impossible because in order to research X it must be compared with not-X.

Wrong.

Furthermore, what unable to compare between X and not-X must be not any one of them.

Incoherent.

The generalization is to get the researchable by using the non-researchable as the fundamental point of view.

Meaningless.

In other words, the researchable cannot be understood from a point of view of the researchable, and the non-researchable cannot be understood in terms of the researchable.

Nonsense.

Not really - there are other sets that are members of S, but which are not members of {S}. Putting it otherwise, {S} has a cardinality of 1, and as for S itself, I'd make a wild guess at infinity.

Yeah, that's the conclusion I was coming to.

So, the set of all sets is weird, but it doesn't satisfy S={S}.

But the set of infinitely nested sets with only one member should work.

 

[doronshadmi]

But the set of infinitely nested sets with only one member should work.

This is exactly the organic paradigm, which is a one thing with non-finite elements with non-finite nested levels, which do not have the totality of the atomic at it self state.

In other words, no member is the final member of the universal set, and this incompleteness can be found in any arbitrarily part of the universal set.

You can think about incompleteness as a property that is equivalent to fractal's self similarity over scales.

 

[nathan]

Does the set of all sets must be a member?

This is not an answer to either of my two questions.

 

[ArmillarySphere]

You still haven't defined "final member".

However, I'd much prefer if you actually defined what you mean by complementation. You use it all over the place, but I have no idea what you mean by it, since it seems to bear no relation to the set theory definition of the complement of a set, either relative or universal.